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
Simon: You can derive the speed of light from Maxwell’s equations.
Me: Because they used to think it was infinite, right?
Simon: Maxwell’s equations aren’t invariant to the Galilean transformation, which means that the Galilean transformation is wrong, which means that Newton’s mechanics is wrong. The actual transformation is the Lorentz transformation, and this is the exciting one. Because that’s what you need for Einstein’s relativity!
Simon told me about strong force and what happens to a quark inside a nucleon if a high energy photon hits it and pushes it outside the nucleon: a new quark and antiquark are created.
But what if the photon was so strong that it pushed the quark even further? It would create another quark and another antiquark.
Then Simon switched over to drawing Feynman diagrams to show how a w boson emitted by a quark or a changes that quark or lepton (charm to strange, bottom to top, electron to electron neutrino, etc.) “We don’t know what the z boson does” , Simon says. “Maybe it’s there for no reason!”
Simon has just graphed this to show how the Lorentz factor or gamma ( on the y axis) is dependent on the speed of the object (the x axis). The 100 on the x axis is the speed of light. You can see how the speed makes virtually no difference to the Lorentz factor (of relativistic time and mass) until the speed of the object reaches about 85 percent of the speed of light. At around 90 percent of the speed of light the Lorentz factor reaches 2 (which means that time is twice as slow by then and the relativistic mass doubles), and at 99 percent the factor is already 7. For 100 percent or the speed of light itself, the Lorentz factor equals infinity, Simon explained.
Simon’s first long boat trip, to see all the artwork presented at the Amsterdam Light Festival this year. Pleasantly surprised at how many pieces were inspired with his favorite themes (glass fiber, RGB perception, string theory, neural networks).
This photograph seems to convey the essence the artwork! It’s about string theory, and when you move relative to the piece the strings flicker (vibrate). Try scrolling up and down and you’ll see the same effect!
We were reading “17 Equations that Changed the World” late last night, the chapter about the wave equation. Simon got all excited about timbres (shapes of sound waves), that are essentially sine waves. He said he knew an alternative way to look for the fundamental frequency (the sin x wave):
“The smallest number that’s divisible by all the numbers in a sequence is the product of all those numbers divided by the greatest common divisor/factor of all those numbers. That’s the Chinese remainder theorem (or rather, a generalisation of it).
If you took a rational frequency and an irrational one and made them into waves, the waves would never ever ever meet, except for one point. So sometimes there’s no fundamental frequency. Because we need at least two points where the waves meet up to define a fundamental frequency.
Sadly, this happens most of the time. In fact, not even most. 100 percent of the time there’s no fundamental frequency. Technically, it’s an infinitely small chance that any number you come up with at random is rational! But fortunately for us, we can approximate the fundamental frequency here: use the two points that are closest to the waves meeting to get an approximate fundamental frequency. And it always works!
This is incredible! We’ve found a connection between a discrete problem, of what’s the smallest number that divides all of the numbers in a given sequence, to a continuous problem, of what is the fundamental frequency of a combination of sine waves. In other words, we found a discrete solution to a continuous problem!”
Simon, what does discrete mean?
“I’ll give you an example. The natural numbers, even though they are infinite, they are still discrete, because there are gaps between them. And a number in between those gaps is not a natural number anymore. A continuous thing however is for example like the real numbers. There’re no gaps. Because if there were gaps, any number in between those gaps was another real number”.
Yesterday we attended one of the hundreds of Science Days venues open for free all over Belgium. Simon particularly enjoyed chemistry demos, even though he was disappointed that some companies showing their inventions didn’t want to share the actual formulas behind the tricks.
The simple non-newtonian fluid remains a favourite.
Making your own bath bombs.
Simon dazzled by how insulator foam (polyurethane) is produced as the result of a reaction between two highly viscous substances, an isocyanate and a polyol (polyether). Another fascinating thing about this demo was that the tool mixing the two ingredients actually employed magnets!
A workshop explaining why ships don’t sink and if they do, why:
Exploring 3D printing:
Heat indicator (material changing color depending on water temperature):
The good old baking soda and vinegar demo revisited: