My first introduction to Mathematica was with Version 2.0 back in the early ’90s as an undergrad in physics at the University of Washington in Seattle. I had occasion to use it from time to time to double-check my math and physics work. Then in my senior year I did an amazing one-on-one project class with one of the department’s more elder mathematical physicists. In the class I did various projects and simulations using Mathematica. As the term went on I began to suspect that I was not so much there to learn from the professor, but to teach him how to use this relatively new amazing application.

My suspicions were confirmed when he gave me my final assignment inspired by an article from a dusty copy of Physical Review Letters from the 1960s. It was an article on the mathematics of Lorentz rotation in special relativity, which is a slightly more complicated version of Lorentz contractions. The professor walked me through the concept of the theory and the math, and then sent me on my way to build a Lorentz rotation simulation in Mathematica.

So I went home and proceeded to work on the simulation on my Macintosh Classic, which barely ran the student version of Mathematica 2. I was pretty pleased with the result. I was able to make a semi-live model that visualized what transformations would be observed of an object when it went through Lorentz rotation as it moved closer and closer to the speed of light.

I returned to the professor’s office to present my work. As he looked through the code, and used the simulator, he sat there humming and mumbling under his breath. Finally he said “So the ‘Old Man’ was right!” He then elaborated that he had got his Ph.D. at Princeton in the 1950s, and that he had spent some time at the Institute for Advanced Study. He explained that none other than Albert Einstein himself had tried to explain to him the concept of Lorentz rotation, and though he easily understood the mathematics, he just couldn’t visual it in his head. But there in his office, with the aid of Mathematica I was finally able to help him see what it “looked like”. That was one of most amazing experiences in my entire education.