**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.**

*Nowadays*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.

Albert Einstein was a great physicist, with all the requisite mathematical tools. However, he rejected

*purely*mathematical abstraction and resorted to

*physical analogy*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 subject to acceleration due to being dragged by a rocket at ever-increasing speeds.

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.

**COMPUTER MODELS FOR**

*VISUALIZATION*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.

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.

*VISUALIZING*EINSTEIN'S SPECIAL AND GENERAL RELATIVITY**Perhaps the most well-known equation in the world is**

**E = mc2**, recognized by virtually every person. But, what does it really mean?

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?

If "everything is relative" why isn't the stay-at-home twin also also younger? So, everything is

*not*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.

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.

Furthermore, what, precisely, is TIME? And how is TIME united with SPACE to form SpaceTime?

When you Google any of this stuff you are quickly buried in equations and tensor mathematics that

*no one*(even an engineer like me) can

*really*understand!

Well, all this bothered me for most of my life until, back in 2012, I decided to answer Alan Alda's

*Flame Challenge*"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.

Time - the fourth dimension (2013 Flame Challenge) from Ira V Glickstein on Vimeo.

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

*understand*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.

**THE MAP IS NOT THE TERRITORY!**

As my principal PhD advisor, Howard Pattee, taught me, "The MAP is NOT the TERRITORY". That sage statement means that

**no model is exactly the same as the thing being modeled**(else it would be the real thing.)

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.

The MAP is NOT the TERRITORY ! |

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.

**Ira Glickstein**
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