Coding, Computer Science, Good Reads, JavaScript, Milestones, Murderous Maths, Notes on everyday life, Set the beautiful mind free, Simon's Own Code, Simon's sketch book

Simon’s first steps in Stephen Wolfram’s Computational Universe

Simon has been enjoying Stephen Wolfram’s huge volume called A New Kind of Science and is generally growingly fascinated with Wolfram’s visionary ideas about the computational universe. We have been reading the 1500-page A New Kind of Science every night for several weeks now, Simon voraciously soaking up the behaviour of hundreds of simple programs like cellular automata.

Wolfram’s main message is that, contrary to our intuition, simple rules can result in complex and often seemingly random behaviour and since humanity now has the computer as a tool to study and simulate that behaviour, it could open a beautiful new alternative to the existing models used in science. According to Wolfram, we may soon realise that the mathematical models we are currently using, based on equations and constraints instead of simple rules, are merely a historical artefact. I’m amazed at how much this is in line with Simon’s own tentative thoughts he was sharing with me earlier this year, about how maths will be taken over by computer science and how algorithms are a more powerful tool than equations. When he came up with those ideas he hadn’t discovered Wolfram’s research and philosophy yet, he used to only know Wolfram as the creator of Wolfram Mathematica and the Wolfram language, both of which Simon greatly admires for being so advanced.

Last night, Simon was watching a TED talk Stephen Wolfram gave in 2010 about the possibilities of computing the much aspired theory of everything, but not in the traditional mathematical way. “It’s about the universe!” Simon whispered to me wide-eyed, when I came to the living room to fetch him. “Mom, and you know who was in the audience there? Benoit Mandelbrot!” (Simon knows Mandelbrot died the same year, he is intrigued by the fact that his and Mandelbrot’s lifetimes have actually overlapped by one year).

We have been informed by the World Science Scholars program that Stephen Wolfram will be one of the professors preparing a course for this year’s scholars cohort, so Simon will have the unique experience of taking that course and engaging in a live session with Stephen Wolfram. It is breathtaking, a chance to connect with someone who is much older, renowned and accomplished, and at the same time so like-minded, a soulmate.

Inspired by reading Stephen Wolfram, Simon has revisited the world of cellular automata and Turing machines, and created a few beautiful Langton’s Ants:

Link to Simon’s sketch on p5: https://editor.p5js.org/simontiger/sketches/sHa6d-AFf
Simon especially likes the last example in the video: “I think of it as triangular houses surrounding a flower garden!”

Simon has also watched a talk by Stephen Wolfram for MIT course 6.S099: Artificial General Intelligence. He said it had things in it about Wolfram Alpha that he didn’t know yet.

Group, In the Media, Milestones, Murderous Maths, Notes on everyday life, Set the beautiful mind free

The Netherlands Chase Away Extreme Talent

This summer, aged 9, Simon @simontigerh was named a World Science Scholar and joined a two-year program for the world’s most exceptional young math talents, as the youngest among the 75 students selected in 2018 and 2019. See the official press release for more info: https://www.businesswire.com/news/home/20190905005166/en/World-Science-Festival-Announces-Newest-Class-%E2%80%9CWorld

Simon’s passion for science and his unique way to see the world have blossomed again once we have pulled him out of school, where he was becoming increasingly unhappy and was considered a problem student. The only way to set his mind free and allow him to follow the path that suits him best, the path of self-directed learning, was to leave Simon’s native Amsterdam and The Netherlands, where school attendance is compulsory.


I am sharing this at the time when educational freedom and parental rights in The Netherlands are in serious danger to become limited even further. It is bittersweet to celebrate Simon’s beautiful journey and at the same time see how The Netherlands are chasing away extreme talent as we are aware of more stories similar to that of Simon’s.

Computer Science, Logic, Milestones, Murderous Maths, Notes on everyday life, Set the beautiful mind free, Simon teaching, Simon's sketch book

Why mathematics may become computer science

Walking home from the swimming pool (where he and Neva had been jumping into the water exactly 24 times, calling out all the permutations of 1,2,3 and 4), Simon suddenly stopped to tell me that some day, mathematics may become engulfed by computer science. Apparently, this was what he was thinking about the whole time he kept silent on the way. Once we got home I sat down to listen to the elaborate proof he had coined for his hypothesis. Here is comes, in his own words:

Someday mathematics may become computer science because most of mathematics uses simple equations and stuff like that, but computer science uses algorithms instead. And of course, algorithms are more powerful than equations. Let me just give you an example.

There’s this set of numbers called algebraic numbers, and there’s this set of numbers called computable numbers. The algebraic numbers are everything you can make with simple equations (finite polynomials), so not like trig numbers, which are actually infinite polynomials, just simple finite equations with arithmetic and power. Computable numbers, however, are a set of numbers that you can actually make with a finite algorithm. It may not represent a finite equation, but the rules for the equation have to be finite. So the algorithm that generates that equation has to be finite. It’s pretty easy to see that every algebraic number is by definition computable. Because the algorithm would just basically be the equation itself.

Is every computable number algebraic? Well, we can easily disprove that. It took very long to prove that Pi is not algebraic, that it is transcendental, as it’s called. But Pi is computable, of course, because, well, that’s how we know what Pi is, to 26 trillion decimal places. So there you go. That’s a number that is computable but not algebraic. So the Euler diagram now looks like this:

Simon drew this illustration later the same evening, when he presented his proof in Russian to his grandma via FaceTime

Now we look back at the beginning and we see that algebraic numbers have to do with equations and computable numbers have to do with algorithms. And because the set of all algebraic numbers is in the set of all computable numbers as we’ve just proved, the set of computable numbers will have more numbers than algebraic numbers. We have given just one example of how algorithms are more powerful than equations.

What about the mathematics that deals with numbers that are incomputable? – I asked.

Well, that’s set theory, a different branch of mathematics. I meant applied mathematics, the mathematics that has application.

Coding, In the Media, Machine Learning, Milestones, Murderous Maths, neural networks, Notes on everyday life, Set the beautiful mind free, Simon's Own Code

Interview with Simon on Repl.it

Repl.it has published a cool interview with Simon! It was interesting how Simon struggling to answer some of the more general questions gave me another glimpse into his beautiful mind that doesn’t tolerate crude dimensionality reductions. The first question, “If you could sum yourself up in one sentence, how would you do it?” really upset him, because he said he just couldn’t figure out a way to sum himself up in one sentence. This is precisely the same reason why Simon has had trouble performing trivial oral English exam tasks, like picking some items from the list and saying why he liked or disliked them. The way he sees the world, some things are simply unfathomable, or in any case, extremely complex, too complex to imagine one can sum them up in one sentence or come up with the chain of causes and consequences of liking something on the spot. He often tells me he sees the patterns, the details. Seeing objects or events in such complexity may mean it feels inappropriate, irresponsible, plain wrong to Simon to reduce those objects and events to a short string of characters.

This made me reflect upon how Simon keeps shaking me awake. I used to find nothing wrong with playing the reductionist game and frankly, had I been asked to sum myself up in one sentence, I would have readily come up with something like “a Russian journalist and a home educator”. It’s thanks to Simon that I am waking up to see how inaccurate that is. I begin to see how many games that we play in our society are forcing us to zoom out too far, to generalize too much. How often don’t we just plug something in, pretending we can answer impossible questions about the hugely complicated world around us and inside us! Well, Simon often honestly tells me that he just doesn’t have the answer.

For that first question in the interview, I suggested Simon answer something like “it’s more difficult to sum myself up in one sentence than to prove that e is irrational”, to which he replied: “But Mom, to prove that e is irrational is easy! It’s hard to prove that Pi is irrational!”

I must add that at the same time, Simon has really enjoyed the fact that Repl.it has written a developer spotlight about him as well as the social interaction on Twitter that the piece has initiated. It gave him a tangible sensation of belonging to the programming community, of being accepted and appreciated, and inspired him to work on his new projects in Repl.it.

Computer Science, Milestones, Murderous Maths, Notes on everyday life, Set the beautiful mind free

E-mail from Ron Graham

Wow! We have received an e-mail from his mathematical majesty Ron Graham today! In reaction to Simon’s Graham Scan project:

“Hi Sophia and Simon, I love the video on Graham’s Scan. I’m sure it was not so easy to make! Simon, you are certainly special! Keep up the good work and keep me posted! Best regards, Ron Graham”

Coding, JavaScript, Machine Learning, Milestones, Murderous Maths, neural networks, Notes on everyday life, Set the beautiful mind free, Simon teaching, Simon's Own Code, Simon's sketch book

What Simon did instead of taking the SAT on Saturday

On Saturday morning, Simon didn’t go to the SAT examination location, although we had registered him to try taking the SAT (with great difficulties, because he is so young). In the course of the past few weeks, after trying a couple of practice SAT tests on the Khan Academy website, we have discovered that the test doesn’t reveal the depth of Simon’s mathematical talent (the tasks don’t touch the fields he is mostly busy with, like trigonometry, topology or calculus and require that instead, he solves much more primitive problems in a strictly timed fashion, while Simon prefers taking time to explore more complex projects). This is what happens with most standardized tests: Simon does have the knowledge but not the speed (because he hasn’t been training these narrow skills for hours on end as his older peers at school have). Nor does he have the desire to play the game (get that grade, guess the answers he deosn’t know), he doesn’t see the point. What did he do instead on his Saturday? He had a good night sleep (instead of having to show up at the remote SAT location at 8 a.m.) and then he…

built an A.I. applying a genetic algorithm, a neural network controlling cars moving on a highway! The cars use rays to avoid the walls of the highway. Implementing neuroevolution. What better illustration does one need to juxtapose true achievement and what today’s school system often wants us to view as achievemnt – getting a high grade on a test? The former is a beautiful page from Simon’s portfolio, showing what he really genuinely can do, a real life skill, something he is passionately motivated to explore deeper, without seeking a reward, his altruist contribution to the world, if you will. The latter says no more than how well one has been trained to apply certain strategies, in a competitive setting.

Simon’s code is online: https://repl.it/@simontiger/Raytracing-AI

Simon has put this version on GitHub: https://github.com/simon-tiger/Raycasting-A.I.

He has also created an improved version with an improved fitness function. “In the improved version, there’s a feature that only shows the best car (and you can toggle that feature on and off). And most importantly, I am now casting relative to where it’s going (so the linearity is gone, but it jiggles a lot, so I might linear interpolate it)”, – Simon explains. You can play with the improved version here: https://repl.it/@simontiger/Raycasting-AI-Improved

Finally, Simon is currently working on a version that combines all the three versions: the original, the improved and the version with relative directions (work in progress): https://repl.it/@simontiger/Raytracing-AI-Full

“I am eventually going to make a version of this using TensorFlow.js because with the toy library I’m using now it’s surprisingly linear. I’m going to put more hidden layers in the network”.

The raytracing part of the code largely comes from Daniel Shiffman.

Simon’s two other videos about this project, that was fully completed in one day:

Part 1
Part 2


Coding, Computer Science, Good Reads, Logic, Milestones, Murderous Maths, Notes on everyday life, Python, Set the beautiful mind free

Fun with Brilliant’s Computer Courses

“Mom, how long would it take a supercomputer running at 10^15 additions per second to calculate the 1000th Fibonacci number?”

Simon has learned this problem from the new course he is following on Brilliant.org: Computer Science Algorithms. Simon worked it out on an A3 sketch book sheet and got the answer correct: it would take longer than the age of the Universe!

Simon working the answer out again to show me the way he solved it

Simon has already finished the Computer Science Fundamentals course! It has been Simon’s idea to take up the courses on Brilliant.org again and he has been working independently, driven entirely by his intrinsic motivation.

The course has also inspired Simon to work on a very large scale project: record a series of tutorials where he explains all the best known sorting algorithms and comes up with the Python code for them on his RaspberryPi!

Milestones, Notes on everyday life, Philosophy, Set the beautiful mind free

What’s Wrong with Traditional School?

In this video, Simon (a 9 year old mathematician and programmer) shares his views on what absolutely needs to change in the educational system and why self-directed learning works better than traditional schooling. Simon’s main points are:

  1. At school, you’re forced to master a few subjects at the same “average” level while when learning at your own pace you tend to follow your talent and passion and learn some subjects at a much higher level. Simon depicts this difference as two bar chart diagrams. On the schooled diagram, there’re fewer subjects/areas of exploration and they are all at about the same level. On the self-directed learning diagram, the bars resemble a diverse metropolis with multiple buildings of varying height (or a garden with many sorts of flowers). Simon also explains that standardized tests and IQ tests expect a child to have developed evenly in all areas, while it may be more natural for a child to be much more developed in a few specific areas depending on her interests, and that there therefore such a thing as a total score simply shouldn’t exist.
  2. Simon’s second point is that the internet, with its online educational opportunities, is going to kill traditional schooling. Simon himself is a perfect example of someone who learns a lot more on than off line.
  3. Simon regrets that the way a student’s proficiency is evaluated today is mainly based on testing the speed at which the student can apply trained strategies as opposed to looking at the student’s original problem solving ability in an untimed setting.
  4. Simon’s final argument against the traditional school system is that it doesn’t allow for failure. Failure is being discouraged and stigmatized, a bad grade can have serious consequences. That is very counterproductive, says Simon, because failure is an important part of the learning process. You don’t learn from your successes (when you have simply used what you already knew), you learn from your failures (because you start to look into why you’ve failed and that makes you a little smarter every time).

Simon has been teaching himself since he was a toddler. He is especially fond of math and sciences, doing university level math and researching serious questions about quantum mechanics and general relativity. He is also fluent in several programming languages. We have had to move from Simon’s native Amsterdam to Belgium to be able to homeschool, because homeschooling is nearly illegal in The Netherlands. Simon is an adamant advocate of educational freedom. There is a growing body of evidence that forced learning is not only ineffective and damaging to the intrinsic motivation, but may also be psychologically detrimental.

Coding, Community Projects, Contributing, JavaScript, live stream, Machine Learning, Milestones, Murderous Maths, neural networks, Notes on everyday life, Set the beautiful mind free, Simon teaching, Trips

Simon took part in a Coding Train livestream in Paris!

Simon and Daniel Shiffman after the livestream

The video below is part of Daniel Shiffman’s livestream hosted by GROW Le Tank in Paris on 6 January 2019 about KNN, machine learning, transfer learning and image recognition. Daniel kindly allowed Simon to take the stage for a few minutes to make a point about image compression (the algorithm that Daniel used was sort of a compression algorithm):

Here is a different recording (in two parts) of the same moment from a different angle: