This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com
Simon has had hours of fun with Test Tube Games, a science games portal featuring interactive explanations and dynamic puzzles on Chemistry and Physics. He has created two simulations based on the games he played. The first one is an electromagnetic field simulator:
Simon is working on a clone of Tchisla, an absorbing number puzzle app from the (Russian!!) creators of Euclidea. The aim is to represent numbers as arithmetical expressions using only one of the digits from 1 to 9 and the shortest way possible. (For example 96 = 99 – √9 or 96 = 4 * 4! or 96 = 2 * 2 * (22 + 2) are all valid representations of 96).
It’s true what the makers say: “You suddenly discover that you know a lot of numbers and their properties: factorials, squares, cubes, prime numbers, roots and others. Tchisla imperceptibly helps you to improve your calculating skills.”
Simon doesn’t like the fact that you can currently only find Tchisla as an app while he wants to screenshare with his friends in a browser, so he has decided to develop his own version. So far he has completed these steps in Glitch:
I wrote a small program that copies itself. When the program doubles itself it executes itself twice. The code that doubles itself is now doubled. The second time you run it you will get 8 times its original copy. The following time it’s going to double 8 copies of itself 8 times. Afterwards it doubles 2048 copies of itself 2048 times — that I can’t run because it would overwhelm the universe 5 times!
You can easily turn every statement into a program. If the program stops, or “halts”, then the statement is true, and if it never stops, or “loops”, the statement is false.
Like, for example, the following program corresponds to the statement: “There’s at least one even number that cannot be expressed as the sum of two primes” (this is the negation of the so-called “Goldbach Conjecture”):
So, if we can figure out if any program will halt or not halt, we can prove everything! Can we do that, though?
This is something Simon worked on for days and he was thrilled to be able to present a working bot to Daniel. The only issue that remains unresolved is whether the mods should control the bot via a secret password or should a more advanced security system be developed. Daniel has decided to take a long break from live streaming, so the whole project probably won’t be revived until the streams resume. In any case, as Simon has put it, “I know, it’s messy, but it works. And that’s what’s important to me”.
Simon has also created several other bots (and built a separate Discord playground where other people can test their bots as well). He has been doing quite a lot of server side programming lately.
How Can Math Help Resolve Racial Segregation? This video and coding project is based on Segregation Solitaire by Thomas Schelling, an American mathematician and economist who was awarded the 2005 Nobel Memorial Prize in Economic Sciences for “having enhanced our understanding of conflict and cooperation through game-theory analysis.”
I don’t like the name ‘Segregation Solitaire’, so I call it Schelling’s Game. This is also inspired by the famous Parable of the Polygons playable essay on the shape of society by Vi Hart and Nicky Case: https://ncase.me/polygons/
Simon binge reads Nicky Case’s essays and has made several remixes of their projects, all the more timely, considering today’s context.
Simon created a physics engine in Python with Turtle. He used Verlet integration (French pronunciation: [vɛʁˈlɛ]), a numerical method for integrating Newton’s equations of motion in calculating trajectories of particles in molecular dynamics simulations and computer graphics.
Verlet Integration is a way to implement a physics engine without having to care about velocity.
Instead of storing the velocity, you store the previous position, and you calculate the velocity on the fly. Then if you add that velocity to the current position, you get the new position. But then you also have to add on the acceleration, because acceleration changes velocity.
If you’re interested in why #covid-19 tracing apps are important and the most privacy-friendly way to implement them, please read this interactive essay by Nicky Case and play with the colorful simulations of all our possible futures. For Simon, this has been the entrance into the Nicky Case @ncasenmare universe (first recommended by 3Blue1Brown). Simon has been gulping down the playable essays on human networks and the spread of complex ideas, self-synchronization in nature, the shape of society and several other burning themes (like coming out and anxiety) and watching Nicky Case’s talks, like this one. Nicky is a self-made indie artist, programmer and writer making very edgy, very 21st century multimedia products that are both profound in content and have an engaging/interactive interface. It’s as if reading an informative piece is turned into a game. And that’s exactly what Nicky stands for: learning through play and messing about. Maybe that’s why Simon has embraced his works so eagerly, Nicky has proven to be one of those perfect matches for our self-directed learning style.
Every polygon can be triangulated into exactly n-2 triangles. So you’ve got the triangulation theorem and the totally opposite theorem in the math universe, Girard’s theorem (the formula for the era of a spherical triangle). I’m going to attempt to put these two together to prove Euler’s polyhedral formula (also known as Euler’s characteristic) V – E + F = 2.
Last Tuesday, May 19, was somewhat a historic day as Simon created his first Discord bot (actually, two bots: one that does polls and count-downs and another programmable one that sends messages). In order to make the bots work, Simon first made a new server called a “bot playground”.
Simon and a friend also practiced in hacking each other:
And finally, he found himself in the centre of a great prank: everyone in his group of friends who wasn’t called Simon changed their names to something containing Simon and all the Simons in the group became Gregs: