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 believes that he has found a mistake in one of the installations at the Technopolis science museum. Or at least that the background description of the exhibit lacks a crucial piece of info. The exhibit that allows to simultaneously roll three equal-weight balls down three differently shaped tracks, with the start and the end at identical height in all the three tracks, supposes that the ball in the steepest track reaches the end the quickest. The explanation on the exhibit says that it is because that ball accelerates the most. Simon has noticed, however, that the middle track highly resembles a cycloid and says a cycloid is known to be the fastest descent, also called the Brachistochrone Curve in mathematics and physics.
In Simon’s own words:
You need the track to be steep, because then it will accelerate more – that’s right. But it also has to be quite a short track, otherwise it takes long to get from A to B – which is not in the explanation. It’s not the steepest track, it’s the balance between the shortest track and the steepest track.
Galileo Galilei thought that it is the arc of a circle. But then, Johan Bernoulli took over, and proved that the cycloid is the fastest.
The (only) most elegant proof I’ve seen so far is in this 3Blue1Brown video: https://www.youtube.com/watch?v=Cld0p3a43fU
There’s also a VSauce1 video, where they made a mechanical version of this (like Technopolis): https://www.youtube.com/watch?v=skvnj67YGmw
Wikipedia Page: https://en.wikipedia.org/wiki/Brachistochrone_curve
We’ve also made some slow motion footage of us using the exhibit (you can see that the cycloid is slightly faster, but as far as I can tell, it’s not precision-made, so it wasn’t the fastest track every time): https://www.youtube.com/watch?v=5Brub0FnpmQ
I hope that you could mention the brachistochrone/ cycloid in your exhibit explanation. I don’t think you can include the proof, because for such a general audience, it can’t fit on a single postcard!
Here Simon explains one more effect he has played with at home, the Magnus effect.
This is Simon’s version of Daniel Shiffman’s 2D Casting code, made on Wednesday last week right after the live session. Link to the live session including the coding challenge.
Code and interactive animation are online at: https://editor.p5js.org/simontiger/sketches/ugHX4yKQC
Play with the animation online at:
Simon has also made one more, optimized version of this project (with fewer rays, runs faster): https://editor.p5js.org/simontiger/present/F6TCHAZs_
Both of Simon’s versions have been added to the community contributions on the Coding Train website: https://thecodingtrain.com/CodingChallenges/145-2d-ray-casting.html
Today we have made beautiful rainbow chrystals! Polarized light iridizes sodium thiosulfate crystals, so we made the crystals in between two polarizing films and then observed them through the microscope. In the video, Simon also explains how polarizing film works.
From the scientific description at the MEL Science website: Sodium thiosulfate crystals contain five molecules of water per one unit of sodium thiosulfate Na2S2O3. Interestingly, when heated, the crystals release the water, while sodium thiosulfate dissolves in this water. This solution solidifies rapidly when cooling, forming beautiful crystals. If these crystals are put between polarizing films, they take on an iridescent sheen. This is because the polarizing films only let light with certain characteristics through, and this light in turn “iridizes” the otherwise-colorless sodium thiosulfate crystals.
Caught Simon’s reaction to Wednesday’s breaking news on video: the first-ever image of a black hole published, made by the Event Horizon Telescope project team. Simon explains why, if you stood next to the black hole, you would be able to see the back of your own head.
Simon loved this video by Veritasium about how the image of the black hole was made (he had watched this one day prior to the actual publication of the black hole image).
Yesterday, wee also watched this beautiful TEDx contribution by Katie Bouman (one of the leading figures behind the algorithm that helped stitch the M87 black hole image data together). The video is from three years ago, when the project was just getting started. Katie is such an inspiration: a computer scientist helping astrophysicists!
Scientists report ‘groundbreaking’ black hole findings from the Event Horizon Telescope: link to the actual press conference.
We have tried using an LED backwards: not get it to shine by letting an electric current pass through it but produce electricity by shining light on an LED (this is how solar panels work). It’s important to use a sensitive LED for this experiment, and as we have observed, it also seems to be important to use light photons of the same frequency as the colour of the LED (red laser didn’t work on a white LED, but it may have to do with the fact that red light is weaker than white light anyway, i.e. has a lower frequency). The picture below shows us measuring the voltage of the current produced by the LED.
We’ve have learned this and a a lot more from Steve Mould’s video on How diodes, LEDs and solar panels work: Photovoltaic cells and LEDs are both made of diodes. Diodes are designed to allow electricity to flow in one direction only but the way we make them (out of semiconductors) means that can absorb and emit light.
In the video, Steve shows how the semiconductor atoms share elctrons. Semiconductors are crystal structures of atoms are replaced by the atoms of neighboring elements, for example a structure where some silicon (Si) atoms are replaced by phosphorus (P) or boron (B) atoms, thus providing for free electrons inside the structure (N-type conductor) or for free “holes” unoccupied by electrons (P-type conductor). A diode is basically two semiconductors pushed together. With enough voltage, the electrones are able to jump from the N-type semiconductor across the depletion zone and into the P-type semiconductor, emitting light (photons) as they fill the holes and go from a high energy state into the low energy state.
If you shine a light at a diode, you can kick some electrons from their shells and thus create free electrons and holes that will move (because of the electric field in the depletion zone) and generate voltage.
Simon showed us this amazing hing with a fidget spinner. It’s called stroboscopic effect. It’s a visual phenomenon that occurs when continuous motion is represented by a series of short or instantaneous samples (like camera shots), distinct from a continuous view.
In the video below, Simon also demonstrates the rolling shutter effect with the same fidget spinner and camera.
Mesmerised by the 3D printed gears on Numberphile: “If you move two of these, the third one appears to be hovering in mid-air!”, Simon made a similar construction of his own – 6 straws forming 3 gears.