@dduque@mathstodon.xyz
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dduque

@dduque@mathstodon.xyz

Physics professor at ETS Ingenieros Navales, UPM, Madrid

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j_bertolotti, to random
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: The "Ashcroft/Mermin Project"
I will try to (likely very slowly) go through the classic textbook "Solid State Physics" by Ashcroft and Mermin and make one or more animation/visualization per chapter.
This will (hopefully) help people digest the topic and/or be useful to lecturers who are teaching about it. As with all my animations, feel free to use them.
The idea is that the animations are a companion to the book, so I will give only very brief explanations here.

dduque,
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@j_bertolotti Ashcroft & Mermin is such a brilliant book. I also liked Kittel, but A&M is just a classic.

dduque,
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@j_bertolotti One of the instances when the Voronoi diagram was re-discovered, if I recall correctly.

dduque, to manjaro
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Trying as an alternative to my beloved

I'm on linux, so this is helpful https://wiki.manjaro.org/index.php/Virt-manager#Install_virt-manager.2C_qemu_and_all_dependencies

johncarlosbaez, (edited ) to random
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The CEO of Exxon just said "we've waited too long" to tackle climate change. He blames "society" and "activists".

Yes, Exxon. Yes, Exxon. Yes, Exxon: the corporation that for decades has been spending millions to slow progress on climate change, despite its own research showing the problem was urgent.

He said:

"We've waited too long to open the aperture on the solution sets in terms of what we need, as a society, to start reducing emissions.... Frankly, society, and the activist — the dominant voice in this discussion — has tried to exclude the industry that has the most capacity and the highest potential for helping with some of the technologies."

What is this — some sort of dark, twisted joke?

The interview is here:

https://web.archive.org/web/20240228015207/https://fortune.com/2024/02/27/exxon-ceo-darren-woods-interview-pay-the-price-for-net-zero/

https://www.salon.com/2024/02/29/exxon-ceo-to-world-climate-isnt-our-fault-now-pay-the-price/

dduque,
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@johncarlosbaez Exxon, as in Exxon Valdes

johncarlosbaez, (edited ) to random
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If you have a line of pendulums each attracting its neighbors, you can form waves of swinging pendulums that move down the line. These can act like particles!

More precisely, when the pendulums form a twist like a 360° twist in a ribbon, you get either a "kink" or an "antikink" depending on whether the twist is clockwise or counterclockwise. Here you see a "kink" and an "antikink" collide and move through each other. The total twist - the number of kinks minus the number of antikinks - is always conserved. At the moment of collision you can see that the total twist is zero in this example.

All this is described by the "sine-Gordon equation". Mathematicians and physicists have studied the hell out of this equation - it turns out to have a lot of depth to it.

I got this animation from Kanehisa Takasaki's webpage:

https://www2.yukawa.kyoto-u.ac.jp/~kanehisa.takasaki/soliton-lab/gallery/solitons/sg-e.html

and he has some more there. Can you guess what happens when two kinks collide?

(1/n)

dduque,
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@johncarlosbaez When two kinks collide... I guess they repel each other, due to the kinky Pauli exclusion principle ?

j_bertolotti, to random
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I need a collaboration between Hayao Miyazaki and Hidetaka Miyazaki.
Just for the LOL

dduque,
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@j_bertolotti The action could take place at this prefecture https://en.wikipedia.org/wiki/Miyazaki_Prefecture

johncarlosbaez, (edited ) to random
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Yes, this guy is playing Scottish folk music in a pub on Christmas eve... on a bouzouki! This instrument jumped from Greece to Ireland in the 60s, but now it's used in Scottish folk music too.

We're having a great evening. I hope you are too.

For more on the Irish bouzouki, try this:

https://en.m.wikipedia.org/wiki/Irish_bouzouki

dduque,
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@johncarlosbaez On my visit to Galway, I was surprised this instrument seemed to be common-place in Irish bands. But I know the banjo had also undergone a similar process. There is also the Peruvian cajón which is now standard in flamenco music. I guess musical instruments slowly evolve and take their places whenever they are neede !

johncarlosbaez, to random
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David Bennett has a great video reminding us that outside the English-speaking world, most people don't call musical notes "C D E F G A B C". Instead they call them "do re mi fa so la si do", which is a system called "solfège" - or they use other systems.

But I was a bit shocked to see his map showing "no data" on what people do in most of Africa, or southeast Asia, or Korea, or Mongolia, or Pakistan, or Turkmenistan, or Uzbekistan.

Mind you, I don't hold it against him. He's an independent video-maker struggling to earn a living explaining music theory. He probably can't afford to spend hours and hours researching every country. But it saddens me to see this map.

I bet some of you here know the systems for naming notes in these greyed-out countries! Please tell us! And if you can find or make a better map, please do.

David Bennett's video is here:

https://www.youtube.com/watch?v=MVA8bgSBt5A

It has some nice info on the history of the solfège system and how it's used differently in English-speaking countries.

dduque,
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@dougmerritt @johncarlosbaez I guess you can restrict your classification to what system people use when learning classical Western music?

BTW, trivia: in Spanish "solfear" is the verb derived from "solfeo" = "solfège". It means reading out loud the notes with their correct lengths, but not their pitches (which would be just singing).

j_bertolotti, to random
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If you sample N points uniformly on the unit sphere, take for each the halfway point to the north pole of the sphere, and then project is on the x-y plane, you obtain N points sampled uniformly on the unit disk.

(A request from @narain )

Black and white visualization on N points on a sphere moving smoothly to their halfway point to the north pole and then being projected on the x-y plane.

dduque,
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@j_bertolotti @narain I know how to generate uniform random points on a sphere (not trivial!, see [1] ). Uniformly spaced points on a sphere, I do not.

I think people used to do some sort of molecular dynamics with repulsive interactions in order to achieve that.

[1] Frenkel & Smit, Understanding Molecular Simulation, one of the appendices

dduque,
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@narain @j_bertolotti Really? I have been digging some algorithms I used to employ and the recipes they provide are more involved. I am a bit proud I remember that Appendix in Frenkel & Smit's book, but they actually refer to an older classic: Allen & Tildesley!

They provided two methods, both of them Monte Carlo-ish. The first one is from von Neumann, and easy to grasp: get a 3D point in the bounding cube, project it radially on the sphere if inside the sphere, reject otherwise.

The other one performs better and is more subtle... but, interestingly, it begins with a disk: get a 2D point in the [0,1]^2 square, reject if outside circle, otherwise make what looks like a sort of stereographic projection onto the sphere.

johncarlosbaez, to random
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No. Succeeding in love is not easy, and there's no formula for it.

Here's the essence of this bad take:

"Since life is itself simply a game in disguise, having a few mathematical tricks up your sleeve can also give you an edge in the game of life."

Life is not simply a game in disguise. There are no fixed rules, apart from possibly the laws of physics. More importantly, there's no fixed definition of what counts as "winning". In fact the whole concept of "winning" doesn't apply, except in very limited realms.

I'm reminded of an anecdote I heard from the statistician Persi Diaconis. I'll probably get the details wrong, but it goes something like this:

Persi Diaconis was friends with an economist who had just gotten two job offers, one on the east coast of the US and one on the west coast. The economist was having a lot of trouble deciding which offer to take: each had its pros and cons. So Diaconis said "Hey, why not use the mathematics you're always talking about? Compute the expected utility in each case, and pick the offer that maximizes it!"

And the economist said "Come on, Persi! This is SERIOUS!"

.....

The article is here:

https://www.theguardian.com/science/2023/nov/05/how-maths-can-help-you-win-at-everything

and I thank @pigworker for pointing it out.

dduque,
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@johncarlosbaez @pigworker As you point out, the mere concept of "life as a game to be won" is quite debatable and open to opinion. To me, it's abhorrent

j_bertolotti, to physics
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:
Signals (e.g. light) move at a finite speed, so there is a time lag between when they are emitted and when they are detected. If the source is moving, the detector will "see" the signal that was emitted at a previous time, not the signal that is being emitted right now, and this time lag can change with time in a complicated way.
(Notice that, as the source is always moving slower than the signal, the detector sees the signals in the same order they were emitted.)

Left panel: a yellow point, representing a source, moving on a thin grey Lissajous curve, and emitting circles at regular time intervals, whose radius grows linearly with time. The colour of the circle changes gradually from red for the first circle to blue for the last one. A white dot just above the Lissajous curve represents a detector. Right panel: a plot of time of emission vs time of detection, with each point appearing when one of the coloured circles hit the detector. The dots form a wavy monotone curve.

dduque,
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@j_bertolotti But... not light in a vacuum, right? That time lag will simply be distance over c in this case

dduque,
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@j_bertolotti Also with light in a medium, a la Cherenkov https://en.wikipedia.org/wiki/Cherenkov_radiation

johncarlosbaez, (edited ) to random
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Though part of me - the worst part - would like to join the clever crowd who endlessly pontificate and interview each other, I'm held back by my intense aversion to publicly talking about:

  1. consciousness
  2. free will
  3. string theory and other theories of everything
  4. are mathematical objects real?
  5. is reality a simulation?
  6. interpretations of quantum mechanics
  7. quantum computers
  8. large language models, machine learning, AI

and most other topics that the "digiterati", the "intellectual dark web", and other quasi-scientific talking heads enjoy bloviating about. I'd much rather curl up with a good solid book on the life cycle of lichens, or the organizational structure of car repair shops.

dduque,
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@johncarlosbaez It's tricky to answer questions that are not well posed

johncarlosbaez, (edited ) to random
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Yesterday I had dinner with some mathematicians including Arthur Jaffe, famous for his work on 'constructive quantum field theory'. This is the subject where you try to make quantum field theory mathematically rigorous beyond the level of perturbation theory. Perturbation theory gives answers to physical questions that are infinite sums. Unfortunately these sums most likely diverge - but physicists usually settle for adding up the first few terms. Constructive quantum field theory tries to do better.

My friend Minhyong Kim asked Jaffe what he thought about the state of quantum field theory. He said there hadn't been much progress in the last couple of decades. It was clear that he meant constructive quantum field theory, not all the other things going on.

He recalled how Balaban had come up with a proof that Yang-Mills theory makes sense nonperturbatively in 4 spacetime dimensions if you assume spacetime is a small enough 4-dimensional box. This would be a first step toward making the box as big as you want, and then letting it become infinite in size.

But Balaban never published this result. In fact he used to save money by leaving his apartment in Cambridge Massachusetts every summer and putting all his belongings in storage. And at some point he lost the manuscript where he had worked on this problem!

Yes, this was sometime in the 1980s before mathematicians wrote papers on computers.

Jaffe said it would be good to redo Balaban's work using new ideas, and in fact also redo all the work on constructive quantum field theory in 2 and 3 spacetime dimensions, which is scattered among many papers and not polished up yet. But nobody seems to have the energy!

dduque,
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@johncarlosbaez Not even closely an expert on this. But, a " a small enough 4-dimensional box" sounds to me as imposing a low-frequency cut-off, which is precisely one of the tricks used in QFT.

j_bertolotti, to random
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I am not sure how many people have a favourite function. I do and it is xˣ. Not because it is particularly useful, but because of the expression any student (me included when I was younger) have on their face the very first time they encounter it 😃

dduque,
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@j_bertolotti That one's related to the Γ(𝑥) function and 𝑥!, which are really important

AstroKatie, to random
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I'm SUPER EXCITED to share with you this series of quantum physics explainer videos I produced with the Perimeter Institute! Check out Episode 1: Wave Particle Duality now ➡️ https://youtu.be/DfQH3o6dKss Subscribe the channel to catch each episode as it’s released! #Quantum101

dduque,
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@AstroKatie You know some people have strong feelings about this duality thing, claiming it obscures the fact that quantum particles are neither. Me, I'm find with it, as long as the "wave function collapse" is not invoked.

johncarlosbaez, (edited ) to random
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Music theory

If you want to learn about modes, you really can't beat the videos of Moss and Dandy. In this one he writes a song in 'Hungarian minor'.

To get Hungarian minor you can start with the natural minor scale

1 2 ♭3 4 5 ♭6 ♭7

then raise the ♭7 a half step to get harmonic minor

1 2 ♭3 4 5 ♭6 7

(okay you knew that), and then do something really drastic - raise the 4 a half step:

1 2 ♭3 #4 5 ♭6 7

👹

This is an intensely dissonant scale, since the #4 is now a tritone above the tonic, and we climb by half tones from the #4 to the 5 to the ♭6 - and there's also a half tone from the 7 up to the octave. All these small steps force there to be big gap somewhere else: 3 half tones from the ♭3 to the #4.

But don't just read me - listen to Moss and Dandy, who explains it with music in a really entertaining yet clear way. (With dancing skeletons.)

https://www.youtube.com/watch?v=bjjijMXIj7g

dduque,
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@johncarlosbaez sounds really Hungarian. More Bartok than Brahms, for sure

dduque, to physics
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I am a professor and researcher at the school of the , Madrid, Spain.

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