tag:blogger.com,1999:blog-65625519029461238392024-01-19T22:11:30.615-08:00VISUALIZE SCIENCE AND TECHNOLOGY WITH IRA<p>VISUALIZATION is the Key to Creatively Understanding Science and Technology</p>
<p>TOPICS: Climate Science, Einstein's Special and General Relativity, Practical "AI Advisers" for Computer-Aided Decision-Making, and Hierarchy Theory</p>Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-6562551902946123839.post-3999331598534616432016-05-16T20:11:00.000-07:002016-05-17T08:11:30.313-07:00Ingenious or Misleading Rationalization for the "Pause" in Global Warming?<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYBN3h0w0njLQiJhN18hpK6eJWv_aVrgBpgvTi-2uivCJRpmF3vhVUvSD-S_2OzSgBZvRMaJj04Hky8uT3OhyuoDhQa5oEoPiFZEEdI74BNZtQILfyR75ZTVWU7ZzT-Lma8YbA_NVaZbg/s1600/2016IceCubeRSSgif.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="470" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYBN3h0w0njLQiJhN18hpK6eJWv_aVrgBpgvTi-2uivCJRpmF3vhVUvSD-S_2OzSgBZvRMaJj04Hky8uT3OhyuoDhQa5oEoPiFZEEdI74BNZtQILfyR75ZTVWU7ZzT-Lma8YbA_NVaZbg/s640/2016IceCubeRSSgif.gif" width="640" /></a></td></tr>
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<span style="font-size: 12.8px;">[Left] The temperature of a glass of ice water "Pauses" at freezing until nearly all the ice melts.</span></div>
<div style="text-align: left;">
<span style="font-size: 12.8px;">[Right] Top: The ice water effect is due to the <i>Heat of Fusion</i> of water. Does that effect apply to the melting of polar ice caps, and explain the statistical "Pause"? </span><span style="font-size: 12.8px;">Bottom: The IPCC's climate theory produced </span><span style="font-size: 12.8px;">climate models that grossly over-estimated warming and failed to predict the "Pause". </span></div>
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"A glass of ice water in a hot place is certainly <i>warming</i>," said the confident questioner, "despite the thermometer <i>'pausing'</i> at freeing until most of the ice has melted. Don't look at the thermometer to detect the warming, watch the ice cubes melt!"<br />
<br />
"Seriously," he continued, "we should watch the alarming melting of glaciers and polar sea ice rather than the 'Pause' in Global Warming according to thermometer readings."<br />
<br />
When <a href="https://wattsupwiththat.com/2014/09/10/a-guide-for-those-perplexed-about-global-warming/">I give talks about climate science to intelligent audiences</a>, my general theme is that <a href="http://visualira.blogspot.com/2015/07/global-warming-is-real-but-not-big-deal.html">Global Warming is REAL, and partly due to human activities, but it is NOT a big DEAL.</a>, <br />
<ul>
<li>Yes, the Atmospheric "Greenhouse" effect is real. It is responsible for the Earth being about 33<span style="font-family: "calibri";">⁰C</span> (60<span style="font-family: "calibri";">⁰F</span>) warmer than it would be absent "Greenhouse" gasses in the Atmosphere.</li>
<li>Yes Carbon Dioxide (CO<sub>2</sub>) is a key "Greenhouse" gas, second only to Water Vapor (H<sub>2</sub>O).</li>
<li>Yes CO<sub>2</sub> has increased by about a third during the past century (from 300 to 400 parts per million), mostly due to unprecedented burning of large quantities of coal, oil, and natural gas.</li>
<li>Yes, temperatures have gone up by about 0.8<span style="font-family: "calibri";">⁰C</span> (1.5<span style="font-family: "calibri";">⁰</span>F) over the past century. </li>
<li>Warming is mostly natural and due to Earth's recovery from the depths of the last ice age, some 18,000 years ago. </li>
<li>No matter what we do, the Earth will warm for hundreds or thousands of years, then plunge into the next ice age. Of course this will not happen monotonically. There will be multi-decade periods of warming and of cooling, just as the Medieval Warm Period (1000-1200s) was considerably warmer than today, and the Little Ice Age (1600-1700s) was much colder.</li>
<li>IPCC climate theory and computer models have failed to match actual satellite temperature data. Alarming predictions have not come to pass. They totally missed the statistical warming "Pause" of the early 2000s. [The IPCC is the<i> Intergovernmental Panel on Climate Change</i>]</li>
<li>[See the lower right section of the figure] For several periods, even the lowest edge of the Yellow error band is warmer than the highest edge of the Blue band! [These error bands are 5%-95% statistical confidence limits, which means there is less than 1 chance in 20 any point outside a band is due to random error. Thus, there is less than 1 chance in 20 x 20 = 400 that any point in the White space between the Yellow and Blue bands is due to random error. Either the NASA satellite sensor systems are badly out of order or the IPCC climate models are terribly wrong!]</li>
<li>The gross failure of the IPCC models to correctly predict warming, despite a significant increase in CO<sub>2</sub>, proves that the models, and the underlying IPCC climate theories, are wrong. </li>
<li>The most generous explanation is that the IPCC climate scientists simply over-estimated the sensitivity of climate to <span style="font-size: 13.3333px;"><span style="font-size: small;">CO</span><sub>2</sub> </span>increase by a factor of two to three. </li>
<li>The most likely explanation is that their climate theory is either incomplete or totally wrong, so their models failed. Either that, or, for political purposes, they purposely jiggered the model parameters to create alarming projections and keep research funding coming from we taxpayers to their organizations. </li>
</ul>
Rationalizations for what happened to the excess heat due to human-made CO<sub>2</sub>:<br />
<ul>
<li>The Oceans absorbed it! </li>
<li>The melting Ice Caps absorbed it!</li>
</ul>
How can the world's leading climate theorists and modelers still be considered competent if they did not know about the heat capacity of the oceans? (Or, apparently, even the Ice Water Experiment! :^)<br />
<br />
The Abstract for the recently published study by Michael <a href="https://wattsupwiththat.com/2016/05/11/study-by-mann-admits-the-pause-in-global-warming-was-not-predictable-but-lets-models-off-the-hook/">"<i>Nature </i>Trick - Hockey Stick"</a> Mann, et. al admits the reality of the <strike>"Pause"</strike> "temporary slowdown". Guess what he blames it on?:<br />
<blockquote>
<b>The temporary slowdown in large-scale surface warming during the early 2000s</b> has been attributed to both external and internal sources of climate variability. Using semiempirical estimates of the internal low-frequency variability component in Northern Hemisphere, Atlantic, and Pacific surface temperatures in concert with statistical hindcast experiments, we investigate whether the slowdown and its recent recovery were predictable. We conclude that the <b>internal variability of the North Pacific</b>, which played a critical role in the slowdown, <b>does not appear to have been predictable using statistical forecast methods</b>... [<b>emphasis </b>mine] </blockquote>
In other words, the unpredictable "internal variability of the North Pacific" <i>ate </i>my alarmist projection! (A variation on the old "dog <i>ate </i>my homework" excuse :^)<br />
<br />
Why was it not predictable?<br />
<ul>
<li>Because statistical forecast methods are weak? </li>
<li>Because the alarmist climate theory is wrong? </li>
<li>Because they knew better but did not dare to reign in their catastrophic predictions for fear of losing research grants?</li>
</ul>
I find it amazing that so many of my friends (who are otherwise intelligent people) cling to their firm belief in a coming human-caused climate catastrophe. Their confidence is based on the alarming predictions rooted in IPCC climate theory and computer models.<br />
<br />
Yet, like the confident questioner I mentioned in the first paragraph, they seem to acknowledge that the IPCC theorists did not know about the relatively simple concepts of ocean heat capacity, or even the temperature profile of ice water due to the <i>Heat of Fusion</i>!<br />
<br />
If these models could not correctly predict a near-term event, such as the "Pause", why put any credence in their catastrophic predictions for 50 or 100 years hence?<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh81AUmDZ81UoA06v-yPp1LX9kV0pyIEYh86bXpoQdtnPMvkbdHzPypmz6i41f9oGAQjIXs8Ni9eYAPPDqHHaxhu86or_iqSlGEqySxfgE3goqoTTZtZT1-GSq42dSETpBIKPYbmqajSAk/s1600/2016+IceCubeRSSbase.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="488" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh81AUmDZ81UoA06v-yPp1LX9kV0pyIEYh86bXpoQdtnPMvkbdHzPypmz6i41f9oGAQjIXs8Ni9eYAPPDqHHaxhu86or_iqSlGEqySxfgE3goqoTTZtZT1-GSq42dSETpBIKPYbmqajSAk/s640/2016+IceCubeRSSbase.jpg" width="640" /></a></div>
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<br />
<b>How Does the Ice Water Experiment Relate to Earth's Proportion of Ice to Liquid Water?</b><br />
<br />
To satisfy my own curiosity, I decided to do some research and figure out how much the melting of glaciers, sea ice, and ice sheets might have reduced Global Warming since 1979. This period includes the statistical "Pause" (or "temporary slowdown in large-scale surface warming during the early 2000s" as Mann refers to it).<br />
<br />
The Ice Water Temperature <i>Pause </i>Experiment works for two reasons:<br />
<ol>
<li>It takes nearly 80 times as much energy to melt a given mass of ice as it does to raise an equivalent mass of water 1<span style="font-family: "calibri";">⁰C</span> (1.8<span style="font-family: "calibri";">⁰F</span>). (This is called the <i>heat of fusion</i> associated with the state transition of water from solid to liquid form.)</li>
<li>The Ice Cubes make up a substantial percentage of the total mass of the ice water mixture. (When the ice cubes melt down to a small proportion of the water, the temperature does rise.)</li>
</ol>
So, what is the percentage of ice to liquid water on Earth, and has enough of it melted to account for the failure of the IPCC models since 1979, or during the "Pause"?<br />
<br />
According to Debenedetti, Pablo G. & H. Eugene Stanley. "Supercooled and Glassy Water."Physics Today. Vol. 56, No. 6 (June 2003): 40 (quoted by <a href="http://hypertextbook.com/facts/2000/HannaBerenblit.shtml">http://hypertextbook.com/facts/2000/HannaBerenblit.shtml</a>) here is what we need to know about the Earth's Ice and Water:<br />
<div>
<ul>
<li><b>1,300 x 10<sup>6</sup> km<sup>3</sup> </b>of water in the oceans [10<sup>6</sup> km<sup>3</sup> = millions of cubic kilometers]</li>
<li> <b>33 x 10<sup>6</sup> km<sup>3</sup></b> of ice in the polar ice caps</li>
<ul>
<li> 3 x 10<sup>6</sup> km<sup>3</sup> in the Greenland ice shelf and</li>
<li>30 x 10<sup>6</sup> km<sup>3</sup> in the Antarctic ice shelf</li>
</ul>
<li> <b>0.2 x 10<sup>6</sup> km<sup>3 </sup></b>of ice in glaciers</li>
<li> <b>0.1 x 10<sup>6</sup> km</b><sup><b>3</b> </sup>of water in lakes</li>
<li> <b>0.0012 x 10<sup>6</sup> km<sup>3 </sup></b>of water in rivers</li>
<li> <b>0.22 x 10<sup>6</sup> km<sup>3 </sup></b>of water in annual precipitation</li>
</ul>
</div>
<div>
We can see from the above that virtually all of the Earth's liquid water is in the oceans and virtually all the ice is in the polar caps. Even if we froze all the water in lakes, rivers, along with annual precipitation, and combined that with the ice in glaciers, the total would be 0.32 x 10<sup>6</sup> km<sup>3</sup>, less than 1% of the total ice caps and less than 0.03% of the total water on Earth!</div>
<div>
<br /></div>
<div>
If both the Arctic/Greenland and Antarctic Ice were to melt, that would account for a reduction in warming of about 33 x 80 / 1300 = 2⁰C (3.6⁰F). Wow! That seems substantial, and there certainly would be catastrophic flooding in some low-lying places if all the Earth's ice melted.<br />
<br />
However, actual ice melt rates are much, much, much less, according to
<a href="https://nsidc.org/cryosphere/sotc/ice_sheets.html">https://nsidc.org/cryosphere/sotc/ice_sheets.html</a>
<br />
<blockquote>
... best estimates of mass balance changes per year for 1992 through 2011: Greenland: lost 142 ± 49 gigatons; East Antarctica: gained 14 ± 43 gigatons; West Antarctica: lost 65 ± 26 gigatons; Antarctic Peninsula: lost 20 ± 14 gigatons. [net annual melt loss 213 gigatons]</blockquote>
Conveniently, 1 gigaton is the weight of one cubic kilometer (km<sup>3</sup>) of fresh water. So, 213 gigatons is equal to 213 km<sup>3 </sup>of ice (momentarily ignoring the fact that 1 km<sup>3 </sup>of ice weighs a bit less than 1 km<sup>3 </sup>of sea water). Lacking more specifics, let us assume an average annual melt rate of 213 km<sup>3 </sup>is at least roughly representative of average annual melt rates from 1979 to 2015. Thus, the total melt for 1979-2015 would be 213 x 36 = 7688 km<sup>3</sup>, which we will round up to 8000 km<sup>3 </sup>to more than make up for the difference in weight of ice and sea water.<br />
<br />
So how much does all that melting amount to in terms of delayed temperature increase? 80 x 8000 / 1,300,000,000 = 0.000492⁰C, which we may round up to 0.0005⁰C (0.0009⁰F) of the warming since 1979, and even less of the missing warming during the "Pause".<br />
<br />
So, total Earth ice melt accounts for less 0.09% of the warming missing from the IPCC's alarming projection. Not so impressive, is it?</div>
<div>
<br /></div>
<div>
So, if anyone hits you with the Ice Cube Temperature <i>Pause</i> Experiment, congratulate them on being 0.09% right (and thus 99.91% wrong :^)</div>
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<div style="text-align: center;">
<span style="color: blue; font-size: large;"><i>Ira Glickstein</i></span></div>
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Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-29494640984221763452016-04-24T17:06:00.001-07:002016-04-24T17:35:44.668-07:00Tips for VISUALIZING Science and Technology<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqEF5rLqmoo3KdSly8KMQcc2vpysxJoeJJXUEE71k1rPTCTjZ8bGhnQpLVbPLVmCXant_DmM2QNuAIHwPCioEcIUJm1PwgxjGhH-5rGNuPuv8CXL5pFgjRDuq5plv_EeFJJagCyDT644/s1600/CivilDisc4+Clock.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="381" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqEF5rLqmoo3KdSly8KMQcc2vpysxJoeJJXUEE71k1rPTCTjZ8bGhnQpLVbPLVmCXant_DmM2QNuAIHwPCioEcIUJm1PwgxjGhH-5rGNuPuv8CXL5pFgjRDuq5plv_EeFJJagCyDT644/s640/CivilDisc4+Clock.jpg" width="640" /></a></div>
I recently presented well-received a talk on "VISUALIZING Science and Technology" to a general audience at the Civil Discourse Club in The Villages, FL. I've also presented more technically deep material to the Science and Technology Club.<br />
<br />
The key to UNDERSTANDING (at least for me) is the ability to "picture" the information, almost as if you had a physical model you could "touch and feel". <br />
<br />
In my talk, I discussed several techniques, including animation, "blick" graphics, and others, and used them to illustrate:<br />
<ul>
<li>Einstein's Relativity (based on his 2005 theories of "Special Relativity" and 2015 "General Relativity"), </li>
<li>A "Nash Bargain" (if you saw the 2001 hit movie "A Beautiful Mind", you know that John Nash earned the 1994 Pulitzer prize in Economics in despite having paranoid schizophrenia), </li>
<li>Bayesian "Inverse Probability" (based on the work of Rev. Thomas Bayes, published in 1763), and </li>
<li>Global Warming (Real but not a big Deal).</li>
</ul>
<br />
<b><span style="color: #660000;">EINSTEIN'S RELATIVITY</span></b><br />
<br />
How to UNDERSTAND the relativistic effects of Kinetic Energy (Special Relativity) and Gravitational Potential Energy (General Relativity)?<br />
<br />
One of the relativistic effects is "Time Dilation". Clocks (of all kinds, including biological clocks) slow down when they are at high levels of either Kinetic or Gravitational Potential Energy.<br />
<br />
<b>Yes, I said it was CLOCKS that slow down (not TIME), and "Kinetic Energy" and (not "Speed"), and "Gravitational Potential Energy (not "Gravity") that cause these relativistic effects. Some readers may think it is TIME that slows down and that it is Relative Speed and Gravity/Acceleration that cause it, but I plan to motivate you otherwise!</b><br />
<br />
<span style="color: #660000; font-weight: bold;">Please refer to the above graphic</span><br />
<br />
The image above is a screen capture from an animated "thought experiment" involving four identical, extraordinarily accurate clocks and an idealized Earth that has a conveniently-located, friction-free Tunnel, cut through the Center, from the left Surface to the right Surface.<br />
<br />
Initially, all clocks are "at rest". The RED and BLUE clocks are at the left edge of the image, very far from the gravitational attraction of the Earth. The GREEN clock is fixed in position at the Earth Surface, and the GREY clock is fixed at the Center.<br />
<br />
OK, let us set the BLUE and RED clocks to zero. Keep the BLUE clock fixed in place and release the RED clock.<br />
<br />
<span style="color: #660000; font-weight: bold;">Release the RED clock</span><br />
<br />
The RED clock slowly "falls" towards the Earth, accelerating as it gets closer. As the RED clock enters the left end of the Tunnel and passes the GREEN clock at the Surface, each clock makes a record of its reading and that of the other. As the RED clock passes the GREY clock at the Center, they each record both readings. The RED clock continues out the right end of the tunnel, decelerates as it gets further from the Earth, momentarily stops moving very far from the Earth, and then "falls" back to the Earth.<br />
<br />
<span style="color: #660000; font-weight: bold;">Compare Intervals recorded by each clock</span><br />
<br />
As the RED clock it passes the GREY and GREEN clocks, and as it stops momentarily next to the BLUE clock they exchange readings and figure out the interval between their first encounter and this one. According to Einstein, the RED clock will measure a shorter interval than the GREY clock, the GREEN clock, and the BLUE clock.<br />
<br />
This difference may be expressed as picoseconds per second (picosec/sec), that is how many trillionths of a second less the interval indicated on the RED clock, divided by the time interval, is less than the interval measured by the other clocks.<br />
<br />
Using the BLUE clock as a reference, the table in the image above indicates that the GREEN clock, at the Earth Surface, will measure a Time Dilation" of 696 picosec/sec, and the GREY clock, at the Surface, will measure 1044 picosec/sec. (These values agree with data found on Wikipedia and other sources.)<br />
<br />
<span style="color: #660000;"><b><i>So, is it Gravity or Gravitational Potential Energy that causes Time Dilation?</i></b></span><br />
<br />
As the graph above shows, Gravity is about zero at the far left, when the RED and BLUE clocks are far from the gravitational attraction of the Earth. Gravity increases to a maximum (negative) value of 32 feet per second squared (32 ft/s2) at the Surface, and then DECREASES to zero at the Center. Gravity is considered negative because it points to the center of the Earth.<br />
<br />
Gravitational Potential Energy (also considered negative) is about zero at the far left, continually increases in (negative) magnitude as the RED clock passes the Surface, and continues to increase in magnitude, reaching a maximum (negative) magnitude at the Center (unlike Gravity which decreases in magnitude to zero at the Center).<br />
<br />
In mathematical terms, Gravitational Potential Energy increases "monotonically" from the far left to the Center, while Gravity increases and then decreases, so it is "non-monotonic" between these points.<br />
<br />
<b>Well, Time Dilation is about zero at the far left, and MONOTONICALLY increases in magnitude from the far left to the Center. Therefore, Time Dilation is more like Gravitational Potential Energy than it is like Gravity. So, it is not Gravity, per se, that causes Time Dilation but it is Gravitational Potential Energy.</b><br />
<br />
The graph indicates that the speed of the RED clock is about zero at the start, increases to 25,000 mph at the Surface, and then to 31,000 mph at the Center. (These values agree with data found on Wikipedia and other sources.)<br />
<br />
<b>Kinetic Energy increases and decreases more like Time Dilation than does Speed. (Kinetic Energy varies as the square of the Speed as does Time Dilation). So, it is not Speed, per se, that causes Time Dilation but it is Kinetic Energy.</b><br />
<br />
<span style="color: #660000; font-weight: bold;">(NOTE: This topic is not complete, I intend to add more material)</span><br />
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<div style="text-align: center;">
<span style="color: blue; font-size: large;"><i>Ira Glickstein</i></span></div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-25113988991436333182016-04-20T17:48:00.003-07:002016-04-20T20:31:08.118-07:00WELCOME to VISUAL IRA ! <div class="separator" style="clear: both; text-align: center;">
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<b><i>The Atmospheric "Greenhouse" Effect is Real, and the Earth is Warming. How Much Global Warming is due to Human Activities?</i></b></center>
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<b><i>Einstein's Special Relativity (1905) and General Relativity (1915) Revolutionized Physics Forever</i></b></center>
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<th><u>CLIMATE SCIENCE TOPICS</u></th>
<th><u>RELATIVITY TOPICS</u></th>
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<td><a href="http://visualira.blogspot.com/2015/07/introduction-to-climate-science.html">INTRODUCTION</a></td>
<td><a href="http://visualira.blogspot.com/2015/07/introduction-to-visualizing-einsteins.html">INTRODUCTION</a></td>
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<td><a href="http://visualira.blogspot.com/2015/07/a-physical-analogy-for-visualizing.html">PHYSICAL ANALOGY</a></td>
<td><a href="http://visualira.blogspot.com/2015/08/energy-kinetic-and-gravitational.html">ENERGY</a></td>
</tr>
<tr>
<td><a href="http://visualira.blogspot.com/2015/07/atmospheric-windows-for-visualizing.html">ATMOSPHERIC WINDOWS</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/visualizing-my-insight-into-lorentz.html?utm_source=BP_recent">INSIGHT</a></td>
</tr>
<tr>
<td><a href="http://visualira.blogspot.com/2015/07/emission-spectra-for-visualizing.html?utm_source=BP_recent">EMISSION SPECTRA</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/visualizing-twin-paradox.html?utm_source=BP_recent">TWIN PARADOX</a></td>
</tr>
<tr>
<td><a href="http://visualira.blogspot.com/2015/07/molecules-and-photons-for-visualizing.html?utm_source=BP_recent">MOLECULES AND PHOTONS</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/visualizing-using-my-excel-spreadsheet.html?utm_source=BP_recent">EXCEL SPREADSHEET MODEL</a></td>
</tr>
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<td><a href="http://visualira.blogspot.com/2015/07/light-and-heat-for-visualizing.html">LIGHT AND HEAT</a></td>
<td></td>
</tr>
<tr>
<td><a href="http://visualira.blogspot.com/2015/07/global-warming-is-real-but-not-big-deal.html">REAL NOT BIG DEAL</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/what-is-time-in-context-of-relativity.html">TIME AND RELATIVITY</a>
</td></tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgme9aHRt5mQ_w92FsIihOtyNhKxCoA-i21GW0QFZRGzlGOPcTVkXPweav13z6P87eo-DyEeEgmgB0sXPUzJiXWJqXMB6Vlhm-6IckBkbjqtWP5fz6YQ66a8y43EtLN9yggF0WHfG4kLjI/s1600/Cube_Animation.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgme9aHRt5mQ_w92FsIihOtyNhKxCoA-i21GW0QFZRGzlGOPcTVkXPweav13z6P87eo-DyEeEgmgB0sXPUzJiXWJqXMB6Vlhm-6IckBkbjqtWP5fz6YQ66a8y43EtLN9yggF0WHfG4kLjI/s1600/Cube_Animation.gif" /></a></div>
<br />
<table>
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<td><center>
<b><i>Practical "Artificial Intelligence Advisers" YOU Can Use - Computer-Aided Decision Making</i></b></center>
</td>
<td><center>
<b><i>Hierarchy Theory - "The Magical Number Seven (plus or minus two) - Optimal Span</i></b></center>
</td>
</tr>
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<td></td>
<td></td>
</tr>
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<th><u>AI ADVISER TOPICS</u></th>
<th><u>HIERARCHY TOPICS</u></th>
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<td></td>
<td></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
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<td>[Click desired Topic]</td>
<td>[Click desired Topic]</td>
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<td></td>
<td></td>
</tr>
<tr>
<td><a href="http://visualira.blogspot.com/2015/09/introduction-to-ai-advisers-and.html">INTRODUCTION</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/introduction-to-hierarchy-topics.html">INTRODUCTION</a></td>
</tr>
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<td><a href="http://visualira.blogspot.com/2015/09/bayesian-inference-advisor.html">BAYESIAN INFERENCE</a></td>
<td><a href="http://visualira.blogspot.com/2015/08/energy-kinetic-and-gravitational.html">tbs</a></td>
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<td><a href="http://visualira.blogspot.com/2016/04/nash-bargain-advisor.html">NASH BARGAIN ADVISOR</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/visualizing-my-insight-into-lorentz.html?utm_source=BP_recent">tbs</a></td>
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<td><a href="http://visualira.blogspot.com/2015/07/emission-spectra-for-visualizing.html?utm_source=BP_recent">tbs</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/visualizing-twin-paradox.html?utm_source=BP_recent">tbs</a></td>
</tr>
<tr>
<td><a href="http://visualira.blogspot.com/2015/07/molecules-and-photons-for-visualizing.html?utm_source=BP_recent">tbs</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/visualizing-using-my-excel-spreadsheet.html?utm_source=BP_recent">tbs</a></td>
</tr>
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<td><a href="http://visualira.blogspot.com/2015/07/light-and-heat-for-visualizing.html">tbs</a></td>
<td></td>
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<td><a href="http://visualira.blogspot.com/2015/07/global-warming-is-real-but-not-big-deal.html">tbs</a></td>
<td><a href="http://visualira.blogspot.com/2015/09/what-is-time-in-context-of-relativity.html">tbs</a>
</td></tr>
</tbody></table>
<h2>
MORE OF MY STUFF YOU MIGHT FIND INTERESTING
</h2>
<ul>
<li><a href="http://tvpclub.blogspot.com/">The Virtual Philosophy Club - Courteous Discussion of Serious Topics</a>
</li>
<li><a href="http://visualira.blogspot.com/">Visual Ira - Visualize Science and Technology With Ira</a></li>
<li><a href="http://2052hp.blogspot.com/">"2052 - The Hawking Plan" (Free online Novel) Amore, amorality and Stephanie Goldenrod's mission to save civilization for an infinite future.</a></li>
<li><a href="http://2052tech.blogspot.com/">Life, Liberty, and Technology - My predictions for the next several decades (companion site to my novel)</a></li>
<li><a href="http://curbfan.blogspot.com/">Curb Your Enthusiasm - Fantasy Episode</a></li>
<li><a href="https://www.youtube.com/user/IraGlickstein">My YouTube Videos</a></li>
<li><a href="https://vimeo.com/60563419">My "What is Time?" Video</a></li>
<li><a href="http://wattsupwiththat.com/author/iraglickstein/">I'm a Guest Contributor to the World's Most Popular Climate Website, Watts Up With That?</a></li>
</ul>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-82709477627739915592016-04-13T19:22:00.002-07:002016-04-20T11:55:22.404-07:00NASH BARGAIN ADVISOR<h1>
Abstract</h1>
John Nash won the 1994 Nobel in Economics for his work on what came to be known as “Nash Equilibrium”, where two or more competing entities “cooperate” (without illegally colluding) to reach a “Nash Bargain”. A Nash Bargain is reached when two or more competitors produce optimal quantities of the same or similar product or service to maximize their own self- interest, assuming others are rational and will do the same. The book and movie “A Beautiful Mind” dramatized Nash’s life story and work.<br />
A relatively simple Excel-based tool helps you calculate a Nash Bargain in a competitive situation. It is available for FREE.<br />
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<h2>
What Can the Nash Bargain Advisor Do For You?</h2>
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Whether you are in a competitive business situation or not, it is important to understand how producers and consumers may come to an effective, mutually-beneficial market solution. If a producer is selling a product or service in an “elastic” market, where demand increases with reduced price, profit may sometimes be maximized by reducing prices to increase sales. </div>
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The <b><i>Nash Bargain Advisor</i></b> can handle a competitive situation where you know: 1) The “Demand Curve” data for the market, namely the relationship between market price and quantity of product on the market, 2) Your own Cost Structure, namely the non-recurring investment to set up your production facilities and the recurring production cost of each item sold, and 3) An estimate of your competitor(s) Cost Structures.</div>
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</div>
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You can download the <i><b>Nash Bargain Advisor</b></i> at:
<a href="http://sites.google.com/site/bigira/stuff-ira-knows/NashBargainAdvisor.xls?attredirects=0&d=1">http://sites.google.com/site/bigira/stuff-ira-knows/NashBargainAdvisor.xls?attredirects=0&d=1</a><br />
(or at) <a href="http://polaris.umuc.edu/~iglickst/swen603/NashBargainAdvisor.xls" rel="nofollow" target="_blank"><span style="color: #0066cc;">http://polaris.umuc.edu/~iglickst/swen603/NashBargainAdvisor.xls</span></a></div>
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The <b><i>Nash Bargain Advisor</i></b> will compute the optimal quantity, market price, and estimated profit (or loss) you are likely to make if you follow the given advice, and if your competitors independently do the same.</div>
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<h2>
About “Elastic” Markets</h2>
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Let us start with a monopoly, the simplest case. Say a given producer is the only source for some unique product or service. Of course, if it is “a necessity of life” they can charge anything they want for it. On the other hand, if people can do without it, the market will be elastic and the monopoly producer will have to set the price and quantity to obtain the highest profit. </div>
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It is a myth that the best way to increase profits is to increase prices. Often reducing prices will increase sales and reduce unit production costs such that overall profits increase. The figure below illustrates that case.</div>
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<div style="text-align: left;">
<a href="https://iraknol.files.wordpress.com/2010/01/knol-nashmonopoly1.jpg"><img border="0" src="https://iraknol.files.wordpress.com/2010/01/knol-nashmonopoly1.jpg" /></a></div>
The heavy black line is the Demand Curve that indicates how the market price declines from about $12 per unit to $4 when the quantity on the market increases from 10 million to 100 million units. (You can change the Demand Curve by entering different numbers on the SETUP sheet of the <i><b>Nash Bargain Advisor</b></i>.)</div>
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The thin red and blue curves indicate the production Cost Structures per unit for two alternate production facilities, as a function of the number of units produced. (You can change the Cost Structures by entering different numbers on the SETUP sheet of the <i><b>Nash Bargain Advisor</b></i>.) </div>
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A producer (whether a monopoly or not) has to decide the optimum level of capital investment. Capital investment in more automated production facilities will increase initial, non-recurring costs, but may reduce incremental production costs by a sufficient amount to pay back the investment -or not- depending upon the number of units eventually sold and the market price when they are sold. The <b><i>Nash Bargain Advisor</i></b> allows you to enter and compare two different sets of Cost Structures. </div>
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</div>
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In the graph above, the thin red curve represents a more highly-automated producer we’ll call “Alpha” and the thin blue dashed curve a less-automated alternative we’ll call “Beta”. Note that, if you produce a smaller number of units, the production cost for each (which is the recurring, incremental cost per unit plus the share of the non-recurring costs) will be higher than if you produce a larger number of units. A more automated facility, corresponding to higher non-recurring investment, will be at a relative disadvantage for low production quantities but may gain an advantage for larger production quantities, as indicated by the thin red and blue curves.</div>
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The heavy red and dashed blue curves indicate the profit per unit as a function of the number of units produced. You might think the maximum overall profit occurs when the profit per unit is maximized, but you would be wrong! The figure below illustrates the overall profit (or loss) for Alpha and Beta alternatives as a function of quantity produced. </div>
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<div style="text-align: left;">
<a href="https://iraknol.files.wordpress.com/2010/01/knol-nashmonopoly1profit.jpg"><img border="0" src="https://iraknol.files.wordpress.com/2010/01/knol-nashmonopoly1profit.jpg" /></a></div>
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The overall profit for the alternative Cost Structures is maximized with a market quantity of 65 million for Alpha and 62 million for Beta, assuming each is a monopoly in a given market. This corresponds to a market price of $7.20 to $7.36 per unit. If the monopoly produces too few units, say 10 to 14 million, it will get $11.68 to $12 per unit, but will lose money overall. On the other hand, if produces too many units, say over 70 million, there will be a glut on the market and overall profits will go down substantially. </div>
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Different Demand Curve and production Cost Structures that you can experiment with on the SETUP sheet of the <b><i>Nash Bargain Advisor</i></b> may result in situations where overall profits increase or decrease monotonically as production quantities increase. However, it is much more typical for profits to maximize with a moderate number of units on the market and for there to be lower profits (or net losses) for very low or very high production quanities. </div>
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<h2>
About Competitive Markets</h2>
<div>
The insight John Nash brought to Economics and that gained him the Nobel in Economics for 1994 is that the situation is the same for multiple producers in a competitive marketplace. If two or more companies produce the same or similar products in an elastic market, such as Burger King and McDonalds or HP and Acer, it is to their advantage to collectively produce a certain number of units, neither too few nor too many.</div>
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If there are too few fast-food restaurants in a given geographic area, they may be able to charge a bit more per burger, but they will sell fewer as potential customers choose to eat at home or to go to full-service eateries. On the other hand, if there are too many fast-food places, they will have to reduce prices drastically to attract customers and their overall profits may decline or turn into losses. </div>
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The same is true for PC makers. As production quantities have multiplied, prices have come down sharply and features have improved dramatically. This, in turn, has increased sales to the point of nearly 100% market penetration in the US and other westernized countries. More and more people have at least one PC and some have a desktop plus a laptop, and other families have one for each member of the family. (My wife and I have one desktop plus three laptops between us.) With the economic slowdown, however, there may be too many units on the market and prices may drop to the point where some producers face losses and have to cut back production or drop out of the market. </div>
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So, how can competitors in an elastic market adjust production quantities such that they can each make a fair profit? Well, they could collude and fix quantities and prices and divide markets to increase their profits. However, that would be totally illegal!</div>
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Using game theory, John Nash came up with a way to reach “equilibrium” without illegal collusion. His solution is for each competitor to use their own Cost Structure and estimate the Cost Structures of competitors and calculate the quantity they should produce, <b>assuming others are rational and will do the same.</b> (The <b>highlighted</b> part of the previous sentence is the most important part. If competitors are not rational, or if they try to “cheat” by producing too many units, the Nash Bargain will not work.)</div>
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The <b><i>Nash Bargain Advisor</i></b> calculates the optimal quanities each competitor should produce to maximize their own self-interest, assuming others “cooperate” by doing the same in a rational way. The <b><i>Nash Bargain Advisor </i></b>also calculates the consequences if one or more producers “cheat” and over-produce more than their optimal quanitiy, or, if one or more producers under-produce due to miscalculation or disruption in supplies or production facilities.</div>
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<h2>
How to Use the Nash Bargain Advisor</h2>
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You have to enter only eight items of data. The SETUP sheet is shown below.</div>
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<div style="text-align: left;">
<a href="https://iraknol.files.wordpress.com/2010/01/knol-nashsetup1.jpg"><img border="0" src="https://iraknol.files.wordpress.com/2010/01/knol-nashsetup1.jpg" /></a></div>
The first four entries define the Demand Curve. In the real world, that data would come from marketing surveys or actual experience with sales volume at various outlets with different prices. It is assumed we are working in the relatively linear portion of the Demand Curve, where market price and quantity available vary inversely.</div>
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Enter the <b>minimum</b> reasonable number of units that may be on the market in the first cell. In the above example, that number is 10 million units. With that number of units available, market demand will support a price of about $12 per unit, entered into the second cell.</div>
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Then, enter the <b>maximum</b> reasonable number of units and the estimated price market demand will support. In the example, 100 million units will drive the price down to about $4 per unit.</div>
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The next four entries define the Cost Structures for two different, competitive producers that we will call Alpha and Beta. </div>
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The first cell for each producer contains the non-recurring costs for setting up the production facility and various fixed costs that do not vary with production volume. In this case, Alpha is assumed to have invested $150 million dollars and Beta $120 million. </div>
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The second cell for each producer contains the incremental production cost per unit, including supplies, factory, distribution, and sales costs. Alpha is assumed to produce units at $1.40 each and Beta at $1.90.</div>
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For this example, the <i><b>Nash Bargain Advisor</b></i> calculates that Alpha should optimally produce about 32 million units and Beta about 31 million, for a total of about 63 million units on the market. </div>
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The graphs on the SETUP sheet indicate the options Alpha and Beta have, assuming their competitor “cooperates” with the Nash Bargain. (A larger version of these graphs is available on the COOPERATION sheet.) The figure below shows the situation for Beta asuming Alpha produces their Nash Bargain quantity.</div>
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<div style="text-align: left;">
<a href="https://iraknol.files.wordpress.com/2010/01/knol-nashalphacoop1.jpg"><img border="0" src="https://iraknol.files.wordpress.com/2010/01/knol-nashalphacoop1.jpg" /></a></div>
Note that Beta could increase their profits by producing about 40 million units, about 9 million more than the Nash Bargain calls for. However, doing so will reduce Alpha’s profits to nearly zero, making Alpha, in game theory terms, the “SUCKER”. That would most likely prompt Alpha to retalliate by also over-producing in the next production cycle. If Beta produces fewer than the Nash Bargain quantity, their profits will decrease. Beta will lose money if they decrease below about 24 million units. If Beta under-produces, Alpha, the cooperator, will see the market price go up and Alpha will earn greater profits.</div>
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The situation is similar for Alpha, assuming Beta produces their Nash Bargain quantity, see the figure below.</div>
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<div style="text-align: left;">
<a href="https://iraknol.files.wordpress.com/2010/01/knol-nashbetacoop1.jpg"><img border="0" src="https://iraknol.files.wordpress.com/2010/01/knol-nashbetacoop1.jpg" /></a></div>
So, for their long-term self-interest, both Alpha and Beta should refrain from cheating and avoid getting into a “price war”.</div>
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<div>
SOME SPECIFIC EXAMPLES OF COOPERATION AND OVER- OR UNDER-PRODUCTION</div>
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The <b><i>Nash Bargain Advisor </i></b>also calculates nine examples for the cases where both Alpha and Beta cooperate and where one or both competitors over- or under-produce. </div>
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Here is a summary based on the SETUP data discussed in the previous paragraphs:</div>
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<ul>
<li>BOTH COOPERATE: Market price is $7.24, Alpha makes a net profit of $40M and Beta $46M.
</li>
<li>ALPHA CHEATS (over-produces by 50%): Market price drops to $5.80, Alpha (Cheater) makes a hefty net profit of $64M and Beta (the SUCKER) is driven down to a profit of $1M.
</li>
<li>BETA CHEATS (over-produces by 50%): Market price drops to $5.86, Beta (Cheater) makes a hefty net profit of $65M and Alpha (the SUCKER) is driven down to a <i>loss</i> of $5M
</li>
<li>BOTH CHEAT: Market Price drops to $4.42, both Alpha and Beta <i>lose</i> about $3M each.
</li>
<li>ALPHA UNDER-PRODUCES (by 50%): Market price is driven up to $8.68. Beta (Cooperator) makes a hefty profit of $91M and Alpha (under-producer) takes a <i>loss</i> of $32M.
</li>
<li>BETA UNDER-PRODUCES (by 50%): Market price is driven up to $8.62. Alpha (Cooperator) makes a hefty profit of $84M and Beta (under-producer) takes a <i>loss</i> of $15M.
</li>
<li>BOTH UNDER-PRODUCE (by 50%): Market price is driven up to $10.06. Alpha takes a loss of $9M and Beta’s profits go down to only $7M.
</li>
<li>ALPHA CHEATS (over-produces by 50%) and BETA UNDER-PRODUCES (by 50%): Market price is $7.18, Alpha (Cheater) makes a hefty profit of $130M and Beta (under-producer) takes a loss of $31M.
</li>
<li>BETA CHEATS (over-produces by 50%) and ALPHA UNDER-PRODUCES (by 50%): Market price is $7.30, Beta (Cheater) makes a hefty profit of $132M and Alpha (under-producer) takes a loss of $54M.</li>
</ul>
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</div>
<div>
Cheating by one or more competitors gluts the market with excess product and drives market price down. That, at least temporarily, benefits consumers. If a price war develops, consumers may benefit for several years. However, there is a risk that one or more competitors may be driven out of business by losses sustained in a price war and that may leave the market to one supplier, which may raise prices for the consumer.</div>
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If one or more competitors under-produces, that hurts consumers by reducing supplies below market needs and raising consumer prices. </div>
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If some of the competitors under-produce while others over-produce such that the net production quantity on the market is around the number called for by the Nash bargain, that will neither hurt nor benefit the consumers. However, the under-producer will see a drop in profit and perhaps endure a loss, while the over-producer will see a hefty profit. Therefore, if one or more competitors is hit by a disruption in production, the best action is for the other competitor(s) to over-produce to make up for the disruption.. </div>
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</div>
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<b><i>Therefore, it appears that the best long-term situation for consumers and producers is a competitive market where producers meet their Nash Bargain quantities and do not cheat. Consumers benefit from reasonable and relatively stable prices while producers make a fair profit.</i></b></div>
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</div>
<h2>
How to Use Nash Bargain Advisor for More Than Two Producers</h2>
<div>
The <b><i>Nash Bargain Advisor</i></b> may be used for more than two producers by combining additional producers into Alpha or Beta. For example, say there are four producers in a given market and two have advanced production facilities while the other two basic facilities. You could use Alpha for the two advanced facility and Beta for the two basic facilities, combining their non-recurring costs and dividing their Nash Bargain quantities.</div>
</div>
</div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-3956140182983564532015-09-16T11:55:00.000-07:002015-09-16T12:48:13.492-07:00INTRODUCTION to Hierarchy Topics - Optimal SpanOptimal Span is at the AMAZING Intersection of Hierarchy Theory, Information Theory, and Complexity Theory!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsSUIAW_fERSUge1zhZjLC4ytRo6Gvg6kX7QlqgytOA802UmiTIOTDW1a0KjZe5jUShh2hyK9I_AmDW-GdSkVGsQd2CIDcEdIyzxAAxU5p8ULDBOBJKweALwK0pxsPddbLk63M3MQcjQjW/s1600/SciTech1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="499" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsSUIAW_fERSUge1zhZjLC4ytRo6Gvg6kX7QlqgytOA802UmiTIOTDW1a0KjZe5jUShh2hyK9I_AmDW-GdSkVGsQd2CIDcEdIyzxAAxU5p8ULDBOBJKweALwK0pxsPddbLk63M3MQcjQjW/s1600/SciTech1.jpg" width="640" /></a></div>
I love Kurt Vonnegut's great poem that captures the very essence of human inquisitiveness:<br />
<blockquote>
<span style="font-size: large;"><b><i>Tiger got to hunt,</i></b></span><br />
<span style="font-size: large;"><b><i>Bird got to fly,</i></b></span><br />
<span style="font-size: large;"><b><i>Man got to sit and wonder 'WHY, WHY, WHY',</i></b></span><br />
<span style="font-size: large;"><b><i><br /></i></b></span>
<span style="font-size: large;"><b><i>Tiger got to sleep,</i></b></span><br />
<span style="font-size: large;"><b><i>Bird got to land,</i></b></span><br />
<span style="font-size: large;"><b><i>Man got to tell himself he UNDERSTAND</i></b></span><br />
<br /></blockquote>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRMjsK_ubEEVZ1PL7dASeSeIXraYkcENhT5Bw2bHehdxvAZ-ewtALOaqLkIfjIuunfwRA3BN-q5mE4bcmR-6pSdUiNsHehb-eQIC-4agt7zO5Ht2jgeE9JfbuQcxkSC1sIBnm7LLcTVLiv/s1600/SciTech2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="499" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRMjsK_ubEEVZ1PL7dASeSeIXraYkcENhT5Bw2bHehdxvAZ-ewtALOaqLkIfjIuunfwRA3BN-q5mE4bcmR-6pSdUiNsHehb-eQIC-4agt7zO5Ht2jgeE9JfbuQcxkSC1sIBnm7LLcTVLiv/s1600/SciTech2.jpg" width="640" /></a></div>
<br />
My contribution to "UNDERSTAND" is my PhD dissertation, "Hierarchy Theory - Some Common Properties of Competitively-Selected Systems", System Science Department, Binghamton University, NY, 1996. If you wish to pursue further research in this area please contact me at <a href="mailto:ira@techie.com">ira</a><a href="mailto:ira@techie.com"></a><a href="mailto:ira@techie.com"></a><a href="mailto:ira@techie.com"></a><a href="mailto:ira@techie.com"></a><a href="mailto:ira@techie.com"></a><a href="mailto:ira@techie.com">@techie.com</a>. A few copies of my dissertation are available.<br />
<strong><br /></strong>
<strong>The OPTIMAL SPAN HYPOTHESIS </strong>is at the heart of my dissertation. Using Hierarchy Theory, Information Theory, and Graph Theory, I proved that Optimal Span is about the same, between five and nine, for virtually all complex structures that have been competitively selected.<br />
<br />
That includes:<br />
<ul>
<li>The products of Natural Selection (Darwinian evolution) and </li>
<li>The products of Artificial Selection (Human inventions that competed for acceptance by human society)</li>
</ul>
My hypothesis is supported by empirical data from varied domains and a derivation from Shannon’s Information Theory and Smith and Morowitz’s concept of intricacy.<br />
<br />
You may download my PowerPoint Show that should run on any Windows PC here:<br />
<a href="https://sites.google.com/site/iraclass/my-forms/SciTechOptimalSpan10Feb2014.pps?attredirects=0&d=1">https://sites.google.com/site/iraclass/my-forms/SciTechOptimalSpan10Feb2014.pps?attredirects=0&d=1</a><br />
<br />
<br />
<b><span style="color: #274e13;">HIERARCHY THEORY</span></b><br />
<br />
Most complex structures are compositional or control hierarchies:<br />
<br />
<ul>
<li>An example of a <b><i>compositional hierarch</i></b>y is written language. A word is composed of characters. A simple sentence is composed of words. A paragraph is composed of simple sentences, and so on. </li>
</ul>
<ul>
<li>An example of a <b><i>control hierarchy</i></b> is a management structure, where a manager controls a number of foremen or team leaders, and they, in turn, control a number of workers.</li>
</ul>
<br />
<b><i><u>Hierarchy </u></i></b>(from Greek:ἱερός — hieros, ‘sacred’, and ἄρχω — arkho, ‘rule’) originally denoted the holy rule ranking of nine orders of angels, from God to Seraphims to Cherubims and so ondown to the Archangels and plain old Angels at the lowest level. Kind of like the organization of God’s Corporation!<br />
<br />
The seminal book on this topic is Hierarchy Theory: The Challenge of Complex Systems[ <a href="http://www.amazon.com/review/product/080760674X/ref=dp_top_cm_cr_acr_txt?%5Fencoding=UTF8&showViewpoints=1" title=""><span style="color: #0867ab;">Pattee, 1973</span></a> ]. This book includes chapters by distinguished academics, including:<br />
<section class="sec"><ul>
<li>Herbert A. Simon (Nobel laureate) on “The Organization of Complex Systems”.</li>
<li>James Bonner “Hierarchical Control Programs in Biological Development”</li>
<li>Howard H. Pattee “The Physical Basis and Origin of Hierarchical Control” and “Postscript: Unsolved Problems and Potential Applications of Hierarchy Theories”</li>
<li>Richard Levins “The Limits of Complexity” </li>
<li>Clifford Grobstein “Hierarchical Order and Neogenesis”.</li>
</ul>
</section><section class="sec">(Howard Pattee was the chairman of my PhD committee)</section><section class="sec"><br /></section><section class="sec">A more recent book, Complexity – The Emerging Science at the Edge of Order and Chaos, observes that the “hierarchical, building-block structure of things is as commonplace as air.” [ <a href="http://books.google.com/books?id=Nb-h3gq9u9MC&dq=waldrop+complexity&pg=PP1&ots=Rqkb7eoVO0&sig=fknvNmelXC8KSELLmLnc_HPcPYw&hl=en&sa=X&oi=book_result&resnum=1&ct=result" title=""><span style="color: #0867ab;">Waldrop, 1992</span></a> ]. Indeed, a bit of contemplation will reveal that nearly all complex structures are hierarchies.<br />
There are two kinds of hierarchy. A few well-known examples will set the stage for more detailed examination of modern Hierarchy Theory:<br />
</section><section class="sec"><h2 class="title">
Examples<sec><br /></sec></h2>
</section><section class="sec">
</section><section class="sec"><h2 class="title">
1 -Management Structure (Control Hierarchy)</h2>
</section><section class="sec">
Workers at the lowest level are controlled by Team Leaders (or Foremen), teams are controlled by First-Level Managers who report to Second-Level managers and so on up to the Top Dog Executive. At each level, the Management Span of Control is the number of subordinates controlled by each superior. </section><section class="sec"><sec><span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span></sec></section><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyHUv0KFOiYDSgxe0Lw-Et0CuV3yRpLEzUQoKKc1mo22k1aqn-asB77D5DKXxN61CVoEAQNYHHLZJNeIYNYBtCIt-YXafA-9cj5s46Ly6QFnX5xfV5dnY7ECJFK936V2sW1wqVRTi3lQC1/s1600-h/hierarchy.jpg" style="background-color: white; color: #7eb8d4; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px; margin-left: auto; margin-right: auto; text-decoration: none;"><img alt="" border="0" height="308" id="BLOGGER_PHOTO_ID_5228269066353484546" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyHUv0KFOiYDSgxe0Lw-Et0CuV3yRpLEzUQoKKc1mo22k1aqn-asB77D5DKXxN61CVoEAQNYHHLZJNeIYNYBtCIt-YXafA-9cj5s46Ly6QFnX5xfV5dnY7ECJFK936V2sW1wqVRTi3lQC1/s640/hierarchy.jpg" style="border: none; float: left; margin: 0px 10px 10px 0px; position: relative;" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px; text-align: start;"><span style="font-size: x-small;">The diagram shows three different ways you might organize 49 workers. In (A) you have ONE manager and 48 workers, which is a BROAD hierarchy. Management experts would say a Management Span of Control of 48 is way too much for anyone to handle! In (B) you have THIRTEEN managers in a three-level management hierarchy and only 36 workers, which is a TALL hierarchy with an average Management Span of Control of only 3.3. Management experts would say this is way too inefficient with too many managers! In (C) you have SEVEN managers and 42 workers in a MODERATE hierarchy with an average Management Span of Control of about 6.5. Management experts would say this is about right for most organizations where the workers have to interact with each other. Optimal Span theory supports this common-sense belief!</span></span></td></tr>
</tbody></table>
<br />
<section class="sec"><h2 class="title">
2 -Software Package (Control Hierarchy)</h2>
</section><section class="sec">
Main Line computer program controls Units (or Modules, etc.) and the Units control Procedures that control Subroutines that control Lines of Code. At each level, the Span of Control is the number of lower-level software entities controlled by a higher-level entity.
<sec><br /></sec></section><section class="sec"><h2 class="title">
3 – Written Language (Containment Hierarchy)</h2>
</section><section class="sec">
Characters at the lowest level are contained in Words. Words are contained in Simple Sentences. Simple Sentences in Paragraphs, and so on up to Sections, Chapters and the Entire Document. At each level, the Span of Containment is the number of smaller entities contained by each larger.<sec><br /></sec></section><section class="sec"><h2 class="title">
4 – “Chinese boxes” (Containment Hierarchy)</h2>
</section><section class="sec">
A Large Box contains a number of Smaller Boxes which each contain Still Smaller Boxes down to the Smallest Box. At each level, the Span of Containment is the number of smaller entities contained by each larger.
<sec><br /></sec></section><section class="sec"><h2 class="title">
Traversing a Hierarchy</h2>
</section><section class="sec">
Note that Examples 1 and 3 above were explained starting at the bottom of the hierarchy and traversing up to the top while Examples 2 and 4 were explained by starting at the top and traversing to the bottom.</section><section class="sec"><br /></section><section class="sec">Simple hierarchies of this type are called “tree structures” because you can traverse them entirely from the top or the bottom and cover all nodes and links between nodes.</section><section class="sec"><h2>
Folding” a “String”</h2>
</section><section class="sec">
A tree structure hierarchy can also be thought of an a one-dimensional “string” that is “folded” (or parsed) to create the tree structure. What does “folding” mean in this context?</section><section class="sec"><br /></section><section class="sec">
As an amusing example, please imagine the Chief Executive of a Company at the head of a parade of all his or her employees. Behind the Chief Exec would be Senior Manager #1 followed by his or her First-Level Manager #1. Behind First-Level Manager #1 would be his or her employees. Behind the employees would be the First-level Manager #2 with his or her employees. After all the First-levels and their employees, Senior Manager #2 would join the parade with his or her First-Levels and their employees, and so on. If you took the long parade and called it a “string”, you could “fold” it at each group of employees, then again at each group of First-Level Managers, and again at the group of Senior Managers, and get the familiar management tree structure!</section><section class="sec"><br />
The above “parade” was described with the Chief Exec at the head of it, but you could just as well turn it around and have the lowest-level employees lead and the Chief Exec at the rear. When military hierarchies go to war, the lowest-level soldiers are usually at the front and the highest-level Generals well behind.<br />
<br />
A more practical example is the text you are reading right now! It was transmitted over the Internet as a string of “bits” – “1″ and “0″ symbols. Each group of eight bits denotes a particular character. Some of the characters are the familiar numbers and upper and lower-case letters of our alphabet and others are special characters, such as the space that demarks a word (and is counted as a character that belongs to the word), punctuation characters such as a period or comma or question mark, and special control characters that denote things like new paragraph and so on.<br />
<br />
You could say the string of 1′s and 0′s is folded every eight bits to form a Character. The string is folded again at each Space Character to form Words. Each group of Words is folded yet again at each comma or period symbol that denotes a Simple Sentence. Each group of Simple Sentences is again folded to make Paragraphs, and so on.<br />
<br />
You could lay out a written document as a tree structure, similar to a Management hierarchy. The Characters would be at the bottom, the Words at the next level up, the Simple Sentences next, the Paragraphs next, and so on up to the whole Section, Chapter, and Book.
<br />
</section><section class="sec"><br /></section><section class="sec"><b><span style="color: #274e13;">OPTIMAL SPAN</span></b></section><section class="sec"><h2 class="title">
<span style="font-size: small;">With all these different types of hierarchical structures, each with its own purpose and use, you might think there is no common property they share other than their hierarchical nature. You might expect a particular Span of Control that is best for Management Structures in Corporations and a significantly different Span of Containment that is best in Written Language.</span></h2>
</section><section class="sec">If you expected the Optimal Span to be significantly different for each case, you would be wrong!</section><section class="sec">
According to System Science research and Information Theory, there is a single equation that may be used to determine the most beneficial Span. That optimum value maximizes the effectiveness of the resources. A Management Structure should have the Span of Control that makes the best use of the number of employees available. A Written Language Structure should have the Span of Containment that makes the best use of the number of characters (or bits in the case of the Internet) available, and so on.</section><section class="sec"><br />
The simple equation for Optimal Span derived by [ <a href="http://web.archive.org/web/20010419115651/http://pages.prodigy.net/ira/fudd.htm#dis" title=""><span style="color: #0867ab;">Glickstein, 1996</span></a> ] is:<br />
<br />
<span style="color: purple; font-size: x-large;"><strong>S<sub>o</sub>= 1 + De</strong></span> <br />(Where D is the degree of the nodes and e is the Natural Number 2.71828459)<br />
<br />
In the examples above, where the hierarchical structure may be described as a single-dimensional folded string where each node has two closest neighbors, the degree of the nodes is, D = 2, so the equation reduces to:<br />
<br /><strong>
S<sub>o</sub>= 1 + De = 1 + 2 x 2.71828459 = 6.43659</strong><br />
<br /><strong>“Take home message”: OPTIMAL SPAN, S<sub>o</sub> = ~ 6.4</strong><br />
<br />
Also see <a href="http://knol.google.com/k/ira-glickstein/quantifying-brooks-mythical-man-month/3ncxde0rz8dtk/3#view" title=""><span style="color: #0867ab;">Quantifying Brooks Mythical Man-Month (Knol)</span></a> , [<a href="http://polaris.umuc.edu/~iglickst/mswe601/optimal_MMM.doc" title=""><span style="color: #0867ab;">Glickstein, 2003</span></a> ] and [ <a href="http://repository.tudelft.nl/consumption/idcplg?IdcService=GET_FILE&RevisionSelectionMethod=latestReleased&dDocName=371262" title=""><span style="color: #0867ab;">Meijer, 2006</span></a> ] for the applicability of Optimal Span to Management Structures.<br />
<br />
[Added 4 April 2013: The Meijer, 2006 link no longer works. His .pdf document is available at <a href="http://repository.tudelft.nl/assets/uuid:843020de-2248-468a-bf19-15b4447b5bce/dep_meijer_20061114.pdf" rel="nofollow"><span style="color: #0867ab;">http://repository.tudelft.nl/assets/uuid:843020de-2248-468a-bf19-15b4447b5bce/dep_meijer_20061114.pdf</span></a> ]<br />
</section><section class="sec"><h2 class="title">
Examples of Competitively-Selected Optimal Span<sec><br /></sec></h2>
<h2 class="title">
Management Span of Control</h2>
Management experts have long recommended that Management Span of Control be in the range of five or six for employees whose work requires considerable interaction. Depending upon the level of interaction, experts recommend up to nine employees per department.This recommendation comes from experience with organizations with different Spans of Control. The most successful tend to have Spans in the recommended range, five to nine,an example of competitive-selection.<br />
<br />
When the lowest level consists of service-type employees, whose interaction with each other is less complex, there may be a dozen or two or more in a department, but there will usually be one or more foremen or team leaders to reduce the effective Management Span of Control to the range five to nine.Corporate hierarchies usually have about the same range of first-level departments reporting to the next level up and so on.<br />
<br />
Say you had a budget for 49 employees and had to organize them to make most effective use of your human resources. Which of the following seems most reasonable?<br />
<br />
(A) you have ONE manager and 48 workers, which is a BROAD hierarchy. Management experts would say a Management Span of Control of 48 is way too much for anyone to handle!<br />
<br />
(B) you have a third-level chief executive, three executive-level managers, each with three department managers, totaling THIRTEEN managers in a three-level management hierarchy and only 36 workers, which is a TALL hierarchy with an average Management Span of Control of only 3.3. Management experts would say this is way too inefficient with too many managers!<br />
<br />
(C) you have a second-level manager and six department managers, totaling SEVEN managers and 42 workers in a MODERATE hierarchy with an average Management Span of Control of about 6.5. Management experts would say this is about right for most organizations where the workers have to interact with each other. Optimal Span theory supports this common-sense belief!
<sec><br /></sec><h2 class="title">
Human Span of Absolute Judgement</h2>
Evolution and Natural Selection have produced the human brain and nervous system and our senses of vision, hearing, and taste. It turns out that these senses are generally limited to five to nine gradations that can be reliably distinguished. It is also the case that we can remember about five to nine chunks of information at any one time. This is another example of competitive-selection, where, over the eons of evolutionary development, biological organisms competed and those that best fit the environment were selected to survive and reproduce.<br /><br />George A Miller wrote a classic paper titled The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information [ <a href="http://web.archive.org/web/20010201193500/www.well.com/user/smalin/miller.html" title=""><span style="color: #0867ab;">Miller, 1956</span></a> ]. He showed that human senses of sight, hearing, and taste were generally limited to five to nine gradations that could be reliably distinguished.<br /><br /><div class="separator" style="background-color: white; clear: both; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhPLTuHXKNv2S6UFpuPxWxf57CqBbBWU6iqwKiVHLIYpuGrrguFOX5FWDHQJgIcGbX45eNoOpcZg_UPHq-slT1Iq-8BYeXQTLCtlprw53YEDO1btTjfD2kXhfIeKNCC4vJRvjC_JkClAwx/s1600/PhiloMagicalSevenMar2014.jpg" imageanchor="1" style="clear: left; color: #7eb8d4; float: left; margin-bottom: 1em; margin-right: 1em; text-decoration: none;"><img border="0" height="253" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhPLTuHXKNv2S6UFpuPxWxf57CqBbBWU6iqwKiVHLIYpuGrrguFOX5FWDHQJgIcGbX45eNoOpcZg_UPHq-slT1Iq-8BYeXQTLCtlprw53YEDO1btTjfD2kXhfIeKNCC4vJRvjC_JkClAwx/s320/PhiloMagicalSevenMar2014.jpg" style="border: none; position: relative;" width="320" /></a></div>
<span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Why do we “chunk” things in groups of about seven – seven days of the week, seven seas, seven sins, etc? The presentation I gave to the Philosophy Club in The Villages, FL, 14 March 2014 provides the theoretical answer. You may download a PowerPoint Show that should run on any Windows computer here:</span><a href="https://sites.google.com/site/iraclass/my-forms/PhiloMAGICALsevenMar2014.ppsx?attredirects=0&d=1" style="background-color: white; color: #7eb8d4; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px; text-decoration: none;">https://sites.google.com/site/iraclass/my-forms/PhiloMAGICALsevenMar2014.ppsx?attredirects=0&d=1</a><span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span><br style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><br style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">This is an easy-to-understand version of a more technical presentation I made to the Science-Technology Club in February, see</span><span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">: </span><a href="http://tvpclub.blogspot.com/2014/02/optimal-span-amazing-intersection-of.html" style="background-color: white; color: #7eb8d4; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px; text-decoration: none;">http://tvpclub.blogspot.com/2014/02/optimal-span-amazing-intersection-of.html</a><br style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><br style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><strong style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><span style="color: #660000;">PERSECUTED BY THE NUMBER SEVEN !</span></strong><br style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.8500022888184px; line-height: 27.7200012207031px;">George A </span><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Miller's classic paper appeared way back in 1956 the </span><em style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Psychological Review</em><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> with the intriguing title: </span><i style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">The Magical Number Seven, Plus or Minus Two – Some Limits on Our Capacity for Processing Information</i><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">. That paper was extremely important and influential and is still available online. George A. Miller contains a strange plea: </span><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><blockquote style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px;">
<span style="font-size: large;">"My problem is that I have been persecuted by an integer seven plus or minus two … </span></blockquote>
Miller’s paper continues as follows:</section><section class="sec"><br /><em>"For seven years this number has followed me around, has intruded in my most private data, and has assaulted me from the pages of our most public journals. This number assumes a variety of disguises, being sometimes a little larger and sometimes a little smaller than usual, but never changing so much as to be unrecognizable.</em><br />
<em><br /></em>
<span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px;"><span style="font-size: large;">"The persistence with which this number plagues me is far more than a random accident …</span></span><br />
<span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px;"><span style="font-size: large;"><br /></span></span>
<em>"There is, to quote a famous senator, a design behind it, some pattern governing its appearances. Either there really is something unusual about the number or else I am suffering from delusions of persecution.Miller’s paper is well worth reading and is available on the Internet at this link [</em><a href="http://web.archive.org/web/20010201193500/www.well.com/user/smalin/miller.html" title=""><em>Miller, 1956</em></a><em>]"</em><br />
<br />
<span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Miller presents the results of twenty experiments where human subjects were tested to determine what he calls our "Span of Absolute Judgment", that is, how many levels of a given stimulus we can </span><i style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">reliably</i><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> distinguish. Most of the results are in the range of five to nine, but some are as low as three or as high as fifteen. For example, our ears can distinguish five or six tones of pitch or about five levels of loudness. Our eyes can distinguish about nine different positions of a pointer in an interval. Using a vibrator placed on a person's chest, he or she can distinguish about four to seven different level of intensity, location, or duration, etc. The average Span of Absolute Judgment is 6.4 for Miller's twenty one-dimensional stimuli.</span><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Miller also presents data for what he calls our "Span of Immediate Memory", that is, how many randomly presented items we can </span><i style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">reliably</i><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> remember. For example, we can remember about nine binary items, such as a series of "1" and "0", or about eight digits, or about six letters of the alphabet, or about five mono-syllabic words randomly selected out of a set of 1000.</span><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">At the end of his paper Miller rambles: </span><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><blockquote style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">
...And finally, what about the magical number seven? What about the seven wonders of the world, the seven seas, the seven deadly sins, the seven daughters of Atlas in the Pleiades, the seven ages of man, the seven notes of the musical scale, and the seven days of the week? What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory?<br />
<br />
For the present, I prefer to withhold judgment.<br />
<br />
<b>Perhaps there is something deep and profound behind all these sevens, something just calling out for us to discover it.</b><span style="background-color: transparent;"> </span></blockquote>
<blockquote style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">
But I suspect that it is only a pernicious, Pythagorean coincidence. [my <b>bold</b>]</blockquote>
<span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Well, it turns out that there IS something DEEP and PROFOUND behind "all these sevens" and I (Ira Glickstein) HAVE DISCOVERED IT. And, my insight applies not only to the span of human senses and memory, but also to the span of written language, management span of control, and even to the way the genetic "language of life" in RNA and DNA is organized. Furthermore, my discovery is not simply based on support from empirical evidence from many different domains, but has been mathematically derived from the basic Information Theory equation published in 1948 by Claude Shannon, and the adaptation of "Shannon Entropy" to the Intricacy of a biograph by Smith and Morowitz in 1982.</span><br /><br /><br />
</section><section class="sec"><h2 class="title">
Glickstein’s Theory of Optimal Span</h2>
</section><section class="sec">Miller’s number also pursued me (Ira Glickstein) until I caught it and showed, as part of my PhD research,[ <a href="http://web.archive.org/web/20010419115651/http://pages.prodigy.net/ira/fudd.htm#dis" title=""><span style="color: #0867ab;">Glickstein, 1996</span></a> ]that, based on empirical data from varied domains, the optimal span for virtually all hierarchical structures falls into Miller’s range, five to nine. Using Shannon’s information theory, I also showed that maximum intricacy is obtained when the Span for single-dimensional structures is S<sub>o</sub> = 1 + 2e = 6.4 (where e is the natural number, 2.71828459). My “magical number” is not the integer 7, but 6.4, a more precise rendition of Miller’s number!</section><section class="sec"><br /></section><section class="sec"><h2 class="title">
Hierarchy and Complexity</h2>
</section><section class="sec">Howard H. Pattee, one of the early researchers in hierarchy theory, posed a serious challenge:</section><section class="sec"><br /></section><section class="sec">Is it possible to have a simple theory of very complex, evolving systems? Can we hope to find common, essential properties of hierarchical organizations that we can usefully apply to the design and management of our growing biological, social, and technological organizations? [<a href="http://www.amazon.com/review/product/080760674X/ref=dp_top_cm_cr_acr_txt?%5Fencoding=UTF8&showViewpoints=1" title=""><span style="color: #0867ab;">Pattee, 1973</span></a>] </section><section class="sec">Pattee was the Chairman of my PhD Committee and I took the challenge very seriously!</section><section class="sec"><br /></section><section class="sec">The hypothesis at the heart of my PhD dissertation is that the optimal span is about the same for virtually all complex structures that have been competitively selected. That includes the products of Natural Selection (Darwinian evolution) and the products of Artificial Selection (Human inventions that competed for acceptance by human society).</section><section class="sec"><br /></section><section class="sec"><h2 class="title">
Weak Statement of Hypothesis</h2>
</section><section class="sec">In the “weak” statement of the hypothesis, it is scientifically plausable to believe that diverse structures tend to have spans in the range of five to nine, based on empirical data from six domains plus a computer simulation. </section><section class="sec"><br /></section><section class="sec">The domains are:</section><section class="sec"><br /></section><section class="sec"><strong>Human Cognition:</strong> Span of Absolute Judgement (one, two and three dimensions), Span of Immediate Memory, Categorical hierarchies and the fine structure of the brain. These all conform to the hypothesis. </section><section class="sec"><br /></section><section class="sec"><strong>Written Language:</strong> Pictographic, Logographic, Logo-Syllabic, Semi-alphabetic, and Alphabetic writing. Hierarchically-folded linear structures in written languages, including English, Chinese, and Japanese writing. These all conform to the hypothesis. </section><section class="sec"><br /></section><section class="sec"><strong>Organization and Management of Human Groups:</strong> Management span of control in business and industrial organizations, military, and church hierarchies. These all conform to the hypothesis. </section><section class="sec"><br /></section><section class="sec"><strong>Animal and Plant Organization and Structure:</strong> Primates, schooling fish, eusocial insects (bees, ants), plants. These all conform to the hypothesis. </section><section class="sec"><br /></section><section class="sec"><strong>Structure and Organization of Cells and Genes:</strong> Prokaryotic and eukaryotic cells, gene regulation hierarchies. These all conform to the hypothesis. </section><section class="sec"><br /></section><section class="sec"><strong>RNA and DNA:</strong> Structure of nucleic acids. These all conform to the hypothesis. </section><section class="sec"><br /></section><section class="sec"><strong>Computer Simulations:</strong> Hierarchical generation of initial conditions for Conway’s Game of Life. (Two-dimensional ). These all conform to the hypothesis. </section><section class="sec"><sec><br /></sec></section><section class="sec"><h2 class="title">
Strong Statement of Hypothesis</h2>
</section><section class="sec">Shannon’s information theory, andthe concept of intricacy of a graphical representation of a structure [ <a href="http://www.springerlink.com/content/k021665p34j75565/" title=""><span style="color: #0867ab;">Smith and Morowitz, 1982</span></a> ] can be used to derive a formula for the optimal span of a hierarchical graph.</section><section class="sec"><br /></section><section class="sec"><br /></section><section class="sec">This work extended the single-dimensional span concepts of management theory and Miller’s “seven plus or minus two” concepts to a general equation for any number of dimensions. I derived an equation that yields Optimal Span for a structure with one-, two-, three- or any number of dimensions!</section><section class="sec"><br /></section><section class="sec">The equation for Span (optimal) is:</section><section class="sec"><br /></section><section class="sec">S<sub>o</sub>= 1 + De </section><section class="sec"><br /></section><section class="sec">(Where D is the degree of the nodes and e is the Natural Number 2.71828459)</section><section class="sec"><br /></section><section class="sec"><br /></section><section class="sec">NOTE: For a one-dimensional structure, such as a management hierarchy or the span of absolute judgement for a single-dimensional visual, taste or sound, the degree of the nodes, D = 2 . This is because each node is a link in a one-dimensional chain or string and so each node has two closest neighbors.</section><section class="sec"><br /></section><section class="sec">For a two-dimensional structure, such as a 2D visual or the pitch and intensity of a sound or a mixture of salt and sugar, D = 4. Each node is a link in a 2D mesh and so each node has four closest neighbors. </section><section class="sec"><br /></section><section class="sec">For a 3D structure, D = 6 because each node is a link in a 3D egg crate and has six closest neighbors. </section><section class="sec"><br /></section><section class="sec">Some of the examples in Miller’s paper were 2D and 3D and his published data agreed with the results ofthe formula. The computer simulation was 2D and also conformed well to the hypothesis.</section><section class="sec"><br /></section><section class="sec">In normal usage, complexity and intricacy are sometimes used interchangeably. However, there is an important distinction between them according to [ <a href="http://www.springerlink.com/content/k021665p34j75565/" title=""><span style="color: #0867ab;">Smith and Morowitz, 1982</span></a> ].</section><section class="sec"><br /></section><section class="sec"><br /></section><section class="sec"><strong>COMPLEXITY -</strong> Something is said to be complex if it has a lot of different parts, interacting in different ways. To completely describe a complex system you would have to completely describe each of the different types of parts and then describe the different ways they interact. Therefore, a measure of complexity is how long a description would be required for one person competent in that domain of knowledge to explain it to another.</section><section class="sec"><br /></section><section class="sec"><br /></section><section class="sec"><strong>INTRICACY</strong> - Something is said to be intricate if it has a lot of parts, but they may all be the same or very similar and they may interact in simple ways. To completely describe an intricate system you would only have to describe one or two or a few different parts and then describe the simple ways they interact. For example, a window screen is intricate but not at all complex. It consists of equally-spaced vertical and horizontal wires criss-crossing in a regular pattern in a frame where the spaces are small enough to exclude bugs down to some size. All you need to know is the material and diameter of the wires, the spacing betwen them, and the size of the window frame. Similarly, a field of grass is intricate but not complex.</section><section class="sec"><br /></section><section class="sec"><br /></section><section class="sec"><strong>If you think about it for a moment, it is clear that, given limited resources, they should be deployed in ways that minimize complexity to the extent possible, and maximize intricacy!</strong></section><section class="sec"><br /></section><section class="sec"><br /></section><section class="sec">Using [ <a href="http://www.springerlink.com/content/k021665p34j75565/" title=""><span style="color: #0867ab;">Smith and Morowitz, 1982</span></a> ] concepts of inticacy, it is possible to compute the theoretical efficiency and effectiveness of a hierarchical structure. If it had the Optimal Span, it is 100% efficient, meaning that it attains 100% of the theoretical intricacy given the resources used.If not, the percentage of efficiency can be computed. For example, a one-dimensional tree structure hierarchy is 100% efficient (maximum theoretical intricacy) with a Span of 6.4. For a Span of five, it is 94% efficient (94% of maximum theoretical intricacy).It is also 94% efficient with a Span of nine. For a Span of four or twelve, it is 80% efficient.</section><section class="sec"><br /></section><section class="sec"><span style="background-color: white; color: #006600; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><strong>OPTIMAL SPAN IN MY NOVEL</strong></span><br style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">In Chapter 6 of</span><span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span><a href="http://2052hp.blogspot.com/2008/02/chapter-6-israeli-adventure.html" style="background-color: white; color: #7eb8d4; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px; text-decoration: none;">my novel</a><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">, Jim and Luke wonder about the control structure for the 1600 scepter-holders:</span><br style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" /><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">
<blockquote>
... After a period of silence, Luke spoke up. “Sixteen hundred people are way too many for there not to be a hierarchical structure,” he began. “If the scepter-holder system was properly designed, according to system science theory at least, there would have to be several grades above the lowest class of scepter-holder.”<br />
<br />
He took out his read-WINs and put them on.<br />
<br />
“Luke,” I observed, “There’s no WIN coverage in this area …”<br />
“Right,” answered Luke, “But there are processors and software in my read-WINs that allows them to operate independently. I’ve got a program for ‘optimal span’ – you know the ‘magical number seven plus or minus two.’”><br />
“What the heck is that?” I asked, “And why would I care? Where are we going here?”<br />
“Well, back about a century ago, a psychologist named Miller discovered that human perception, such as sight and smell and taste and memory and so on, is limited to five to nine gradations. He called it 'the magical number seven, plus or minus two' or, more scientifically, the 'span of human perception'."<br />
“Another guy, an engineer named Glickstein, about sixty years ago, proved the optimal span for any structure is one plus the degree of the nodes times 2.71828459, the natural number ‘e.’ For a one-dimensional string, the degree is two and the formula comes out to be around six and a third, or a little more. He also showed with Shannon’s information theory that the range five to nine was, at least theoretically, over ninety-six percent efficient and four to twelve was over eighty percent efficient. And that’s not just for control hierarchies like a management chain, but also containment hierarchies in all types of physical systems and even software systems like …”<br />
“You just told me how to build a clock,” I laughed, interrupting Luke. “All I want to know is what time it is! Please, tell me why I give a hoot about the range five to nine or the number six and a third or a bit more?”<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span></blockquote>
<blockquote>
<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">“About forty years ago,” continued Luke, “A management expert rediscovered the optimal span theory and proclaimed that all management structures must adhere to it! Did you ever notice how nearly all departments at TABB have either six or seven workers to each manager? How each second-level manager has six or seven first-level managers working for him or her?”</span><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span></blockquote>
<blockquote>
<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">“Yeah, come to think of it,” I replied, “That’s how it is. On the other hand, when I worked in a factory as a college summer job, we had about a dozen guys and gals in our team.”</span><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span></blockquote>
<blockquote>
<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">“Well,” replied Luke, “The lowest level, like a platoon in the military, can have ten or twelve or sometimes a bit more. The theory only applies when the workers have to interact with each other in complex ways, not when they’re doing grunt work.”</span><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span></blockquote>
<blockquote>
<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">“If you’d quit interrupting, I’ll tell you,” Luke said good-naturedly, “According to the optimal span program in my read-WINs, sixteen-hundred scepter-holders would break down into about two-hundred-fifty first-level ‘departments,’ each with six or seven scepter-holders and one higher-level scepter-holder ‘managing’ them. The two-hundred-fifty second-level scepter-holders would report to thirty-six third-level scepter-holders who, in turn, would report to six fourth-level scepter-holders who would report to the top dog scepter-holder if there was one.”</span><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span></blockquote>
<blockquote>
<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">“Yeah,” replied Luke, “There should be </span><em style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">thirty-six</em><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> scepter-holders at the third level. What about it?”</span><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span></blockquote>
<blockquote>
<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">“Well,” I began, very seriously, “We have a tradition in Judaism that there are </span><em style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">thirty-six ‘tzadikim’</em><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> or ‘righteous ones’ for whose sake the world exists. No one knows who they are. When one dies, he, or she I guess, is replaced by another, chosen by God. They are sometimes called the ‘</span><em style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">Lamed Vovniks’</em><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> because, according to gematria, which we discussed some months ago, the Hebrew letter </span><em style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">Lamed</em><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> stands for thirty and the letter </span><em style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">Vuv</em><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">for six, which adds up to thirty-six.”</span><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> </span></blockquote>
<blockquote>
<span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">“So,” replied Luke with a level of interest that surprised me at the time, “There would be </span><em style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">thirty-six</em><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> especially powerful scepter-holders who would regulate the rest! And they do need regulation. I’m not one-hundred percent pleased with Stephanie’s ethics ..."</span></blockquote>
</span></section><section class="sec"><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span></section>
<section class="sec"><div style="text-align: center;">
<span style="color: blue; font-size: x-large;"><em>Ira Glickstein</em></span></div>
</section>Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-91819990891113680452015-09-15T12:55:00.002-07:002015-09-15T12:57:35.336-07:00INTRODUCTION to "AI ADVISERS" and COMPUTER-AIDED DECISION-MAKING<strong><span style="color: #003300;">ARE WE IN CONTROL OF OUR OWN DECISION-MAKING?</span></strong><br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghXZ-infUqTTUzmeERiExnh2clNzAc8XGY_OZKbr-YJLH1oB3WWjgz155cs2xpGW9N3uM0FduZKFdIi22W6gVi0Ou4uIyGNcmHL1cX89i5vinSXAPPwYMnrJCU8f15XsKPWzt24dI4lwI/s1600/DECISION.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="182" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghXZ-infUqTTUzmeERiExnh2clNzAc8XGY_OZKbr-YJLH1oB3WWjgz155cs2xpGW9N3uM0FduZKFdIi22W6gVi0Ou4uIyGNcmHL1cX89i5vinSXAPPwYMnrJCU8f15XsKPWzt24dI4lwI/s640/DECISION.jpg" width="640" /></a></div>
How are decisions made where you work? In your personal life? In government and politics?<br />
<br />
<div style="text-align: center;">
<span style="font-size: large;">Are we really in control of our own decision-making?</span></div>
<div style="text-align: center;">
<span style="font-size: large;">Is it a completely objective, fact-based, unemotional process? </span></div>
<div style="text-align: center;">
<span style="font-size: large;">(If you answered "YES" you are almost certainly WRONG!)</span></div>
<br />
EMOTION generally plays a key role in virtually all decision-making. As I was taught in IBM Marketing School "You buy WHAT you like from WHO you like!"<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghrnXgVXldStnB6x4K3lDG7LrUr9AcUJzRU91vJb4GgCT7s-S8DySCI49bVxstfH_p6rww9CdT4k0nRNhU4iSTgVmxjZqPAoblYI8PVP23-qAdiBeK_zkRzxYG-roHeyplCS9ArfoUqElb/s1600-h/TED-+Tom+Jerry.JPG" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5343499156423667554" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghrnXgVXldStnB6x4K3lDG7LrUr9AcUJzRU91vJb4GgCT7s-S8DySCI49bVxstfH_p6rww9CdT4k0nRNhU4iSTgVmxjZqPAoblYI8PVP23-qAdiBeK_zkRzxYG-roHeyplCS9ArfoUqElb/s400/TED-+Tom+Jerry.JPG" style="float: left; height: 269px; margin: 0px 10px 10px 0px; width: 385px;" /></a><br />
The image is from a great <a href="http://www.ted.com/index.php/talks/dan_ariely_asks_are_we_in_control_of_our_own_decisions.html">TED talk</a> that asks the question: "Are we in control of our own decisions?"<br />
<br />
The answer is NO!<br />
<br />
This TED talk clearly demonstrates how our emotions and other non-rational factors control our decision-making much more strongly than reasonable logic.<br />
<br />
For example, the person on the far left is "Tom" and the one on the far right is "Jerry". The figure in the top middle is a distorted version of "Jerry" to make him look ugly. The middle bottom is an ugly version of "Tom".<br />
<br />
When presented with the top form, and asked who they would date, most picked good-looking Jerry. When shown the bottom form, they picked good-looking Tom. Amazingly, the ugly choice totally changed the results of the selection process!<br />
<br />
The TED presenter, Dan Ariely, uses several other examples to show how our decision process may be totally altered by the presentation of undesirable, non-chosen alternatives.<br />
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<strong><span style="color: #003300;">HOW DOES THIS BEAR ON PROFESSIONAL DECISION-MAKING?</span></strong><br />
<br />
Well, if a decision is close between two alternatives, which is always the case for hard decisions in business (or the Supreme Court, where, by definition, cases are almost always close choices), a good strategy could be to introduce a slightly "ugly" version of the choice you want the deciders to make.<br />
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For example, a prosecutor could include the death penalty as an option, even if he or she thought a 20-year sentence is most appropriate. The "ugly" death penalty option would make it more likely the jurors would settle on a long sentence. Given a choice between 10 years and 20 years, they might pick 10. If the death penalty was added to the menu, they would be more likely to choose 20 years.<br />
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The other lesson I take from this TED talk is that professionals should adopt methodologies that, to the extent possible, exclude emotional factors.<br />
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<strong><span style="color: #003300;">FREE INTERACTIVE DECISION-AIDING "AI ADVISERS" YOU CAN USE</span></strong><br />
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I have used Excel to construct several "AI Advisers" - Computer-Aided tools that you may use to reduce the emotional quotient in your personal and professional decision-making. They are all totally FREE (and well worth it :^).<br />
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<b><u>Decision-Making In the Face of Uncertainty Utilizing Multiple Evaluation Factors and Weights</u></b><br />
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my <a href="http://knol.google.com/k/ira-glickstein/decision-aiding-tool-do-a-trade-study/3ncxde0rz8dtk/5#">Decision tool</a> "forces" the deciders to consider multiple factors and weights in reaching a decision.<br />
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<b><u>Bayesian Inference (Inverse Probability)</u></b><br />
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xx<br />
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<b><u>Nash Bargain (Setting the most advantageous price in a competitive market)</u></b><br />
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xx<br />
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<b><u>Management Span of Control Based on Hierarchy Theory and Information Theory</u></b><br />
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xx<br />
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<b><u>Visual Acuity</u></b><br />
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How big and what size fonts should you use for signs, PowerPoint presentations, and printed documents. How big should your new High Definition television display be in your living room, your den, your meeting room, etc.<br />
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<span style="color: #000066; font-size: 20.7999992370605px;"><em>Ira Glickstein</em></span></div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-8280148658209207272015-09-15T11:46:00.000-07:002015-09-15T13:06:53.692-07:00Bayesian Inference Adviser<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7qkbHJt8X9p781-_IisQtx11-578ZaOXSFURHMO6jeFjg47HBQ2ssBBIJikKRdRny-IrEt_BIpSPkJ2NXetjCMjIu1l8YedTWAfsc5kKSdGuwERpZLNGNIyAhl0eV81a2yzZ4VZ8dF4JF/s1600/bayes-tshirt201.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7qkbHJt8X9p781-_IisQtx11-578ZaOXSFURHMO6jeFjg47HBQ2ssBBIJikKRdRny-IrEt_BIpSPkJ2NXetjCMjIu1l8YedTWAfsc5kKSdGuwERpZLNGNIyAhl0eV81a2yzZ4VZ8dF4JF/s320/bayes-tshirt201.jpg" width="640" /></a><br />
Bayes Theorem has practical applications. Use it to make real world decisions.<br />
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Bayes Theorem is not just an obscure artifact of the statistics of probability handed down to us from centuries ago. You can use it now to make decisions that will affect your financial well-being.<br />
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A relatively simple Excel-based tool helps you choose the right course of action in the face of uncertain probabilities and inexact test results. It is available for FREE.<br />
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<strong><span style="color: #660000;">What can the <em>Bayesian Inference Adviser</em> Tool do for You?</span></strong><br />
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I know you are probably not in the oil business (and neither am I), but the best way to understand an abstract concept is to go through a practical example. The example below has to do with oil exploration and drilling, but the <em><strong>Bayesian Inference Adviser </strong></em>can handle any problem where you know: <br />
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1) the probability of success if you take action without doing further testing, <br />
2) the cost of further testing and the probability the test results will be reliable,<br />
3) the cost of taking some action, <br />
4) the financial benefit to you if the action is successful, and<br />
5) the compensation you expect for taking the risk. <br />
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You can download the <em>Bayesian Inference Adviser</em> at:<br />
<a href="https://sites.google.com/site/bigira/stuff-ira-knows/BayesianInferenceAdvisorV3.xls?attredirects=0&d=1">https://sites.google.com/site/bigira/stuff-ira-knows/BayesianInferenceAdvisorV3.xls?attredirects=0&d=1</a><br />
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The<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian Inference Adviser</b></i> will compute the most likely financial implications of your actions. What if you proceed without further testing? What if you get a positive test result and proceed? What if you get a negative test result and proceed? Several other examples in very different domains are included later in this posting, but for now, put on your hard hat and let us imagine we are in the oil business!<br />
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<strong><span style="color: #660000;">Example #1- Should we drill here, drill now?</span></strong><br />
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<strong>Situation</strong><br />
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Twenty oil wells have been drilled in a particular area and only three of them have yielded commercially-viable quantities of petroleum. The others were “dry holes”. So the chances of a newly-drilled hole striking oil are about 15%. You could do just go ahead and drill without further testing, but that would be relatively expensive and you could turn up a dry hole. Seismic testing is less expensive than actually drilling, but even if you get a positive result, that doesn’t guarantee oil will be found. The probability of getting a positive seismic test result in this area is 25%. The tests results have a probability of 80% of being positive if there is indeed oil at the site. You input the three probabilities (15%, 25%, and 80%) into the<span class="Apple-converted-space"> </span><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian Inference Adviser</i></b><span class="Apple-converted-space"> </span>INPUT panel as indicated above.</div>
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The<span class="Apple-converted-space"> </span><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian Inference Adviser</i></b><span class="Apple-converted-space"> </span>uses Bayes Theorem to calculate that there is an<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">inverse</b></i><span class="Apple-converted-space"> </span>probability of 48% that you will be successful finding oil given a positive seismic test. OK, now that Bayes has spoken, what should you do?</div>
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To answer that question you first have to input four pieces of financial data. According to experienced oilmen in the area, it will cost $1M to do a seismic test and an additional $20M if you decide to drill. if you do strike oil, you could get $70M based on current prices, but you need a 15% return on investment (ROI) to account for the risk and the possibility petroleum prices could go down further. ROI is: { Gain from Investment – Cost of Investment } / {Cost of Investment}<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiItUFwsCK9G54dSt-csb21kWGby2GBquNoOiIkkxQG0nTbTI0igHtHfd6mTHXFvkys4LEA6e4PJmdfukYgDBqqvk3-pKwvEv10ixGAUiTH6ToPKt6B51cKO7grNWeDTrooDqbsM8yneV0H/s1600/BayesOil1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiItUFwsCK9G54dSt-csb21kWGby2GBquNoOiIkkxQG0nTbTI0igHtHfd6mTHXFvkys4LEA6e4PJmdfukYgDBqqvk3-pKwvEv10ixGAUiTH6ToPKt6B51cKO7grNWeDTrooDqbsM8yneV0H/s320/BayesOil1.JPG" width="640" /></a></div>
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The figure above shows the numbers you would input into the<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian Inference Adviser</b></i><span class="Apple-converted-space"> </span>for the given situation, and the output you would get. The <strong><em>Bayesian Inference Adviser </em></strong>is pretty sure what you should do in this case: <br />
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<strong><em> Test first. If Test is Positive, do the Procedure.</em></strong> Proceed with the seismic testing and, if you get a positive result, go ahead and drill and get rich. If you get a negative test result you are advised to abandon the plan to drill at that point. Do not throw good money after the “bad” $1M you spent on the seismic testing. Move to another spot and continue seismic testing and hope for better test results.<br />
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But what if you and your investors happened to be more greedy (or cautions) and demanded at least a 30% ROI?</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkhK-nBKjKK_MfknoDvoVs-tlh5dOUiTAYdwhThl0mSCE4enmhtYfr_-bbWpbvr6YGC7u2vVekFY3s5nVseujA0oafIJmtEt9s5Y2Ho29Qa3fHhQ0bymIaRbvP51G2gVctBtfHzerdRN1P/s1600/BayesOil.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkhK-nBKjKK_MfknoDvoVs-tlh5dOUiTAYdwhThl0mSCE4enmhtYfr_-bbWpbvr6YGC7u2vVekFY3s5nVseujA0oafIJmtEt9s5Y2Ho29Qa3fHhQ0bymIaRbvP51G2gVctBtfHzerdRN1P/s320/BayesOil.jpg" width="640" /></a></div>
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The figure above shows the numbers you would input into the<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian Inference Adviser</b></i><span class="Apple-converted-space"> </span>for the given situation, and the output you would get. The <strong><em>Bayesian Inference Adviser </em></strong>is pretty sure what you should do in this case:<br />
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<strong><em> Hopeless venture. (Can you reduce expected ROI?)</em></strong> Forget about it unless you and your investors will accept a lower ROI. Given these inputs, if you absolutely need 30% ROI, it is HOPELESS. However, if you and your investors are willing to reduce expected ROI to 20%, you should TEST FIRST, then GIVEN A POSITIVE TEST RESULT, DRILL.<br />
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On the other hand, what if you are in a different oil patch where the PRIOR probability of striking oil or gas is much higher, say 80%?<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHNGG3s10t9ZQBBPzSPSeH4S5cdbXIvP3UFX-BCDIzI8jJ8qwEQuogSaqFKWGcdGME_b3TNa_6PRbV5FkjZBzvcL3opnzMnoA1KAtHXzibK6T4MdW5osw26kNYvHk4PamXCY3g8M-4B5JP/s1600/BayesOil2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHNGG3s10t9ZQBBPzSPSeH4S5cdbXIvP3UFX-BCDIzI8jJ8qwEQuogSaqFKWGcdGME_b3TNa_6PRbV5FkjZBzvcL3opnzMnoA1KAtHXzibK6T4MdW5osw26kNYvHk4PamXCY3g8M-4B5JP/s320/BayesOil2.JPG" width="640" /></a></div>
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The figure above shows the numbers you would input into the<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian Inference Adviser</b></i><span class="Apple-converted-space"> </span>for the given situation, and the output you would get. The <strong><em>Bayesian Inference Adviser </em></strong>is pretty sure what you should do in this case:<br />
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<strong><em> No need to Test. Go ahead with Procedure. </em></strong>Here, with such a high expectation of hitting oil or gas, you don't even have to test. <br />
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NOTE: These are just made-up values to illustrate the process and may or may not represent the actual financial situation in any real-world situation. If you use this tool to make money, please send me my share. If you lose money, you are on you own :^)</div>
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<strong>Choices</strong> What to do? </div>
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1) Go ahead and drill without seismic testing? </div>
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2) Do the seismic testing and, if you get a positive result, go ahead and drill? </div>
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3) Forget about it – all these numbers hurt my head!</div>
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The <strong><em>Bayesian Inference Adviser </em></strong>crunches the numbers you entered and gives you the results and recommendations on what to do! </div>
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According to analysis using Bayes Law, in the first situation above, if you drill for oil or gas without doing the seismic testing, you are most likely to invest $133M, for a net loss of $73M and an ROI of -55%. OUCH! Not a good result!</div>
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If you go ahead and invest the $1M for the seismic testing of several locations and eventually get a positive result and then drill, you are most likely to invest $50M for each successful oil well, for a net gain of $10M and an ROI of +20%. WOW! That would be great!</div>
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What happens when oil prices go up or down and other variables change? Given different circumstances, the <strong><em>Bayesian Inference Adviser </em></strong>is capable of recommending that you proceed to drill without testing or that you abandon plans to get into the oil business in that area entirely. </div>
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<span style="color: #660000;"><strong>Background – What is Bayes Theorem?</strong></span> If you really want to know all the intimate statistical probabilistic stuff, just Google “Bayes Theorem” or “Bayesian” and you will get lots of links replete with mathematical symbols in all their glory. (Don’t worry if you can’t really understand all those symbols -perhaps your daughter could play them on her flute :^)</div>
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<span style="color: #660000;"><strong>Here is All You Really Need to Know about Bayes</strong></span> The Rev. Thomas Bayes was a Presbyterian minister and mathematician who lived in the 1700′s. His great contribution to mathematics was the concept of “<strong><em>inverse </em></strong>probability”. He came up with it at a time when only “<strong>forward </strong>probabilty” was generally known. </div>
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<section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><strong>Forward </strong>Probability is Easy <div>
<strong>Forward </strong>probability has to do with making predictions based on previous knowledge. Say you know the following about <em>Poupon University</em>: </div>
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1) There are a total of 3000 students, </div>
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2) 2340 are Liberal Arts majors, </div>
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3) 60 are Math majors, and </div>
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4) 600 are Engineering majors. </div>
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If you go to Commons and pick a student at random, what is the probability you’ll pick a Liberal Arts major? A Math major? An Engineer? (Assuming, of course, that Engineers are as likely as, say English majors, to take a break from their studies and to go to the Commons :^)</div>
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That is easy using <strong>forward </strong>probability: </div>
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1) Liberal Arts: 2340/3000 = 0.4 or a 78% chance of picking a Liberal Arts major. </div>
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2) Math: 60/3000 = 0.02 or a 2% chance of picking a Math major. </div>
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3) Engineering: 600/3000 = 0.2 or a 20% chance you’ll pick an Engineer.</div>
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</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><strong><em>Inverse </em></strong>Probability is Hard </section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><div>
What Bayes figured out, <strong><em>inverse </em></strong>probability, is harder. (An English major once told me that “<em>backward </em>poets rhyme <em>inverse</em>” but that is a different matter :^) </div>
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Hey, here’s a student wearing a Bayes Theorem T-Shirt! Based on the facts given above, what is the probability he or she is a Liberal Arts major? A Math major? an Engineer? The formula on his shirt can help you do the <strong><em>inverse </em></strong>probability to figure that out. </div>
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See the top figure in this posting, a T-Shirt with Bayes Theorem in Mathematical Symbols</div>
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But first you need some additional facts: </div>
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a) Based on sales by the college store, about 300 students out of the 3000 on campus, or 10%, own a Bayes T-shirt. </div>
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b) 100% of the Math majors own them (of course :^). </div>
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c) 30% of the engineeers.</div>
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d) Only 2.6% of the Liberal Arts majors.</div>
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e) You are in luck, today is April 7, the day Rev. Thomas Bayes died 1761, so everybody who owns a Bayes T-Shirt will be wearing one today!</div>
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If you pick a student <strong>who is wearing a Bayes T-Shirt</strong>, at random, what is the <strong>inverse </strong>probability that he or she is a Liberal Arts major? A Math major? An Engineer? Why don’t you guess right now – please write your answers down so you will be properly amazed when you find out how wrong (or right) you were!</div>
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Bayes Theorem is shown in mathematical symbols on the T-Shirt at the top of this posting. It translates to mathematical English as follows:</div>
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<strong> Probability of A <em>given</em> B equals Probability of B <em>given</em> A multiplied by the Probability of A and divided by the Probability of B</strong><strong> </strong> In case you did not understand that translation, here it is in plain English using the Bayes T-shirt and Engineering students as an example:</div>
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<strong> The Probability a Student is an Engineer <em>given</em> that he or she is wearing a Bayes T-Shirt, is equal to the Probability of wearing a Bayes T-Shirt <em>given</em> a student is an Engineer multiplied by the Probability a Randomly-selected student is an Engineer, all divided by the Probability a Randomly-selected student is wearing a Bayes T-Shirt. </strong> Let’s run the numbers:</div>
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<strong>P(Wearing Bayes T-Shirt given Engineer)</strong>=30% [from a few paragraphs above]</li>
<li><strong>P(Engineer) = 20% </strong>[from the forward probability stuff]</li>
<li><strong>P(Wearing Bayes T-Shirt) = 10% </strong>[from a few paragraphs above]</li>
<li><strong>P(Engineer <em>given</em> Wearing Bayes T-Shirt) = P(Wearing Bayes T-Shirt <em>given</em> Engineer) </strong><strong> x P(Engineer) / P(Wearing Bayes T-Shirt) = 30 x 20 / 10 = 60% </strong> </li>
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</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"></section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">So, <em>given </em>that the student you pick at random is actually wearing a Bayes T-Shirt, there is a 60% chance he or she is an Engineer! WOW! What did you guess? 60% is a higher percentage than I would have guessed because only 20% of the students on campus are Engineers.<div>
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So, using the “test” that a student is wearing a Bayes T-Shirt <em>increases </em>your chances of picking an Engineer by a factor of three. WOW, the power of Bayes Theorem is impressive. </div>
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If you run the numbers for Math majors you get 100x 2 / 10 = 20%. There is a 20% chance he or she is a Math major. WOW! A surprising result because only 2% of the students on campus are Math majors! So using the “test” that a student is wearing a Bayes T-Shirt <em>increases </em>your chances of picking a Math major by a factor of ten. WOW, the power of Bayes Theorem is impressive.</div>
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If you run the numbers for Liberal Arts majors you get: 1x 40 / 10 = 4%. There is only a 4% chance he or she is a Liberal Arts major, surprising because they make up 40% of the student body. Bayes predicts you are ten times <em>less </em>likely to pick a Liberal Arts major using the Bayes T-Shirt test, a negative result. (You could use that test to <em>avoid </em>Liberal Arts majors -or they could use the same test to avoid Engineers and Math majors:^) </div>
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So, in summary, if a student happens to be wearing a Bayes T-Shirt on this campus today, there is an 80% chance he or she is in Math or Engineering even though only 22% of the students are in those two majors.</div>
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<strong><span style="color: #660000;">Bayesian Controversy</span></strong> </div>
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According to <a href="http://psychology.wikia.com/wiki/Bayesian_probability" rel="nofollow"><span style="color: #0867ab;">http://psychology.wikia.com/wiki/Bayesian_probability</span></a> there is considerable controversy between “Bayesians” and “Frequentists” as to the true meaning and interpretation of “probability”. (IMHO, the controversy is like the legendary spat between the "Hatfields" and the "McCoys" - as a practical matter it does not mean anything TO ME. There are situations where standard "Frequentist" probability is most applicable and situations where "Bayesian" probability is most applicable. Both are valid in their own ways.)</div>
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</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><strong><em>Bayesian </em></strong>Interpretation <div>
“In the philosophy of mathematics <strong>Bayesianism </strong>is the tenet that the mathematical theory of probability is applicable to the degree to which a person believes a proposition. Bayesians also hold that Bayes’ theorem can be used as the basis for a rule for updating beliefs in the light of new information —such updating is known as <em>Bayesian inference . </em>In this sense, Bayesianism is an application of the probability calculus and a probability interpretation of the term <em>probable</em>, or —as it is usually put —an <em>interpretation of probability</em>.”</div>
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“A quite different interpretation of the term <em>probable </em>has been developed by frequentists . In this interpretation, what are <em>probable </em>are not propositions entertained by believers, but events considered as members of collectives to which the tools of statistical analysis can be applied.”</div>
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</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Discussion</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"> </section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">The <strong>frequentists </strong>demand that probability statements be based on hard data derived from actual observation and experiments. On the other hand, <strong><em>Bayesians </em></strong>allow each person to assign different Bayesian probabilities to the same proposition.<div>
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</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">“Although there is no reason why different interpretations (senses) of a word cannot be used in different contexts, there is a history of antagonism between Bayesians and frequentists, with the latter often rejecting the Bayesian interpretation as ill-grounded. The groups have also disagreed about which of the two senses reflects what is commonly meant by the term ‘probable’.”<div>
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An interesting example would be if ten coin tosses resulted in seven heads and three tails. A <strong>frequentist </strong>would say the probability is 70/30 heads unless and until further tosses proved otherwise. A <strong><em>Bayesian </em></strong>would consider the situation from a larger prospective. Was the coin provided by a trusted person or some stranger in a bar? Is there reason to believe the coin is fair or loaded? Based on that consideration, one <strong><em>Bayesian </em></strong>might assign a probability of 50/50, since ten tosses with a 70/30 result is statistically possible with a fair coin. Another <strong><em>Bayesian </em></strong>might conclude, from the situation, that the coin is probably loaded and assign a 70/30 probability. Yet another might split the difference and assign 60/40, … </div>
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</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Of course, if the coin is tossed another hundred times, both the <strong>frequentists </strong>and the <strong><em>Bayesians </em></strong>may change their assigned probabilities. It may turn out that the <strong>frequentist </strong>70/30 was closer to the truth -or- that the <em><strong>Bayesian </strong></em>50/50 was a better call. <div>
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<span style="color: #660000;">Targeted Marketing Example</span> </h2>
Guess what, the <strong><em>Bayesian Inference Adviser </em></strong>loves targeted marketing problems!<br />
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Say we are marketing something fairly expensive, with a correspondingly high profit margin. Suppose it would appeal only to a highly specialized audience. For example, something that only mathematically and technologically-oriented college students would buy. Indeed, what if ownership of a Bayes T-Shirt turned out to be an excellent “test indicator” to qualify a prospect? If we could get hold of a list of students who bought those shirts -or just go on campus and approach anyone wearing one- we could restrict our sales pitches to them.</div>
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If the Bayesian <em><strong>Inverse </strong></em>probability was high enough for this select group, we could afford to lure them to our sales pitch with the promise of a gift or a free meal. </div>
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Bad Reputation of “Free Bait” Not Always Justified Of course you are familiar with this type of targeted marketing approach. Offer a free trial subscription to a magazine or a 30-day free trial for a software program or computer game. Give a lower monthly price for cell phone service or cable-TV for a year and jack it up after the customer is hooked. Offer a free vacation to a time share property, etc. The key to the success of these plans is to qualify the targets and then offer them the “free bait”. You better qualify them well because the “free bait” can be costly to you if all you attract are people who have no intention of buying and are just looking for a free meal or gift!</div>
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Although some instances of targeted marketing have given the genre a bad reputation, there is nothing wrong, in principle, with offering something of value to qualified people to get them to listen to your sales pitch. For example, when I interviewed seniors on a college campus for possible jobs as engineers at the company where I worked, I was allowed to invite up to 25% of the top candidates for an expense-paid trip to our facility – if they met certain GPA and other qualifications.</div>
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The key is to make sure that the qualifying “test” is effective enough to justify the “free bait”.</div>
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TARGETED MARKETING Case</section><br />
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Marketing Case - Test the Person, Offer Free Bait if Qualified </div>
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This is a situation where the “Prior” Probability is very low – only about <strong>five </strong>out of <strong>one-thousand </strong>people would want our product and be able to afford it. That is only 0.5%. </div>
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Assume we have developed some type of “qualifying test” that identifies about <strong>ten </strong>out of <strong>one-thousand </strong>people as targets. That is only1%. (This “test” might be a prospect list we could buy from a market data company that tracks interests and buying habits and disposable income of specific types of people. Alternatively, we might send agents to yacht clubs or professional societies or whatever type of affinity group that tends to have people who qualify for our product. Our agents would glad-hand people and identify likely prospects. Another possibility would be to have our current customers recommend their associates with similar interests and income.) </div>
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Notice that these two probabilities 0.5 and 1% are very much lower than the probabilities we used for the oil exploration cases. Targeted marketing makes sense only when the targets are a very select population and our product has a high markup. (If the targets were a higher percentage of the general population, we would use the mass media such as the internet, TV, and print publications.) </div>
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The third probability we need to input is <strong>conditional </strong>probability, the probability that someone who would buy our product would pass our qualifying test. We could survey current customers using the “test” we have devised and determine what percentage of them would pass the “test”. In this case, let us assume 75% of our current customers would pass the test. </div>
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We input these three probabilities and the <strong><em>Bayesian AI Adviser </em></strong>calculates the <strong><em>inverse </em></strong>probability that we will be successful in selling our product to a person who passed the test. In this case that comes out to be 37.5%. </div>
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</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Input the Financial Assumptions </section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"></section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Now we need the four essential financial inputs. Let us assume we will have to spend about $2 per person for the qualifying test. We’ll offer qualified prospects a gift or meal that costs us about $40 each. If they buy our product or service we’ll get a gross return of about $750 and we need an ROI of 20% to justify the risk.</section><section class="sec" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><div>
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In this case, with such a small percentage of the population as our audience, it would be foolish to invite everybody for the “free bait” – we would lose big! According to the <strong><em>Bayesian Inference Adviser</em></strong>, an untargeted approach would cost us about $8000 for each person who buys, a net loss of $7250 and a ROI of -90%. We expected results like that which is why we intend to do targeted marketing. </div>
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The <strong><em>Bayesian Inference Adviser </em></strong>is pretty sure what you should do in this case: </div>
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<strong><em> Hopeless venture. (Can you reduce expected ROI?)</em></strong> Forget about it unless you and your investors will accept a lower ROI. Given these inputs, if you absolutely need 20% ROI, it is HOPELESS. However, if you and your investors are willing to reduce expected ROI to 17%, you should <strong><em>Test first. If Test is Positive, do the Procedure.</em></strong> Proceed with the qualification testing and, if you get a positive result, go ahead offer them the free vacation or gift or meal and get rich. </div>
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<span style="color: #660000;">Medical Testing - Highly Accurate Tests but Ultra-Low “Probability of Success”</span> </h2>
Medical testing illustrates another aspect of the value of analysis based on Bayesian <em><strong>inverse </strong></em>probability. Generally, medical tests, such as tests for early detection of serious diseases or use of illegal drugs in the workplace are very good (with 95% to 99.99%accuracy) but the targets are rare in the population. Of course it is good that only a very small percentage of people have these serious diseases or use illegal drugs in the workplace, but, as you will see based on Bayesian analysis, that leads to a fairly high level of false positives. <br />
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<span style="color: #660000;"><strong>Screening Tests for Serious but Rare Diseases</strong></span></div>
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Assume one in ten-thousand people in a given population is in the initial stages of some serious disease. Early testing could detect the disease in time to take preventive action. P(S) = 0.01% expresses that<span class="Apple-converted-space"> </span><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">one in a ten-thousand</b><span class="Apple-converted-space"> </span>probability.</div>
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Assume further that there is a test that can detect the disease in its early stages with a 99.99% probability. That is, if a person has the disease and takes the test, there is a 99.99% probability the test will come back positive. However, the probability of a positive test is 0.1%, which means that, while 99.9% of the population will get a negative result, 0.1% will get a positive, and nine out of ten of the positives will be <strong><em>false</em></strong> positives.</div>
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The computed Bayes<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">inverse</b></i><span class="Apple-converted-space"> </span>probability is 10% which means that only one in ten people who get a positive test result will actually have the disease. There will be about nine <strong><em>false</em></strong> positives for every ten-thousand people tested. All ten people will have to be called back in for more intensive and intrusive (and expensive) re-testing using other techniques to assure they do not have the disease. For every person who has the disease, nineteen will be alarmed and inconvenienced unnecessarily.</div>
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If we assume the cost of the initial testing is about $10 per person, which is quite reasonable for any kind of medical test, and that the cost of follow-up testing will be about $500 for each person identified as possibly having the disease, the cost of finding that one person in ten-thousand will be over $100,000 dollars! If we have to test one-million people, we will find about one-hundred with the disease and unnecessarily alarm and inconvenience nearly two-thousand, and spend over $2M! If we have to test three-hundred million people, it will cost over $3B! </div>
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<span style="color: #660000;">Testing for Illegal Drugs in the Workplace</span></h3>
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The<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</b></i><span class="Apple-converted-space"> </span>could be used to determine the cost of doing screening tests in the workplace to identify employees who may be using hard drugs. They are putting themselves and their co-workers in jeopardy through their actions and risking liability actions against their employer if a co-worker or a member of the public is affected by their actions.</div>
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However, even if the tests are highly accurate and correctly catch 99% of the employees who have used illegal drugs recently, they are likely to have <strong><em>false</em></strong> positives for even more innocent employees. This will necessitate follow-up testing that may be more intrusive and alarming, as well as very expensive. The<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</b></i><span class="Apple-converted-space"> </span>will compute the likely costs of such a screening program. Management will have to determine if the elimination of various types of drugs among employees is worth the overall expense and disruption.</div>
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For example, it may well be worth the expense and disruption of innocent employee’s lives to do complete screening for airline pilots, bus drivers, employees in high-security jobs where drug use may expose them to blackmail, and others whose actions could cost lives and expose employers to gigantic liability claims. On the other hand, employees in less critical jobs might be screened only if evidence comes up that they are behaving strangely at work, are in financial stress, are having domestic troubles, etc. </div>
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<span style="color: #660000;">Error Testing Feature of <em>Bayesian Inference Adviser</em></span></h2>
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What if we enter probabilities that don’t make sense? Well, the <strong><em>Bayesian AI Adviser </em></strong>has some error detection capabilities, as illustrated by the red boxes in the rightmost panel. </div>
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Notice the far right column in the above examples, where four red "OK" notices indicate error checking has found no problems. If there was an error, a red "Error" notice would appear on the affected line. For example, a red “Error” would denote that P(+) < P(S) x P(+|S), which is not possible, or that the combination of P(S), P(+), and P(+|S) causes P(S|+) > 0.999. </div>
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The <strong><em>Bayesian Inference Adviser </em></strong>also checks that the Gross Benefit if Successful is greater than the Cost of Procedure and that the Cost of Procedure is greater than the Cost of Test. A little red “OK” indicates that those values are not in error. </div>
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<span style="color: #660000;">Sensitivity Analysis – How Robust Are Your Results?</span></h2>
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<span style="color: #660000;">Why Do Sensitivity Analysis?</span></h3>
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The results and recommendations of the<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</b></i><span class="Apple-converted-space"> </span>are, of course, dependent upon the probabilities and cost factors you input. There are two reasons to do sensitivity analysis and the<b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><span class="Apple-converted-space"> </span>Bayesian AI Adviser</i></b><span class="Apple-converted-space"> </span>provides graphical aids for both:</div>
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<span style="color: #660000;">YOU ARE UNCERTAIN ABOUT YOUR INPUT PARAMETERS</span></h4>
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The inputs are “just estimates”. What if they are off by 10%? 20%? – or more? The<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</b></i><span class="Apple-converted-space"> </span>graphically indicates what would happen to your ROI if the true value was lower than you estimated, down to half what you input. It also shows what the ROI would be if any of your input variables were double what you input. (If you can’t estimate a variable closer than a factor of two, you are really not ready to do anything that will put real money at risk!) </div>
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<span style="color: #660000;">YOU MISSED YOUR ROI GOAL</span> </h4>
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If the<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</b></i><span class="Apple-converted-space"> </span>indicates you missed your ROI goal you may be able to make changes to achieve it. The most obvious change is to reduce your desired ROI. For example, if you expected to achieve 30% and the<span class="Apple-converted-space"> </span><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</i></b><span class="Apple-converted-space"> </span>indicates you will only meet 20%, perhaps you should settle for that.</div>
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If reducing minimum acceptable ROI is a deal-breaker for your investors, then you need to consider more difficult changes. These include: <br />
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1) Improving the qualification test to tighten the limits, <br />
2) Changing the drilling location or market sector to an area where you are more likely to strike oil and/or find customers, <br />
3) Modifying your product so it has more appeal, <br />
4) Raising the price to gain more benefit from each sale, <br />
5) Reducing the price to increase volume of sales, <br />
6) Reducing the cost of the qualification tests, etc.<br />
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The<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</b></i><span class="Apple-converted-space"> </span>graphically indicates which of these changes are most likely to have the best pay-off for you. </div>
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<span style="color: #660000;">Example of Sensitivity Analysis – Oil Exploration Case #2</span></h3>
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FINANCIAL FACTOR SENSITIVITY</h4>
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<a href="http://web.archive.org/web/20120616172412/http://iraknol.files.wordpress.com/2010/01/bayes-oil2costsensitivity1.jpg" style="color: #0867ab; text-decoration: none;"><img border="0" src="http://web.archive.org/web/20120616172412im_/http://iraknol.files.wordpress.com/2010/01/bayes-oil2costsensitivity1.jpg" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;" /></a></div>
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The figure shows your financial factors (see Oil Exploration Case #2 subsection above): Your minimum acceptable ROI is 30% (indicated by the horizontal dashed line) . The most likely achieved ROI is indicated as the point where the other curves cross. It is about 20%.</div>
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Here is how to use the sensitivity analysis graph:</div>
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<b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Benefit if Successful:</b><span class="Apple-converted-space"> </span>The blue line marked with diamonds represents changes to the Benefit if Successful. If you can increase that by 10%, indicated as where it crosses the ROI line, you will be at 30% ROI. That means waiting for oil prices to go up or reducing your refining or transport costs, etc. In the marketing case, it means raising your prices, but that may be self-defeating if sales decline as a result, or reducing your prices to gain volume, but that too may be self-defeating if profits decrease as a result of a smaller margin per item sold.</div>
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<b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Procedure Cost:</b><span class="Apple-converted-space"> </span>Alternatively, according to the green line marked with triangles, if you reduce your Procedure Cost by about 15%, you meet the ROI. That means reducing the cost of drilling that well. In the targeted marketing case, perhaps you can just serve coffee and donuts rather than a full meal.</div>
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<b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Test Cost:</b><span class="Apple-converted-space"> </span>The third possibility is reducing your Test Cost, as indicated by the pink line with squares, but that would require reducing the Test Cost by over 20%. Perhaps you can get the seismic test company to lower their price? Perhaps the market research company will sell you that list of hot prospects for less money?</div>
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PROBABILITY FACTOR SENSITIVITY</h4>
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<a href="http://web.archive.org/web/20120616172412/http://iraknol.files.wordpress.com/2010/01/bayes-oil2probsensitivity1.jpg" style="color: #0867ab; text-decoration: none;"><img border="0" src="http://web.archive.org/web/20120616172412im_/http://iraknol.files.wordpress.com/2010/01/bayes-oil2probsensitivity1.jpg" style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;" /></a></div>
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The figure shows your probability factors: Again, your minimum acceptable ROI is 30% (indicated by the horizontal dashed line) and the achieved ROI, indicated as the point where the other curves cross) is about 20%.</div>
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Here is how to use the sensitivity analysis graph:</div>
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<b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Probability of Success:</b><span class="Apple-converted-space"> </span>The black line marked with starry squares represents changes to P(S), Probability of Success. If you could improve that by about 10% you would meet your ROI goal. P(S) is determined by where you intend to drill or the market segment you are addressing, etc., so you would have to move to a different area or market segment to improve that value.</div>
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<b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Probability of Positive Test:</b><span class="Apple-converted-space"> </span>Alternatively, according to the blue line marked with circles, if you reduce your Probability of Positive Test by about 10%, you meet the ROI. That would require making the qualification test tighter, so it discriminates the chances of success more sharply and has fewer <strong><em>false</em></strong> positives.</div>
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<b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Probability of Positive Test<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">given</i><span class="Apple-converted-space"> </span>Success:</b><span class="Apple-converted-space"> </span>The third possibility is increasing your Probability of Positive Test<span class="Apple-converted-space"> </span><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">given</i><span class="Apple-converted-space"> </span>Success by about 10%. This requires tighter classification of your previous customers in the targeted marketing case or of the geological assumptions in an oil exploration case.</div>
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<span style="color: #660000;">Please Let Me Know How this Tool Has Helped You</span></h2>
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I’d appreciate it if you would Comment on this (former Google Knol) posting and let me and others know your experiences with the<span class="Apple-converted-space"> </span><b style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;"><i style="border: 0px currentColor; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline;">Bayesian AI Adviser</i></b>, ideas for improvement, etc. You may also reach me by email at<span class="Apple-converted-space"> </span><a href="mailto:Ira@techie.com" style="color: #0867ab; text-decoration: none;">Ira@techie.com</a>. advTHANKSance! </div>
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<span style="color: #0b5394; font-family: "Helvetica Neue", Arial, Helvetica, sans-serif; font-size: x-large;"><em>Ira Glickstein</em></span></div>
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Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-18586954540142057292015-09-03T08:51:00.000-07:002015-09-03T08:53:01.887-07:00What is TIME? (In the context of Relativity)<iframe allowfullscreen="" frameborder="0" height="375" mozallowfullscreen="" src="http://player.vimeo.com/video/60563419" webkitallowfullscreen="" width="500"></iframe> <br />
<a href="http://vimeo.com/60563419">Time - the fourth dimension (2013 Flame Challenge)</a> from <a href="http://vimeo.com/user16712038">Ira Glickstein</a> on <a href="http://vimeo.com/">Vimeo</a>.<br />
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My entry for Alan Alda's 2013 <em>Flame Challenge</em> was submitted way back in February 2011. It is in the form of a short video answering the deceptively simple question "What is Time?" (click above to view the video).<br />
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Alan Alda is on a mission to help youngsters become interested in science. In conjuction with the <a href="http://www.centerforcommunicatingscience.org/the-flCenter">Center for Communicating Science at SUNY Stony Brook</a>, he started the <em>Flame Challenge</em> in 2012 with the question "What is Flame?" They received some 800 entries.<br />
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I expect they will get even more this year with the question "What is Time?"<br />
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<div style="text-align: center;">
<strong>ABOUT MY ENTRY</strong></div>
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I think I've come up with a unique way of viewing "<em>Time</em> - the fourth dimension". Due to a strict limit on the length of the video, and the fact that it is aimed at 11-year old students, I have had to greatly simplify the material. This Blog posting includes additional material that will be useful to adult readers and science teachers who wish to know more about my way of viewing <em>Time</em>.<br />
<br />
There are three big ideas here:<br />
<ol>
<li><em><strong>TIME</strong></em> is NOT a clock (any more than Space is a ruler or Heat is a thermometer), nor is it rotation of the Earth or motion or the order of events, etc. </li>
<li><em><strong>TIME</strong></em> is <strong><em>the fourth dimension</em></strong>, plain and simple. It appears different to us because the whole Universe is speeding along the <em>Time</em> axis at the speed of light. </li>
<li><em><strong>TIME</strong></em> slows down when we move in Space because nothing can move faster than the speed of light, so any motion in Space must take away from the speed in <em>Time</em> such that the vector sum of the Space and <em>Time</em> velocities exactly equals the speed of light.</li>
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<div style="text-align: center;">
<strong>WHAT <em>TIME</em>
IS NOT</strong></div>
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<div>
<em>Time</em> is not the tick, tick, tock of a click, click,
clock, any more than Space is a ruler or Heat is a thermometer!</div>
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</div>
<div>
Nor is <em>Time</em> the rotation of the Earth on its axis
that gives us day and night divided into 24 hours. Nor is it the movement of the
tilted Earth in orbit around the Sun that gives us the seasons, nor any other
kind of motion. Nor is it the spontaneous decay of certain atoms that give
radioactive materials a half-life. Nor is it simply the ordering of events.</div>
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<div style="text-align: center;">
<strong>WHAT TIME
IS</strong></div>
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<div>
<em>Time</em>,
plain and simple, is
the fourth dimension,
very much like the first three dimensions of Space. </div>
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</div>
<div>
The <em>Time</em>
dimension appears different to us because you and I and the whole Universe are
hurtling along it at very nearly the speed of light as a consequence of the
“Big Bang” expansion some 13.7 billion years ago, in which our Universe, along with the dimensions of Space and <em>Time</em>, originated. <br />
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Since <em>Time</em> itself originated with the "Big Bang" it may not be meaningful to even ask the question "What happened <em>before</em> the Big Bang?" In any case, we may never know what caused it.</div>
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The Universe originated as an incredibly energetic and dense point of Energy/Matter that suddenly expanded. During the initial moments of the expansion, it is not clear if there was anything like the sub-atomic and atomic particles of Matter or the radiation of Energy with which we are familiar today. However, when Matter and Energy, as we know it, formed, all particles with mass were expelled along the <em>Time</em> axis, or at very tiny angles with respect to that axis. You and I, along with everyone and everything else, are still moving along or near that dimension at very close to the speed of light, <em><strong>c</strong></em>, which is as fast as anything can go. </div>
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We do not notice our ultra-rapid travel along the <em>Time</em> dimension as motion because the whole Universe is moving along with us. Therefore, we notice only <em>relative</em> motion between ourselves and other people and between ourselves and other things. </div>
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<div>
For example, people on the equator are happily unaware that they are moving Eastward at about 1,000 miles per hour due to the rotation of the Earth on its axis. Unless you live in one of the polar regions, you are moving Eastward at hundreds of miles per hour. Even if you are on an airplane, travelling "Westward" from New York to Chicago or Los Angeles at 500 miles per hour, your net velocity is Eastward, due to the rotation of the Earth! We are equally unaware that the whole Earth is speeding along at over 67,000 miles per hour on its orbit around the Sun!</div>
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<span style="font-family: Times New Roman;">
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<strong>WHY <em>TIME</em>
CAN BE SLOWED A BIT</strong></div>
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</div>
<div>
We live in four-dimensional Space<em>Time</em>
where everything must move at the speed of light, <strong><em>c</em></strong>,
either along the <em>Time</em> axis, along a Space axis, or in a
combination of <em>Time</em> and Space at an angle, <strong><em>Θ</em></strong>, to
the
<em>Time</em> axis.
If movement is totally aligned with the Time axis, <strong><em>Θ = 0</em></strong> and we are said to be “at rest” in
Space, and we move along the <em>Time</em> axis at the normal rate (<em><strong>c</strong></em>,
about one foot per nanosecond).</div>
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<div>
If we are not "at rest" in Space, <strong><em>Θ > 0</em></strong>, and we move through Space<em>Time</em> in a combination of Space and <em>Time</em> such that the vector sum of our Space and <em>Time</em> velocities is exactly <em><strong>c</strong></em>. Since nothing can go faster than <em><strong>c</strong></em>, any movement in Space must slow down our movement in <em>Time</em>. This was recognized over 100 years ago by Lorentz, Minkowski, and Einstein, who use the terms "Dilation of Time" and "Contraction of Space". This is usually expressed in terms of the Lorentz factor:</div>
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<br />
<br />
<dd><img alt=" \gamma = \frac{1}{\sqrt{1-v^2/c^2}} \," class="tex" src="http://rpmedia.ask.com/ts?u=/math/e/c/e/ece36c4d0f9e2f93d3f04810f7519e40.png" /></dd>where <em><strong>c</strong></em> is the velocity of light and <strong><em>v</em></strong> is the velocity of an object in Space. <br />
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<span style="color: red; font-size: large;"><strong><em>As an engineer, I found that way of expressing relativistic effects of travel at significant fractions of the speed of light not to be "understandable" from my physical (and perhaps anal) point of view.</em></strong></span></div>
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After <em>knocking my head against the wall</em> over an inordinate amount of <em>Time</em>, I finally realized that I could get an exactly equivalent Lorentz factor by considering the angle <em><strong>Θ</strong></em>, between the Time axis and the velocity vector of an object through SpaceTime.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH3MOfwXrQS-cddvsbIZ2TTPKiZDRzDF8rGauv4AyG7K2z_PhoR_VblDIUtPUVPeczKCOtG8kSdPY7tanXs9_WGVyWXTLGfKiJFBe9wK50pXlCxLkptLS1cp9TzdyPhUp4tfsa9gfB53O1/s1600/TimeDilation.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH3MOfwXrQS-cddvsbIZ2TTPKiZDRzDF8rGauv4AyG7K2z_PhoR_VblDIUtPUVPeczKCOtG8kSdPY7tanXs9_WGVyWXTLGfKiJFBe9wK50pXlCxLkptLS1cp9TzdyPhUp4tfsa9gfB53O1/s320/TimeDilation.JPG" width="520" /></a></div>
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[above image modified 12 April 2013]</div>
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It turns out that <em><strong>v</strong></em> (the velocity of the object in Space) divided by <strong><em>c</em></strong> is equal to the <strong><em>Sin
Θ</em></strong>, and that 1/<em><strong>ϒ</strong></em>, the Lorenz factor, is equal to the <strong><em>Cos Θ</em></strong>. </div>
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<strong>WHAT ARE DIMENSIONS?</strong><br />
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This may sound like a simple question, and the answer is pretty simple, but, just to be sure we are all on the same page (see figure below):</div>
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0 - A POINT has ZERO dimensions</div>
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1 - Drag the point along the FIRST dimension ("x" of Space) and you get a LINE, that has ONE dimension.</div>
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2 - Drag the line along the SECOND dimension ("y" of Space) and you get a SQUARE (or rectangle) that has TWO dimensions.</div>
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3 - Drag the square along the THIRD dimenson ("z" of Space) and you get a CUBE (or rectangular solid) that has THREE dimensions.</div>
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4 - Drag the cube along the FOURTH dimension ("t" of Time) and you get a HYPER-CUBE (or hyper-rectangular solid) that has FOUR dimensions.</div>
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<strong>SUMMARY</strong></div>
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When movement is a combination of <em>Time</em> and Space, and the velocity in Space is <em><strong>v</strong></em>, an object is moving through Space<em>Time</em> at an angle <em><strong>Θ</strong></em>, such that: <strong><em>v/c = SinΘ</em></strong>, and 1/<strong><em>ϒ</em></strong> (the Lorentz factor) <strong><em>= Cos Θ</em></strong>.<br />
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The figure below shows the situation for seven different values for the angle of travel through Space<em>Time</em>, from <strong><em>Θ = </em></strong><strong><em>0</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong> to <strong><em>Θ = 90</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span><em> </em></strong>.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjywTmN6cHPANxbo1dFIMEVfUHZfRlDQ3RcQcNEENl7CQHOxkewdKW4qcfvjPc4PBNX7V1Cv4Tm9zQMWmIIgJmbE_lKTFIhTX34tW0d7CdE_iNy5MWiQJuuQ85Q1Wp4iXpEeZgNaQZ_-wFI/s1600/time+angles.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="504" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjywTmN6cHPANxbo1dFIMEVfUHZfRlDQ3RcQcNEENl7CQHOxkewdKW4qcfvjPc4PBNX7V1Cv4Tm9zQMWmIIgJmbE_lKTFIhTX34tW0d7CdE_iNy5MWiQJuuQ85Q1Wp4iXpEeZgNaQZ_-wFI/s320/time+angles.jpg" width="520" /></a></div>
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<strong><em>Θ = 0</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰ [<em>Sin</em> <span style="font-family: Times New Roman;"><em>Θ = 0.0000, Cos Θ = 1.0000</em>] <span style="color: #274e13;">AT REST IN SPACE</span></span></span></span></strong><br />
<strong><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"></span></strong>For an object that is "at rest" in Space, <span style="color: black;"><strong><em>Θ = 0</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong>. Even when an object is not moving along the Space axis, it is moving along the <em>Time</em> axis. Since everything in Space<em>Time</em> must have a speed of <strong><em>c</em></strong>, an object "at rest" in Space must be moving at speed <strong><em>c</em></strong> in <em>Time</em>. Note that for this condition, <strong><em>v/c = 0</em></strong> and the Lorentz factor <strong><em>ϒ = 1</em></strong>. Note also that, for this case <strong><span style="font-family: Calibri;"><em>Sin</em> </span><em><span style="font-family: Times New Roman;">Θ</span></em><span style="font-family: Times New Roman;"></span></strong><span style="font-family: Times New Roman;"></span> is equal to <em><strong>v/c</strong></em> and <strong><em>Cos Θ </em></strong>is equal to 1/<strong><em>ϒ</em></strong>.</span><br />
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Even the fastest rockets and satellites developed so far go only a tiny, tiny fraction of c. Therefore, for all practical purposes, the angle, <strong><em>Θ</em></strong>, is <span style="color: black; font-family: Calibri; font-size: 18pt; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-color-index: 1; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: black; mso-style-textfill-fill-themecolor: text1; mso-style-textfill-type: solid;">≈ </span><em><strong>0</strong></em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;"><strong>⁰</strong> (approximately equal to ZERO degrees).<strong> For example, the Earth is travelling around the Sun at a speed of 67,000 miles per hour, faster than any rocket, but that is only 0.001 % of the speed of light. At 67,000 miles per hour,<em> v/c</em> = 0.00001 and <em><span style="font-family: Times New Roman;">Θ </span></em>= 0.0000017</strong><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;"><strong>⁰.</strong> </span></span></span></span><br />
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<strong><em>Θ = 15</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰ [<em>Sin</em> <span style="font-family: Times New Roman;"><em>Θ = 0.2588, Cos Θ = 0.9659</em>] <span style="color: blue;">MOVING 26% OF<span style="color: black;"> <em>c</em></span> IN SPACE</span></span></span></span></strong><br />
<strong><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"></span></strong>An object is moving through Space<em>Time</em> at an angle of <span style="color: black;"><strong><em>Θ = 15</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong>. It moves through Space at 26% of <strong><em>c</em></strong> and through Time at 97% of <strong><em>c</em></strong>. Note that for this condition, <strong><em>v/c = 0.2588</em></strong> and the Lorentz factor <strong><em>ϒ = 0.9659</em></strong>. Note also that, for this case <strong><span style="font-family: Calibri;"><em>Sin</em> </span><em><span style="font-family: Times New Roman;">Θ</span></em><span style="font-family: Times New Roman;"></span></strong><span style="font-family: Times New Roman;"></span> is equal to <em><strong>v/c</strong></em> and <strong><em>Cos Θ </em></strong>is equal to 1/<strong><em>ϒ</em></strong>.</span><br />
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<strong><em>Θ = 30</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰ [<em>Sin</em> <span style="font-family: Times New Roman;"><em>Θ = 0.5000, Cos Θ = 0.8660</em>] <span style="color: #b45f06;">MOVING 50% OF <em><span style="color: black;">c</span></em> IN SPACE</span></span></span></span></strong><br />
<strong><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"></span></strong>An object is moving through Space<em>Time</em> at an angle of <span style="color: black;"><strong><em>Θ = 30</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong>. It moves through Space at 50% of <strong><em>c</em></strong> and through Time at 87% of <strong><em>c</em></strong>. Note that for this condition, <strong><em>v/c = 0.5000</em></strong> and the Lorentz factor <strong><em>ϒ = 0.8660</em></strong>. Note also that, for this case <strong><span style="font-family: Calibri;"><em>Sin</em> </span><em><span style="font-family: Times New Roman;">Θ</span></em><span style="font-family: Times New Roman;"></span></strong><span style="font-family: Times New Roman;"></span> is equal to <em><strong>v/c</strong></em> and <strong><em>Cos Θ </em></strong>is equal to 1/<strong><em>ϒ</em></strong>.</span><br />
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<strong><em>Θ = 45</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰ [<em>Sin</em> <span style="font-family: Times New Roman;"><em>Θ = 0.7071, Cos Θ = 0.7071</em>] <span style="color: #b45f06;"><span style="color: #660000;">MO</span><span style="color: #783f04;">VING 71% OF</span> <em><span style="color: black;">c</span></em> </span><span style="color: #783f04;">IN SPACE</span></span></span></span></strong><br />
<strong><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"></span></strong>An object is moving through Space<em>Time</em> at an angle of <span style="color: black;"><strong><em>Θ =45</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong>. It moves through Space at 71% of <strong><em>c</em></strong> and through <em>Time</em> at 71% of <strong><em>c</em></strong>. Note that for this condition, <strong><em>v/c = 0.7071</em></strong> and the Lorentz factor <strong><em>ϒ = 0.7071</em></strong>. Note also that, for this case <strong><span style="font-family: Calibri;"><em>Sin</em> </span><em><span style="font-family: Times New Roman;">Θ</span></em><span style="font-family: Times New Roman;"></span></strong><span style="font-family: Times New Roman;"></span> is equal to <em><strong>v/c</strong></em> and <strong><em>Cos Θ </em></strong>is equal to 1/<strong><em>ϒ</em></strong>.</span><br />
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<strong><em>Θ = 60</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰ [<em>Sin</em> <span style="font-family: Times New Roman;"><em>Θ = 0.8660, Cos Θ = 0.5000</em>] <span style="color: #b45f06;"><span style="color: purple;">MOVING 87% OF</span> <em><span style="color: black;">c</span></em> </span><span style="color: purple;">IN SPACE</span></span></span></span></strong><br />
<strong><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"></span></strong>An object is moving through Space<em>Time</em> at an angle of <span style="color: black;"><strong><em>Θ = 60</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong>. It moves through Space at 87% of <strong><em>c</em></strong> and through <em>Time</em> at 50% of <strong><em>c</em></strong>. Note that for this condition, <strong><em>v/c = 0.8660</em></strong> and the Lorentz factor <strong><em>ϒ = 0.5000</em></strong>. Note also that, for this case <strong><span style="font-family: Calibri;"><em>Sin</em> </span><em><span style="font-family: Times New Roman;">Θ</span></em><span style="font-family: Times New Roman;"></span></strong><span style="font-family: Times New Roman;"></span> is equal to <em><strong>v/c</strong></em> and <strong><em>Cos Θ </em></strong>is equal to 1/<strong><em>ϒ</em></strong>.</span><br />
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<strong><em>Θ = 75</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰ [<em>Sin</em> <span style="font-family: Times New Roman;"><em>Θ = 0.9659, Cos Θ = 0.2558</em>] <span style="color: #b45f06;"><span style="color: #444444;">MOVING 97% OF</span> <em><span style="color: black;">c</span></em> </span><span style="color: #444444;">IN SPACE</span></span></span></span></strong><br />
<strong><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"></span></strong>An object is moving through Space<em>Time</em> at an angle of <span style="color: black;"><strong><em>Θ = 75</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong>. It moves through Space at 97% of <strong><em>c</em></strong> and through <em>Time</em> at 26% of <strong><em>c</em></strong>. Note that for this condition, <strong><em>v/c = 0.9659</em></strong> and the Lorentz factor <strong><em>ϒ = 0.2558</em></strong>. Note also that, for this case <strong><span style="font-family: Calibri;"><em>Sin</em> </span><em><span style="font-family: Times New Roman;">Θ</span></em><span style="font-family: Times New Roman;"></span></strong><span style="font-family: Times New Roman;"></span> is equal to <em><strong>v/c</strong></em> and <strong><em>Cos Θ </em></strong>is equal to 1/<strong><em>ϒ</em></strong>.</span><br />
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<strong><em>Θ = 90</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰ [<em>Sin</em> <span style="font-family: Times New Roman;"><em>Θ = 1.0000, Cos Θ = 0.0000</em>] <span style="background-color: #783f04; color: yellow;">TIME STANDS STILL</span><span style="color: #b45f06;"> </span></span></span></span></strong><br />
Light (and other forms of electro-magnetic radiation) move through Space<em>Time</em> at an angle of <span style="color: black;"><strong><em>Θ = 90</em><span style="color: #00b050; font-family: Calibri; font-weight: bold; language: en-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-effects-shadow-align: topleft; mso-effects-shadow-alpha: 43.0%; mso-effects-shadow-angledirection: 2700000; mso-effects-shadow-anglekx: 0; mso-effects-shadow-angleky: 0; mso-effects-shadow-color: black; mso-effects-shadow-dpidistance: 3.0pt; mso-effects-shadow-dpiradius: 3.0pt; mso-effects-shadow-pctsx: 100.0%; mso-effects-shadow-pctsy: 100.0%; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #00B050; mso-style-textfill-type: solid; text-shadow: none;"><span style="color: black;">⁰</span></span></strong>. Light moves through Space at 100% of <strong><em>c</em></strong> and, therefore, since nothing can go faster than <strong><em>c</em></strong>, <em>Time</em> stands still. Note that for this condition, <strong><em>v/c = 1.0000</em></strong> and the Lorentz factor <strong><em>ϒ = 0.0000</em></strong>. Note also that, for this case <strong><span style="font-family: Calibri;"><em>Sin</em> </span><em><span style="font-family: Times New Roman;">Θ</span></em><span style="font-family: Times New Roman;"></span></strong><span style="font-family: Times New Roman;"></span> is equal to <em><strong>v/c</strong></em> and <strong><em>Cos Θ </em></strong>is equal to 1/<strong><em>ϒ</em></strong>.</span> Anything with mass cannot achieve this speed in Space because it would take an infinite amount of energy to get it up to this speed in Space.<br />
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<strong><span style="color: purple;">[ADDED 11 March 2013]</span></strong> In response to some skepticism about my contention that the whole known Universe is speeding along the <em>Time</em> dimension at nearly the speed of light, I did more research and found support from Brian Greene, Professor of Physics and Mathematics at Columbia U, who has been featured on the PBS Nova series. He writes:<br />
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<b><i>“Special relativity declares a similar law for all motion: the combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light”</i></b> [Excerpt From: Greene, Brian. “The Fabric of the Cosmos.” Vintage Books, 2007. See <a href="http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.htm" rel="nofollow"><span style="color: blue;">http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.htm</span></a> for his PBS series.]<br />
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<span style="font-size: large;"><em>Ira Glickstein</em></span></div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-60171106170695835402015-09-01T13:19:00.001-07:002015-09-01T21:58:01.606-07:00VISUALIZING - Using My FREE Excel Spreadsheet for Special and General Relativity<div style="text-align: right;">
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<b style="font-size: medium;"><i><span style="font-size: large;">Nowadays</span></i></b><span style="font-size: small;"> it is common to use computer models to help us VISUALIZE and better understand complex situations and systems. Prior to the advent of computer models, we had to use mental models in our "mind's eye", along with physical aids such as paper maps and diagrams, modelling clay, and so on. I've created an interactive Excel Spreadsheet for Special and General Relativity.</span></div>
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<span style="font-family: Calibri; font-size: 12pt;"><span style="font-family: Calibri; font-size: 12pt;">User selects a Star, Planet, or Set Angle Option. </span></span><br />
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<span style="font-family: Calibri; font-size: 12pt;"><span style="font-family: Calibri; font-size: 12pt;">Right side shows Special Relativity Effects due to the Kinetic Energy of moving at half the speed of light in empty Space. </span></span><br />
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<span style="font-family: Calibri; font-size: 12pt;"><span style="font-family: Calibri; font-size: 12pt;">Left side shows equivalent General Relativity Effects, where Time "curves" due to the Potential Energy of being "at rest" close to a Black Hole.</span></span><br />
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Albert Einstein was a great physicist, with all the requisite mathematical tools. However, he rejected <em style="background-color: white; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border: 0px; color: #404040; line-height: 22.8800029754639px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">purely</em><span style="background-color: white; line-height: 22.8800029754639px;"> mathematical abstraction and resorted to </span><em style="background-color: white; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border: 0px; color: #404040; line-height: 22.8800029754639px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">physical analogy</em><span style="background-color: white; line-height: 22.8800029754639px;"> for his most basic insights. For example, as part of the thought process that resulted in his theories of Special Relativity (1905) and General Relativity (1915) he imagined himself riding along a beam of light; or as an observer standing along the tracks as a train zipped by at near-light-speed; or as a scientist sealed in a closed box and not able to tell if the box was stationary on the surface of the Earth, subject to gravity, or in deep space, far from massive objects, but </span><span style="background-color: white; line-height: 22.8800029754639px;">subject to acceleration due to </span><span style="background-color: white; line-height: 22.8800029754639px;">being dragged by a rocket at ever-increasing speeds.</span><br />
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Of course, Einstein and virtually all scientists and technologists use mathematical abstractions to quantify the meaning in our visualization models. We change the initial conditions and run these models to simulate what may or may not happen in different situations.<br />
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<b><span style="color: #4c1130;">COMPUTER MODELS FOR <i><span style="font-size: large;">VISUALIZATION</span></i></span></b><br />
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As personal computers and the Internet have become endemic, manual typewriters, paper maps, physical books, and so much else has been displaced by automated versions. Similarly, computer visualizations and models have displaced older methods - except for that old reliable "mind's eye" which remains as important as ever.<br />
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During my career as a Senior System Engineer at IBM and Lockheed-Martin I made extensive use of computer models and visualizations and have continued to do so since retirement.<br />
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<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;"><b><span style="color: #4c1130;"><i><span style="font-size: large;">VISUALIZING</span></i> EINSTEIN'S SPECIAL AND GENERAL RELATIVITY</span></b></span><br />
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Perhaps the most well-known equation in the world is <span style="font-family: Georgia, Times New Roman, serif;"><b>E = m<span style="text-indent: -0.38in;">c</span><span style="text-indent: -0.38in; vertical-align: super;">2</span></b>,</span> recognized by virtually every person. But, what does it really mean?<br />
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And, many people know about the so-called "twin paradox", where one twin goes off on long mission at high speeds into space, and comes back younger. But why does this happen and exactly what causes it?<br />
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If "everything is relative" why isn't the stay-at-home twin also also younger? So, everything is <i>not</i> relative, and perhaps Einstein's original name for his theories "Invariance" is more apt -for the fact all observers, including those moving at different speeds, measure the same speed for light.<br />
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If the traveling twin is younger due to experiencing high speed and acceleration, then it is aging that has slowed down, not time, per se.<br />
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Furthermore, what, precisely, is TIME? And how is TIME united with SPACE to form SpaceTime?<br />
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When you Google any of this stuff you are quickly buried in equations and tensor mathematics that <i>no one</i> (even an engineer like me) can <i>really</i> understand!<br />
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Well, all this bothered me for most of my life until, back in 2012, I decided to answer Alan Alda's <i>Flame Challenge</i> "What is Time?" and produce a short video. In the research process for that project, I think I had a critical insight into TIME, SPACE, and RELATIVITY that may help you VISUALIZE this important scientific theory.<br />
<iframe allowfullscreen="" frameborder="0" height="375" mozallowfullscreen="" src="https://player.vimeo.com/video/60563419" webkitallowfullscreen="" width="500"></iframe> <br />
<a href="https://vimeo.com/60563419">Time - the fourth dimension (2013 Flame Challenge)</a> from <a href="https://vimeo.com/user16712038">Ira V Glickstein</a> on <a href="https://vimeo.com/">Vimeo</a>.<br />
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Since that time, I've continued to delve into Relativity and I've come up with what I think is a unique way to visualize and ... perhaps ... even <i>understand </i>it. The following images are screenshots from an Excel spreadsheet I created to provide myself (and you :^) a "hands-on" experience with the relativistic effects of high speed (kinetic energy) and high acceleration (potential energy), including time dilation, length contraction, and the curvature of SPACE and TIME. It is available free.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTq30ISKwNm3q026WWhC9ZyKgxiyc6MZHfLZbiMhYk5gevLWBBtlcz1rBQCYhy2YEvH_BGni-yaE88b-J9S0gF8C6wvwahyphenhyphenh0a4h-DDBOJfAI8nsRKGsyI7ZSy8kkmcBg1WHNo9z7LaWao/s1600/Excel+Main+Panel.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="408" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTq30ISKwNm3q026WWhC9ZyKgxiyc6MZHfLZbiMhYk5gevLWBBtlcz1rBQCYhy2YEvH_BGni-yaE88b-J9S0gF8C6wvwahyphenhyphenh0a4h-DDBOJfAI8nsRKGsyI7ZSy8kkmcBg1WHNo9z7LaWao/s640/Excel+Main+Panel.JPG" width="640" /></a></td></tr>
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<div style="text-align: left;">
<span style="font-family: Calibri; font-size: 12pt; font-weight: bold;">Free
Excel Spreadsheet for VISUALIZATION of Einstein's Special and General
Relativity. </span></div>
<span style="font-family: Calibri; font-size: 12pt;"></span><br />
<div style="text-align: left;">
<span style="font-family: Calibri; font-size: 12pt;"><span style="font-family: Calibri; font-size: 12pt;">Image
is of the Main Panel where user selects a Star, Planet, or Set Angle Option. In
the case illustrated, the </span><span style="font-family: Calibri; font-size: 12pt;">SpaceTime</span><span style="font-family: Calibri; font-size: 12pt;">
angle is set to 30º, where velocity is half the speed of light</span><span style="font-family: Calibri; font-size: 12pt;">.
</span><span style="font-family: Calibri; font-size: 12pt;">T</span><span style="font-family: Calibri; font-size: 12pt;">his
</span><span style="font-family: Calibri; font-size: 12pt;">causes
clocks to slow down by 13.4%, which corresponds to 49 days per year or 482
seconds per hour. Right side shows Special Relativity Effects due to the
Kinetic Energy of moving at half the speed of light in empty Space. Left side
shows equivalent General Relativity Effects, where Time "curves" due
to the Potential Energy of being "at rest" close to a Black Hole.</span></span></div>
<span style="font-family: Calibri; font-size: 12pt;">
</span></div>
</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR_TRdFwsUB0USx9vTeJCGyUxUt82KM4wqRQlszWF4tf715RHb_o9Rn3Ynh3-H39g7bLiVoXEURu7CSFHxVsVklS_wHvklRJ7le1u6XfhgYXx-8i4zwnIMnX-xS5qybmg2TzrUFTa1WPRy/s1600/Excel+Kinetic+Minkowski.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="382" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR_TRdFwsUB0USx9vTeJCGyUxUt82KM4wqRQlszWF4tf715RHb_o9Rn3Ynh3-H39g7bLiVoXEURu7CSFHxVsVklS_wHvklRJ7le1u6XfhgYXx-8i4zwnIMnX-xS5qybmg2TzrUFTa1WPRy/s640/Excel+Kinetic+Minkowski.JPG" width="640" /></a></td></tr>
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<div style="text-align: left;">
<span style="font-family: Calibri; font-size: 12pt; font-weight: bold;">Free
Excel Spreadsheet for VISUALIZATION of Einstein's Special and General
Relativity. </span></div>
<span style="font-family: Calibri; font-size: 12pt;"></span><br />
<div style="text-align: left;">
<span style="font-family: Calibri; font-size: 12pt;"><span style="font-size: 12pt;">Image
is of the SpaceTime view of the right side of the Main Panel (where the vector sum of TRAVEL + AGING = 1) plus the Minkowski-Like SpaceTime view (where the simple sum of TRAVEL + AGING =1). </span></span></div>
<span style="font-family: Calibri; font-size: 12pt;">
</span></div>
</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPrUY7sbS7QM6f9w3r5xO_SgX4gjuyOc9SmuxXLlceZiBpwDC4cpalxwqiEG26aeAYA8BbXgbKEjPrx05Zx8SYvu7fpYrhfNWBDta8Sh52fq5y759AmQwToR3TOKNBFt5cZ7DgZAaQYEfV/s1600/Excel+Minkowski+Planck.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPrUY7sbS7QM6f9w3r5xO_SgX4gjuyOc9SmuxXLlceZiBpwDC4cpalxwqiEG26aeAYA8BbXgbKEjPrx05Zx8SYvu7fpYrhfNWBDta8Sh52fq5y759AmQwToR3TOKNBFt5cZ7DgZAaQYEfV/s640/Excel+Minkowski+Planck.JPG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><div style="text-align: center;">
<span style="font-family: Calibri; font-size: 12pt; font-weight: bold; text-align: left;">Free Excel Spreadsheet for VISUALIZATION of Einstein's Special and General Relativity. </span></div>
<div style="text-align: left;">
<span style="font-size: small; text-align: left;"><span style="font-family: Calibri;">Image is of the Minkowski-Like view (described above) compared to a Planck view, where both Space and Time are assumed to be discrete, and </span><span style="font-family: Calibri; text-align: right; text-indent: 0in;">Each tiny cell is </span><span style="font-family: Calibri; text-align: right; text-indent: 0in;">1</span><span style="font-family: Calibri; text-align: right; text-indent: 0in; vertical-align: baseline;"> Planck Time (</span><span style="font-family: Calibri; font-style: italic; text-align: right; text-indent: 0in;">t</span><span style="font-family: Calibri; font-style: italic; text-align: right; text-indent: 0in; vertical-align: sub;">P </span><span style="font-family: Calibri; text-align: right; text-indent: 0in; vertical-align: baseline;">) </span><span style="font-family: Calibri; text-align: right; text-indent: 0in;">by</span><span style="font-family: Calibri; text-align: right; text-indent: 0in; vertical-align: baseline;"> </span><span style="font-family: Calibri; text-align: right; text-indent: 0in; vertical-align: baseline;">1 Planck Length (</span><span style="font-family: Calibri; font-style: italic; text-align: right; text-indent: 0in;">ℓ</span><span style="font-family: Calibri; font-style: italic; text-align: right; text-indent: 0in; vertical-align: sub;">P</span><span style="font-family: Calibri; text-align: right; text-indent: 0in; vertical-align: baseline;">).</span></span></div>
<span style="font-size: small; text-align: left;">
</span></td></tr>
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<b><span style="color: #4c1130;">THE MAP IS NOT THE TERRITORY!</span></b><br />
<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;"><br /></span>
<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;">As </span>my principal PhD advisor, Howard Pattee, taught me, "The MAP is NOT the TERRITORY". That sage statement means that <b>no model is exactly the same as the thing being modeled</b> (else it would be the real thing.)<br />
<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;"><br /></span><span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;">We make models because the real thing is too complex and difficult for us to visualize, or -like the Global Climate- is not readily available for us to experiment upon.</span><br />
<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;"><br /></span>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia3gTyw_yBNxkPUizcFrdXH5NJOqk4MGU4jTvB4IllEhGl7bzZzjhF71fPQwjLJeTrkD6e2EzXva5_i1j0lxNUDKHKzhTAv7soyfA2SkKv9l0dIQFL_fIo5ijYRjHL_H6AAhFhmqQWSJ4G/s1600/CatMilitaryStrategy.gif" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><span style="color: black;"><img border="0" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia3gTyw_yBNxkPUizcFrdXH5NJOqk4MGU4jTvB4IllEhGl7bzZzjhF71fPQwjLJeTrkD6e2EzXva5_i1j0lxNUDKHKzhTAv7soyfA2SkKv9l0dIQFL_fIo5ijYRjHL_H6AAhFhmqQWSJ4G/s200/CatMilitaryStrategy.gif" width="200" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The MAP is NOT the TERRITORY !</td></tr>
</tbody></table>
<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;">Many a General (or football coach) has moved symbols around on a map of the field of battle, convincing himself and his staff of inevitable victory, only to find his opponent also had a model, perhaps a better one plus superior forces to carry it to victory. </span><br />
<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;"><br /></span>
<span style="background-color: white; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 17.6000003814697px; line-height: 22.8800029754639px;">We generally model only the most important or critical parts of the situation or complex system we are trying to visualize. We consider the model to have been successful if the results match actuality to some level of fidelity, at least for those significant portions. If subsequent testing reveals that the model does not comport with reality, we must improve or discard it.</span><br />
<br />
<div style="text-align: center;">
<i><b><span style="color: blue; font-size: large;">Ira Glickstein</span></b></i></div>
</div>
<br />
<span style="font-family: inherit;">
</span>Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com3tag:blogger.com,1999:blog-6562551902946123839.post-13558211395148014172015-09-01T13:13:00.001-07:002021-07-24T13:00:56.767-07:00VISUALIZING My "Insight" into Lorentz "Gamma" and SpaceTimeA key aspect of Einstein's Special Relativity is that, at high speeds, there is significant "Time Dilation" and "Length Contraction". In his 1905 Theory of Relativity paper, Einstein derives the equation that <i>quantifies </i>these Relativistic Effects, apparently unaware that Hendrick Lorentz had earlier come up with the same equation. The "Lorentz Transform" or "Lorentz Gamma" (equation near the top of the graphic below) solves for <span style="background-color: white; color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-size: 16.52px; font-style: italic; font-weight: 700; white-space: nowrap;">γ</span> (Greek lower-case letter Gamma) given knowledge of the relative velocity of a body (<i><b>v</b></i>) divided by the speed of light (<i><b>c</b></i>).<br />
<br />
Simple enough, but, in my (perhaps overly anal :^) Engineering Mind it bothered me that I could not "picture" it in <i>physical </i>terms.<br />
<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAV6vEOnLO6P_VqToVix3wsCFCihJHoWsz92EPlUMivAxhrmUBm_F5605Dwt0-ZBONIU787Oqx9lutOiCzLFa01Eqnq9YuMLSnbBAHOQFsHFR5uLFyIfTBWhr37EX1rvQS874hnCjDhc_X/s1600/VIZLorentz.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="490" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAV6vEOnLO6P_VqToVix3wsCFCihJHoWsz92EPlUMivAxhrmUBm_F5605Dwt0-ZBONIU787Oqx9lutOiCzLFa01Eqnq9YuMLSnbBAHOQFsHFR5uLFyIfTBWhr37EX1rvQS874hnCjDhc_X/s640/VIZLorentz.jpg" width="640" /></a></div>
<span style="color: blue; font-size: x-small;">LINKS TO RELATED POSTINGS AND RESOURCES</span><br />
<a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxpcmFiZXN0cHBzfGd4OjFiYzE5YTZhNjA1YTQ4YjY"><span style="color: blue; font-size: x-small;">VISUALIZING Relativity - PowerPoint Show</span></a><br />
<a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxpcmFiZXN0cHBzfGd4OjFjZWZjZTY2ZDRlOTRkNWM"><span style="color: blue; font-size: x-small;">VISUALIZING Relativity - Excel Spreadsheet</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/05/visualization-for-science-and-technology.html?utm_source=BP_recent"><span style="color: blue; font-size: x-small;">VISUALIZING for Science and Technology - Blog Posting</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/06/visualizing-einsteins-miracle-year.html?utm_source=BP_recent"><span style="color: blue; font-size: x-small;">VISUALIZING Einstein's "Miracle Year" - Blog Posting</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/06/visualizing-my-insight-into-lorentz.html"><span style="color: blue; font-size: x-small;">VISUALIZING My Insight Into Lorentz Gamma - Blog Posting</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/06/visualizing-twin-paradox.html"><span style="color: blue; font-size: x-small;">VISUALIZING the "Twin Paradox" - Blog Posting</span></a><br />
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<b><span style="color: #660000;">AN OLD JOKE</span></b><br />
<br />
This situation reminds me of the old joke about the Historian, the Physicist, and the Engineer who happened to be waiting for a bus outside an office building. They noticed <i>three </i>people (a man and two women) enter the building, and, some time later, <i>five </i>emerge (a woman and four men).<br />
<br />
Making conversation, the Historian asked, "How many people are in that building?"<br />
<br />
The Physicist immediately answered, "<i>Three </i>went in and <i>five </i>came out, so there are <i>minus two</i> people in that building!"<br />
<br />
The Engineer shook his head. "Mathematically correct," he noted, "But, what in hell does '<i>minus two</i> people' mean?"<br />
<br />
"Do you have a better answer?" asked the Historian.<br />
<br />
The Engineer thought for a while and replied. "Well, if we assume that is the only entrance and exit for that building, we can deduce that, prior to our arriving here, there were <i>at least three men</i> in that building, and now there is <i>at least one woman</i> in there."<br />
<br />
<b><span style="color: #660000;">BACK TO LORENTZ</span></b><br />
<br />
Well, a couple of years ago, I ran the Lorentz Transform for several different values of <i><b>v/c</b></i> and was startled to find some <i>familiar </i>numbers come up, among them <i><b>0.5000, 0.7071, and 0.8660</b></i>.<br />
<br />
Early in my engineering career I memorized the sines and cosines of <i><b>30⁰, 45⁰, and 60⁰</b></i>. Those were the familiar numbers that popped up in my results for the Square Root of <b><i>1-(v/c)²</i></b>. (The fact that I still remember those numbers, half a century later, confirms how anal my Engineering Mind really is. :^)<br />
<br />
For example, if you pick the simple case of half the speed of light (i.e., <i><b>v/c = 0.5000</b></i>), the Square Root term turns out to be <i><b>0.8660</b></i>, which is the <i><b>Cosine </b></i>of <i><b>30⁰</b></i>. As the graphic above illustrates, if you plot Time vs Space with commensurate scales (i.e., Time in <i>nanoseconds </i>and Space in <i>feet</i>, since, as I also memorized those many years ago, light travels about <i>one foot</i> in <i>one nanosecond</i>), a unit long <i>SpaceTime</i> vector, tipped <i><b>30⁰</b></i> from the Time axis, has its point at <i><b>0.5000 </b></i>along the Space axis and <i><b>0.8660 </b></i>along the Time axis!<br />
<br />
<b><span style="color: #660000;">SOME EXAMPLES</span></b><br />
<br />
Let us call the Square Root part of the Lorentz Transform term <b><i>α</i></b> (Greek letter Alpha) from here on, and notice that <b><i>α = 1/</i></b><i><b>ϒ</b></i>. Furthermore, let us call the <i><b>v/c</b></i> term <i><b>β</b></i> (Greek letter Beta), and the angle between the Time axis and the unit long<i> SpaceTime</i> vector <i><b>Θ </b></i>(Greek letter Theta).<br />
<br />
For <i><b>Θ =</b></i> <i><b>0</b></i><i><b>⁰ </b></i>: <b><i>α = 1.0000 = Cos(</i></b><i><b>0</b></i><i><b>⁰</b></i><b><i>) </i></b>and <i><b>β</b></i><b> = <i>0.0000</i> = <i>Sin</i></b><b><i>(</i></b><i><b>0</b></i><i><b>⁰</b></i><b><i>)</i></b><br />
For <i><b>Θ =</b></i> <i><b>30</b></i><i><b>⁰ </b></i>: <b><i>α = 0.8660 = Cos(</i></b><i><b>30</b></i><i><b>⁰</b></i><b><i>) </i></b>and <i><b>β</b></i><b> = <i>0.5000</i> = <i>Sin</i></b><b><i>(</i></b><i><b>30</b></i><i><b>⁰</b></i><b><i>)</i></b><br />
For <i><b>Θ =</b></i> <i><b>45</b></i><i><b>⁰ </b></i>: <b><i>α = 0.7071 = Cos(</i></b><i><b>45</b></i><i><b>⁰</b></i><b><i>) </i></b>and <i><b>β</b></i><b> = <i>0.7071</i> = <i>Sin</i></b><b><i>(</i></b><i><b>45</b></i><i><b>⁰</b></i><b><i>)</i></b><br />
For <i><b>Θ =</b></i> <i><b>60</b></i><i><b>⁰ </b></i>: <b><i>α = 0.5000 = Cos(</i></b><i><b>60</b></i><i><b>⁰</b></i><b><i>) </i></b>and <i><b>β</b></i><b> = <i>0.8660</i> = <i>Sin</i></b><b><i>(6</i></b><i><b>0</b></i><i><b>⁰</b></i><b><i>)</i></b><br />
For <i><b>Θ =</b></i> <i><b>90</b></i><i><b>⁰ </b></i>: <b><i>α = 0.0000 = Cos(</i></b><i><b>90</b></i><i><b>⁰</b></i><b><i>) </i></b>and <i><b>β</b></i><b> = <i>1.0000</i> = <i>Sin</i></b><b><i>(</i></b><i><b>90</b></i><i><b>⁰</b></i><b><i>)</i></b><br />
<br />
So, now it all makes sense (at least to an old engineer like me :^)! All the Square Root part of the Lorentz Transform is telling us is that if we pick a value for <i><b>v/c </b></i>that is equal to the Sine of some angle, <i><b>Θ</b></i>, we'll get a value for the Square Root part that is the Cosine of that <i>same </i>angle, <i><b>Θ</b></i>.<br />
<br />
The simple VISUALIZATION is a unit vector in <i>SpaceTime</i> tipped <i><b>Θ</b></i><i><b>⁰</b></i> from the Time axis, and it works for any <i><b>Θ </b></i>between <i><b>0</b></i><i><b>⁰ </b></i>and <i><b>90</b></i><i><b>⁰</b></i>. <br />
<br />
<b><span style="color: #660000;">OK, BUT WHAT IS THIS VISUALIZATION TELLING US?</span></b><br />
<br />
In the above graphic, the Time axis extends up to <i><b>1.0</b></i>, but the projection of the unit long <i>SpaceTime</i> vector onto the Time axis reaches only to <i><b>0.8660</b></i>. So, what does <b><i>α = 0.8660 </i></b>tell us?<br />
<br />
I used to have the impression that Relativistic Effects "slowed down time", and I believe quite a few of you who are reading this Blog accept that idea. However, the well known "Twin Paradox" (to be discussed in more detail the next Blog Posting in this VISUALIZING Series) tells us, IMHO, that it is not Time, per se, that "slows down" but rather AGING. For every year the stay-at-home Twin ages, the travelling twin ages only <b><i>α</i></b> years. So, if <b><i>α = 0.8660</i></b>, and the stay-at-home twin ages <i><b>10</b></i> years, the traveling twin will age only <i><b>8.66</b></i> years.<br />
<br />
What do<i> I</i> mean by AGING? Well, it is simply the number read from a good-quality clock at some final Event, assuming the clock was set to zero at some initial Event, and that the clock was present at both Events. The clock may be a mechanical or electronic device, or a chemical or radioactive reaction, or a biological life form, such as bacteria, plants, or animals.<br />
<br />
In the Twin Paradox example, both siblings are present at the separation Event and the reunion Event, each usually denoted by numerical values for <b><i>t, x, y,</i></b> and <i><b>z</b></i>, for Time and the three dimensions of Space. Thus, when reunited, they are both at the exact same Time (and Space), the only difference is how much each of them has AGED.<br />
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<div style="text-align: center;">
<span style="color: blue; font-size: large;"><b><i>Ira Glickstein</i></b></span></div>
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<br />Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-83526803097190330122015-09-01T13:07:00.001-07:002015-09-01T13:10:25.674-07:00VISUALIZING the "Twin Paradox"In Einstein's ground-breaking 1905 paper<span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">, </span><a href="https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf" style="background-color: white; color: #7eb8d4; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px; text-decoration: none;">On the Electrodynamics of Moving Bodies</a>, he provides the basis for the well-known "Twin Paradox" (where one twin takes a space journey at high speeds, and finds, upon returning home, that he or she has AGED less than the stay-at-home sibling). Quoting Einstein:<br />
<blockquote>
<i>If one of two synchronous
clocks at A is moved in a closed curve with constant velocity until it returns to
A, the journey lasting t seconds, then by the clock which has remained at rest
the traveled clock on its arrival at A will be [<b>1 - <span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">α</span></b>] seconds slow</i>*.</blockquote>
* Note: I've substituted "<i><b>1 - <span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px;">α</span></b></i>" for the equivalent, but more complex equation in Einstein's original paper, where <i><b><span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px;">α </span></b></i>is the Square Root portion of the Lorentz Transformation ( <span style="border-color: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border-width: initial; line-height: 29.8666667938232px;"><img alt="\scriptstyle{\epsilon = \sqrt{1 - v^2/c^2}}" class="mwe-math-fallback-image-inline tex" src="https://upload.wikimedia.org/math/5/4/3/543bc9f7c0c227c945a5f37f66234cad.png" style="background-color: white; border: none; color: #252525; display: inline-block; font-family: sans-serif; line-height: 29.8666667938232px; margin: 0px; vertical-align: middle;" /></span>) as described in my <a href="http://tvpclub.blogspot.com/2015/06/visualizing-my-insight-into-lorentz.html">previous Blog posting</a>.<br />
<br />
To VISUALIZE Einstein's thought experiment, let "A" be a location on Earth, where the stay-at-home twin resides, and the "closed curve" be the path followed by the traveling twin, moving at 87% of the speed of light (<i><b>v/c = </b><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; font-weight: bold; line-height: 27.7200012207031px;">β</span><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; font-weight: bold; line-height: 27.7200012207031px;"> = 0.8660</span></i>) where <b><i><span style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">α = 0.5</span> </i></b>as depicted below.<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0Hafzn7RgIEdH0tfxLuz2p8pFtbR83x6CZq7B1c8JNomtOe_DkeswxN-zSXFIVFb2dLca0v6YgeVS3JCT-nrmLlMaDK__LAGEXAzZ_Ktz7A0BX2fAfvPfVgz73ZZTb7IsOceTmZoGhJy6/s1600/VIZTwins.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="490" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0Hafzn7RgIEdH0tfxLuz2p8pFtbR83x6CZq7B1c8JNomtOe_DkeswxN-zSXFIVFb2dLca0v6YgeVS3JCT-nrmLlMaDK__LAGEXAzZ_Ktz7A0BX2fAfvPfVgz73ZZTb7IsOceTmZoGhJy6/s640/VIZTwins.jpg" width="640" /></a><br />
<span style="color: blue; font-size: x-small;">LINKS TO RELATED POSTINGS AND RESOURCES</span><br />
<a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxpcmFiZXN0cHBzfGd4OjFiYzE5YTZhNjA1YTQ4YjY"><span style="color: blue; font-size: x-small;">VISUALIZING Relativity - PowerPoint Show</span></a><br />
<a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxpcmFiZXN0cHBzfGd4OjFjZWZjZTY2ZDRlOTRkNWM"><span style="color: blue; font-size: x-small;">VISUALIZING Relativity - Excel Spreadsheet</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/05/visualization-for-science-and-technology.html?utm_source=BP_recent"><span style="color: blue; font-size: x-small;">VISUALIZING for Science and Technology - Blog Posting</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/06/visualizing-einsteins-miracle-year.html?utm_source=BP_recent"><span style="color: blue; font-size: x-small;">VISUALIZING Einstein's "Miracle Year" - Blog Posting</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/06/visualizing-my-insight-into-lorentz.html"><span style="color: blue; font-size: x-small;">VISUALIZING My Insight Into Lorentz Gamma - Blog Posting</span></a><br />
<a href="http://tvpclub.blogspot.com/2015/06/visualizing-twin-paradox.html"><span style="color: blue; font-size: x-small;">VISUALIZING the "Twin Paradox" - Blog Posting</span></a><br />
<br />
As depicted, Blair and Aden are 20 years old when Aden takes off on a long space journey at ultra-high speed while Blair remains home. Aden's journey, at an average speed of 87% the speed of light, extends out to the vicinity of a Neutron Star (or a Black Hole) where Aden's spaceship "slingshots" and speeds back to Earth.<br />
<br />
When Aden is at the half-way point, Blair has AGED 30 Earth-years and is 50 years old. However Aden, due to being in a state of high Kinetic Energy with respect to Blair, has AGED only 15 years and is only 30 years old.<br />
<br />
By the time Aden returns from the journey, Blair has AGED an additional 30 Earth-years and has reached the ripe old age of 80. However Aden has only AGED an additional 15 years, and returns home a sprightly 50 year-old!<br />
<br />
<b><span style="color: #660000;">WHAT DOES THIS VISUALIZATION TELL US?</span></b><br />
<br />
First of all, this is only a "thought experiment" and there are many practical limitations that make it unrealistic. None of our current spacecraft are capable of even 1% of the speed of light, much less the 87% imagined for Aden. Furthermore, even if we had such a spacecraft, and even if it carried only a clock and not a fragile human being, considering the G-forces involved, it would take a number of years to accelerate up to 87% of the speed of light, perform the "slingshot", and decelerate to land safely on Earth.<br />
<br />
A more realistic depiction would include those years of acceleration and deceleration and would require some portions of the journey to be faster than 87% of the speed of light so as to average 87%.<br />
<br />
Note that the Einstein quote is from Einstein's 1905 SPECIAL RELATIVITY paper and he (wisely) specifies that the "closed curve" be at "constant velocity". It would take an additional ten years, and Einstein's 1915 GENERAL RELATIVITY paper to account for the Relativistic Effects of the acceleration and deceleration required for a practical journey. It turns out that the acceleration and deceleration of the traveling twin in the spacecraft would actually increase the difference in AGING somewhat. However, 60 years of Earth gravity, to which the stay-at-home twin would be exposed, would actually decrease the difference in AGING a bit.<br />
<br />
On the other hand, some of the explanations of the "Twin Paradox" I found on the Internet expose what I think are misinterpretations of inertial reference frames and simultaneity.<br />
<br />
<b><span style="color: #660000;">CONFUSION IN EXPLANATIONS OF THE "TWIN PARADOX"</span></b><br />
<br />
<b>Symmetry and Simultaneity Run Riot !</b><br />
<br />
In my explanation above, I state that, at the half-way point, Aden, on the spaceship, has aged 15 years while Blair, on Earth, has aged 30 years. Well, some would complain, if Aden has not yet done the "slingshot" turn-around, it is improper to state anything about difference in aging between Blair and Aden since both are still in their original frames of reference! They claim a symmetry where each twin sees the other as moving and the other as having a slower clock. They claim there is no such thing as simultaneity.<br />
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<b>Different Inertial Frames</b><br />
<b><br /></b>
For example, right near the top of the <a href="https://en.wikipedia.org/wiki/Twin_paradox">Wikipedia</a> explanation:<br />
<blockquote>
<i>... each twin sees the other twin as moving, and so, according to an incorrect naive application of time dilation and the principle of relativity, each should paradoxically find the other to have aged more slowly. However, this scenario can be resolved within the standard framework of special relativity: the travelling twin's trajectory involves <b>two different inertial frames</b>, one for the outbound journey and one for the inbound journey, and so there is no symmetry between the spacetime paths of the two twins. [My <b>emphasis</b>]</i></blockquote>
Well, <b>prior to the turn-around</b>, each twin had one and only one inertial frame, not "two different inertial frames". So, does this explanation mean to say they <i>both </i>aged more slowly, or <i>neither </i>aged more slowly? Does it mean to say that, during the turn-around, the traveling twin <i>suddenly </i>got younger or the stay-at-home twin <i>suddenly </i>got older?<br />
<br />
Sadly for me (an old engineer who cannot understand the meaning of <i>minus two people -</i> see the Physist/Engineer joke in <a href="http://tvpclub.blogspot.com/2015/06/visualizing-my-insight-into-lorentz.html"> my prevous posting</a> ) YES, they do seem to think that the ages of the twins can <i>suddenly </i>change, based on how they do their <i>calculations</i>!<br />
<br />
<b>Gravitational Time Dilation</b><br />
<br />
Further confusion in the Wikipedia explanation:<br />
<blockquote>
<i> .... Explanations put forth by Albert Einstein and Max Born invoked <b>gravitational time dilation</b> to explain the aging as a direct effect of acceleration.</i></blockquote>
According to this Wikipedia quote, the Einstein/Born explanations invoke "gravitational time dilation to explain the aging as a direct effect of acceleration." Well, the traveling twin certainly had to be accelerated and decelerated during launch and recovery and during the turn-around, and we learn from General Relativity that Relativistic Effects of gravity are equivalent to high-speed effects at certain levels of acceleration and speed. However, the amount of reduction in aging is proportional to the total length of time the traveling twin is at ultra-high speed, and the thought experiment could be lengthened to hundreds or millions of years, such that the acceleration/deceleration periods are an insignificant fraction of the travelling twin's journey.<br />
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<b>Age Jump Instantly At the Turn-around</b><br />
<br />
Yet further confusion in the Wikipedia explanation:<br />
<blockquote>
<i>... For a moment-by-moment understanding of how the time difference between the two twins unfolds, one must understand that in special relativity there is no concept of absolute present. ...For different inertial frames there are different sets of events that are simultaneous in that frame. This relativity of simultaneity means that switching from one inertial frame to another requires an adjustment in what slice through spacetime counts as the "present". ...</i></blockquote>
<blockquote>
<i>... <b>Just before turnaround</b>, the traveling twin calculates the age of the Earth-based twin ... [but] ... Just after turnaround, if he recalculates, ... <b>there is a jump discontinuity in the age of the Earth-based twin</b>. ... [If the twins] regularly update each other on the status of their clocks by way of sending radio signals (which travel at light speed), then all parties will note an incremental buildup of asymmetry in time-keeping, <b>beginning at the "turn around" point</b>. Prior to the "turn around", each party regards the other party's clock to be recording time differently from his own, but the noted difference is symmetrical between the two parties. After the "turn around", the noted differences are not symmetrical, and the asymmetry grows incrementally until the two parties are reunited. Upon finally reuniting, this asymmetry can be seen in the actual difference showing on the two reunited clocks. </i><i>[My <b>emphasis</b>]</i></blockquote>
OK, the twins are far apart for much of this thought experiment so radio signals between them will take years to reach their destinations. Therefore, even if the turn-around plans have been settled and the Relativistic Effects calculated before the launch, the stay-at-home twin will not know for sure whether or not they have been successful. The spacecraft may have blown up or gone off the planned course. Similarly, the traveling twin will not know the status of the stay-at-home. The Earth may have been destroyed by a meteor, etc. <br />
<br />
But, it blows my mind that some physicists can imagine an <i>instantaneous </i>jump in age by any human being (much less a clock) due to a spacecraft turning around, or a calculation based on a delayed radio message.<br />
<br />
<b><span style="color: #660000;">MY (SIMPLE) EXPLANATION OF THE "TWIN PARADOX"</span></b><br />
<br />
Yes, if two spaceships pass in the night, all they can measure is <i>relative </i>speed (even if one happens to be Spaceship Earth). According to all that is currently known, observers on each spaceship will measure the other as being shorter in the direction of travel than it really is (length contraction) and that the other's clock is running slow (time dilation). I got that.<br />
<br />
As one Internet source noted, when two cars pass on a highway and each driver looks in their rear-view mirror, the other car <i>appears </i>to be getting smaller. Of course, in the case of the cars, we know that <i>neither </i>is really getting smaller.<br />
<br />
So, what is different in the case of the twins?<br />
<br />
Well, for one thing, the spacecraft was loaded with fuel and the stay-at-home twin watched it blast off and accelerate. The traveling twin felt the acceleration to ultra-high speed. Due to that expenditure of fuel, the spacecraft was raised to a higher level of Kinetic Energy than it had when it was sitting on the launch pad.<br />
<br />
Throughout its journey, the spacecraft continued at high speed relative to the Earth (assuming that any frictional losses of energy were made up by further expenditure of fuel).<br />
<br />
I maintain that the Relativistic Effects of a slowdown of aging (clock rate) for the travelling twin compared to the stay-at-home twin is due to a relatively higher level of Kinetic Energy. (When we get to General Relativity later in this Blog series, we will learn that high levels of Potential Energy due to the acceleration of gravity have similar Relativistic Effects.)<br />
<br />
<div style="text-align: center;">
<span style="color: blue; font-size: large;"><b><i>Ira Glickstein</i></b></span></div>
<span style="font-size: x-small;"><br /></span>
* Note: I've substituted "<i><b>1 - <span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px;">α</span></b></i>" for the equivalent, but more complex equation in Einstein's original paper, where <i><b><span style="background-color: white; color: #6f6f6f; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 27.7200012207031px;">α </span></b></i>is the Square Root portion of the Lorentz Transformation ( <span style="border-color: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border-width: initial; line-height: 29.8666667938232px;"><img alt="\scriptstyle{\epsilon = \sqrt{1 - v^2/c^2}}" class="mwe-math-fallback-image-inline tex" src="https://upload.wikimedia.org/math/5/4/3/543bc9f7c0c227c945a5f37f66234cad.png" style="background-color: white; border: none; color: #252525; display: inline-block; font-family: sans-serif; line-height: 29.8666667938232px; margin: 0px; vertical-align: middle;" /></span>) as described in my <a href="http://tvpclub.blogspot.com/2015/06/visualizing-my-insight-into-lorentz.html">previous Blog posting</a>.<br />
<br />Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-5451290286733460802015-08-29T21:51:00.004-07:002021-07-24T15:52:37.930-07:00Relative ENERGY (Kinetic and Gravitational Potential Energy) Determines Relativistic Effects<div class="MsoNormal">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcIjSrNpIIs01q47EfObivgR3B7QSFXHfs66bbD57DxIsIVZ9URfuxUrazPtH3dRM1Cidaee7igv4mmgH3U-VZgOc_eaVl3OyblM6bBSU72JTZ6PMr5VHPIzjOyXp3mepxttNelg0wDxg/s1600/RelEpicasion.gif" style="margin-left: auto; margin-right: auto;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcIjSrNpIIs01q47EfObivgR3B7QSFXHfs66bbD57DxIsIVZ9URfuxUrazPtH3dRM1Cidaee7igv4mmgH3U-VZgOc_eaVl3OyblM6bBSU72JTZ6PMr5VHPIzjOyXp3mepxttNelg0wDxg/s640/RelEpicasion.gif" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><div style="text-align: left;">
<span style="font-size: small;"><b>LEFT:</b> <i><b>Jumpy Jill</b></i> is in a friction-free tunnel and cycles forever. She is "at rest" at the top and bottom of the hole and therefore has zero Kinetic Energy (<i><b>KE</b></i>). She does have positive Gravitational Potential Energy (<i><b>GPE</b></i>) with respect to the center of the tunnel. Her maximum speed is achieved at the center. </span></div>
<div style="text-align: left;">
<span style="font-size: small;"><br /></span></div>
<div>
<div style="text-align: left;">
<span style="font-size: small;"><b>RIGHT</b>: <b><i>Far-Out Fred</i></b> is launched into space at <i>a hair less</i> than Escape Velocity. He travels a very long distance over nearly infinite time before he runs out of <i><b>KE </b></i>and is momentarily "at rest". He falls back towards the planet, enters the friction-free hole at <i>a hair less</i> than Escape Velocity, reaches maximum speed at center, decelerates, exits hole at <i>a hair less</i> than Escape Velocity, heads into space, and cycles forever. </span><br />
<span style="font-size: small;"><br />
Note: All speeds and relative energy are with respect to an observer "at rest" at the very center of the planet.</span></div><div style="text-align: left;"><span style="font-size: small;"><br /></span></div>
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</td></tr>
</tbody></table>
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<b>Relativistic
Effects are Proportional to Kinetic Energy and Gravitational Potential Energy</b><span face=""segoe ui" , sans-serif"> <o:p></o:p></span></div>
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<b><br /></b></div>
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<span face=""arial" , "helvetica" , sans-serif">Does relative TOTAL ENERGY determine the magnitude of Time Dilation and Length Contraction? Here are some equations, arguments and examples that support the idea that these Relativistic Effects are due to Total Energy with respect to a reference observer. I will appreciate comments and corrections.</span></div>
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<span face=""arial" , "helvetica" , sans-serif"><b>Time Dilation</b> is a relativistic
effect that slows the rate of a clock that is moving and/or accelerating with
respect to an “at rest” reference clock. </span><br />
<span face=""arial" , "helvetica" , sans-serif"><br /></span>
<span face=""arial" , "helvetica" , sans-serif"><b>"Coordinate" Time Interval </b>between two events, </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δ</span></i></b><b style="font-family: Arial, Helvetica, sans-serif;"><i>t</i></b><span face=""arial" , "helvetica" , sans-serif">, ("delta tee") </span><span face=""arial" , "helvetica" , sans-serif">measured by a clock "at rest" in a reference frame (zero speed, zero gravity). </span><br />
<span face=""arial" , "helvetica" , sans-serif"><br /></span>
<span face=""arial" , "helvetica" , sans-serif"><b>"Proper" Time Interval</b> between the same two events, </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δτ</span></i></b><span face=""arial" , "helvetica" , sans-serif">, </span><span face=""arial" , "helvetica" , sans-serif">("delta tau") </span><span face=""arial" , "helvetica" , sans-serif">measured by a clock that is moving and/or accelerating with respect to the reference frame (due to relative gravity and/or speed).</span><br />
<span face=""arial" , "helvetica" , sans-serif"><br /></span>
<b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δτ </span></i></b><span face=""arial" , "helvetica" , sans-serif">is equal to or greater than </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δt </span></i></b><span face=""arial" , "helvetica" , sans-serif">due to Time Dilation. </span><br />
<span face=""arial" , "helvetica" , sans-serif"><br /></span>
<span face=""arial" , "helvetica" , sans-serif"><b>Lorentz Factor</b>, </span><span face="Arial, Helvetica, sans-serif"><b><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><i style="font-weight: bold;">=</i></span><span face=""arial" , "helvetica" , sans-serif"> </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δ</span></i></b><b style="font-family: Arial, Helvetica, sans-serif;"><i>t</i></b><span face=""arial" , "helvetica" , sans-serif">/</span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δτ</span></i></b><span face=""arial" , "helvetica" , sans-serif">, </span><span face=""arial" , "helvetica" , sans-serif">equal to or greater than 1.0. (</span><span face="Arial, Helvetica, sans-serif"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; font-weight: bold; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"><b> </b>is lower-case </span></span>"gamma")</div><div class="MsoNormal" style="background: white; margin-bottom: 0.0001pt;">
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<span face=""arial" , "helvetica" , sans-serif"><b>Lorentz Factor due to relative speed</b>, </span><b style="font-family: Arial, Helvetica, sans-serif;"><b><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><i><sub>K</sub> = 1/SQRT(1-v<sup>2</sup>/c<sup>2</sup>) </i></b><span face=""arial" , "helvetica" , sans-serif">where <i><b>v</b></i> is the relative velocity between the "at rest" clock and the moving clock, and <i><b>c</b></i> is the speed of light in a vacuum.</span><span face=""arial" , "helvetica" , sans-serif"> </span><br />
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<span face=""arial" , "helvetica" , sans-serif"><b>Lorentz Factor due to relative gravity</b>, </span><b style="font-family: Arial, Helvetica, sans-serif;"><b><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><i><sub>G</sub> = 1/SQRT(1-2GM/rc<sup>2</sup>)</i></b><i style="font-family: Arial, Helvetica, sans-serif;">,</i><b style="font-family: Arial, Helvetica, sans-serif;"><i> </i></b><span face=""arial" , "helvetica" , sans-serif">where <i><b>G </b></i></span><span face=""arial" , "helvetica" , sans-serif">is the gravitational constant, <i><b>M</b></i> is the mass of the spherical planet (or massive object) that is the source of the gravitational field, </span><span face=""arial" , "helvetica" , sans-serif">and </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>r</i></b><span face=""arial" , "helvetica" , sans-serif"> (which must be equal to or greater than the radius of the planet</span><span face=""arial" , "helvetica" , sans-serif">) is the distance of the clock from the center of the planet</span><span face=""arial" , "helvetica" , sans-serif">.</span><br />
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<span face=""arial" , "helvetica" , sans-serif"><b>Time Dilation</b>,</span><b style="font-family: Arial, Helvetica, sans-serif;"><i>TD = </i></b><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δ</span></i></b><span face=""arial" , "helvetica" , sans-serif"><i style="font-weight: bold;">t -</i> </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δτ</span></i></b><b style="font-family: Arial, Helvetica, sans-serif;"><i>,</i></b><span face=""arial" , "helvetica" , sans-serif"> is the "coordinate" time interval minus the "proper" time interval. </span><br />
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<span face=""arial" , "helvetica" , sans-serif"><b>Time Dilation</b>,</span><b style="font-family: Arial, Helvetica, sans-serif;"><i>TD = <span style="color: purple;">(</span></i></b><b style="color: purple; font-family: Arial, Helvetica, sans-serif; line-height: 24.64px;"><b style="color: black;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><i>- 1)</i></b><b style="font-family: Arial, Helvetica, sans-serif; line-height: 24.64px;"><i><span lang="EL">Δτ</span></i></b><span face=""arial" , "helvetica" , sans-serif">, an equivalent way to express Time Dilation. Please note that the </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span style="color: purple;">(</span></i></b><b style="color: purple; font-family: Arial, Helvetica, sans-serif; line-height: 24.64px;"><b style="color: black;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><i>- 1)</i></b><span face=""arial" , "helvetica" , sans-serif"> factor is common to the equation for Time Dilation as well as the expressions for <i><b>KE </b></i>and <i><b>GPE</b></i>.</span><br />
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<span face=""arial" , "helvetica" , sans-serif"><b>Kinetic Energy</b> of the clock, </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>KE</i></b><span face=""arial" , "helvetica" , sans-serif"> =</span><b style="font-family: Arial, Helvetica, sans-serif;"><i> <span style="color: purple;">(</span></i></b><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><b style="font-family: Arial, Helvetica, sans-serif;"><i><span style="color: purple;"><sub>K </sub></span></i></b><b style="font-family: Arial, Helvetica, sans-serif;"><span style="color: purple;"><span style="line-height: 18.4px;">– </span><i>1)</i></span></b><b style="font-family: Arial, Helvetica, sans-serif;"><i>m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif">, where </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif"> is the "rest mass" of the clock.</span></div>
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<span face=""arial" , "helvetica" , sans-serif" style="background-color: white;"><b>Gravitational Potential Energy</b> of the clock with respect to infinity, </span><b style="background-color: white; font-family: Arial, Helvetica, sans-serif;"><i>-GPE</i></b><span face=""arial" , "helvetica" , sans-serif" style="background-color: white;"> =</span><b style="background-color: white; font-family: Arial, Helvetica, sans-serif;"><i> <span style="color: purple;">(</span></i></b><b style="background-color: white; font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><b style="background-color: white; font-family: Arial, Helvetica, sans-serif;"><i><span style="color: purple;"><sub>G </sub></span></i></b><b style="background-color: white; font-family: Arial, Helvetica, sans-serif;"><span style="color: purple;"><span style="line-height: 18.4px;">– </span><i>1)</i></span></b><b style="background-color: white; font-family: Arial, Helvetica, sans-serif;"><i>m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="background-color: white; font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif" style="background-color: white; font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: white;">.</span></div><div class="MsoNormal">
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<span face=""arial" , "helvetica" , sans-serif"><span style="line-height: 115%;"><b>Escape Velocity</b>, <b><i>v<sub>E</sub></i></b>, from a non-rotating, no atmosphere planet, <b><i>P</i></b>,
is the speed, perpendicular to the surface, where <b><i>KE</i></b> is exactly equal to <b><i>-GPE</i></b>. (The
minus sign is due to <b><i>GPE</i></b> being defined as zero at infinite distance from <b><i>P</i></b>, increasing in magnitude to its largest <i>NEGATIVE</i> value at the center, and then increasing asymptotically
to zero an infinite distance from <b><i>P</i></b>.) A rocket launched at <b><i>v<sub>E</sub></i></b>
will just break free of the gravity of <b><i>P</i></b> and continue into space forever, with
no need for further propulsion. </span> <b><i>v<sub>E</sub> = SQRT(2GM/r), </i></b>where <b><i>G</i></b> is the gravitational
constant, <b><i>M</i></b> is the mass of <b><i>P</i></b>, and <b><i>r</i></b> (which must be equal to
or greater than the radius of <b><i>P</i></b>) is the distance of the object from
the center of <b><i>P</i></b>.</span></div>
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<span face=""arial" , "helvetica" , sans-serif"><o:p></o:p></span></div>
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<span face=""arial" , "helvetica" , sans-serif" style="line-height: 115%;">A
clock moving at <b><i>v<sub>E</sub></i></b> (the Escape velocity associated with the surface
of <b><i>P</i></b>),
but far from any massive object (zero gravity), will have exactly the same <i><b>TD </b></i>as a clock “at rest” (zero speed) on the surface of <b><i>P</i></b>.
Note that this occurs when the <b><i>KE</i></b> of the
former is exactly equal to the <b><i>-GPE</i></b> with respect to infinity of the latter.<i><o:p></o:p></i></span><br />
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<span face=""arial" , "helvetica" , sans-serif">As an Engineer (not a
Physicist) these facts scream out that relative <b><i>ENERGY</i></b> (<b><i>KINETIC</i></b> and/or <b><i>-GRAVITATIONAL POTENTIAL</i></b>) <i>causes</i> <i><b>TD</b></i>. I find it surprising that these facts are <i>not</i> mentioned at all in the Wikipedia entries for <a href="https://en.wikipedia.org/wiki/Escape_velocity">Escape_velocity</a> nor <a href="https://en.wikipedia.org/wiki/Time_dilation">Time_dilation</a>, nor by
most internet resources for relativistic effects. In the few instances where
mentioned, the <i>exact</i> relationship of <b><i>ENERGY</i></b>
to <b><i>RELATIVISTIC
EFFECTS</i></b><i> </i>is treated as an
unimportant coincidence. It seems to me that <b>RELATIVE ENERGY IS THE PRIME CAUSATIVE FACTOR FOR RELATIVISTIC EFFECTS</b>,
as confirmed by simple examination of the applicable equations.<o:p></o:p></span></div>
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<span face=""arial" , "helvetica" , sans-serif"><b><i><u>Summary</u></i></b></span><br />
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<span face=""arial" , "helvetica" , sans-serif">A change in kinetic energy causes
a </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>linear</i></b><span face=""arial" , "helvetica" , sans-serif">
change in <i><b>TD</b></i>. A change in
speed will cause a change in <i><b>TD</b></i>, but </span><i style="font-family: Arial, Helvetica, sans-serif;">not</i><span face=""arial" , "helvetica" , sans-serif"> in a way that is </span><i style="font-family: Arial, Helvetica, sans-serif;">linearly</i><span face=""arial" , "helvetica" , sans-serif">
related to the Lorentz factor. For example, a 1% increase in speed, from 0.098c to 0.099c will cause a 0.01% increase in <i><b>TD</b></i>, while a 1% increase from 0.98c to 0.99c will cause a 41% increase!</span><br />
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<span face=""arial" , "helvetica" , sans-serif">A change in <i><b>GPE </b></i>causes a </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>linear</i></b><span face=""arial" , "helvetica" , sans-serif"> change in Time dilation. A
change in gravity will cause a change in <i><b>TD</b></i>, but </span><i style="font-family: Arial, Helvetica, sans-serif;">not</i><span face=""arial" , "helvetica" , sans-serif"> in a way that is </span><i style="font-family: Arial, Helvetica, sans-serif;">linearly</i><span face=""arial" , "helvetica" , sans-serif"> related to the Lorentz factor. (Indeed, the relationship between gravity and Time dilation is not even monotonic! When a clock is within a massive object, gravity decreases while Time dilation increases! [Thanks to John Rennie at the physics stack exchange for kindly (and with extraordinary patience) corrected my misconceptions about gravitational potential energy, see <a href="http://physics.stackexchange.com/questions/213507/does-a-clock-oscillating-in-a-friction-free-hole-through-the-center-of-a-planet">here</a>.]</span></div>
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<span face=""arial" , "helvetica" , sans-serif">The equations for <b><i>TD</i></b>, <b style="background-color: transparent; color: #222222; line-height: 15.3333px;"><i>E<sub>K </sub></i></b>, and <b style="color: #222222; line-height: 15.18px;"><i>-E<sub>G</sub></i></b>. share a common element: <b><i><span style="color: purple;">(</span></i></b><span style="background-color: transparent; color: purple;"><b style="line-height: 24.64px;"><b style="color: black; font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><i>- 1)</i></b></span></span></div>
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<span face=""arial" , "helvetica" , sans-serif"><b><i>TD = </i></b><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><sub> </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span><b style="background-color: transparent; line-height: 24.64px;"><i><span lang="EL">Δτ</span></i></b>.</span></div>
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<span face=""arial" , "helvetica" , sans-serif"><span style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.3333px;"> </span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;">E<sub>K</sub></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span style="font-style: italic; font-weight: bold;">=</span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"> <span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>K </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><br />
<span face=""arial" , "helvetica" , sans-serif" style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.18px;">-E<sub>G</sub></span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold;"> =</span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent;"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"> <span style="color: purple;">(</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent;"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><sub>G </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;">c</span><sup style="background-color: transparent; font-family: Arial, Helvetica, sans-serif; font-style: italic; font-weight: bold; line-height: 24.64px;">2</sup></div><div style="background-color: white;">
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<span face=""arial" , "helvetica" , sans-serif">When </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;">E<sub>K</sub></span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold;">= </span><span face=""arial" , "helvetica" , sans-serif" style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.18px;">-E</span><sub style="color: #222222; font-family: Arial, Helvetica, sans-serif; font-style: italic; font-weight: bold; line-height: 15.18px;">G </sub><span face=""arial" , "helvetica" , sans-serif"> then </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(</span></span><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><sub>K </sub></span></span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span><span face=""arial" , "helvetica" , sans-serif"> </span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold;">= </span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(</span></span><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><sub>G </sub></span></span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold;">= </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(</span></span><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><sub> </sub></span></span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span></div><div style="background-color: white;">
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<span face=""arial" , "helvetica" , sans-serif">Therefore, for a clock with unit mass (1 kg), the time dilation per second of "proper" time, is </span><span face=""arial" , "helvetica" , sans-serif"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><span face=""arial" , "helvetica" , sans-serif"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><sub>K </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>/m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif">, due to relative speed, and </span><span face=""arial" , "helvetica" , sans-serif"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><span face=""arial" , "helvetica" , sans-serif"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><sub>G </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>/m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif">, due to relative gravity.</span></div><div style="background-color: white;">
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<span face=""arial" , "helvetica" , sans-serif">It should be "obvious" that </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>TD</i></b><span face=""arial" , "helvetica" , sans-serif"> experienced by a clock "at rest" on the surface of </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>P</i></b><span face=""arial" , "helvetica" , sans-serif"> is exactly equal to the </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>TD</i></b><span face=""arial" , "helvetica" , sans-serif"> experienced by a clock in deep space moving at the Escape velocity, </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span style="color: #222222; line-height: 15.3333px;">v<sub>E</sub></span></i></b><span face=""arial" , "helvetica" , sans-serif">, associated with the surface of </span><b style="font-family: Arial, Helvetica, sans-serif;"><i>P</i></b><span face=""arial" , "helvetica" , sans-serif">.</span></div>
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<b><u><span face=""arial" , "helvetica" , sans-serif">LINEAR and MONOTONIC Relationship between ENERGY and Relativistic Effects<o:p></o:p></span></u></b><br />
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<span face=""arial" , "helvetica" , sans-serif">The Excel graphs below compare ENERGY, Velocity, and Gravity with the Time Dilation.</span><br />
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<span face=""arial" , "helvetica" , sans-serif">The analysis is based on the Kinetic Energy resulting from relative velocities from zero to 295,599,350 meters per second (0 to 98.6% of <i><b>c</b></i>, the speed of light) in deep space -or- the Gravitational Potential Energy resulting from being "at rest" within the gravitational attraction of either an Earth-like massive sphere or a compact Neutron Star-like massive sphere (with a mass of two Suns and a radius of only 13 km, experienced from an infinite distance down to the center. </span><br />
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<b style="font-family: arial, helvetica, sans-serif;">Time Dilation is LINEAR with Respect to Kinetic Energy and NON-Linear with Respect to Velocity</b></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggsUAYRIyBtQwyCIf-YYfgPApu8Ju0kTrIk3TW8PD0B59WaNARNhm9a3UiSKVtgvlminllfaATmjiy9QugmCggZsjvyHclYZSFbXX-P3Prk8yCW6az0jyO0Mcj37kvMgUIhqJF5mcsuLY/s1600/EnergyTDspeed.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="440" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggsUAYRIyBtQwyCIf-YYfgPApu8Ju0kTrIk3TW8PD0B59WaNARNhm9a3UiSKVtgvlminllfaATmjiy9QugmCggZsjvyHclYZSFbXX-P3Prk8yCW6az0jyO0Mcj37kvMgUIhqJF5mcsuLY/s640/EnergyTDspeed.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The above graphic shows the relationship between Time Dilation, Velocity, and Kinetic Energy. Note that, for all speeds from zero to the speed of light, <i><b>TD </b></i>is exactly proportional to <i><b>KE</b></i>, and <i><b>TD </b></i>is not proportional to Velocity.</td></tr>
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<b style="font-family: arial, helvetica, sans-serif;">Time Dilation is LINEAR with Respect to Gravitational Potential Energy and NON-Linear and NON-Monotonic with Respect to Gravity (Example for Earth-Like Spherical Massive Object)</b><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXdnynge9Y6j7qT9zC-rEhGTq_IQYtqdarxDW6anbVOXk3gXE_lfuOIGVrsGe4qEaT9UTaFQQERIc1gaMomKGZIj6b0DN2UVOxCXUj5vMUN8lRx6xspgTn81P1vEEE8WPZncTbD-rfz5g/s1600/EnergyTDGPEEarth.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="504" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXdnynge9Y6j7qT9zC-rEhGTq_IQYtqdarxDW6anbVOXk3gXE_lfuOIGVrsGe4qEaT9UTaFQQERIc1gaMomKGZIj6b0DN2UVOxCXUj5vMUN8lRx6xspgTn81P1vEEE8WPZncTbD-rfz5g/s640/EnergyTDGPEEarth.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: 12.8px;">The above graphic shows the relationship between <i><b>Time Dilation</b></i>, <i><b>Gravity</b></i>, and <i><b>Gravitational Potential Energy</b></i>. Note that, for this example, using a spherical mass with the same mass and radius of the Earth, </span><i style="font-size: 12.8px;"><b>TD </b></i><span style="font-size: 12.8px;">is exactly proportional to </span><i style="font-size: 12.8px;"><b>GPE</b></i><span style="font-size: 12.8px;">. Note also that the relationship between </span><i style="font-size: 12.8px;"><b>TD </b></i><span style="font-size: 12.8px;">and <i><b>Gravity </b></i>is not even monotonic! <br />From Infinity to the Surface, as <i><b>Gravity INCREASES</b></i> in (negative) magnitude, <i><b>TD </b></i>increases, but non-linearly. <br />From the Surface to the Center, as <i><b>Gravity DECREASES</b></i> in (negative) magnitude, <i><b>TD </b></i>increases, also non-linearly.</span></td></tr>
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<span face=""arial" , "helvetica" , sans-serif"><br /></span><b style="font-family: arial, helvetica, sans-serif;">Time Dilation is LINEAR with Respect to Gravitational Potential Energy and NON-Linear and NON-Monotonic with Respect to Gravity (Example for Neutron Star-Like Spherical Massive Object)</b><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1u15BGOsr6KzUiCm2sXQHii2ly3Gl8SBadIyelXHsOQW7AOE_uEpJ8K2JKDhZ-CBG2_fZegebcOjzbt2XmOIv8zVcVImNsLV6DY57-FWCtUk6mXmQkgopQQQJZ6-J0zZpam6LrUIX9fU/s1600/EnergyTDGPENeutron.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="476" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1u15BGOsr6KzUiCm2sXQHii2ly3Gl8SBadIyelXHsOQW7AOE_uEpJ8K2JKDhZ-CBG2_fZegebcOjzbt2XmOIv8zVcVImNsLV6DY57-FWCtUk6mXmQkgopQQQJZ6-J0zZpam6LrUIX9fU/s640/EnergyTDGPENeutron.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: 12.8px;">The above graphic shows the relationship between <i><b>Time Dilation</b></i>, <i><b>Gravity</b></i>, and <i><b>Gravitational Potential Energy</b></i>. Note that, for this example, using a spherical mass with the same mass and radius of a Neutron Star, which is much, much more massive than the Earth, and very much smaller, so its density is far greater than the Earth, </span><i style="font-size: 12.8px;"><b>TD </b></i><span style="font-size: 12.8px;">is exactly proportional to </span><i style="font-size: 12.8px;"><b>GPE</b></i><span style="font-size: 12.8px;">. Note also that the relationship between </span><i style="font-size: 12.8px;"><b>TD </b></i><span style="font-size: 12.8px;">and <i><b>Gravity </b></i>is not even monotonic!<br />From Infinity to the Surface, as <i><b>Gravity INCREASES</b></i> in (negative) magnitude, <i><b>TD </b></i>increases, but non-linearly.<br />From the Surface to the Center, as <i><b>Gravity DECREASES</b></i> in (negative) magnitude, <i><b>TD </b></i>increases, also non-linearly.</span></td></tr>
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<b><u><span face=""arial" , "helvetica" , sans-serif">Conclusion<o:p></o:p></span></u></b></div>
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<span face=""arial" , "helvetica" , sans-serif">TOTAL ENERGY with respect to the center of <b><i>P</i></b>
determines the magnitude of Time Dilation and Length Contraction for the entire
journeys of both <b><i>Fred</i></b> and <b><i>Jill</i></b>. These journeys involve
movement at various speeds, including momentary instants of being “at rest”,
and various levels of gravitational attraction, including momentary instants of
zero gravity.</span><br />
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<span face=""arial" , "helvetica" , sans-serif">The equations for <b><i>TD</i></b>, <b style="background-color: transparent; color: #222222; line-height: 15.3333px;"><i>E<sub>K </sub></i></b>, and <b style="color: #222222; line-height: 15.18px;"><i>-E<sub>G</sub></i></b>. share a common element: <b><i><span style="color: purple;">(</span></i></b><span style="background-color: transparent; color: purple;"><b style="line-height: 24.64px;"><b style="color: black; font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><i>- 1)</i></b></span></span></div>
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<span face=""arial" , "helvetica" , sans-serif"><b><i>TD = </i></b><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><sub> </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span><b style="background-color: transparent; line-height: 24.64px;"><i><span lang="EL">Δτ</span></i></b>. where </span><b style="font-family: Arial, Helvetica, sans-serif;"><b><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><i>=</i></b><span face=""arial" , "helvetica" , sans-serif"> </span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δ</span></i></b><b style="font-family: Arial, Helvetica, sans-serif;"><i>t</i></b><span face=""arial" , "helvetica" , sans-serif">/</span><b style="font-family: Arial, Helvetica, sans-serif;"><i><span lang="EL">Δτ</span></i></b><span face=""arial" , "helvetica" , sans-serif">,</span></div>
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<span face=""arial" , "helvetica" , sans-serif"><span style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.3333px;"> </span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;">E<sub>K</sub></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span style="font-style: italic; font-weight: bold;">=</span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"> <span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>K </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif">, where</span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"><b style="font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>K</sub> = 1/SQRT(1-v<sup>2</sup>/c<sup>2</sup>)</span><b style="font-family: Arial, Helvetica, sans-serif; font-style: italic;"> </b><b style="font-family: Arial, Helvetica, sans-serif; font-style: italic;"> </b><br />
<span face=""arial" , "helvetica" , sans-serif" style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.18px;">-E<sub>G</sub></span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold;"> =</span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent;"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"> <span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>G </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;">c</span><sup style="background-color: transparent; font-family: Arial, Helvetica, sans-serif; font-style: italic; font-weight: bold; line-height: 24.64px;">2</sup><span face=""arial" , "helvetica" , sans-serif">, where</span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"><b style="font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>G</sub> = 1/SQRT(1-2GM/rc<sup>2</sup>)</span><br />
<span face=""arial" , "helvetica" , sans-serif">When </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;">E<sub>K</sub></span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold;">= </span><span face=""arial" , "helvetica" , sans-serif" style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.18px;">-E</span><sub style="color: #222222; font-family: Arial, Helvetica, sans-serif; font-style: italic; font-weight: bold; line-height: 15.18px;">G </sub><span face=""arial" , "helvetica" , sans-serif"> then </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>K </sub></span></span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span><span face=""arial" , "helvetica" , sans-serif"> </span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold;">= </span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>G </sub></span></span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold;">= </span><span face=""arial" , "helvetica" , sans-serif" style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(</span></span><b style="font-family: Arial, Helvetica, sans-serif;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span><span face="sans-serif" style="color: #202122; font-size: 14px;"> </span></b><span style="background-color: transparent; color: purple; font-style: italic; font-weight: bold; line-height: 15.18px;">– </span><span style="background-color: transparent; color: purple; font-style: italic; font-weight: bold;">1) </span></div><div>
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<span face=""arial" , "helvetica" , sans-serif">Therefore, for a clock with unit mass (1 kg), the time dilation per second of "proper" time, is </span><span face=""arial" , "helvetica" , sans-serif"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>K </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>/m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif">, due to relative speed, and </span><span face=""arial" , "helvetica" , sans-serif"><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>G </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1)</span></span></span><b style="font-family: Arial, Helvetica, sans-serif;"><i>/m<sub>0</sub></i></b><span face=""arial" , "helvetica" , sans-serif" style="font-style: italic; font-weight: bold; line-height: 24.64px;">c<sup>2</sup></span><span face=""arial" , "helvetica" , sans-serif">, due to relative gravity.</span></div>
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<span face=""arial" , "helvetica" , sans-serif">When <span style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;">E<sub>K</sub></span><span style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"> </span><span style="background-color: transparent; font-style: italic; font-weight: bold;">= </span><span style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.18px;">-E</span><sub style="color: #222222; font-style: italic; font-weight: bold; line-height: 15.18px;">G </sub> then <span style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>K </sub></span></span><span style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span> <span style="font-style: italic; font-weight: bold;">= </span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub>G </sub></span></span><span style="font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span><span style="font-style: italic; font-weight: bold;">= </span><span style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;">(<b style="color: black; font-family: Arial, Helvetica, sans-serif; font-style: normal;"><span class="texhtml" style="color: #202122; font-family: "Nimbus Roman No9 L", "Times New Roman", Times, serif; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-size: 16.52px; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><i>γ</i></span></b><sub> </sub></span></span><span style="background-color: transparent; font-style: italic; font-weight: bold; line-height: 24.64px;"><span style="color: purple;"><span style="line-height: 15.18px;">– </span>1) </span></span></span></div>
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<span face=""arial" , "helvetica" , sans-serif">My Excel analysis confirms, for a wide range of relative velocities and gravitational situations, ENERGY remains linearly related to Time Dilation and Length Contraction This is definitely NOT the case for Velocity nor Gravity, each of which are asymptotically limited.</span><br />
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<span face=""arial" , "helvetica" , sans-serif">Therefore it is reasonable to conclude that relative TOTAL ENERGY
determines the Relativistic Effects of any combination of speed and gravity.</span><o:p></o:p></div><div class="MsoNormal"><span face=""arial" , "helvetica" , sans-serif"><br /></span></div><div class="MsoNormal"><span face=""arial" , "helvetica" , sans-serif">[Edited 24 July 2021. I fixed a couple of typos and changed "</span><span style="background-color: white; color: purple; font-style: italic; font-weight: 700;">ϒ"</span><sub style="background-color: white; color: purple; font-style: italic; font-weight: 700;"> </sub><span face=""arial" , "helvetica" , sans-serif">to "</span><span style="background-color: white;"><span class="texhtml" style="color: #202122; font-feature-settings: "lnum", "tnum", "kern" 0; font-kerning: none; font-variant-numeric: lining-nums tabular-nums; line-height: 1; white-space: nowrap;"><span style="font-family: Nimbus Roman No9 L, Times New Roman, Times, serif; font-style: italic; font-weight: bold;"><span style="font-size: 16.52px;">γ</span></span><span face="sans-serif"><span style="font-size: 14px;"><i><b>"</b>.</i>]</span></span></span></span></div>
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<span style="color: blue; font-size: large;"><i><b>Ira Glickstein</b></i></span></div>
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Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-86053248956177298772015-07-31T10:54:00.000-07:002020-04-24T21:02:57.109-07:00Introduction to VISUALIZING Einstein's Relativity<div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: left; unicode-bidi: embed; word-break: normal;">
<span style="font-family: "calibri";"><b><span style="color: #660000;">WHY VISUALIZATION IS IMPORTANT</span></b></span></div>
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<span style="font-family: "calibri";">Although </span><span style="font-family: "calibri";">the
he could </span><span style="font-family: "calibri";">"</span><span style="font-family: "calibri";">do
the math", </span><span style="font-family: "calibri";">Albert </span><span style="font-family: "calibri";">Einstein
relied on VISUAL ANALOGIES </span><span style="font-family: "calibri";">for </span><span style="font-family: "calibri";">his
greatest <b>insights</b> </span><span style="font-family: "calibri";">that </span><span style="font-family: "calibri";">revolutionized
the world of science.</span></div>
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<span style="font-family: "calibri";">Let me share some of his </span><span style="font-family: "calibri";"><i>insights </i>(and a couple of mine)<i> </i></span><span style="font-family: "calibri";">that </span><span style="font-family: "calibri";">may
help </span><span style="font-family: "calibri";">you </span><span style="font-family: "calibri";">better </span><span style="font-family: "calibri";">VISUALIZE </span><span style="font-family: "calibri";">and </span><span style="font-family: "calibri";">even
understand a bit </span><span style="font-family: "calibri";">of </span><span style="font-family: "calibri";">Einstein's
Theories </span><span style="font-family: "calibri";">of </span><span style="font-family: "calibri";">Special
and General Relativity. (C</span><span style="font-family: "calibri";">lick <a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxpcmFiZXN0cHBzfGd4OjRjNGViMDI3ZTRhMmY5ZjI">here</a> to download the PowerPoint charts </span><span style="font-family: "calibri";">I used to presented some of this material to the Philosophy Club of The Villages, FL, on 31 July 2015.)</span></div>
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<span style="font-family: "calibri";">For example, in his famous 1905 paper that introduced what has come to be called the theory of "Special Relativity", Einstein starts with a simple VISUALIZATION, depicted in my graphic below.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilSFbq3JURO3DA64oKtjTX_9kzD0ZJXNyifV-4dN-DUjYGiRhPYR1bQ55Bk8sSuMINRH94THNOoLnc6kwdXQRrHgtDnQNjKGKRD9DOLVQUhL6mNMhM7GRXduy06S9KU8duxhLFhY2FAnE/s1600/RelCoil.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="251" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilSFbq3JURO3DA64oKtjTX_9kzD0ZJXNyifV-4dN-DUjYGiRhPYR1bQ55Bk8sSuMINRH94THNOoLnc6kwdXQRrHgtDnQNjKGKRD9DOLVQUhL6mNMhM7GRXduy06S9KU8duxhLFhY2FAnE/s640/RelCoil.gif" width="640" /></a></div>
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Prior to attending Zurich Polytechnic, where he earned a degree in Mathematics and Physics, Einstein had worked with his father who owned an electrical equipment business. Therefore, young Albert had some practical ENGINEERING experience as a foundation upon which he could "do the MATH" and create the PHYSICS theories that revolutionized our understanding of the workings of the Universe, and made him famous.<br />
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He knew, from practical experience working with his father on electrical equipment, that a stationary coil of wire would generate an electric current if a magnet was moved back and forth within it. He also knew the reverse was true. A stationary magnet would generate an electric current in a coil of wire if the coil was moved back and forth over the magnet. The key, of course, was the RELATIVE movement of the coil and the magnet.<br />
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<b><span style="color: #660000;">VISUALIZATION AS AN AID TO CREATIVITY AND UNDERSTANDING</span></b><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHMUnXyrk_QaBLZLLvL5oTjwmCH6LNnfhh4TfHWlJRXp2awnaeTUzwOGo-qBKiXPAZI5T89FnrXS_5P3H9uEx4Q2NFg2S3IXIO6FY3wc1CoymqSrQ2EHJBYJGUM6_gTFlobkVMT99iWcE/s1600/RelSimple.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHMUnXyrk_QaBLZLLvL5oTjwmCH6LNnfhh4TfHWlJRXp2awnaeTUzwOGo-qBKiXPAZI5T89FnrXS_5P3H9uEx4Q2NFg2S3IXIO6FY3wc1CoymqSrQ2EHJBYJGUM6_gTFlobkVMT99iWcE/s320/RelSimple.jpg" width="225" /></a></div>
I agree with Einstein that there are (<b><i>relatively </i>:^</b>) simple descriptions that can help "even a child" understand "all physical theories" (apart from their mathematical expressions).<br />
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The key to this level of understanding is VISUALIZATION aids, such as the graphic above and the ones I will use in this series of Blog posts.<br />
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Yes, of course the mathematics is important for a full understanding, but, as an ENGINEER (and not a PHYSICIST), I tend to approach science and technology via the VISUALIZATION route first.<br />
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My bachelors degree is in Electrical Engineering (1961) and my Masters (1990) and PhD (1996) are in System Science, so I have some academic ability to understand physics and "do the math". During my long, creative, and successful engineering career (at IBM and Lockheed-Martin) I collaborated with some brilliant mathematicians and physicists, along with system, hardware and software engineers without whom my creative concepts would never have seen the light of day.<br />
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It seems to me that (at least some) physicists, including some who are (justifiably) well recognized and honored for their contributions to science, get confused and even mislead by the mathematics.<br />
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For example, it is common for physicists to say that some physical reaction is "governed by this equation". NOPE! The physical reaction is in accordance with the Laws of Nature, and our equations (and, now, computer models) are mere approximations of actual reality. As my PhD adviser (Howard Pattee, a physicist) taught me, "the map is not the territory!"<br />
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OK, back to Einstein's Relativity!<br />
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<span style="color: #660000;"><b>ESSENCE OF EINSTEIN'S THEORY OF SPECIAL RELATIVITY (SR)</b></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtlSi6k0k9_ZDNXtPlKqKFkblawk9mGlhtoMQUYd5ihtCBFtxweQsfBVgz3TFC8J5eHfG4OvOfrYCdsOzSoX9Qw1DnF-qyZmiE0_jkPthoJp__lGPILuRdQUpt_WaAI1upY1YPpueg3wc/s1600/RelTrainStation.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtlSi6k0k9_ZDNXtPlKqKFkblawk9mGlhtoMQUYd5ihtCBFtxweQsfBVgz3TFC8J5eHfG4OvOfrYCdsOzSoX9Qw1DnF-qyZmiE0_jkPthoJp__lGPILuRdQUpt_WaAI1upY1YPpueg3wc/s320/RelTrainStation.jpg" width="309" /></a></div>
The graphic depicts a moving observer <b><i>A</i></b> who is on a train going at a substantial fraction of the speed of light, and a stationary observer <b><i>B</i></b> who is at a station that is the same length as the train. Both observers have identical clocks, flashing beacons, and instruments they may use to measure clock rates, the length of the train and the station, and the speed of the light emanating from the flashing beacons.<br />
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<b>Starting with the idea that <i>relative </i>motion is the key to generation of electricity, Einstein takes a gigantic leap of insightful imagination and states, as a postulate, that the speed of light (in a vacuum) is constant for all observers, no matter the speed of the source or of the observer. Einstein referred to his concept of the measured speed of light being constant as "invariability".</b><br />
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Thus, observers <i><b>A</b></i> and <i><b>B</b></i> will measure the exact same speed of light for the light emanating from their own as well as the other's flashing beacons, no matter how fast they, or the other, is moving.<br />
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NOTE THAT THIS IS COUNTER-INTUITIVE. For example, if observer <i><b>A</b></i>, on the train, fired a gun towards the station, the speed of the bullet, as measured by stationary observer <i><b>B</b></i>, would be the muzzle velocity PLUS the train velocity. If observer <i><b>B </b></i>fired a gun and measured the speed of the bullet, it would be just the muzzle velocity. So, for bullets fired from guns, observer <i><b>B </b></i>would measure a greater speed for bullets from observer <b><i>A</i></b>'s gun than from her own. Not so with a light beam, according to Einstein (and he turned out to be correct).<br />
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Furthermore, observer <i><b>B</b></i> will measure the length of the train as being <i>contracted </i>(that is, shorter than the length of her station) and the rate of the clock on the train being <i>dilated </i>(that is, slower than the clock at her station).<br />
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Perhaps surprisingly, observer <i><b>A </b></i>will measure the length of the station as being <i>contracted </i>(that is, shorter than the length of his train) and the rate of the clock at the station being <i>dilated </i>(that is, slower than the clock on his train).<br />
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So, each measures the length and clock rates of the other as being less than their own! How can that be? Well, an internet site suggests it is like two cars passing on a road. When the drivers look into their rear view mirrors, the other car appears to be getting smaller. Of course, we know that both cars are the same length, regardless of what the drivers observe in their rear-view mirrors.<br />
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However, according to Einstein's Special Relativity (and all experiments to date), one of the two bodies in relative motion (in this case the train or the station) <i><b>actually </b></i>does have its length contracted and clock speed reduced relative to the other. Which one? Stay tuned and you will find out. (HINT: If you think it is the train that actually experiences relativistic effects in this case, you are correct!)<br />
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<span style="color: #660000;"><b>ESSENCE OF EINSTEIN'S THEORY OF GENERAL RELATIVITY (GR)</b></span><br />
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Special Relativity applies only to bodies in relative motion at <i><b>constant </b></i>speed. In 1915, Einstein extended his theory to the more general case of accelerating bodies, that is bodies that change speed or turn during observation.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXOlGDBOG6wEPoO3GamL9ib7bOcR9X2fTBxjOmfdQ9rnarbQVBTfaRwNvImvQ1a5PDEpaVcdcT885s3E31-3PeQS67wZFbc516yBEoV_nr99roqjFopxRpnl4V8M_m5rUrb0n-31HLeus/s1600/RelGR.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXOlGDBOG6wEPoO3GamL9ib7bOcR9X2fTBxjOmfdQ9rnarbQVBTfaRwNvImvQ1a5PDEpaVcdcT885s3E31-3PeQS67wZFbc516yBEoV_nr99roqjFopxRpnl4V8M_m5rUrb0n-31HLeus/s400/RelGR.jpg" width="400" /></a></div>
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The graphic depicts two scientists, equipped with identical instruments. who are confined to sealed boxes.<br />
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One scientist is in a sealed box on Earth, where GRAVITY is 32.2 feet per second squared (9.8 meters per second squared).<br />
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<span style="vertical-align: sub;">The other is in Deep Space, far from any massive bodies, on a rocket that is ACCELERATING at the rate of 32.2 feet per second squared.</span><br />
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<span style="vertical-align: sub;">Einstein reasoned that the scientists could not tell whether they were on Earth (experiencing GRAVITY) or in Deep Space (experiencing ACCELERATION).</span><br />
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<span style="vertical-align: sub;">From this basic </span><i style="vertical-align: sub;"><b>insight</b></i><span style="vertical-align: sub;">, Einstein concluded that the relativistic effects of GRAVITY were equivalent to the relativistic effects of ACCELERATION. He also "pictured" the effect of a massive body on </span><b style="vertical-align: sub;"><i>SpaceTime </i></b><span style="vertical-align: sub;">as causing it to "curve".</span><br />
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<sup><sub>
</sub></sup><b style="color: #660000;">HOW ARE SPECIAL RELATIVITY AND GENERAL RELATIVITY RELATED?</b><br />
<sup><sub><span style="color: #660000; font-size: small;"><b><br /></b></span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">In my research for this project, I happened upon a fact that is not prominently mentioned by many Internet expositions of Relativity. Namely that:</span><br />
</sub></sup><br />
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<b><span style="font-size: medium;">Time Dilation, <i>TD</i>, due to General Relativity</span></b><br />
<b><span style="font-size: medium;">at a location near</span></b><b style="font-size: 14.85px; line-height: 27.72px;"><span style="font-size: medium;"> a massive body </span></b></div>
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<b><span style="font-size: medium;">is <i>exactly equal</i> to </span></b></div>
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<b><span style="font-size: medium;">the <i>TD </i>due to Special Relativity for a spacecraft </span></b></div>
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<b><span style="font-size: medium;">(in deep space far from any massive body) </span></b></div>
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<b><span style="font-size: medium;">moving at the <i>Escape Velocity </i></span></b></div>
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<b><span style="font-size: medium;">corresponding to that location!</span></b><br />
<b><span style="font-size: medium;"><br /></span></b>
<b><span style="font-size: medium;">At any location near a massive sphere,<i> Escape Velocity</i> is the speed at which the Kinetic Energy is <i>exactly equal and opposite</i> to Gravitational Potential Energy, such that a rocket moving at that speed will continue out to space forever without any need for further propulsion. </span></b><br />
<b><span style="font-size: medium;"><br /></span></b>
<b><span style="color: blue; font-size: medium;">Kinetic ENERGY, <i>KE </i>is LINEARLY related to <i>TD</i>. An increase (or decrease) in <i>KE </i>will result in an <i>exactly proportional</i> increase (or decrease) in <i>TD</i>.</span></b><br />
<b><span style="font-size: medium;"><br /></span></b>
<b><span style="font-size: medium;">Speed is NOT linearly related to <i>TD</i>. At <i>low </i>speeds, a given <i>increase </i>in speed results in a <i>minuscule </i>increase in <i>TD</i>. However, at <i>high </i>speeds (a substantial fraction of the speed of light), the same <i>increase </i>in speed results in a <i>large </i>increase in <i>TD</i>. </span></b><br />
<b><span style="font-size: medium;"><br /></span></b>
<span style="color: red;"><b><span style="font-size: medium;">Gravitational Potential ENERGY, <i>GPE </i>is LINEARLY related to <i>TD</i>. </span></b><b style="font-size: 14.85px; line-height: 27.72px;"><span style="font-size: medium;">An increase (or decrease) in <i>GPE </i>will result in an <i>exactly proportional </i>increase (or decrease) in <i>TD</i>.</span></b></span><br />
<b><span style="font-size: medium;"><br /></span></b><b style="font-size: 14.85px; line-height: 27.72px;"><span style="font-size: medium;">Gravity, <i>g</i>, per se, is NOT linearly related to <i>TD</i>. Indeed, it is NOT even monotonic. At the center of a massive object, where <i>TD </i>is maximized, <i>g </i>is zero. At the surface, where <i>g </i>reaches its maximum (negative) value, <i>TD </i>is less than at the center, but more than at infinity. At an infinity, where <i>TD </i>is zero, <i>g </i>is also zero. The fact that the relationship is non-monotonic is clear because within a massive object, <i>smaller</i> levels of <i>g </i>are associated with <i>increasing TD</i>. Outside a massive object, <i>smaller </i>levels of <i>g </i>are associated with <i>decreasing TD</i>.</span></b><b style="font-size: 14.85px; line-height: 27.72px;"><span style="font-size: medium;"> </span></b></div>
<br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;" />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">When you throw a ball straight up into the air at some initial vertical speed, it will not continue to go up forever. As it rises it will slow its upward speed until it reaches the point where its speed is zero. Then it falls, continuously increasing downward speed, until it returns to your glove. If we ignore air friction, the ball will strike your glove at exactly the same speed as your initial throw.</span><br />
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<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">This is a perfect illustration of the exchange of <i style="font-weight: bold;">Kinetic Energy</i><i style="font-weight: bold;"> </i>for <b><i>Gravitational Potential Energy</i></b>. </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Your initial throw imparts a given vertical speed to the ball. From that speed, you can compute the <i><b>KE</b></i>. As the ball rises and slows due to the force of Gravity, the <i><b>KE </b></i>is converted to <i><b>GPE </b></i>(ignoring loss to air friction). At the highest point, the ball has zero Kinetic Energy, and maximum <i><b>GPE </b></i>relative to your glove. By conservation of Energy, the <i><b>GPE </b></i>at the peak is <i>exactly equal</i> to the initial <i><b>KE </b></i>of the throw. As the ball falls, the process is reversed, with the <i><b>GPE </b></i>being converted to <i><b>KE</b></i>. </span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">(NOTE: By convention, <i><b>GPE </b></i>is considered </span><i style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">negative </i><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">- because it points downward towards the massive object that is the source of the gravitational field. <i><b>GPE </b></i>is zero at an infinite distance, and gains in magnitude (becomes more <i>negative</i>) closer to the massive object. <i><b>KE </b></i>is considered <i>positive</i>. So, in the preceding paragraph, when I say that the <i><b>GPE </b></i>at the highest point is </span><i style="font-size: 14.850001335144px; line-height: 27.7200012207031px;">exactly equal</i><span style="font-size: 14.850001335144px; line-height: 27.7200012207031px;"> to the initial <i><b>KE </b></i>of the throw, what actually happens is that, as the ball rises and slows, <i><b>KE </b></i>goes from some high positive value to zero (<i>reduces</i>), while <i><b>GPE </b></i>goes from some high <i>negative </i>value to a<i> less negative</i> value (<i>increases</i>). The <i>reduction </i>in <i><b>KE </b></i>is <i>exactly equal</i> to the <i>increase </i>in <i><b>GPE</b></i>. Keep that in mind as you read the following.) </span></span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Is there a speed at which you could throw that ball such that it will keep going up forever? In other words, could you give it the <i><b>KE </b></i>that corresponds to the <i><b>GPE </b></i>of a ball that is infinitely far from Earth? The answer is YES, and that speed is called the <b><i>Escape Velocity</i></b> from Earth. Of course, you could not throw a ball that fast, but you could if you had a rocket!</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd6Zc05t0kkyCdmcUNEocQX9GDe3vyfM5yoFlwVUKjVDaPQlwNCT-xRdTelExq1aIFO2gM-ky6YNkqzL2bu_84LasdUFz_Sef9pulX5Yda0YGsHb8bzdfVCe4lF9Kh7pftaeutGL18J2A/s1600/RelEscVel.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="251" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd6Zc05t0kkyCdmcUNEocQX9GDe3vyfM5yoFlwVUKjVDaPQlwNCT-xRdTelExq1aIFO2gM-ky6YNkqzL2bu_84LasdUFz_Sef9pulX5Yda0YGsHb8bzdfVCe4lF9Kh7pftaeutGL18J2A/s400/RelEscVel.jpg" width="400" /></a></div>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Escape Velocity from the Earth Surface is about </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><i><b>25,000 MPH (40,000 km/hr)</b></i></span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><b>.</b> It is defined as the launch speed required for a spacecraft, pointing straight up, such that it will have just enough <i><b>KE </b></i>so it will not fall back to Earth (ignoring air friction and rotation of the Earth).</span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">The graphic illustrates the equivalence between the effects of GRAVITY (<b><span style="color: red;">GENERAL RELATIVITY</span><span style="color: blue;"> </span></b>- on the left) and SPEED (<b><span style="color: blue;">SPECIAL RELATIVITY</span></b> - on the right). </span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">An observer "at rest" on the Earth will experience relativistic effects (length contraction and time dilation) due to his <i><b>GPE </b></i>with respect to infinity. That <i><b>GPE </b></i>is the energy required to move an object from the surface of the Earth to infinity. </span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">At that level of <i><b>GPE</b></i>, it would take an equivalent level of <i><b>KE </b></i>for a rocket to leave the Earth and never return. That level of <i><b>KE </b></i>corresponds to the Escape Velocity from the Earth's surface.</span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">An observer in a rocket in Deep Space, far from any massive object and <i>moving </i>at 25,000 MPH will experience exactly the same relativistic effects </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">(length contraction and time dilation)</span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> due to her <i><b>KE </b></i>with respect to the Earth </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">as the "at rest" rocket on Earth. </span><br />
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<b style="color: #660000;">PUTTING IT ALL TOGETHER - JUMP INTO A TUNNEL THROUGH THE EARTH</b><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHLetQRV1X31aLNZ25IU518tsNKYgs6gf2aZHcCim4EJsZnxP1GxO4lkkwtachVP8raGuo4fdxIekLfWDDmkp_e-JfN58wOaMZ6Csnu6Yin9m8CMc-MrqdiLNE7QkAuiE5jX4Slx2BCyg/s1600/RelEarthHole.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="496" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHLetQRV1X31aLNZ25IU518tsNKYgs6gf2aZHcCim4EJsZnxP1GxO4lkkwtachVP8raGuo4fdxIekLfWDDmkp_e-JfN58wOaMZ6Csnu6Yin9m8CMc-MrqdiLNE7QkAuiE5jX4Slx2BCyg/s640/RelEarthHole.gif" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">In the above graphic, POTENTIAL ENERGY is with respect to the center of the Earth, and is related to, but NOT the same, as Gravitational Potential Energy, <i><b>GPE</b></i>. <br />
For good (but confusing) reasons, <i><b>GPE</b></i> is always ZERO or NEGATIVE.<br />
<i><b>GPE(Infinity)</b></i> is defined as ZERO. <i><b>GPE(Surface)</b></i> and <i style="font-size: 12.8px;"><b>GPE(Center)</b></i><span style="font-size: 12.8px;"> are defined as the work (energy) required to raise an object from the Center or the Surface to Infinity. The magnitude of </span><i style="font-size: 12.8px;"><b>GPE(Center)</b></i><span style="font-size: 12.8px;"> is larger than the magnitude of </span><i style="font-size: 12.8px;"><b>GPE(Surface)</b></i><span style="font-size: 12.8px;">, however, since both are negative quantities, </span><i style="font-size: 12.8px;"><b>GPE(Center)</b></i><span style="font-size: 12.8px;">, on the real number scale, is numerically LESS than </span><i style="font-size: 12.8px;"><b>GPE(Surface)</b></i><span style="font-size: 12.8px;">. <br />The POTENTIAL ENERGY in the above graphic is the <i><b>GPE</b></i> at a given location in the tunnel (either </span><i style="font-size: 12.8px;"><b>GPE(Surface)</b></i><span style="font-size: 12.8px;"> or </span><i style="font-size: 12.8px;"><b>GPE(Midway) </b></i><span style="font-size: 12.8px;">MINUS </span><i style="font-size: 12.8px;"><b>GPE(Center)</b></i><span style="font-size: 12.8px;">, and is therefore a positive quantity.</span><span style="font-size: 12.8px;"> </span></td></tr>
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Consider three observers:<br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><b><i>A </i></b>is "at rest" on the surface of the Earth. He has zero SPEED, so he has zero <i><b>KE</b></i>. But, what is his POTENTIAL ENERGY, <i><b>PE(Surface)</b></i>? Since POTENTIAL ENERGY is with respect to the Center, it is </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>GPE(Surface)</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">, MINUS </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>GPE(Center)</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">, a POSITIVE quantity</span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">. At the Surface, Gravity, <i><b>g = 32.2</b></i> feet per second squared.</span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><i>B </i></b><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">is "at rest" in the very center of the Earth. He has zero SPEED, so he has zero <i><b>KE</b></i>. </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">But, what is POTENTIAL ENERGY. </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>PE(Center)</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">? Since </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">POTENTIAL ENERGY is with respect to the Center, it is </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>GPE(Center)</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">, MINUS </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>GPE(Center)</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">, which is ZERO.</span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;"> </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">At the Center, </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>g = 0.0</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;"> feet per second squared.</span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><i>C </i></b><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">starts "at rest" on the surface of the Earth. At that point, She</span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> has zero SPEED, so she has zero <i><b>KE</b></i>. And, like <b><i>A</i></b>, she </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>PE(surface)</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">, a POSITIVE Quantity. </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">At the Surface, Gravity, </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>g = 32.2</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;"> feet per second squared.</span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><i>C </i></b><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">jumps into the tunnel! She falls at increasing SPEED, so her <i><b>KE </b></i>increases. By conservation of energy, assuming a friction-free tunnel, her <i><b>PE </b></i>must decrease by the same amount as her <i><b>KE </b></i>increases. So, when she is about halfway from the surface to the center, she has medium <i><b>KE </b></i>and medium <i><b>PE</b></i>. Since GRAVITY decreases linearly within a spherical mass, a</span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">t the midway point, </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>g = 16.1</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;"> feet per second squared.</span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><i>C </i></b><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">comes to the center of the Earth! At this point, she is moving very fast, so she has maximum <i><b>KE</b></i>. However, being at the center of the Earth, she zero </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>PE</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;"> with respect to the Center. </span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">At the Center, </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>g = 0.0</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;"> feet per second squared.</span><br />
<br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><i>C </i></b><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">continues towards the other side of the Earth, <i><b>g </b></i>increases in magnitude from zero towards its eventual value of -<i><b>32.2</b></i> feet per second squared at the surface, her SPEED decreases, and her <i><b>KE </b></i>decreases. So, at this point, she has medium <i><b>KE </b></i>and <i><b>PE</b></i>. </span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><i>C </i></b><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">reaches the other side of the Earth. At this point (but only momentarily) she is again "at rest" on the surface of the Earth. At that point, She</span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"> has zero SPEED, so she has <i><b>KE = 0</b></i>, and </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>PE(Surface)</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">. </span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">So what happens? <b><i>C</i></b> falls back into the hole, and repeats the process of exchanging <i><b>PE </b></i>and <i><b>KE</b></i>. If the hole is friction-free, she neither gains nor looses net Energy (the simple sum of </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>PE PLUS</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;"> </span><i style="font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 14.85px; line-height: 27.72px;"><b>KE</b></i><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">). T</span><span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px; line-height: 27.72px;">his process will continue forever, and it turns out that the journey from top Surface to bottom Surface is about 42 minutes, or about 84 minutes for the round trip.</span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;">Please notice that <b><i>C</i></b> will experience the relativistic effects of Special Relativity plus the relativistic effects of General Relativity when passing through the center of the Earth. When momentarily "at rest" at the surface, she will experience only the relativistic Effects of General Relativity. Thus, her <i><b>TD</b></i> will be greater at the center due to more <i><b>KE </b></i>and also greater at the center due to more <i><b>GPE</b></i>. </span><br />
<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.850001335144px; line-height: 27.7200012207031px;"><br /></span>
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<br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 24.6399993896484px;" />
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<div style="text-align: center;">
<b><span style="color: blue; font-size: large;"><i>Ira Glickstein</i></span></b></div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-81099477343698788282015-07-24T17:49:00.001-07:002015-07-24T17:54:50.885-07:00Light and Heat for VISUALIZING the Atmospheric "Greenhouse" Effect<div style="color: #222222; font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 26.4444446563721px; margin-bottom: 0.825em;">
Guest Post by <a data-mce-href="http://tvpclub.blogspot.com/" href="http://tvpclub.blogspot.com/" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Ira</a> <a data-mce-href="http://2052tech.blogspot.com/" href="http://2052tech.blogspot.com/" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Glickstein</a> </div>
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<em style="font-weight: inherit; line-height: 1.7;">Solar "light" </em>radiation in = <em style="font-weight: inherit; line-height: 1.7;">Earth "heat" </em>radiation to Space out! That's old news to those of us who understand <em style="font-weight: inherit; line-height: 1.7;">all </em>energy is <em style="font-weight: inherit; line-height: 1.7;">fungible </em>(may be converted to different forms of energy) and energy/mass is <em style="font-weight: inherit; line-height: 1.7;">conserved </em>(cannot be created nor destroyed).<br />
<i style="background-color: white; color: black; font-family: 'Times New Roman'; font-size: 13.1999998092651px; line-height: 26.4444446563721px; text-align: center;"><span style="color: blue; font-size: xx-small;"><span style="line-height: 26.4444446563721px;">Originally Posted by me to Watts Up With That, the world's most popular climate website</span>, where it attracted almost 12,000 page views and 958 comments. (Click <a href="http://wattsupwiththat.com/2011/05/07/visualizing-the-greenhouse-effect-light-and-heat/" style="color: #888888; text-decoration: none;">here</a> to view my original posting and read the Comments.</span></i></div>
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My <em style="font-weight: inherit; line-height: 1.7;">Visualizing </em>series [<a data-mce-href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/" href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Physical Analogy</a>, <a data-mce-href="http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/" href="http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Atmospheric Windows</a>, <a data-mce-href="http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra" href="http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Emission Spectra</a>, and <a data-mce-href="http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/" href="http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Molecules/Photons</a>] has garnered almost 2000 comments, mostly positive. I've learned a lot from WUWT readers who know more than I do. However, some commenters seem to have been taken in by scientific-sounding objections to the basic science behind the Atmospheric "Greenhouse Effect". Their objections seemed to add more <em style="font-weight: inherit; line-height: 1.7;">heat </em>than <em style="font-weight: inherit; line-height: 1.7;">light </em>to the discussion. This posting is designed to get back to basics and perhaps transform our <em style="font-weight: inherit; line-height: 1.7;">heat</em>ed arguments into more en<em style="font-weight: inherit; line-height: 1.7;">light</em>ened understanding :^)</div>
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<dt class="wp-caption-dt" style="-webkit-user-drag: none; font-size: 15px; font-style: inherit; font-weight: bold; line-height: 1.7;"><a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/05/gw-light-heat.jpg" href="http://wattsupwiththat.files.wordpress.com/2011/05/gw-light-heat.jpg" style="-webkit-user-drag: none; color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="size-full wp-image-39426" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/05/gw-light-heat.jpg" src="http://wattsupwiththat.files.wordpress.com/2011/05/gw-light-heat.jpg" height="400" style="-webkit-user-drag: none; border: 0px none rgb(238, 238, 238); color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 5px auto 0px !important; max-width: 98%; padding: 0px;" title="GW-Light-Heat" width="640" /></a></dt>
<dd class="wp-caption-dd" style="-webkit-user-drag: none; color: #666666; font-family: Georgia, serif !important; font-size: 12px; font-style: inherit; font-weight: inherit; line-height: 17px; margin: 0px 0px 0.6em !important; padding: 0px 0px 5px 40px; position: relative; text-align: left;">Solar "light" energy in is equal to Earth "heat" energy out.</dd></dl>
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[Click on image for larger version]</div>
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As I've mentioned before, during my long career as a system engineer I've worked with many talented mathematical analysts who always provided <em style="font-weight: inherit; line-height: 1.7;">precise </em>results, mostly correct, but some <em style="font-weight: inherit; line-height: 1.7;">precisely wrong</em>, usually due to mistaken assumptions. I got into the habit of doing a "back of the envelope" calculation of my own as a "sanity check" on their results. If their results matched within reasonable limits, I accepted them. If not, I investigated further. In those days my analysis was really done using a slide rule and scrap paper, but I now use spreadsheets.<img alt="" class="wp-more-tag mce-wp-more" data-mce-placeholder="1" data-mce-resize="false" data-mce-src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" data-wp-more-text="" data-wp-more="more" src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" style="-webkit-box-shadow: none; background-attachment: scroll; background-clip: initial; background-image: url(https://wordpress.com/wp-includes/js/tinymce/skins/wordpress/images/more-2x.png); background-origin: initial; background-position: 50% 50%; background-repeat: repeat-y; background-size: 1900px 20px; border-radius: 0px; border: 0px; box-shadow: none; cursor: default; display: block; font-style: inherit; font-weight: inherit; height: 16px; line-height: 1.7; margin: 15px auto 0px; max-width: 100%; outline: 0px; padding: 0px; width: 692.256958007813px;" title="Read more..." /></div>
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The graphic above is based on an excellent spreadsheet from <a data-mce-href="http://serc.carleton.edu/files/introgeo/models/mathematical/examples/XLPlanck.xls" href="http://serc.carleton.edu/files/introgeo/models/mathematical/examples/XLPlanck.xls" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">http://serc.carleton.edu/files/introgeo/models/mathematical/examples/XLPlanck.xls</a>. It uses Planck's Law to calculate the <em style="font-weight: inherit; line-height: 1.7;">black body</em> radiation spectrum from the Sun, as observed at the top of the Earth's Atmosphere. It also may be used to calculate the radiation spectrum from the Earth System (Atmosphere and Surface, see below for explanation) at any assumed temperature. (I will refer to this spreadsheet as "Carleton" in this posting.)</div>
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I modified the Carleton spreadsheet to compute the mean Solar radiation per square meter absorbed by the Earth System, which turns out to be 240 Watts/m^2. I then used the spreadsheet to determine the effective mean temperature of the Earth System that would emit an equal amount of energy to Space, and that turned out to be 255 Kelvins (-18ºC which is 1ºF).</div>
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<strong style="font-style: inherit; line-height: 1.7;">Since the mean temperature at the surface of the Earth is 288 Kelvins (+15ºC which is 59ºF), that leaves 33 Kelvins (33ºC which is 58ºF) to be accounted for. Guess how we acount for it?</strong></div>
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The yellow curve (above left) shows that Solar radiation is in a tall, narrow "shortwave" range, from about 0.1μm (microns, or millionths of a meter) to about 4μm, which we call ultra-violet, visual, and near-infrared. The vertical axis is Intensity of the radiation, measured in Watts/m^2/μm, and the horizontal axis is Wavelength, measured in μm. If you divide the area under the yellow curve into vertical strips, and add up the total area, you get 240 Watts/m^2.</div>
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Since we humans sense the visual portion of this radiation as "light", that is the name we give it, and that has led to the false assumption that it contains no "heat" (or "thermal") energy.</div>
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The violet curve (above right) shows that, assuming a mean temperature of 255 K, Earth System radiation to Space is in a squat, wide "longwave" range, from about 5μm to beyond 40μm, which we call mid- and far-infrared. If you divide the area under the violet curve into vertical strips, and add up the total area, you get the same 240 Watts/m^2 as is under the yellow curve.</div>
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<strong style="font-style: inherit; line-height: 1.7;">DETAILED EXPLANATION</strong></div>
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<dt class="wp-caption-dt" style="-webkit-user-drag: none; font-size: 15px; font-style: inherit; font-weight: bold; line-height: 1.7;"><a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/05/gw-heat-light-detail.jpg" href="http://wattsupwiththat.files.wordpress.com/2011/05/gw-heat-light-detail.jpg" style="-webkit-user-drag: none; color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="size-full wp-image-39441" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/05/gw-heat-light-detail.jpg" src="http://wattsupwiththat.files.wordpress.com/2011/05/gw-heat-light-detail.jpg" height="265" style="-webkit-user-drag: none; border: 0px none rgb(238, 238, 238); color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 5px auto 0px !important; max-width: 98%; padding: 0px;" title="GW-heat-light-detail" width="640" /></a></dt>
<dd class="wp-caption-dd" style="-webkit-user-drag: none; color: #666666; font-family: Georgia, serif !important; font-size: 12px; font-style: inherit; font-weight: inherit; line-height: 17px; margin: 0px 0px 0.6em !important; padding: 0px 0px 5px 40px; position: relative; text-align: left;">Left: Actual Solar radiation spectrum observed at top of Atmosphere, compared to black body model. Right: Black body Earth System radiation spectrum out to Space.</dd></dl>
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The graph on the left shows the actual observed Solar radiation spectrum (in red) as measured at the top of the Atmosphere. It is superimposed on a black body model (in blue) showing very good correlation. Thus, while the Sun is not exactly a black body, it is OK to assume it is for this type of "sanity check" exercise.</div>
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If you calculate the area under the curve you get about 1366 Watts/m^2. That means that a square meter of perfect black body material, held perpendicular to the Sun, would absorb 1366 Watts.</div>
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However, the Earth is not a perfect black body, neither is it a flat surface perpendicular to the Sun! So, to plot the yellow curve at the top of this posting, I had to adjust that value accordingly. There are two adjustments:</div>
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<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">The Earth may be approximated as a sphere, with the Sun shining on only half of it at any given time. The adjustment factor for this correction is 0.25.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">The albedo (reflectiveness) of the Earth system, primarily clouds and light-colored areas on the Surface such as ice, causes some of the Solar radiation to be reflected back out to Space without contributing any energy to the Earth System. The adjustment factor for this correction is 0.7.</li>
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After applying these adjustments, the net Solar energy absorbed by the Earth System is 240 Watts/m^2.</div>
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The graph on the right shows the black body model for an Earth System at a mean temperature of 255 K, a temperature that results in the same 240 Watts/m^2 being emitted out to Space.</div>
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Of course, the Earth System is not a perfect black body, as shown by the graph in the upper panel of the illustration below, which plots actual observations from 20 km looking down. (Adapted from Grant Petty, <em style="font-weight: inherit; line-height: 1.7;">A First Course in Atmospheric Radiation</em>, Figure 8.2, <a data-mce-href="http://www.sundogpublishing.com/AtmosRad/Excerpts/index.html" href="http://www.sundogpublishing.com/AtmosRad/Excerpts/index.html" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">http://www.sundogpublishing.com/AtmosRad/Excerpts/index.html</a>.)</div>
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The actual measured radiation is the dark squiggly curve. Note that it jigs and jags up and down between the topmost dashed curve, which is the black body spectrum for a temperature of 270 K and a lower dashed curve which is the black body spectrum for 230 K. This data was taken over the Arctic, most likely during the daytime. The Petty book also has a graph looking down from over the Tropical Pacific which ranges from 300 K down to 210 K. Observations will vary by tens of degrees from day to night, summer to winter, and Tropical to Polar.</div>
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<strong style="font-style: inherit; line-height: 1.7;">However, it is clear that my result, based on matching 240 Watts/m^2, is within a reasonable range of the true mean temperature of the Earth System as viewed from Space.</strong></div>
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<a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/05/gw-spectrum-atmemi.jpg" href="http://wattsupwiththat.files.wordpress.com/2011/05/gw-spectrum-atmemi.jpg" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="aligncenter size-full wp-image-39453" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/05/gw-spectrum-atmemi.jpg" src="http://wattsupwiththat.files.wordpress.com/2011/05/gw-spectrum-atmemi.jpg" height="482" style="border: 1px solid rgb(221, 221, 221); clear: both; color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 0.4em auto 1.625em; max-width: 100%; padding: 6px;" title="GW Spectrum AtmEmi" width="640" /></a></div>
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<strong style="font-style: inherit; line-height: 1.7;">NOTE ABOUT THE ABOVE ILLUSTRATION</strong></div>
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WUWT readers will notice some <em style="font-weight: inherit; line-height: 1.7;">apparent </em>inconsistencies in the graphs above. The top and bottom panels, from Petty, peak at 15μm to 20μm, while the purple, blue, and black curves in the middle panel, and the Earth System curves from the Carleton spreadsheet I used (see above) peak in the 9μm to 11μm range. Also, the Petty black body curves peak at a "Radiance" around 100 mW/m^2/sr cm^-1 while the black body curves from Carleton peak at an "Intensity" of around 14 W/m^2/μm. Furthermore, if you look closely at the Petty curves, the labels on the black body curves are mirror image! What is going on?</div>
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Well, I know some of the reasons, but not all. (I hope commenters who are more fluent in this than I am will confirm my explanations and provide more information about the differences between "Radiance" and "Intensity".) I have Googled and Wikied the Internet and am still somewhat confused. Here is what I know:</div>
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<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">The horizontal axis in Petty's plots are what he calls "Wavenumber", increasing from left to right, which is the number of waves that fit into a cm (centimeter, one hundredth of a meter).</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">This is proportional to the frequency of the radiation, and the frequency is the inverse of the wavelength. Thus, his plots are the mirror image of plots based on wavelength increasing from left to right.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">The spreadsheet I used, and my previous experience with visual, and near-, mid-, and far-IR as used in military systems, always uses wavelength increasing from left to right.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">So, when I constructed the above illustration, I reversed Petty's curves, which explains why the labels on the black body curves are mirror image.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">Fortunately, Petty also included a wavelength legend, which I faithfully reproduced, in non-mirror image, at the top of each plot.</li>
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But, that still does not explain why the Petty black body curves peak at a longer wavelength than the Carleton spreadsheet and other graphics on the Internet. I tried to reproduce Petty's blackbody curves by multiplying the Carleton values by the wavelength (μm) and that did not move the peak to the right enough. So, I multiplied by the wavelength again (μm^2) and, <em style="font-weight: inherit; line-height: 1.7;">voila</em>, the peaks agreed! (I hope some WUWT reader will explain why the Petty graphs have this perverse effect. advTHANKSance!)</div>
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<strong style="font-style: inherit; line-height: 1.7;">ANSWERING THE OBJECTIONS TO BASIC ATMOSPHERIC "GREENHOUSE EFFECT" SCIENCE</strong></div>
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First of all, let me be clear where <strong style="font-style: inherit; line-height: 1.7;"><em style="font-weight: inherit; line-height: 1.7;">I</em></strong> am coming from. I'm a Lukewarmer-Skeptic who accepts that H2O, CO2 and other so-called "greenhouse gases" in the Atmosphere <em style="font-weight: inherit; line-height: 1.7;">do</em> cause the mean temperature of the Earth Surface and Atmosphere to be higher than they would be if everything was the same (Solar radiation, Earth System Albedo, ...) but the Atmosphere was pure nitrogen. The main <em style="font-weight: inherit; line-height: 1.7;">scientific </em>question for me, is <em style="font-weight: inherit; line-height: 1.7;">how much</em> does the increase in human-caused CO2 and human-caused albedo reduction increase the mean temperature above what it would be with natural cycles and processes? My answer is "not much", because perhaps 0.1ºC to 0.2ºC of the supposed 0.8ºC increase since 1880 is due to human activities. The rest is due to natural cycles and processes over which we humans have no control. The main <em style="font-weight: inherit; line-height: 1.7;">public policy </em>question for me, is <em style="font-weight: inherit; line-height: 1.7;">how much</em> should we (society) do about it? Again, my answer is "not much", because the effect is small and a limited increase in temperatures and CO2 may turn out to have a net benefit.</div>
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So, my motivation for this <em style="font-weight: inherit; line-height: 1.7;">Visualizing </em>series is <em style="font-weight: inherit; line-height: 1.7;">not </em>to add to the Alarmist "the sky is falling" panic, but rather to help my fellow Skeptics avoid the natural temptation to fall into an "equal and opposite" falsehood, which some of those on my side, who I call "Disbelievers", do when they fail to acknowledge the basic facts of the role of H2O and CO2 and other gases in helping to keep temperatures in a livable range.</div>
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Objection #1: Visual and near-visual radiation is merely "light" which lacks the "quality" or "oomph" to impart warmth to objects upon which it happens to fall.</div>
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Answer #1: A NASA webpage targeted at children is sometimes cited because they say the near-IR beam from a TV remote control is not warm to the touch. Of course, that is <em style="font-weight: inherit; line-height: 1.7;">not </em>because it is near-visual radiation, but rather because it is very low power. All energy is fungible, and can be changed from one form to another. Thus, the 240 Watts/m^2 of visible and near-visible Solar energy that reaches and is absorbed by the Earth System, has the effect of warming the Earth System exactly as much as an equal number of Watts/m^2 of "thermal" mid- and far-IR radiation.</div>
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Objection #2: The Atmosphere, which is cooler than the Earth Surface, cannot warm the Earth Surface.</div>
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Answer #2: The Second law of Thermodynamics is often cited as the source of this falsehood. The correct interpretation is that the Second Law refers to <em style="font-weight: inherit; line-height: 1.7;">net </em>warming, which can only pass from the warmer to the cooler object. The back-radiation from the Atmosphere to the Earth Surface has been measured (see lower panel in the above illustration). All matter above absolute zero emits radiation and, once emitted, that radiation does not know if it is travelling from a warmer to a cooler surface or vice-versa. Once it arrives it will either be reflected or absorbed, according to its wavelength and the characteristics of the material it happens to impact.</div>
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Objection #3: The Atmospheric "Greenhouse Effect" is fictional. A glass greenhouse works mainly by preventing or reducing convection and the Atmosphere does not work that way at all.</div>
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Answer #3: I always try to put "scare quotes" around the word "greenhouse" unless referring to the glass variety because the term is misleading. Yes, a glass greenhouse works by restricting convection, and the fact that glass passes shortwave radiation and not longwave makes only a minor contribution. Thus, I agree it is unfortunate that the established term for the Atmospheric warming effect is a bit of a misnomer. However, we are stuck with it. But, enough of semantics. Notice that the Earth System mean temperature I had to use to provide 240 Watts/m^2 of radiation to Space to balance the input absorbed from by the Earth System from the Sun was 255 K. However, the actual mean temperature at the Surface is closer to 288 K. How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.</div>
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<i><span style="color: blue; font-size: large;">Ira Glickstein</span></i></div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-9769504711716574592015-07-24T17:41:00.003-07:002015-07-24T17:41:37.541-07:00Global Warming is REAL, but NOT a Big DEAL<div style="background-color: white; border: 0px; color: #404040; font-family: pt-serif-1, pt-serif-2, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 1.1em; line-height: 1.3em; margin-bottom: 1em; outline: 0px; padding: 0px; vertical-align: baseline;">
<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Guest essay by Ira Glickstein, PhD</strong></div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Originally Published January 12, 2014 at <a href="http://wattsupwiththat.com/2014/01/12/global-warming-is-real-but-not-a-big-deal-2/">Watts Up With That?</a></strong></div>
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We’ve reached a turning point where it is hard for any Global Warming Alarmist to claim (with a straight face) that the world as we know it is about to end in the coming decades unless we stop burning fossil fuels. Anyone deluded or foolish enough to make such a claim would be laughed at by many audiences.<br />
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">GLOBAL WARMING IS REAL</strong><br />
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Yes, the world has warmed 1°F to 1.5°F (0.6°C to 0.8°C) since 1880 when relatively good thermometers became available. Yes, part of that warming is due to human activities, mainly burning unprecedented quantities of fossil fuels that continue to drive an increase in carbon dioxide (CO2) levels. The Atmospheric “Greenhouse” Effect is a scientific fact!</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">BUT GLOBAL WARMING IS NOT A BIG DEAL</strong></div>
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<a href="http://wattsupwiththat.files.wordpress.com/2014/01/2014-visualize-picasion_com_a68ec0d7e36577af229fe99a4e4c3212.gif" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;"><img alt="Image" height="476" id="i-101058" originalh="356" originalw="404" scale="1.5" src="http://wattsupwiththat.files.wordpress.com/2014/01/2014-visualize-picasion_com_a68ec0d7e36577af229fe99a4e4c3212.gif?w=404&h=356" style="border: 0px; max-width: 100%;" width="640" /></a></div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; line-height: 1.3em; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Alarmist <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Theory</em> is <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Handcuffed</em> to High Estimates of Climate Sensitivity</strong></div>
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As the animated graphic clearly indicates, the <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">theoretical</em> climate models used by the Intergovernmental Panel on Climate Change (IPCC) are <strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">handcuffed</em> </strong>to inordinately high estimates of climate sensitivity (how much temperatures are expected to rise given a doubling of CO2). Since the advent of good satellite-based global temperature data in 1979, observed temperatures have risen at a fraction of the IPCC predicted rate even as CO2 continues to rise.</div>
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Relax, there is not and never has been any near-term “tipping point”. The actual Earth Climate System is far less sensitive to CO2 than claimed the IPCC climate theory, as represented by their computer models. Global Warming since 1880 is mainly due to Natural Cycles and Processes not under human control. Yes, the same Natural Cycles and Processes that were responsible for the many Ice Age cycles that repeatedly occurred about every 100,000 years or so.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">A GREAT TIME TO PUT ALARMISTS IN THEIR PLACE</strong></div>
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Last week, by a stroke of good fortune, I happened to be scheduled to present<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">“Visualizing the Atmospheric ‘Greenhouse’ Effect – <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Global warming is real, but how much is due to human activities and how big is the risk</em>?”</strong> to the <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Philosophy Club</em> in the Central Florida retirement community where I live.</div>
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Everyone in the highly interactive and supportive audience was aware of newspaper and TV reports of the drama of those ill-fated Global Warming “Research” activists whose Russian ship, the <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Academik Shokalskiy</em>, got stuck in the summer ice of the Antarctic. (Fortunately, those people are safe, having been rescued by a helicopter from a Chinese icebreaker.) In addition to the Antarctic adventure gone wrong, in the week leading up to and following my talk, the media was overrun by stories of the “polar vortex” literally freezing large parts of the US and even causing Florida temperatures to drop below 30°F (0°C).</div>
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Of course, everyone knows that the cold wave is only <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">anecdotal</em> evidence and “weather is not climate”. However, photos and videos of researchers stuck in the Antarctic summer ice as well as scenes of American life frozen in place for days on end, when combined with clear and irrefutable evidence of a slowdown in warming since 1979 and no statistically significant warming since 1996 (as depicted in the graphic above), has considerable <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">emotional</em> impact. Audiences often react more to <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">emotions</em> than their <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">reason</em>.</div>
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My animated PowerPoint Show, which should run on any Windows PC, is available for download <a href="https://sites.google.com/site/iraclass/my-forms/2014%20Visualizing%20Atmospheric%20Greenhouse.ppsx?attredirects=0&d=1" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">here</a>. (NOTE: I knew that many members of the <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Philosophy Club</em> audience, while highly intelligent and informed, are not particularly scientifically astute. Therefore, I kept to the basics and invited questions as I proceeded. Since most of them think in Fahrenheit, I was careful to give temperatures in that system. By contrast, my 2011 talk to the more scientifically astute members of our local <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Science and Technology Club</em> <a href="http://wattsupwiththat.com/2011/05/30/skeptic-strategy-for-talking-about-global-warming/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">Skeptic Strategy for Talking about Global Warming</a> was more technical. Both presentations make use of animated PowerPoint charts and you are free to download and use them as you wish.)</div>
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My presentation is based on my five-part WUWT series entitled “Visualizing the ‘Greenhouse Effect'” – <a href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">1 – A Physical Analogy</a>, <a href="http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">2 – Atmospheric Windows</a>, <a href="http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">3 – Emission Spectra</a>, <a href="http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">4 – Molecules and Photons</a>, and <a href="http://wattsupwiththat.com/2011/05/07/visualizing-the-greenhouse-effect-light-and-heat/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">5 – Light and Heat</a>. The series, which ran in 2011, generated tens of thousands of page views at WUWT, along with thousands of comments. I wrote the series this website attracts some viewers who reject the basic physics of the Atmospheric “Greenhouse” Effect.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">HOW A REAL GREENHOUSE WORKS</strong></div>
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I explained how a real physical Greenhouse works and how that is both similar and different from the Atmospheric “Greenhouse” Effect. The Greenhouse descriptions I learned in high school, as well as those available on the Internet, consider only the RADIATIVE effect. The glass roof of the Greenhouse allows visible light to pass through freely, heating the soil, plants, and air, but is opaque to the resultant infrared radiation, which is partly re-radiated back down into the Greenhouse, warming it further. That part is true, but far from the whole story. The MAIN reason a Greenhouse <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">stays</em> warm is that it is airtight to restrict CONVECTION and it is insulated to restrict CONDUCTION. In fact, it is possible to construct a successful Greenhouse using a roof made from materials that allow both visible and infrared to pass freely, but is impossible to make a working Greenhouse that is not both airtight and insulated.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">HOW THE ATMOSPHERIC “GREENHOUSE” EFFECT WORKS</strong></div>
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All warm objects emit radiation at a wavelength dependent upon the temperature of the object. The Sun, at around 10,000 °F, emits “short-wavelength” infrared radiation, centered around 1/2 micron (one millionth of a meter). The soil, plants, and air in the Greenhouse, at around 60°F to 100°F (15°C to 40°C), emit “long wavelength” radiation, centered around 10 microns (with most of the energy between 4 and 25 microns).</div>
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The Atmospheric “Greenhouse” Effect works because:</div>
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<li style="border: 0px; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 6px; outline: 0px; padding: 0px; vertical-align: baseline;">Short-wavelength radiation from the Sun passes freely through the gases that make up the Atmosphere,</li>
<li style="border: 0px; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 6px; outline: 0px; padding: 0px; vertical-align: baseline;">About a third of this Sunlight is reflected back by white clouds, dust, and light-colored objects on the Surface, and that energy is lost to Space,</li>
<li style="border: 0px; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 6px; outline: 0px; padding: 0px; vertical-align: baseline;">The remaining two-thirds of the Sunlight energy is absorbed by the Sea and Land Surface and causes it to warm,</li>
<li style="border: 0px; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 6px; outline: 0px; padding: 0px; vertical-align: baseline;">The warm Surface cools by emitting long-wavelength radiation at the Bottom of the Atmosphere, and this radiation passes towards the Top of the Atmosphere, where it is ultimately lost to Space,</li>
<li style="border: 0px; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 6px; outline: 0px; padding: 0px; vertical-align: baseline;">On the way to the Top of the Atmosphere, much of this radiation is absorbed by so-called “Greenhouse” gases (mostly water vapor and carbon dioxide) which causes the Atmosphere to warm,</li>
<li style="border: 0px; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 6px; outline: 0px; padding: 0px; vertical-align: baseline;">The warmed Atmosphere emits infrared radiation in all directions, some into Space where it is lost, and some back towards the Surface where it is once again absorbed and further warms the Surface.</li>
<li style="border: 0px; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 6px; outline: 0px; padding: 0px; vertical-align: baseline;">In addition to the RADIATIVE effects noted in points 1 through 6, the Surface is cooled by CONVECTION and CONDUCTION (thunderstorms, winds, rain, etc.)</li>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">THANK GOODNESS FOR THE ATMOSPHERIC “GREENHOUSE” EFFECT</strong></div>
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If not for the warming effect of “Greenhouse” gases, the Surface of the Earth would average below 0°F (-18°C), which would prevent life as we know it. This effect is responsible for about 60°F (33°C) of warming. According to the Intergovernmental Panel on Climate Change (IPCC), the Earth Surface has warmed about 1.5°F (0.8°C) since good thermometer data became available around 1880. Some skeptics (including me) believe the actual warming is closer to 1°F, and that government agencies have adjusted the thermometer record to exaggerate the warming by 30% or more. However, it doesn’t really matter whether the actual warming is 1°F or 1.5°F (0.6°C or 0.8°C) because we are arguing about only 0.5°F (0.2°C), which is less than 1% of the total warming due to the Atmospheric “Greenhouse” Effect.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">HOW SENSITIVE IS THE CLIMATE TO HUMAN ACTIVITIES?</strong></div>
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The IPCC claims that the majority of the warming since 1880 is due to human activities. It is true that we are burning unprecedented amounts of fossil fuel (coal, oil, gas), and that we are making land use changes that may reduce the albedo (reflectiveness) of the Surface. Most of the increase in Atmospheric CO2 (a 40% rise from about 270 to nearly 400 parts per million by volume) is due to human activities.</div>
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The IPCC claims that Climate Sensitivity (the average increase in Surface temperatures due to a doubling of CO2) is between 3°F and 8°F (1.5°C and 4.5°C). Some skeptics (including me) believe they are off by at least a factor of two, and possibly a factor of three, and that Climate Sensitivity is closer to 1°F to 3°F (0.5°C to 1.5°C). As evidence for our conclusions, we point to the fact that virtually ALL of the IPCC climate models have consistently over-estimated future temperature predictions as compared to the actual temperature record. Indeed, for the past 17 years as CO2 levels continue their rapid climb, temperatures have leveled off, which is proof that Natural Cycles, not under human control or influence, have cancelled out warming due to CO2 increases. Thus, Natural Cycles must have a larger effect than CO2.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">VISUALIZING THE ATMOSPHERIC “GREENHOUSE” EFFECT</strong></div>
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As I noted above, I wrote the “Visualizing” series for WUWT (<a href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">1 – A Physical Analogy</a>, <a href="http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">2 – Atmospheric Windows</a>, <a href="http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">3 – Emission Spectra</a>, <a href="http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">4 – Molecules and Photons</a>, and <a href="http://wattsupwiththat.com/2011/05/07/visualizing-the-greenhouse-effect-light-and-heat/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">5 – Light and Heat</a>) because some WUWT viewers are “Disbelievers” who have had an “equal and opposite” reaction to the “end of the world” excesses of the Global Warming “Alarmists”. By failing to understand and accept the basic science of the Atmospheric “Greenhouse” Effect, they have, IMHO, “thrown the baby out with the bathwater”.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Answering Some Objections to the Atmospheric “Greenhouse”Effect</strong></div>
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Some WUWT commenters seem to have been taken in by scientific-sounding objections to the basic science behind the Atmospheric “Greenhouse” Effect. Their objections seemed to add more <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">heat </em>than <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">light </em>to the discussion. This section is designed to get back to basics and perhaps transform our <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">heat</em>ed arguments into more en<em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">light</em>ened understanding :^)</div>
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<a href="http://wattsupwiththat.files.wordpress.com/2011/05/gw-light-heat.jpg" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;"><img alt="" height="400" scale="0" src="https://blogger.googleusercontent.com/img/proxy/AVvXsEgttU9tuEpYS5DH1urh-DFK0Er2btnpAA79ozsH-amiNh1bLyfYvOy6J4L4LG2uzMJT1Z33HtFwVchd-mHxlTX3T9PvazpJ9eGobMLl2T8x0g60UXR5Wxf35uRfQeQHY7ybmhvHHHjQv9KWCgSvoju3NWv2xMu3sPdMWBwyKNZ7URccvTCx_XiLkApTw4AyJ94" style="border: 0px; height: auto; max-width: 100%;" title="GW-Light-Heat" width="640" /></a></div>
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The main <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">scientific </em>question for me, is <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">how much</em> does the increase in human-caused CO2 and human-caused albedo reduction increase the mean temperature above what it would be with natural cycles and processes? My answer is “not much”, because perhaps 0.2ºC to 0.4ºC (0.1ºC to 0.2ºC) of the supposed 1.5ºF (0.8ºC) increase since 1880 is due to human activities. The rest is due to natural cycles and processes over which we humans have no control. The main <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">public policy </em>question for me, is <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">how much</em> should we (society) do about it? Again, my answer is “not much”, because the effect is small and a limited increase in temperatures and CO2 may turn out to have a net benefit.</div>
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So, my motivation for this <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Visualizing </em>series was <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">not </em>to add to the Alarmist “the sky is falling” panic, but rather to help my fellow Skeptics avoid the natural temptation to fall into an “equal and opposite” falsehood, which some of those on my side, who I call “Disbelievers”, do when they fail to acknowledge the basic facts of the role of H2O and CO2 and other gases in helping to keep temperatures in a livable range.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Objection #1:</strong> Visual and near-visual radiation is merely “light” which lacks the “quality” or “oomph” to impart warmth to objects upon which it happens to fall.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Answer #1:</strong> A NASA webpage targeted at children is sometimes cited because they say the near-IR beam from a TV remote control is not warm to the touch. Of course, that is<em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">not </em>because it is near-visual radiation, but rather because it is very low power. All energy is fungible, and can be changed from one form to another. Thus, the 240 Watts/m^2 of visible and near-visible Solar energy that reaches and is absorbed by the Earth System, has the effect of warming the Earth System exactly as much as an equal number of Watts/m^2 of “thermal” mid- and far-IR radiation.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Objection #2:</strong> The Atmosphere, which is cooler than the Earth Surface, cannot warm the Earth Surface.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Answer #2:</strong> The Second law of Thermodynamics is often cited as the source of this falsehood. The correct interpretation is that the Second Law refers to <em style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">net </em>warming, which can only pass from the warmer to the cooler object. The back-radiation from the Atmosphere to the Earth Surface has been measured (see lower panel in the above illustration). All matter above absolute zero emits radiation and, once emitted, that radiation does not know if it is travelling from a warmer to a cooler surface or vice-versa. Once it arrives it will either be reflected or absorbed, according to its wavelength and the characteristics of the material it happens to impact.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Objection #3:</strong> The Atmospheric “Greenhouse” Effect is fictional. A glass greenhouse works mainly by preventing or reducing convection and the Atmosphere does not work that way at all.</div>
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<strong style="border: 0px; font-family: inherit; font-size: 17.6000003814697px; font-style: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Answer #3:</strong> I always try to put “scare quotes” around the word “greenhouse” unless referring to the glass variety because the term is misleading. Yes, a glass greenhouse works mainly by restricting convection, and the fact that glass passes shortwave radiation and not longwave makes only a minor contribution.</div>
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Thus, I agree it is unfortunate that the established term for the Atmospheric warming effect is a bit of a misnomer. However, we are stuck with it. But, enough of semantics. Notice that the Earth System mean temperature I had to use to provide 240 Watts/m^2 of radiation to Space to balance the input absorbed from by the Earth System from the Sun was 255 K. However, the actual mean temperature at the Surface is closer to 288 K. How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.</div>
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<i><span style="color: blue; font-size: large;">Ira Glickstein</span></i></div>
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<a href="http://wattsupwiththat.com/2011/05/07/visualizing-the-greenhouse-effect-light-and-heat/" style="border: 0px; color: #b26600; font-family: Arial; font-size: 17.6000003814697px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; text-decoration: none; vertical-align: baseline;">Read more detail, including the 958 responses</a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzLahAB4Mxcz6QlMYbne0-xKtmPIdalKYFSG_UaVSoyts1jXK-YS3iHDZSgZsmixqrU0hiepQwjpB56nP_ne7xK1xch6ugQJsIN35qCVH-pIe7qnWwPkg19O680ryJI7_ICfNef7h_iBs/s1600/ClimateScienceViewpoints.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="476" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzLahAB4Mxcz6QlMYbne0-xKtmPIdalKYFSG_UaVSoyts1jXK-YS3iHDZSgZsmixqrU0hiepQwjpB56nP_ne7xK1xch6ugQJsIN35qCVH-pIe7qnWwPkg19O680ryJI7_ICfNef7h_iBs/s640/ClimateScienceViewpoints.jpg" width="640" /></a></td></tr>
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<li style="text-align: left;"><span style="font-size: 12.8000001907349px;">"Global Warming" (aka "Climate Change") attracts a diverse range of viewpoints. </span></li>
<li style="text-align: left;"><span style="font-size: 12.8000001907349px;">Those I call "Alarmists" spout loud-mouthed propaganda predicting imminent "tipping point" disaster unless we humans immediately cease burning unprecedented amounts of coal, oil and gas and stop land development that reduces the albedo (reflectivity) of the Earth surface. </span></li>
<li style="text-align: left;"><span style="font-size: 12.8000001907349px;">Their irrational counterparts on the other side, who I call "Disbelievers", reject the basic scientific proof of the Atmospheric "Greenhouse" gas effect, and claim it is all a political ruse. </span></li>
<li style="text-align: left;"><span style="font-size: 12.8000001907349px;">Those in the middle (Warmists, Lukewarmers, and Skeptics) accept the basic science, but make different estimates of how much human activities have actually increased world-wide temperatures and the danger inherent in moderate temperature rise. They therefore differ on how much needs to be done in response. </span></li>
<li style="text-align: left;"><span style="font-size: 12.8000001907349px;">Those I call "Warmists" argue for maximum reasonable responses to what they perceive as a serious human-caused warming problem,. </span></li>
<li style="text-align: left;"><span style="font-size: 12.8000001907349px;">The Skeptics" argue for minimal action for what they perceive as mostly natural climate cycles that are only slightly due to human activities. </span></li>
<li style="text-align: left;"><span style="font-size: 12.8000001907349px;">The "Lukewarmers" argue for moderate corrective action. </span><span style="font-size: 12.8000001907349px;">I count myself as a "Lukewarm Skeptic".</span></li>
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<b><span style="color: #660000;">WHY CLIMATE SCIENCE IS IMPORTANT </span></b><br />
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There is no doubt that:<br />
<ul>
<li>Average surface temperatures on Earth have increased by about 1.5⁰F (0.8⁰C) over the past century. </li>
<li>The so-called Atmospheric "Greenhouse" Effect is real. That is, the presence of "Greenhouse" Gases in the Atmosphere, mainly water vapor (H2O) and carbon dioxide (CO2), makes the Earth surface some 60⁰F (33⁰C) warmer than it would be absent those gases. All else being equal, increases in Atmospheric CO2 tend to raise average global temperatures.</li>
<li>Some of the temperature increase is due to human activities. Most of the recent rise in Atmospheric CO2 is due to human activities, mainly burning unprecedented amounts of fossil fuels (coal,oil, gas). Changes in land use due to worldwide agricultural and industrial development have reduced the albedo (reflectivity) of the Earth's surface, which contributes to warming.</li>
</ul>
<b><span style="color: #660000;">KEY ISSUES OF CLIMATE SCIENCE</span></b><br />
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The issues (and my answers):<br />
<ul>
<li>How much of the average global temperature increase is due to human activities? </li>
<ul>
<li>Most likely less than a third of the net warming over the past 100 years is due to human activities. That amounts to only about 0.5⁰F (0.3⁰C). </li>
<li>The official Intergovernmental Panel on Climate Change (IPCC) claims that human activities are responsible for more than half of the warming. However, the lack of any statistically significant net warming over the past two decades, despite continued, mostly human-caused CO2 rise, casts serious doubt on that claim.</li>
</ul>
<li>How much of the warming is due to natural cycles not under human control or influence, and how dangerous is moderate warming?</li>
<ul>
<li>Most likely more than two-thirds of the warming is totally natural and due to the Earth's recovery from the <a href="https://en.wikipedia.org/wiki/Little_Ice_Age">"Little Ice Age"</a> (LIA), a near-disastrous time of low crop yields that occurred between the years 1650 and 1850. </li>
<li>The LIA followed the Medieval Warm Period (MWP) that occurred between 900 and 1200. History shows that the MWP and other moderately warm periods such as that associated with advances in the Roman empire, are generally beneficial to human life and civilization.</li>
<li>Geological evidence and ice core data indicate that, well-prior to the appearance of humans on Earth, natural cycles of ice ages have recurred every 100,000 years or so. We are currently in a warming inter-glacial period between ice ages.</li>
</ul>
<li>Why have the predictions of continued rapid warming based on the official Climate Theory put forth by the IPCC failed to materialize?</li>
<ul>
<li>IPCC Climate Models, based on their Climate Theory, predicted that average surface temperatures would rise more than 0.7⁰F (0.4⁰C) between 1980 and 2015, in tandem with rising CO2 levels . </li>
<li>Actual increases during this thirty-five year period have been less than a third of that estimate. The excellent, and highly reliable global satellite record, available since 1979, shows absolutely no net increase since 1998. The terrestrial record (surface-based thermometers) has recently been "adjusted" to yield a tiny increase, but nowhere near what had been predicted. </li>
<li>The IPCC computer climate models are based on a Climate Theory that is far too sensitive to CO2 levels. The theory predicts that a doubling of Atmospheric CO2 will cause warming of between 1.5 to 4.5⁰C (3 to 8⁰F). Based on several decades of observations, the actual sensitivity of Climate to CO2 is most likely 0.5 to 1.5⁰C (1 to 3⁰F). That is the only reasonable explanation of the failure of the IPCC Climate Theory.</li>
<li>According to <a href="https://www.blogger.com/null">Nobel Laureate Richard Feynman</a> <i><b>"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."</b></i> Instead of following Feynman's advice and changing an obviously flawed Climate Theory, the IPCC scientists have "adjusted" the data! But, even the "adjusted" data fails to match up with the outlandish predictions of the IPCC Climate Models.</li>
</ul>
<li>What can and should be done to mitigate that increase? </li>
<ul>
<li>Very little beyond moderate "green" energy conservation along with transition from fossil fuels to alternatives such as water, wind, solar, nuclear, recycling of biowaste, and so on. </li>
<li>Even if we in the US and Europe and other highly-developed countries take maximum "green" action, China, India, and other rapidly-developing economies will continue to increase their use of coal, oil, and gas, totally cancelling out any effect our actions may have. </li>
</ul>
</ul>
<b><span style="color: #660000;"> MY QUALIFICATIONS TO COMMENT ON CLIMATE SCIENCE</span></b><br />
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<u><b>Academic System Science Credentials</b></u><br />
The Global Climate System is very complex, with innumerable interacting parts. I earned a PhD in System Science (1996) and therefore have academic credentials and knowledge of how to analyze, model, and attempt to understand complex systems. For example:<br />
<ul>
<li>Some components of the Climate System tend to provide <i>positive </i>feedback that increases warming, such as rising CO2 levels that cause surface temperature increases that, in turn, cause less CO2 to be absorbed by the oceans and rivers and more CO2 to out-gas from these water features, further increasing Atmospheric CO2. </li>
<li>Other components cause <i>negative </i>feedback, such as the tendency of higher morning temperatures to produce greater evaporation and therefore more daytime clouds and thunderstorms earlier in the day. </li>
<li>Thunderstorms and daytime clouds have a net <i>cooling </i>effect, making this process a type of automatic "thermostat". with the result stabilizing temperatures despite CO2 rise.</li>
<li>Daytime clouds increase the albedo (reflectivity) of the Earth surface and therefore have a net <i>cooling </i>effect </li>
<li>Nighttime clouds absorb and re-emit long-wave radiation, causing a net <i>warming </i>effect.</li>
<li>Here is a simplified model constructed by a leading Warmist, <a href="https://en.wikipedia.org/wiki/Kevin_E._Trenberth">Kevin Trenberth</a>, a lead IPCC author and US NCAR researcher. See comments <a href="http://wattsupwiththat.com/2014/01/17/nasa-revises-earths-radiation-budget-diminishing-some-of-trenberths-claims-in-the-process/">here</a>.</li>
</ul>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA2v0E5upLZAWq6IXnDpmx7vqDw9R1x2LfaWlGY-wfm3oOA2UO6jKV278g71HnU-fxC4X_fLsOdXCZzSrQs6BSLxKvg5vGw1n06LWN5MBFMc7Mze8JjjsO0Euzv7TrNDweQRUjZacLG7o/s1600/ClimateBudgetTrenberth2009.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="460" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA2v0E5upLZAWq6IXnDpmx7vqDw9R1x2LfaWlGY-wfm3oOA2UO6jKV278g71HnU-fxC4X_fLsOdXCZzSrQs6BSLxKvg5vGw1n06LWN5MBFMc7Mze8JjjsO0Euzv7TrNDweQRUjZacLG7o/s640/ClimateBudgetTrenberth2009.jpg" width="640" /></a></td></tr>
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<span style="background-color: #efefef; color: #999999; font-family: Arial; font-size: 12.8000001907349px; line-height: 16.6400012969971px;">The Earth’s annual radiation budget. The numbers are all in W/m2 (Watts per square meter), a measure of energy. Of the incoming radiation, 49% (168÷342) is absorbed by the Earth’s surface. That heat is returned to the atmosphere in a variety of forms (evaporation processes and thermal radiation, for example). Most of this back-scattered heat is absorbed by the atmosphere, which then re-emits it both up and down. Some is lost to space, and some stays in the Earth’s climate system. This is what drives the Greenhouse Effect [Figure from Trenberth et al. 2009].</span></div>
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<u><b>Professional System Engineering Credentials</b></u><br />
My decades-long professional career was in System Engineering (IBM, Lockheed-Martin) so I have practical experience with really complex human-made systems.</div>
<div>
<ul>
<li>I have actual "hands-on" experience attempting to properly construct and evaluate computer models of complex avionics systems. </li>
<ul>
<li>I've "burnt my fingers" on models of the Doppler-Inertial Navigation systems that were in use prior to the advent of GPS.</li>
<li>I've "stubbed my toes" on models of the multiple redundant data bus systems interconnecting multiple computers, sensors, displays, and actuators on modern aircraft.</li>
</ul>
<li>I know, from sometimes bitter experience, how difficult this task may become, and how easy it may be to fool ones-self.</li>
</ul>
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<u><b>Academic System Engineering Teaching Credentials</b></u><br />
I've also been an adjunct professor at the Thomas J. Watson School of Engineering at Binghamton University (NY) and the University of Maryland University College, teaching both under-graduate and graduate-level courses in Computer Science, Artificial Intelligence, Artificial Life, and System Engineering.<br />
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<u><b>Online Climate Publication Credentials</b></u></div>
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Since 2010, I've been a Guest Contributor to the world's most popular Climate website, <a href="http://wattsupwiththat.com/author/iraglickstein/">Watts Up With That?</a>, where my topic postings have attracted hundreds of thousands of page views and thousands of comments.<br />
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<span style="color: #660000;"><b>CONCLUSION</b></span><br />
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So, please click on each of the <u>CLIMATE SCIENCE TOPICS</u> listed at the top of the right-hand column under the Blog title.<br />
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advTHANKSance !<br />
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<b><span style="font-size: large;">Ira Glickstein</span></b></div>
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Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-30767103287835151732015-07-14T19:35:00.000-07:002015-07-14T19:47:23.799-07:00A Physical Analogy for VISUALIZING the Atmospheric "Greenhouse" Effect Albert Einstein was a great </span><em style="font-weight: inherit; line-height: 1.7;">theoretical</em><span style="line-height: 26.4444446563721px;"> physicist, with all the requisite mathematical tools. However, he rejected </span><em style="font-weight: inherit; line-height: 1.7;">purely</em><span style="line-height: 26.4444446563721px;"> mathematical abstraction and resorted to </span><em style="font-weight: inherit; line-height: 1.7;">physical analogy</em><span style="line-height: 26.4444446563721px;"> for his most basic insights. For example, he imagined a man in a closed elevator being transported to space far from any external mass and then subjected to accelerating speeds. That man could not tell the difference between gravity on Earth and acceleration in space, thus, concluded Einstein, gravity and acceleration are equivalent, which is the cornerstone of his theory of relativity. Einstein never fully bought into the mainstream interpretation of quantum mechanics that he and others have called </span><em style="font-weight: inherit; line-height: 1.7;">quantum weirdness</em><span style="line-height: 26.4444446563721px;"> and </span><em style="font-weight: inherit; line-height: 1.7;">spooky action at a distance</em><span style="line-height: 26.4444446563721px;">.
<dt class="wp-caption-dt" style="-webkit-user-drag: none; font-size: 15px; font-style: inherit; font-weight: bold; line-height: 1.7;"><i style="background-color: white; font-size: 13.1999998092651px; line-height: 26.4444446563721px; text-align: center;"><span style="color: blue; font-size: xx-small;"><span style="line-height: 26.4444446563721px;">Originally Posted by me to Watts Up With That, the world's most popular climate website</span>, where it attracted over 12,000 page views and 340 comments. (Click <a href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/" style="color: #888888; text-decoration: none;">here</a> to view my original posting and read the Comments.</span></i></dt>
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So, if some <em style="font-weight: inherit; line-height: 1.7;">Watts Up With That?</em> readers have trouble accepting the atmospheric "greenhouse" effect because of the lack of a good physical analogy, you are in fine company.</div>
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For example, in the discussion following Willis Eschenbach's excellent <a data-mce-href="http://wattsupwiththat.com/2010/11/27/people-living-in-glass-planets/" href="http://wattsupwiththat.com/2010/11/27/people-living-in-glass-planets/" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">People Living in Glass Planets</a>, a commenter "PJP", challenged the atmospheric "greenhouse" effect:</div>
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"The incoming energy (from the sun) you express in w/m^2, lets simplify it even more and say that energy is delivered in truckloads. Lets say we get 2 truckloads per hour. ... when we come to your semi-transparent shell [representing greenhouse gases (GHG) in the atmosphere], you are still getting two truckloads per hour, but you say that these two truckloads are delivered to both the earth and to the shell — that makes 4 truckloads/hr. Where did the extra two truckloads come from?"</div>
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In that thread, I posted a comment with an analogy of truckloads of orange juice, representing short-wave radiation from Sun to Earth, and truckloads of blueberry juice, representing longwave radiation between Earth and the Atmosphere and back out to Space. A later commenter, "davidmhoffer" said <em style="font-weight: inherit; line-height: 1.7;">"Ira, That was a brilliant explanation. ..."</em></div>
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This Post is a further elaboration of my physical analogy, using a pitching machine and yellow and purple balls in place of the truckfulls of juice.<br />
<a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale1.jpg" href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale1.jpg" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="aligncenter size-full wp-image-34338" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale1.jpg" src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale1.jpg" height="480" style="border: 1px solid rgb(221, 221, 221); clear: both; color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 0.4em auto 1.625em; max-width: 100%; padding: 6px;" title="GW scale1" width="640" /></a><br />
Graphic 1 shows the initial conditions. The Sun is a ball pitching machine that, when we turn it on, will throw a steady stream of yellow balls towards the tray of a weight scale, which represents the Earth. The reading on the scale is analogized to "temperature" and, with the Sun turned off, reads "0" arbitrary units.</div>
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<strong style="font-style: inherit; line-height: 1.7;">TURN ON THE "SUN"</strong></div>
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Graphic 2 shows what happens when the Sun is turned on and there are no GHG in the Atmosphere. The stream of yellow balls impact the tray atop the weight scale and compress the springs within the well-damped scale until equilibrium is reached. The scale reads "1". This is analogous to the temperature the Earth would reach in the absence of GHG.</div>
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The balls bounce off the tray and, for illustrative purposes, turn purple in color. This is my way of showing that Sun radiative energy is mostly in the "shortwave" visible and near-visible region (about 0.3μ to 1μ) and that radiative energy from the warmed Earth is mostly in the "longwave" infrared region (about 6μ to 20μ). The Greek letter "μ" (mu) stands for a unit of length called the "micron" which is a millionth of a meter.</div>
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Since, at this stage of my physical analogy, there are no GHG in the Atmosphere, the purple balls go off into Space where they are not heard from again. You can assume the balls simply "bounce" off like reflected light in a mirror, but, in the actual case, the energy in the visible and near-visible light from the Sun is absorbed and warms the Earth and then the Earth emits infrared radiation out towards Space. Although "bounce" is different from "absorb and re-emit" the net effect is the same in terms of energy transfer.</div>
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If we assume the balls and traytop are perfectly elastic, and if the well-damped scale does not move once the springs are compressed and equilibrium is reached, there is no work done to the weight scale. Therefore, Energy IN = Energy OUT. The purple balls going out to Space have the same amount of energy as the yellow balls that impacted the Earth.</div>
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<strong style="font-style: inherit; line-height: 1.7;">ADD GHG TO THE "ATMOSPHERE"</strong></div>
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<a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale3.jpg" href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale3.jpg" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="aligncenter size-full wp-image-34353" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale3.jpg" src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale3.jpg" height="480" style="border: 1px solid rgb(221, 221, 221); clear: both; color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 0.4em auto 1.625em; max-width: 100%; padding: 6px;" title="GW scale3" width="640" /></a><br />
Graphic 3 shows what happens when we introduce GHG into the Atmosphere. The yellow balls, representing shortwave radiation from the Sun to which GHG are transparent, whiz right through and impact the weight scale and push it down as before.</div>
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However, the purple balls, representing longwave radiation from the Earth, are intercepted by the Atmosphere. In my simplified physical analogy, the Atmosphere splits each purple ball in two, re-emiting one half-ball back towards the Earth and the other half-ball out to Space. Again, you can assume that half of the balls "bounce" off the Atmosphere back to Earth like reflected light from a half-silvered mirror and the other half pass through out towards Space. In the actual case, it is "absorb and re-emit half in each direction" but the net effect is the same in terms of energy transfer.</div>
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<strong style="font-style: inherit; line-height: 1.7;">OK, here is the part where you should pay close attention.</strong> The purple half-balls that are re-emitted by the Atmosphere towards Earth impact the tray of the weight scale and press against the springs with about half the force of the original yellow balls. So, at this stage, when equilibrium is reached, the well-damped scale reads "1.5" arbitrary units.</div>
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But, we are not done yet. The purple half-balls are absorbed by the Earth, and re-emitted towards Space. Then they are re-absorbed by the Atmosphere and once again split into quarter-balls, half of which head back down to Earth and re-impact the weight scale. Now it reads "1.75". As you can see, the purple balls continue to get split into ever smaller balls as they bounce back and forth and half head out to Space. The net effect on the weight scale is the sum of 1 (from the yellow balls) + 1/2 + 1/4 + 1/8 + 1/16 and so on (from the purple balls). That expression has a limit of "2", which is approximately what the scale will read when equilibrium is reached.</div>
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Again, the well-damped scale does not move once the springs are compressed and equilibrium is reached, so there is no work done to the weight scale. Therefore, Energy IN = Energy OUT. The purple balls going out to Space have the same amount of energy as the yellow balls that impacted the Earth. <strong style="font-style: inherit; line-height: 1.7;">But the "temperature" of the Earth, as analogized by the reading on the weight scale, has increased.</strong></div>
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<strong style="font-style: inherit; line-height: 1.7;">DOUBLE THE GHG IN THE "ATMOSPHERE"</strong></div>
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<a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale4.jpg" href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale4.jpg" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="aligncenter size-full wp-image-34366" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale4.jpg" src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-scale4.jpg" height="477" style="border: 1px solid rgb(221, 221, 221); clear: both; color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 0.4em auto 1.625em; max-width: 100%; padding: 6px;" title="GW scale4" width="640" /></a><br />
Graphic 4 is the final step in my physical analogy. Let us double the GHG in the Atmosphere. (NOTE: I am assuming that the doubling includes ALL the GHG, most especially water vapor, and not simply CO2!) This is represented by putting a second layer of Atmosphere into the physical analogy.</div>
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The purple balls emitted towards Space by the first layer of the Atmosphere are intercepted by the second layer, where they are absorbed, and smaller balls are re-emited in each direction. The downward heading balls from the upper atmosphere are intercepted by the lower Atmosphere and half is re-emitted down towards the weight scale that represents Earth. Once again, they compress the springs in the weight scale increasing the reading a bit, and are re-emitted back up. The purple balls get halved and bounce around up and down between Earth and the two layers of the Atmosphere, further increasing the reading on the scale once equilibrium is reached.</div>
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Again, the well-damped scale does not move once the springs are compressed and equilibrium is reached, so there is no work done to the weight scale. Therefore, Energy IN = Energy OUT. The purple balls going out to Space have the same amount of energy as the yellow balls that impacted the Earth. <strong style="font-style: inherit; line-height: 1.7;">But the "temperature" of the Earth, as analogized by the reading on the weight scale, has increased due to the doubling of GHG in the Atmosphere.</strong></div>
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<strong style="font-style: inherit; line-height: 1.7;">WHAT I LEFT OUT OF THE PHYSICAL ANALOGY</strong></div>
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Any simplified analogy is, by its very nature, much less than the very complex situation it is meant to analogize. Here is some of what is left out:</div>
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<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">My purple balls are re-emitted in only two directions, either up or down. In the real world, longwave radiation is emitted in all directions, including sideways.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">My purple balls are all totally absorbed by the Atmosphere and re-emitted. In the real-world, a substantial amount of longwave radiation is re-emitted from the Earth and the Atmosphere in the 9μ to 12μ band where the Atmosphere is nearly-transparent. A substantial portion of the radiation from Earth and the Atmosphere thus passes through the Atmosphere to Space without interception.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">My physical analogy addresses only radiative energy transfer. In the real-world, energy transfer from the Sun to Earth and Earth to Space <em style="font-weight: inherit; line-height: 1.7;">is</em> purely radiative. However, the Earth transfers a considerable amount of energy to the Atmosphere via convection and conduction, in the form of winds, precipitation, thunderstorms, etc. These effects are absent from my analogy.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">I represent the Atmosphere as a single shell, when, in fact, it has many layers with lots of interaction between layers.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">I represent doubling of GHG as adding another shell, when, in fact, doubling of GHG, if it occured (and if it included not just CO2 but also a doubling of water vapor and other GHG) would increase the density of those gases in the Atmosphere and not necessarily increase its height significantly.</li>
<li style="font-style: inherit; font-weight: inherit; line-height: 1.7;">In my analogy, all the energy from the Sun strikes and is absorbed by the Earth. In the real-world, up to a third of it is reflected back to Space from light-colored surfaces (albedo) such as snow, ice, clouds, and the white roof of Energy Secretary Chu's home :^). If a moderately warmer Earth, due to increased GHG, evaporates more water vapor into the atmosphere, and if that causes more clouds to form, that could increase the Earth's albedo to counteract a substantial portion of the additional warming.</li>
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I am sure WUWT readers will find other issues with my <em style="font-weight: inherit; line-height: 1.7;">physical analogy</em>. However, the point of this posting is to convince those WUWT readers, who, like Einstein, need a physical analogy before they will accept any mathematical abstraction, that the atmospheric "greenhouse" effect is indeed real, even though estimates of climate <em style="font-weight: inherit; line-height: 1.7;">sensitivity</em> to doubling of CO2 are most likely way over-estimated by the official climate <em style="font-weight: inherit; line-height: 1.7;">Team</em>. When I was an Electrical Engineering undergrad, I earned a well-deserved "D" in <em style="font-weight: inherit; line-height: 1.7;">Fields and Waves</em> because I could not create a physical analogy in my overly-anal mind of Maxwell's equations or <em style="font-weight: inherit; line-height: 1.7;">picture</em> the "curl" or any of the other esoteric stuff in that course. Therefore, those WUWT readers who need a <em style="font-weight: inherit; line-height: 1.7;">physical analogy</em> are in great company - <a data-mce-href="http://tvpclub.blogspot.com/2010/12/einsteins-cosmological-philosophy.html" href="http://tvpclub.blogspot.com/2010/12/einsteins-cosmological-philosophy.html" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Einstein and Glickstein</a> :^).</div>
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I plan to make additional postings in this series, addressing some implications of the 9μ to 12μ portion of the longwave radiation band where the Atmosphere is nearly-transparent, as well as other atmospheric "greenhouse" issues. I look forward to your comments!</div>Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-71919281003354649872015-07-14T12:33:00.003-07:002015-07-14T12:34:09.496-07:00Molecules and Photons for VISUALIZING the Atmospheric "Greenhouse" EffectThis series began with a <a href="https://www.blogger.com/null">mechanical analogy</a> for the Atmospheric "Greenhouse Effect" and progressed a bit more deeply into <a href="https://www.blogger.com/null">Atmospheric Windows</a> and <a href="https://www.blogger.com/null">Emission Spectra</a>. In this posting, we consider the interaction between air molecules, including Nitrogen (N2), Oxygen (O2), Water Vapor (H2O) and Carbon Dioxide (CO2), with Photons of various wavelengths. This may help us visualize how energy, in the form of Photons radiated by the Sun and the Surface of the Earth, is absorbed and re-emited by Atmospheric molecules.<br />
<i style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 26.4444446563721px; text-align: center;"><span style="color: blue; font-size: x-small;"><span style="line-height: 26.4444446563721px;">Originally Posted by me to Watts Up With That, the world's most popular climate website</span>, where it attracted over 18,000 page views and 743 comments. (Click <a href="http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/">here</a> to view my original posting and read the Comments.)</span></i><a href="http://wattsupwiththat.files.wordpress.com/2011/03/gw-photons-animated.gif"><img alt="" class="aligncenter size-full wp-image-36788" src="http://wattsupwiththat.files.wordpress.com/2011/03/gw-photons-animated.gif" height="338" title="GW Photons Animated" width="450" /></a><strong>DESCRIPTION OF THE GRAPHIC</strong>
The animated graphic has eight frames, as indicated by the counter in the lower right corner. Molecules are symbolized by letter pairs or triplets and Photons by ovals and arrows. The view is of a small portion of the cloud-free Atmosphere. (Thanks to WUWT commenter <a href="http://knowledgedrift.wordpress.com/">davidmhoffer</a> for some of the ideas incorporated in this graphic.)<br />
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<li>During the daytime, Solar energy enters the Atmosphere in the form of Photons at wavelengths from about 0.1μ (micron - millionth of a meter) to 4μ, which is called "shortwave" radiation and is represented as ~1/2μ and symbolized as orange ovals. Most of this energy gets a free pass through the cloud-free Atmosphere. It continues down to the Surface of the Earth where some is reflected back by light areas (not shown in the animation) and where most is absorbed and warms the Surface.</li>
<li>Since Earth's temperature is well above absolute zero, both day and night, the Surface radiates Photons in all directions with the energy distributed approximately according to a "blackbody" at a given temperature. This energy is in the form of Photons at wavelengths from about 4μ to 50μ, which is called "longwave" radiation and is represented as ~7μ, ~10μ, and ~15μ and symbolized as violet, light blue, and purple ovals, respectively. The primary "greenhouse" gases (GHG) are Water Vapor (H2O) and Carbon Dioxide (CO2). The ~7μ Photon is absorbed by an H2O molecule because Water Vapor has an absorption peak in that region, the ~10μ Photon gets a free pass because neither H2O nor CO2 absorb strongly in that region, and one of the 15μ Photons gets absorbed by an H2O molecule while the other gets absorbed by a CO2 molecule because these gases have absorption peaks in that region.</li>
<li>The absorbed Photons raise the energy level of their respective molecules (symbolized by red outlines).</li>
<li>The energized molecules re-emit the Photons in random directions, some upwards, some downwards, and some sideways. Some of the re-emitted Photons make their way out to Space and their energy is lost there, others back down to the Surface where their energy is absorbed, further heating the Earth, and others travel through the Atmosphere for a random distance until they encounter another GHG molecule.</li>
<li>This frame and the next two illustrate another way Photons are emitted, namely due to collisions between energized GHG molecules and other air molecules. As in frame (2) the Surface radiates Photons in all directions and various wavelengths.</li>
<li>The Photons cause the GHG molecules to become energized and they speed up and collide with other gas molecules, energizing them. NOTE: In a gas, the molecules are in constant motion, moving in random directions at different speeds, colliding and bouncing off one another, etc. Indeed the "temperature" of a gas is something like the average speed of the molecules. In this animation, the gas molecules are fixed in position because it would be too confusing if they were all shown moving and because the speed of the Photons is so much greater than the speed of the molecules that they hardly move in the time indicated.</li>
<li>The energized air molecules emit radiation at various wavelengths and in random directions, some upwards, some downwards, and some sideways. Some of the re-emitted Photons make their way out to Space and their energy is lost there, others back down to the Surface where their energy is absorbed, further heating the Earth, and others travel through the Atmosphere for a random distance until they encounter another GHG molecule.</li>
<li>Having emitted the energy, the molecules cool down.</li>
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<strong>DISCUSSION</strong>
As in the other postings in this series, <strong>only radiation effects are considered</strong> because they are the key to understanding the Atmospheric "Greenhouse Effect". I recognize that other effects are as important, and perhaps more so, in the overall heat balance of the Earth. These include clouds which reflect much of the Sun's radiation back out to Space, and which, due to negative feedback, counteract Global Warming. Other effects include convection (wind, thunderstorms, ...), precipitation (rain, snow) and conduction that are responsible for transferring energy from the Surface to the Atmosphere. It is also important to note that the Atmospheric "Greenhouse Effect" and a physical greenhouse are similar in that they both limit the rate of thermal energy flowing out of the system, but the mechanisms by which heat is retained are different. A greenhouse works primarily by preventing absorbed heat from leaving the structure through convection, i.e. sensible heat transport. The greenhouse effect heats the earth because greenhouse gases absorb outgoing radiative energy and re-emit some of it back towards earth.
That said, how does this visualization help us understand the issue of "CO2 sensitivity" which is the additional warming of the Earth Surface due to an increase in atmospheric CO2? Well, given a greater density of CO2 (and H2O) molecules in the air, there is a greater chance that a given photon will get absorbed. Stated differently, a given photon will travel a shorter distance, on average, before being absorbed by a GHG molecule and be re-emitted in a random direction, including downwards towards the Surface. That will result in more energy being recycled back to the Surface, increasing average temperatures a bit.<br />
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<i><span style="color: blue; font-size: large;">Ira Glickstein</span></i></div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com0tag:blogger.com,1999:blog-6562551902946123839.post-20857841280752834172015-07-14T12:24:00.001-07:002015-07-14T12:34:09.489-07:00Atmospheric Windows for VISUALIZING the Atmospheric "Greenhouse" Effect<div style="color: #222222; font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 26.4444446563721px; margin-bottom: 0.825em;">
<span style="line-height: 26.4444446563721px;">A real greenhouse has windows. So does the Atmospheric "greenhouse effect". They are similar in that they allow Sunlight in and restrict the outward flow of thermal energy. However, they differ in the mechanism. A real greenhouse primarily restricts heat escape by preventing convection while the "greenhouse effect" heats the Earth because "greenhouse gases" (GHG) absorb outgoing radiative energy and re-emit some of it back towards Earth.</span></div>
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<i style="color: black; line-height: 26.4444446563721px; text-align: center;"><span style="color: blue; font-size: x-small;"><span style="line-height: 26.4444446563721px;">Originally Posted by me to Watts Up With That, the world's most popular climate website</span>, where it attracted over 21,000 page views and 489 comments. (Click <a href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/">here</a> to view my original posting and read the Comments.)</span></i></div>
<a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-summary1.jpg" href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-summary1.jpg" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="aligncenter size-full wp-image-34921" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-summary1.jpg" src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-summary1.jpg" height="388" style="border: 1px solid rgb(221, 221, 221); clear: both; color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 0.4em auto 1.625em; max-width: 100%; padding: 6px;" title="GW Spectrum summary" width="640" /></a><br />
The base graphic is from <a data-mce-href="http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png" href="http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">Wikipedia</a>, with my annotations. There are two main "windows" in the Atmospheric "greenhouse effect". The first, the <strong style="font-style: inherit; line-height: 1.7;">Visible Light Window</strong>, on the left side of the graphic, allows visible and near-visible light from the Sun to pass through with small losses, and the second, the <strong style="font-style: inherit; line-height: 1.7;">Longwave Window</strong>, on the right, allows the central portion of the longwave radiation band from the Earth to pass through with small losses, while absorbing and re-emitting the left and right portions.</div>
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<strong style="font-style: inherit; line-height: 1.7;">The Visible Light Window</strong><br />
To understand how these Atmospheric windows work, we need to review some basics of so-called "blackbody" radiation. As indicated by the red curve in the graphic, the surface of the Sun is, in effect, at a temperature of 5525ºK (about 9500ºF), and therefore emits radiation with a wavelenth centered around 1/2μ (half a micron which is half a millionth of a meter). Solar light ranges from about 0.1μ to 3μ, covering the ultraviolet (UV), the visible, and the near-infrared (near-IR) bands. Most Sunlight is in the visible band from 0.38μ (which we see as violet) to 0.76μ (which we see as red), which is why our eyes evolved to be sensitive in that range. Sunlight is called "shortwave" radiation because it ranges from fractional microns to a few microns.</div>
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As the graphic indicates with the solid red area, about 70 to 75% of the downgoing Solar radiation gets through the Atmosphere, because much of the UV, and some of the visible and near-IR are blocked. (The graphic does not account for the portion of Sunlight that gets through the Atmosphere, and is then reflected back to Space by clouds and other high-albedo surfaces such as ice and white roofs. I will discuss and account for that later in this posting.)</div>
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My annotations represent the light that passes through the Visible Light Window as an orange ball with the designation <strong style="font-style: inherit; line-height: 1.7;">1/2μ</strong>, but please interpret that to include all the visible and near-visible light in the shortwave band.</div>
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<strong style="font-style: inherit; line-height: 1.7;">The Longwave Window</strong><br />
As indicated by the pink, blue, and black curves in the graphic, the Earth is, in effect, at a temperature that ranges between a high of about 310ºK (about 98ºF) and a low of about 210ºK (about -82ºF). The reason for the range is that the temperature varies by season, by day or night, and by latitude. The portion of the Earth at about 310ºK radiates energy towards the Atmosphere at slightly shorter wavelengths than that at about 210ºK, but nearly all Earth-emitted radiation is between 5μ to 30μ, and is centered at about 10μ.</div>
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As the graphic indicates with the solid blue area, only 15% to 30% of the upgoing thermal radiation is transmitted through the Atmosphere, because nearly all the radiation in the left portion of the longwave band (from about 5μ to 8μ) and the right portion (from about 13μ to 30μ) is totally absorbed and scattered by GHG, primarily H2O (water vapor) and CO2 (carbon dioxide). Only the radiation near the center (from about 8μ to 13μ) gets a nearly free pass through the Atmosphere.</div>
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My annotations represent the thermal radiation from the Earth as a pink pentagon with the designation <strong style="font-style: inherit; line-height: 1.7;">7μ</strong> for the left-hand portion, a blue diamond <strong style="font-style: inherit; line-height: 1.7;">10μ</strong> for the center portion, and a dark blue hexagon <strong style="font-style: inherit; line-height: 1.7;">15μ</strong> for the right-hand portion, but please interpret these symbols to include all the radiation in their respective portions of the longwave band.</div>
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<strong style="font-style: inherit; line-height: 1.7;">Sunlight Energy In = Thermal Energy Out</strong><br />
The graphic is an animated depiction of the Atmospheric "greenhouse effect" process.</div>
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<a data-mce-href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-123a.gif" href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-123a.gif" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;"><img alt="" class="aligncenter size-full wp-image-34922" data-mce-src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-123a.gif" src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-123a.gif" height="338" style="border: 1px solid rgb(221, 221, 221); clear: both; color: #222222; display: block; font-style: inherit; font-weight: inherit; height: auto; line-height: 1.7; margin: 0.4em auto 1.625em; max-width: 100%; padding: 6px;" title="GW Spectrum 123a" width="450" /></a></div>
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On the left side:<br />
(1) Sunlight streams through the Atmosphere towards the surface of the Earth.<br />
(2) A portion of the Sunlight is reflected by clouds and other high-albedo surfaces and heads back through the Atmosphere towards Space. The remainder is absorbed by the Surface of the Earth, warming it.<br />
(3) The reflected portion is lost to Space.</div>
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On the right side:<br />
(1) The warmed Earth emits longwave radiation towards the Atmosphere. According to the first graphic, above, this consists of thermal energy in all bands <strong style="font-style: inherit; line-height: 1.7;">~7μ</strong>, <strong style="font-style: inherit; line-height: 1.7;">~10μ</strong>, and <strong style="font-style: inherit; line-height: 1.7;">~15μ</strong>.<br />
(2) The <strong style="font-style: inherit; line-height: 1.7;">~10μ</strong> portion passes through the Atmosphere with litttle loss. The <strong style="font-style: inherit; line-height: 1.7;">~7μ</strong> portion gets absorbed, primarily by H2O, and the <strong style="font-style: inherit; line-height: 1.7;">15μ</strong> portion gets absorbed, primarily by CO2 and H2O. The absorbed radiation heats the H2O and CO2 molecules and, at their higher energy states, they collide with the other molecules that make up the air, mostly nitrogen (N2), oxygen (O2), ozone (O3), and argon (A) and heat them by something like conduction. The molecules in the heated air emit radiation in random directions at all bands (<strong style="font-style: inherit; line-height: 1.7;">~7μ</strong>, <strong style="font-style: inherit; line-height: 1.7;">~10μ</strong>, and <strong style="font-style: inherit; line-height: 1.7;">~15μ</strong>). The <strong style="font-style: inherit; line-height: 1.7;">~10μ</strong> photons pass, nearly unimpeded, in whatever direction they happen to be emitted, some going towards Space and some towards Earth. The <strong style="font-style: inherit; line-height: 1.7;">~7μ</strong> and <strong style="font-style: inherit; line-height: 1.7;">~15μ</strong> photons go off in all directions until they run into an H2O or CO2 molecule, and repeat the absorption and re-emittance process, or until they emerge from the Atmosphere or hit the surface of the Earth.<br />
(3) The <strong style="font-style: inherit; line-height: 1.7;">~10μ</strong> photons that got a free-pass from the Earth through the Atmosphere emerge and their energy is lost to Space. The <strong style="font-style: inherit; line-height: 1.7;">~10μ</strong> photons generated by the heating of the air emerge from the top of the Atmosphere and their energy is lost to Space, or they impact the surface of the Earth and are re-absorbed. The <strong style="font-style: inherit; line-height: 1.7;">~7μ</strong> and <strong style="font-style: inherit; line-height: 1.7;">~15μ</strong> generated by the heating of the air also emerge from the top or bottom of the Atmosphere, but there are fewer of them because they keep getting absorbed and re-emitted, each time with some transfered to the central <strong style="font-style: inherit; line-height: 1.7;">~10μ</strong> portion of the longwave band.</div>
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The symbols <strong style="font-style: inherit; line-height: 1.7;">1/2μ</strong>, <strong style="font-style: inherit; line-height: 1.7;">7μ</strong>, <strong style="font-style: inherit; line-height: 1.7;">10μ</strong>, and <strong style="font-style: inherit; line-height: 1.7;">15μ</strong> represent quanties of photon energy, averaged over the day and night and the seasons. Of course, Sunlight is available for only half the day and less of it falls on each square meter of surface near the poles than near the equator. Thermal radiation emitted by the Earth also varies by day and night, season, local cloud cover that blocks Sunlight, local albedo, and other factors. The graphic is designed to provide some insight into the Atmospheric "greenhouse effect".</div>
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<strong style="font-style: inherit; line-height: 1.7;">Conclusions</strong><br />
Even though estimates of climate <em style="font-weight: inherit; line-height: 1.7;">sensitivity</em> to doubling of CO2 are most likely way over-estimated by the official climate <em style="font-weight: inherit; line-height: 1.7;">Team</em>, it is a scientific truth that GHGs, mainly H2O but also CO2 and others, play an important role in warming the Earth via the Atmospheric "greenhouse effect".</div>
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This and my <a data-mce-href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/" href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/" style="color: #1b8be0; font-style: inherit; font-weight: inherit; line-height: 1.7; text-decoration: none;">previous posting in this series</a> address ONLY the radiative exchange of energy. Other aspects that control the temperature range at the surface of the Earth are at least as important and they include convection (winds, storms, etc.) and precipitation that transfer a great deal of energy from the surface to the higher levels of the Atmosphere.</div>
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I plan to do a subsequent posting that looks into the violet and blue boxes in the above graphic and provides insight into the process the photons and molecules go through.</div>
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I am sure WUWT readers will find issues with my <em style="font-weight: inherit; line-height: 1.7;">Atmospheric Windows</em> description and graphics. I encourage each of you to make comments, all of which I will read, and some to which I will respond, most likely learning a great deal from you in the process. However, please consider that the main point of this posting, like the previous one in this series, is to give insight to those WUWT readers, who, like Einstein (and me :^) need a graphic visual before they understand and really accept any mathematical abstraction.</div>
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<span style="color: blue; font-size: large;"><i>Ira Glickstein</i></span></div>
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Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com1tag:blogger.com,1999:blog-6562551902946123839.post-81473791507509381752015-07-14T12:21:00.002-07:002015-07-14T12:34:09.500-07:00Emission Spectra for VISUALIZING the Atmospheric "Greenhouse" EffectThe Atmospheric “greenhouse effect” has been analogized to a <em>blanket</em> that insulates the Sun-warmed Earth and slows the rate of heat transmission, thus increasing mean temperatures above what they would be absent “greenhouse gases” (GHGs). Perhaps a better analogy would be an <em>electric blanket</em> that, in addition to its insulating properties, also emits thermal radiation both down and up. A real greenhouse primarily restricts heat escape by preventing convection while the “greenhouse effect” heats the Earth because GHGs absorb outgoing radiative energy and re-emit some of it back towards Earth.<br />
<i style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 26.4444446563721px; text-align: center;"><span style="color: blue; font-size: x-small;"><span style="line-height: 26.4444446563721px;">Originally Posted by me to Watts Up With That, the world's most popular climate website</span>, where it attracted over 14,000 page views and 476 comments. (Click <a href="http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/">here</a> to view my original posting and read the Comments.)</span></i><br />
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Many thanks to Dave Springer and Jim Folkerts who, in comments to my previous posting <a href="http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/">Atmospheric Windows</a>, provided links to emission graphs and a textbook <a href="http://www.sundogpublishing.com/AtmosRad/Excerpts/index.html">“A First Course in Atmospheric Radiation”</a> by Grant Petty, Sundog Publishing Company.<br />
<a href="http://wattsupwiththat.files.wordpress.com/2011/03/gw-spectrum-tropical-pacific.jpg"><img class="aligncenter size-full wp-image-35580" title="GW Spectrum Tropical Pacific" src="http://wattsupwiththat.files.wordpress.com/2011/03/gw-spectrum-tropical-pacific.jpg" alt="" width="640" height="476" /></a><br />
<strong>Description of graphic (from bottom to top):</strong><br />
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<strong><!--more--><br />
</strong><br />
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<strong>Earth Surface:</strong> Warmed by shortwave (~1/2μ) radiation from the Sun, the surface emits upward radiation in the ~7μ, ~10μ, and ~15μ regions of the longwave band. This radiation approximates a smooth “blackbody” curve that peaks at the wavelength corresponding to the surface temperature.<br />
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<strong>Bottom of the Atmosphere:</strong> On its way out to Space, the radiation encounters the Atmosphere, in particular the GHGs, which absorb and re-emit radiation in the ~7μ and ~15μ regions in all directions. Most of the ~10μ radiation is allowed to pass through.<br />
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The lower violet/purple curve (adapted from figure 8.1 in Petty and based on measurements from the Tropical Pacific looking UP) indicates how the bottom of the Atmosphere re-emits selected portions back down towards the surface of the Earth. The dashed line represents a “blackbody” curve characteristic of 300ºK (equivalent to 27ºC or 80ºF). Note how the ~7μ and ~15μ regions approximate that curve, while much of the ~10μ region is not re-emitted downward.<br />
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<strong>“Greenhouse Gases”:</strong> The reason for the shape of the downwelling radiation curve is clear when we look at the absorption spectra for the most important GHGs: H2O, H2O, H2O, … H2O, and CO2. (I’ve included multiple H2O’s because water vapor, particularly in the tropical latitudes, is many times more prevalent than carbon dioxide.)<br />
Note that H2O absorbs at up to 100% in the ~7μ region. H2O also absorbs strongly in the ~15μ region, particularly above 20μ, where it reaches 100%. CO2 absorbs at up to 100% in the ~15μ region.<br />
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Neither H2O nor CO2 absorb strongly in the ~10μ region.<br />
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Since gases tend to re-emit most strongly at the same wavelength region where they absorb, the ~7μ and ~15μ are well-represented, while the ~10μ region is weaker.<br />
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<strong>Top of the Atmosphere:</strong> The upper violet/purple curve (adapted from figure 6.6 in Petty and based on satellite measurements from the Tropical Pacific looking DOWN) indicates how the top of the Atmosphere passes certain portions of radiation from the surface of the Earth out to Space and re-emits selected portions up towards Space. The dashed line represents a “blackbody” curve characteristic of 300ºK. Note that much of the ~10μ region approximates a 295ºK curve while the ~7μ region approximates a cooler 260ºK curve. The ~15μ region is more complicated. Part of it, from about 17μ and up approximates a 260ºK or 270ºK curve, but the region from about 14μ to 17μ has had quite a big <em>bite</em> taken out of it. Note how this <em>bite</em> corresponds roughly with the CO2 absorption spectrum.<br />
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<strong>What Does This All Mean in Plain Language?</strong><br />
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Well, if a piece of blueberry pie has gone missing, and little Johnny has blueberry juice dripping from his mouth and chin, and that is pretty good circumstantial evidence of who took it.<br />
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Clearly, the GHGs in the Atmosphere are responsible. H2O has taken its toll in the ~7μ and ~15μ regions, while CO2 has taken its <em>bite</em> in its special part of the ~15μ region. Radiation in the ~10μ region has taken a pretty-much <em>free pass</em> through the Atmosphere.<br />
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The top of the Atmosphere curve is mostly due to the lapse rate, where higher levels of the Atmosphere tend to be cooler. The ~10μ region is warmer because it is a view of the surface radiation of the Earth through an almost transparent window. The ~7μ and 15μ regions are cooler because they are radiated from closer to the top of the Atmosphere. The CO2 <em>bite</em> portion of the curve is still cooler because CO2 tends to be better represented at higher altitudes than H2O which is more prevalent towards the bottom.<br />
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That is a good explanation, as far as it goes. However, it seems there is something else going on. The ~7μ and ~15μ radiation emitted from the bottom of the Atmosphere is absorbed by the Earth, further warming it, and the Earth, approximating a “blackbody”, re-emits them at a variety of wavelengths, including ~10μ. This additional ~10μ radiation gets a nearly <em>free pass</em> through the Atmosphere and heads out towards Space, which explains why it is better represented in the top of the Atmosphere curve. In addition, some of the radiation due to collisions of energized H2O and CO2 molecules with each other and the N2 (nitrogen), O2 (oxygen) and trace gases, may produce radiation in the ~10μ region which similarly makes its way out to Space without being re-absorbed.<br />
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There is less ~15μ radiation emitted from the top of the Atmosphere than entered it from the bottom because some of the ~15μ radiation is transformed into ~10μ radiation during the process of absorption and re-emission by GHGs in the atmosphere and longwave radiation absorbed and re-emitted by the surface of the Earth.<br />
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<strong>Source Material</strong><br />
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My graphic is adapted from two curves from Petty. For clearer presentation, I smoothed them and flipped them horizontally, so wavelength would increase from left to right, as in the diagrams in my previous topics in this series. (<a href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/">Physical Analogy</a> and <a href="http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/">Atmospheric Windows</a>.)<br />
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Here they are in their original form, where the inverse of wavelength (called “wavenumber”) increases from left to right.<br />
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Source for the upper section of my graphic.<br />
<strong>Top of the Atmosphere from Satellite Over Tropical Pacific.</strong><br />
<a href="http://wattsupwiththat.files.wordpress.com/2011/03/gw-petty-6-6.jpg"><img class="aligncenter size-full wp-image-35616" title="GW Petty 6.6" src="http://wattsupwiththat.files.wordpress.com/2011/03/gw-petty-6-6.jpg" alt="" width="640" height="411" /></a>[Caption from Petty: <em>Fig. 6.6: Example of an actual infrared emission spectrum observed by the Nimbus 4 satellite over a point in the tropical Pacific Ocean. Dashed curves represent blackbody radiances at the indicated temperatures in Kelvin. (IRIS data courtesy of the Goddard EOS Distributed Active Archive Center (DAAC) and instrument team leader Dr. Rudolf A. Hanel.)</em>]<br />
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Source for the lower section of my graphic.<br />
<strong>Bottom of the Atmosphere from Surface of Tropical Pacific (and, lower curve, from Alaska).</strong><br />
<a href="http://wattsupwiththat.files.wordpress.com/2011/03/gw-petty-fig-8-1.jpg"><img class="aligncenter size-full wp-image-35607" title="GW Petty Fig 8.1" src="http://wattsupwiththat.files.wordpress.com/2011/03/gw-petty-fig-8-1.jpg" alt="" width="640" height="614" /></a>[Caption from Petty: <em>Fig. 8.1 Two examples of measured atmospheric emission spectra as seen from ground level looking up. Planck function curves corresponding to the approximate surface temperature in each case are superimposed (dashed lines). (Data courtesy of Robert Knutson, Space Science and Engineering Center, University of Wisconsin-Madison.)</em>]<br />
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The figures originally cited by Dave Springer and Tim Folkerts are based on measurements taken in the Arctic, where there is far less water vapor in the Atmosphere.<br />
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<img class="aligncenter size-full wp-image-34921" src="http://www.skepticalscience.com/images/infrared_spectrum.jpg" alt="" width="640" height="388" />[Fig. 8.2 from Petty] (a) Top of the Atmosphere from 20km and (b) Bottom of the Atmosphere from surface in the Arctic. Note that this is similar to the Tropical Pacific, at temperatures that are about 30ºK to 40ºK cooler. The CO2 <em>bite</em> is more well-defined. Also, the <em>bite</em> in the 9.5μ to 10μ area is more apparent. That <em>bite</em> is due to O2 and O3 absorption spectra.<br />
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<strong>Concluding Comments</strong><br />
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This and my previous two postings in this series <a href="http://wattsupwiththat.com/2011/02/20/visualizing-the-greenhouse-effect-a-physical-analogy/">Physical Analogy</a> and <a href="http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/">Atmospheric Windows</a> address ONLY the radiative exchange of energy. Other aspects that control the temperature range at the surface of the Earth are at least as important and they include convection (winds, storms, etc.) and precipitation (clouds, rain, snow, etc.) that transfer a great deal of energy from the surface to the higher levels of the Atmosphere.<br />
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For those who may have missed my previous posting, here is my <strong>Sunlight Energy In = Thermal Energy Out</strong> animated graphic that depicts the Atmospheric "greenhouse effect" process in a simlified form.<br />
<a href="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-123a.gif"><img class="aligncenter size-full wp-image-34922" title="GW Spectrum 123a" src="http://wattsupwiththat.files.wordpress.com/2011/02/gw-spectrum-123a.gif" alt="" width="450" height="338" /></a><br />
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I plan to do a subsequent posting that looks into the violet and blue boxes in the above graphic and provides insight into the process the photons and molecules go through.<br />
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I am sure WUWT readers will find issues with my <em>Emissions Spectra</em> description and graphics. I encourage each of you to make comments, all of which I will read, and some to which I will respond, most likely learning a great deal from you in the process. However, please consider that the main point of this posting, like the previous ones in this series, is to give insight to those WUWT readers, who, like Einstein (and me :^) need a graphic visual before they understand and really accept any mathematical abstraction.<br />
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<div style="text-align: center;">
<span style="color: blue; font-size: large;"><i>Ira Glickstein</i></span></div>
Ira Glicksteinhttp://www.blogger.com/profile/10800080810596424897noreply@blogger.com1