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More Stephen Wolfram and Brian Greene

What has been your silver lining during this COVID-19 crisis so far, in terms of self-directed learning? Simon is happy that Grant Sanderson, Stephen Wolfram and Brian Greene all have more time now to make frequent streams and tutorials. In fact, he can’t even follow all of them live as they often overlap!

Luckily, years of homeschooling have allowed us to develop a very flexible approach to daily routine, enabling us to embrace learning opportunities from across the Atlantic, that mostly present themselves in the evening hours. Our learning is circular, cyclical, not linear (we learn around the clock and Simon often returns to the topics he has already covered before but at a new level).

Simon delirious watching a Stephen Wolfram livestream
A screenshot from the live chat in Stephen Wolfram’s stream

Brian Greene publishes daily videos called “Your Daily Equations” on the World Science Festival channel, and viewers can “order” which equation they want to discuss next. He also does a weekly live Q&A.

It’s funny how both Wolfram and Greene are Simon’s professors as part of the World Science Scholars program, but he seems to have gotten a better chance to engage with them personally now that we’re all stuck at home (through the live chat and comments) than during the official World Science Scholars sessions!

Every day, Simon feels like he’s sitting right next to Brian Greene in his living room. There’s this atmosphere of informal talk and human warmth, as one of the world’s top flight professors is accessible for questions and gives Simon and other students so much of his precious time to explain all the quantum physics fundamentals. So touching yesterday, as Brian Greene just took off his socks and held them up in the air to visualise spin.
On April 2: there’re equations for relativistic mass and rest mass. The speed of light equation that Brain Greene talks about is with relativistic mass. — Do you know the equation with the rest mass? — No… In fact, let’s derive it right now!
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World Science Scholars Feature Simon’s visit to CERN in a newsletter. The current course is about neurons. Reading Stephen Wolfram.

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”).

September 2019: Simon at a hotel room in Geneva taking pat in his first WSS live session, with Professor Brian Greene
September 2019: screenshot from Professor Brian Greene’s course module on quantum physics

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.

Screenshots of the course’s quizzes. Simon has learned about scale invariance, the number of neurons in the human brain, allometric and isometric scaling relationships.

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.

screenshot from the course by Professor Herculano-Houzel

Simon has also contributed to the discussion pages, trying out an experiment where paper surface represented cerebral cortex:

The top paper represents the cerebral cortex of a smaller animal. Cerebral cortex follows the same physical laws when folding is applied.

Simon: “Humans are not outliers because they’re outliers, they are outliers because there’s a hidden variable”.

screenshot from Professor Herculano-Houzel’s course: after colour has been added to the plot, the patterns reveal themselves

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 playing around in Wolfram Mathematica, after reading about minor changes to the initial conditions of an idealised version of the kneading process
Simon working out a “study plan” for his Chinese lessons using a network system model he saw in Stephen Wolfram’s book “A New Kind of Science”
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Simon introducing himself for the World Science Scholars program

This is Simon’s introductory video for the World Science Scholars program (initiative of The World Science Festival). In May this year, Simon has been chosen as one of the 30 young students worldwide, joining the 2019 cohort for exceptional talents in mathematics. Most of the other students are 14 to 17 years old, age was not a factor in the selection process. To help the students and their future mentors to get to know one another, every World Science Scholar was asked to record an introductory video, no longer than 3 minutes, answering a few questions such as what is the biggest misconception about math, what your favourite branches of math and science are and who among the living mathematicians you’d like to meet.

Throughout the program, the students are given access to over a dozen unique interdisciplinary online courses and have the option to complete an applied math project, alone or as a team, consulting real experts in the field of their project. Simon has already started the first course module, on Special Relativity by Professor Brian Greene. The course has been specifically recorded for the World Science Scholars and reflects the program’s ethos: it’s self-paced, no grades, it relies on beautiful animations and visualizations, it’s full of subtle humour, is dynamic, thought-provoking and quite advanced (exactly in The Goldilocks Zone for Simon, as far as I could judge), yet broken up into easy-to-digest pieces. It’s difficult to predict how Simon’s path as a World Science Scholar will unfold (I’m afraid of making any predictions as he is extremely autodidact), but so far we have been very pleased with the nature of this program and it seems to match our non-coercive, self-directed learning style. I have especially liked one of the course’s main postulates: “Simultaneity is in the eye of the beholder”.

Simon watching Brian Greene’s Special Relativity course
Studying light clocks
Light clocks. Does the moving light clock tick slower?
Simon thinking about the question: Does the moving light clock tick slower?