art, Coding, Geometry Joys, Murderous Maths, Museum Time, Notes on everyday life, Together with sis, Trips

Back at Stedelijk

As for Morellet’s RGB colored cells, very inspiring for a sandpiles coding project. (The photographs don’t convey half of the effect the original canvasses invoke. Morellet’s cells actually appear to be moving when you gaze at the original).
Installation by Barbara Kruger
Installation by Barbara Kruger
Read this poem from top to bottom and it’s depressing, from bottom to top and it’s empowering.
Group, Math Riddles, Murderous Maths, Notes on everyday life

MathsJam 18 June 2019

This was the last MathsJam this academic year and a very social one. Simon has enjoyed the outside setting and mingled with the other mathematicians.
Simon had also contributed two problems (numbers 3 and 5). Unfortunately we haven’t seen anyone solve them (the problems come from the Russian math olympiad published in the magazine Kvantik).
Simon had recognized two problems he knew the answers to. Here he is explaining the persistences problem (number 13).
The smallest number with persistence 5 is 679
Simon trying to prove that the solution to problem number 2 is e.
Math Riddles, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book, Together with sis

Teaching Mathematical Fundamentals

Simon loves challenging other people with math problems. Most often it’s his younger sister Neva who gets served a new portion of colourful riddles, but guests visiting our home also get their share, as do Simon’s Russian grandparents via FaceTime. Simon picks many of his teaching materials in the Mathematical Fundamentals course on Brilliant.org, and now Neva actually associates “fundamentals” with “fun”!

Math Riddles, Murderous Maths, Notes on everyday life, Simon's sketch book

Trinagular birthday probabilities

“What is the chance that two people in a group of, say, 30 people would have their birthday on the same day?” I asked Simon as we were sitting on a bench by the river Schelde late last night, waiting for his Dad and sister to arrive by boat. The reason for this question was that one of the professors at Simon’s MathsJam club turned out to have celebrated his birthday exactly on the same day as I the week before. Besides I was afraid of Simon getting bored just sitting there, “enjoying the warm evening”. At first, I thought he didn’t hear my question and repeated myself a couple of times. Then I noticed he was so silent simply because he was completely immersed in the birthday problem.

Eventually, at that time already on Antwerp’s central square, Simon screamed with joy as he told me the formula he came up with involved triangle numbers! “It’s one minus 364/365 to the power of the 29th triangle number!” he shouted. “It’s a binomial coefficient, the choose function!”

Simon’s solution defining the probability of two people having the same birthday in a group of n people. The highlighted diagonal in the Pascal triangle are the triangle numbers. For example, 15 is the 5th triangle number. So in a group of 6 people, the probability would be 1 minus 364/365 tothe power of 15.
A few days later Simon told me his previous formula wouldn’t work for a group of 366 people and quickly came up with a simpler formula, without any triangle numbers.
Coding, Community Projects, Contributing, Notes on everyday life, Python, Simon teaching, Simon's Own Code, Together with sis

Drawing with Turtle

Here we are, on the day of my 40th birthday, while recording a lesson of drawing with turtle in Python. It was meant to be my birthday present, a beginner-friendly hour of code, in which Neva would also be able to take an active part. We ended up recording two beautiful sessions only to find out later that our screen capture video was irreparably corrupted (never record in mp4 in OBS). Simon was inconsolable. We also thought this webcam recording was gone but rediscovered it a day later. So nice to have it as a memory.

And I’m relieved to say that we have managed to redo the whole project from scratch today (sadly without Neva’s participation this time as she had better things to do, so I look rather redundant sitting there next to Simon giving the lesson). Once Simon is done with the editing (which is another two days of work I’m afraid), he will upload the hour of code on YouTube. He also plans to create a website for this project to enable his “students” to draw in a built-in application.

From our session today:

And here is an example of Simon drawing with turtle for his own pleasure, a Serpinski triangle in Python (a few days ago):

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.

Exercise, Experiments, Notes on everyday life, Physics, Simon teaching, Together with sis, Trips

A lot of fluid dynamics at Technopolis

Today we celebrated my 40th birthday with a family trip to Technopolis, a mekka for science-minded kids in the Belgian town of Mechelen. (Technically, my real birthday is in two days from now, but I have messed with the arrow of time a little, to speed things up).
The entrance to the museum is adorned with a red lever that anyone can use to lift up a car!
Simon and Neva lifting up the car
The beautiful marble run and math and physics demo in one
Galton’s board and Gaussian distribution
Simon explaining the general relativity demo, which is part of the marble run
This was probably the winner among all the exhibits: a wall to climb with a mission (Simon figured it out rather quickly – one had to turn “mirrors” to change the direction of light (green projection) and have the light rays extinguish the targets.
Simon tried to explain this to other children, but they only seemed to want to climb. It was sad to see how no one cared to listen (well, except for Neva of course).
Simon was already familiar with this optical illusion. Later he saw another version of this on an Antwerp facade.
The logic gates were too easy.
the center of gravity
Huge catenaroids! Something Simon had already demonstrated to us at home, but now in XXL!
cof
And huge vortices! Another passion.
Hydrodynamic levitation! Hydrodynamic levitation!
Look! A standing wave!
And another standing wave!

Here Simon explains one more effect he has played with at home, the Magnus effect.

Exercise, Math Riddles, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book, Together with sis, Trips

Math on the Beach

Sunday at the beach, Simon was reenacting the 5 doors and a cat puzzle (he had learned this puzzle from the Mind Your Decisions channel). The puzzle is about guessing behind which door the cat is hiding in as few guesses as possible, while the cat is allowed to move one door further after every wrong guess.

the little houses served as “doors”, and Simon’s little sister Neva as “the cat”

“Here’s a fun fact!” Simon said all of a sudden. “If you add up all the grains of sand on all the beaches all over the world, you are going to get several quintillion sand grains or several times 10^18!” He then proceeded to try to calculate how many sand grains there might be at the beach around us…

In the evening, while having a meal by the sea, Simon challenged Dad with a Brilliant.org problem he particularly liked:

Simon’s explanation sheet (The general formulas are written by Simon, the numbers underneath the table are his Dad’s, who just couldn’t believe Simon’s counterintuitive solution at first and wanted check the concrete sums. He later accepted his defeat):

Logic, Murderous Maths, Notes on everyday life

Benford’s Law

Simon is looking at his subscribers count on YouTube. We speculate if he gets to 1000 before the end of the academic year. Simon tells me that’s because subscriber count is just another example of Benford’s law in action. What is Benford’s law? – I ask.

“If you take some data that spans a few orders of magnitude and take the leading digits of all numbers, then you’re most likely not going to get a uniform distribution. Instead, 30% of the time, the numbers will start with a 1, a little bit less of the time – with a 2, even less – with a 3, and so on all the way to 9 (which has a low chance of occurring). For example, the populations of countries would follow that law. If something is not random enough, though (like human height in meters), then it wouldn’t follow that law. If something is too random, it also wouldn’t follow that law.”

Simon explains further: “Consider YouTube subscriber count over time. If you have 100 subscribers, then to get up to 200 is an increase of 100% (which is pretty big). But to get from 200 to 300 is only a 50% increase. From 900 to 1000 is just 11 %.”.

Then his dad asks: “What about going from 1000 subscribers to 1100 subscribers?”

“Well, Benford’s law only cares about the leading digit (and that’s what you want to increase as well). So you don’t want to increase from 1000 to 1100, you want to increase from 1000 to 2000! In other words, start a new Benford’s law ‘Epoch’.”