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
Today, Simon returned to a problem he first encountered at a MathsJam in summer: “Pick random numbers between 0 and 1, until the sum exceeds 1. What is the expected number of numbers you’ll pick?” Back in June, Simon already knew the answer was e, but his attempt to prove it didn’t quite work back then. Today, he managed to prove his answer!
The same proof in a more concise way:
At MathsJam last night, Simon was really eager to show his proof to Rudi Penne, a professor from the University of Antwerp who was sitting next to Simon last time he gave it a go back in June. Rudi kept Simon’s notes and told me he really admired the way Simon’s reasoning spans borders between subjects (the way Simon can start with combinatorics and jump to geometry), something that many students nurtured within the structured subject system are incapable of doing, Rudi said. Who needs borders?
Later the same evening, Simon had a blast demonstrating the proof to a similar problem to a larger grateful and patient audience, including Professor David Eelbode. The first proof was Simon’s own, the second problem (puzzle with a shrinking bullseye) and proof came from Grant Sanderson (3Blue1Brown) on Numberphile.
“Don’t allow any constraints to dull his excitement and motivation!” Rudi told me as Simon was waiting for us to leave. “That’s a huge responsibility you’ve got there, in front of the world”.
Simon’s sister Neva has started a vlog and Simon, busy as he is, enjoys editing her videos. For the first 17-minute video he has also done all the subtitles (translating from Dutch to English), which was a project that took him two days and something like 7 hours of work! Neva, in her turn, has got Simon increasingly interested in environmental issues.
Such a pleasant play date last week with another eager learner. Simon shared his GeoGebra skills and some geometrical paper tricks, among other things. It’s heartwarming to see Simon blossom socially, he is growingly attentive to younger kids and generally engaging with people of various ages, as long as they show interest in anything Simon has an understanding of.
Simon’s September visit to CERN has been featured in a World Science Scholars newsletter:
Here’s our update on the World Science Scholars program. Simon has finished the first bootcamp course on the theory and quantum mechanics by one of program’s founders, string theorist Professor Brian Greene and has taken part in three live sessions: with Professor Brian Greene, Professor Justin Khoury (dark matter research, alternatives to the inflationary paradigm, such as the Ekpyrotic Universe), and Professor Barry Barish (one of the leading experts in gravitational waves and particle detectors; won the Nobel Prize in Physics along with Rainer Weiss and Kip Thorne “for decisive contributions to the LIGO detector and the observation of gravitational waves”).
At the moment, there isn’t much going on. Simon is following the second course offered by the program, at his own pace. It’s a course about neurology and neurological statistics by Professor Suzana Herculano-Houzel and is called “Big Brains, Small Brains: The Conundrum of Comparing Brains and Intelligence”. The course is compiled from Professor Herculano-Houzel’s presentations made at the World Science Festival so it doesn’t seem to have been recorded specifically for the scholars, like Professor Brian Greene’s course was.
Professor Herculano-Houzel has made “brain soup” (also called “isotropic fractionator”) out of dozens of animal species and has counted exactly how many neurons different brains are made of. Contrary to what Simon saw in Professor Greene’s course (mainly already familiar stuff as both relativity theory and quantum mechanics have been within his area of interest for quite some time), most of the material in this second course is very new to him. And possibly also less exciting. Although what helps is the mathematical way in which the data is presented. After all, the World Science Scholars program is about interdisciplinary themes that are intertwined with mathematical thinking.
Another mathematical example: in Professor Herculano-Houzel’s course on brains we have witnessed nested patterns, as if they escaped from Stephen Wolfram’s book we’re reading now.
Simon has also contributed to the discussion pages, trying out an experiment where paper surface represented cerebral cortex:
Simon: “Humans are not outliers because they’re outliers, they are outliers because there’s a hidden variable”.
Simon is looking forward to Stephen Wolfram’s course (that he is recording for world science scholars) and, of course, to the live sessions with him. The information that Stephen Wolfram will be the next lecturer has stimulated Simon to dive deep into his writings (we are already nearly 400 pages through his “bible” A New Kind of Science) and sparked a renewed and more profound understanding of cellular automata and Turing machines and of ways to connect those to our observations in nature. I’m pretty sure this is just the beginning.
It’s amazing to observe how quickly Simon grasps the concepts described in A New Kind of Science; on several occasions he has tried to recreate the examples he read about the night before.
Simon loves the Maths Is Fun website and has borrowed a couple of ideas for cool games from there. He wrote the code completely on his own, from scratch. Below is a video where he presents his Connect games:
In October and early November, Simon was busy with another attempt to simulate SAP-1 (simple as possible processor, an 8-bit computer) in Circuitverse (something that he hadn’t managed to complete when he tried it last time). I’m not even sure if anyone uses Circuitverse for such large-scale projects.
On November 7, Simon finally managed to finish the RAM on his simulated 8-bit computer (a computer where every general-purpose register contains 8 bits and therefore can only process 8 bits of data)! Although he is far from the end of the project, he is convinced that the RAM is the hardest part, so “now everything is going to be okay!”
“RAM was the hardest mainly because I have been trying to build the subcircuit for the RAM myself, which is not going to do it for SAP-2”,(Simon’s next ambition, also an 8-bit computer but with 64K memory, 2K PROM + 62K RAM). “This time the RAM I needed was particularly small, so I built a mini-RAM myself”.
Simon has worked really hard for several days on his first machine learning community contribution! He has created this mini-series about building a game of Make 24 with Google’s Teachable Machine that he trained to recognise gestures as a game controller.
“It’s the first time I’m using ml5 from scratch! I’ve also built in a feature to enable the users to train their own models!”
During Chinese lesson yesterday, Simon came up with what he calls his “Cycle formula” to calculate all the permutations of placing n numbers in a cyclical order (like on a clock face). He also proved the formula. Wait, Chinese lesson? Yes, I know, this guy manages to squeeze some math everywhere. His Chinese tutor loved it by the way. “Well, we’ve both learned something!” Simon exclaimed delightfully.
This is an example of the learning style that Simon enjoys most. He really likes doing the daily challenges on Brilliant.org. He later sometimes discusses them with other participants or even writes wikis!