Infinities Driving You Mad. Part 3: Inaccessible Numbers.

This is the third (and in my opinion, the best so far) video in Simon’s short series Infinities Driving You Mad. In this episode, Simon takes us into the strange world of inaccessible numbers. “People are just going to click this video and not notice that they’re going to be mad after they watched it”, Simon comments.

Link to Part 2 about ordinal numbers: https://youtu.be/D0l-EwPmx-w

Link to Part 1 about cardinal numbers: https://youtu.be/jyOnxdJHWOU

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Water Fountain Powered by Sound Waves

We built a water fountain powered by sound waves! There is a little speaker attached to the bottom of the water basin. Warning: the sound frequencies in the video may be unpleasant!

And here we tried the same with sand. Again, warning: the frequencies may be unpleasant to your ear, so make sure you lower the volume on your device.

Microstructures Interfering With Light

What looks like strange planets in dark space are actually glimpses of the microstructures forming the Giant Blue Morpho’s wings, as seen through a microscope. Simon told me about how a Blue Morpho’s wings aren’t actually blue (have no blue pigment) but appear blue as a result of a physical phenomenon called structural coloration — microstructures interfering with light. This is almost the same phenomenon as iridescence (making a surface appear to change colours as the observer’s angle of view or the illumination angle changes, think of the soap film in a bubble).

We had found Blue Morpho’s wings in the street about half a year ago. Someone threw a small butterfly collection away — several butterflies pinned to a stick. It looked very cruel and we would have never killed a Blue Morpho for the sake of an experiment, but since we stumbled upon such a rare treasure, we picked up one wing and stored it in a book.

Horizontal force

Going for a walk quickly turns into yet another Physics experiment. “Here’s a challenge: what if you can force the ball down so much and induce so much horizontal motion (when the ball bounces off of a wooden wedge) into the system that it goes all the way to the other side?” Simon shouts as he runs after a small bouncy ball in a large space that once used to be a tram depot. “With a back spin the ball goes horizontally! “

Why Cookies Get Bigger in the Oven

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Simon is baking Dutch traditional “pepernootjes” (“pepper nuts” or spicy cookies) and explains why they get bigger in size after you put them in the oven and what the optimal tiling pattern is to fit a maximal number of cookies on the baking sheet.

Upon waking up

Simon said today upon waking up: “If a Physics constant suddenly popped up in pure mathematics, that would be really weird. If there is more than one universe, that would mean either that mathematics only exists in this particular universe, or that one of the laws of physics in our universe would go through mathematics to all other universes in existence. So for example, the speed of light would be the same in all universes, or Planck’s constant”.

Infinities Driving You Mad. Part 2: There’re Infinitely Many Infinities

This is the second part in a series of four videos that Simon is recording about Infinities Driving You Mad (on Set Theory) and is devoted to ordinal numbers. If you would like a little more explanation about what ω-one is, please see this short footnote video where Simon explains in more detail how he moves from the first infinite ordinal ω to ω-one:

Link to Part 1 about cardinal numbers: https://youtu.be/jyOnxdJHWOU

Serious answers

Simon told me this morning that he has found the answer to a question that bothered him so much lately -why photons (and gluons) violate E = mc². “It’s because photons are not real particles, they are virtual! That means that you cannot directly detect them. You need a photon to bounce off of an object to detect it. And gluons you cannot detect at all!”

Photons also don’t satisfy Eistein’s more complicated and less well-known equation about energy momentum relation: E² = (c²) + p²c², he added enthusiastically.

Sugar and Salt

Want some me sugar in your tea?

Simon built this sucrose (table sugar) molecule with the help of Theodore Gray’s Molecules book (although he is pretty sure there is a mistake in the Dutch version of the book, on a different page, where the fructose, glucose and galactose molecular structures seem to be mixed up – the sucrose description helped him discover this as the table sugar molecule is made up of one fructose and one glucose molecule).

Simon is also fascinated how sugar and salt, substances that are easy to confuse on the kitchen table, are made of molecules that are so “wildly different”: