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
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?
Simon is obsessed with Euclidea https://www.euclidea.xyz/ — a learning environment for geometric constructions and proofs. He has also downloaded the Euclidea app (which has more features), so that he could continue engaging with it while at the beach.
Yesterday, he finished the whole first section (called Alpha), completing all of its 7 tasks in several ways, most of which he solved himself without using hints. The goal is to solve a problem using the minimum number of moves:
Each solution is scored in two types of moves: L (straight or curved lines) and E (elementary Euclidean constructions). Points are not taken into account.
L counts tool actions: constructing a line, a perpendicular, and so on. E counts moves as if a construction was made with real compass and straightedge. (Each advanced tool has its own E cost).
Each level has L and E goals. They are independent. A lot of problems have universal solution that satisfies both goals. But some problems should be solved twice: one solution to reach L goal and another solution to reach E goal.
You can receive the following stars on each level:
* the challenge was solved * the L goal was reached * the E goal was reached * all variants (V) of answer were found
If there are several objects satisfying the statement of a problem, you can get a hidden V-star by constructing all the answers (solutions) at the same drawing. Usually this implies some kind of symmetry. You need to guess on what levels it is possible because the presence of a V-star is not shown until you find it.
– Euclidea Manual
The five images below are an example of solving a Euclidea puzzle:
Simon also loves recreating all the puzzles:
For the last puzzle, Simon couldn’t find the minimum number of moves independently and looked the solution up on stackexchange. “It would have taken me a year to figure this out”, he said:
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.
Pondering over the future, I told the kids the universal basic income and Doughnut Economics should be the next step. Simon game me an improvised lecture on doughnut topology. Well, what do you know? The very next day, Simon’s native city of Amsterdam announced it would be the first city in the world to embrace Kate Raworth’s doughnut model!
In the long run, this may even mean we’ll be able to return to our home in Amsterdam we left 4 yrs ago to be able to homeschool. Raworth’s model views the child as much more than simply future “workforce” and that could help personalise education and create legal bearing for Self-Directed Learning. Because let’s face it: Can Industrial-Age schooling really serve as a foundation for a new sustainable mindset?
Below are some impressions of Simon’s doughnut topology tutorial on April 7:
Simon emphasised that this trick won’t work with a real doughnut, as Simon explains:
in topology, we’re talking about 2-dimensional manifolds (which means that they are hollow or that they’re just a flat surface). It doesn’t really make sense (not like it doesn’t make sense mathematically, but it just isn’t as interesting) to talk about 3-dimensional manifolds (filled 3D objects, not hollow) unless we’re doing it in 4-dimensional space. In other words, it doesn’t make sense to talk about 3-dimensional manifolds unless they’re embedded in 4-dimensional space.
At the beginning of April, Simon started working on his COVID-19 epidemic simulation project, implementing a number of scenarios (like various degrees of hygiene, quarantine, social distancing), explaining his code live on camera so that anyone can code along and create their own simulations.
The programming language I used is Processing (Java), optimized for Creative Coding purposes. To run the code on your computer, you’ll need to install Processing https://processing.org (I provide more detailed instructions in my GitHub readme).
The project is still in progress, as Simon plans to implement a few more realistic scenarios. He recorded Part III live on Discord (The Coding Train’s Discord channel) and will probably do the same for the upcoming parts, so stay tuned!
On March 17, Simon started a series of math and coding projects about COVID-19. The first projects he called Corona Math: Why Social Isolation?
This is part I of my Corona Math series. In this video, I calculate how many people will be infected with the coronavirus after 10 spreads (I call them iterations). I also calculate how many days there are in each iteration.
In the second video Corona Math: Where is the Inflection Point? (recorded on March 19), I attempt to calculate the “inflection point” for COVID-19, and ultimately fail. I come to the conclusion that it’s too unpredictable, and we’re now only at the very beginning. I used the Wolfram Language for this video, so here’s a link: https://www.wolframcloud.com/obj/721d493e-156b-4131-818c-e59476d1d2aa
10 days later Simon recorded another Corona Math project. In Belgium, we’re having a #Covid_19 “light #lockdown“, which means we’re allowed to walk within a 2km radius from our home. Simon calculated how many people would fit into his designated walking area, considering #SocialDistancing:
December was all about computer science and machine learning. Simon endlessly watched Welch Labs fantastic but freakishly challenging series Learning to See and even showed me all the 15 episodes, patiently explaining every concept as we went along (like underfitting and overfitting, recall, precision and accuracy, bias and variance). Below is the table of contents he made of the series:
While watching the series, he also calculated the solutions to some of the problems that Welch Labs presented, like the question about the number of possible rules (= grains of sand) for a simple ML problem if memorisation is applied. His answer was that the grains of sand would cover all land on earth:
Simon loved the historical/philosophical part of the course, too. Especially the juxtaposition of memorising vs. learning, the importance of learning to make assumptions, futility of bias-free learning, and the beautiful quotes from Richard Feynman!
I have since then found another Feynman quote that fits Simon’s learning style perfectly (and I believe is the recipe to anyone’s successful learning as opposed to teaching to the test): “Study hard what interests you the most in the most undisciplined, irreverent and original manner possible.” We have discussed the possibilities of continuing at the university again. I have also asked Simon how he sees himself applying his knowledge down the road, trying to understand what academic or career goals he may have set for himself, if any. Does he have a picture of himself in five years from now, where does he want to be by then? He got very upset, just like when asked to sum himself up in one sentence for an interview last spring. “Mom, I’m just having fun!”
Every live session Daniel Shiffman mentions Simon several times, usually because Simon gives good feedback/ advice. On the other end, Simon is invigorated and jumping about the room. Sometimes resulting in serious bumps against the furniture.