#PhysicsFactlet
An attempt to explain what tensors are for people with high-school Math (if you are a mathematician, this thread is not for you).

Not sure why, but tensors are often introduced in a very confused way, that makes them look more scary than they actually are.

1/ Let's assume you are familiar with matrices (if you aren't, chances are you don't care what a tensor is), so the fact that multiplying rows by columns a row vector with a column vector yields a scalar (i.e. a single number) should be no surprise to you.

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#PhysicsFactlet (346)
A few days back I stumbled on a @AAPTHQ paper that has the words "Space pirates" in the tile, read it, and decided it was a lot of fun, so now you get a mini-thread and a couple of simple animations 😉
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aapt.scitation.org/doi/full/10.11… Sadly the paper is not truly about space pirates, but about the "pursuit curve"problem. I.e. object A is moving, object B follows it (pointing toward A at each time), and you want the path traced by B in the pursuit.
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#PhysicsFactlet (342) Lagrange multipliers
Strictly speaking Lagrange multipliers are not "Physics", but they are so useful to solve so many Physical problems, that it is definitively worth looking at them.
1/ Before we even introduce them, let's solve a super-simple problem, which will form the basis for our motivation to look into Lagrange multipliers:
Find the minimum of the function f=x²+y².

Yes, I can hear you shouting x=y=0, but let's still do the calculation.
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#PersonalOpinionOnOldishGame
You can't really finish #MonsterHunterWorld, but I have played as much as I am going to (100+ hours), so here are a few thoughts about it.
TL;DR: it is a good game with some incomprehensible flaws.
1/ Monster Hunter: World is the Nth (with N being a large integer) game in the the Monster Hunter series, but it was the first one I ever played (the new one, Monster Hunter: Rise is only on Nintendo Switch).
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#PhysicsFactlet (335)
Yesterday, at a small playground where my son was playing, I saw this Kugel fountain, so here comes a short thread about Kugel fountains and how they work.
🧵 1/

(Alt Text: a Kugel fountain slowly rotating in a sunny day.) First of all, what is a Kugel fountain?
There are a few variations on the theme, but usually they are big stone spheres, sitting on a hemispherical hole, with water flowing from below. Despite their weight, they can spin with a small push, and keep spinning for a long time.
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#PhysicsFactlet (331)
"Anderson localization" is a weird phenomenon that is not well known even among Physicists, but has the habit of popping up essentially everywhere.
An introductory thread 🧵
1/ The idea of "localization" originally came about as an explanation (by P.W. Anderson, hence the name) of why the spins in certain materials did not relax as fast as expected.
nobelprize.org/prizes/physics…
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New paper on #ArXiv!
"Tracking moving objects through scattering media via speckle correlations"
With @YJaureguiS, and Harry Penketh.

Short(?) thread explaining what it is about.
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arxiv.org/abs/2202.10804 Scattering is a major problem for imaging, and it doesn't take very much of it before we can't see essentially anything of what it is happening.
Not surprisingly, imaging in the presence of scattering is a very active field of research.
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https://twitter.com/j_bertolotti/status/1481215310178967554?s=20&t=Y7yXVQG90DQF4NuY-7FPqg

#TheLongRoadToLearnSomethingNew
I decided it is high time I learn something about machine learning. I couldn't care less about learning how to use Tensorflow or any other package that do machine learning for you. I "just" want a Physicist's intuition for how and why it works.
1/ A million years ago I asked here for advices on resources. Some were very good advices, some were not. But I am mow armed with a textbook, and will irregularly update here on my progresses.
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#PhysicsFactlet The ones I am most proud of from 2021 (in chronological order)
A visualization of what an eigenvector is (at least for 2x2 matrices)

https://twitter.com/j_bertolotti/status/1354822527487340550?t=OqQyzEQbi08lgTRfyCySfQ&s=19

Pulse chirping (keeping the pulse duration constant for ease of visualization, although in reality one usually keeps the bandwidth constant)

https://twitter.com/j_bertolotti/status/1359088862396612612?t=OqQyzEQbi08lgTRfyCySfQ&s=19

#PhysicsFactlet (308)
There are not many problems in Physics that can be solved exactly, so we tend to rely on perturbation theory a lot. One of the problems with perturbation theory is that infinities have the bad habit of popping up everywhere when you use it.
(A thread 1/ ) If you know anything about Physics you are probably thinking about quantum field theory and all the nasty infinities that we need to "renormalize". But quantum field theory is difficult, so let's look at a MUCH simpler problem: the anharmonic oscillator.
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In celebration of 10k followers, here is a new edition of "people you should follow, but that (given their follower count) probably you don't".
i.e. people I follow, with <5k followers, non-locked, active, that in my personal opinion you should follow too.
1/ In random order:
@LCademartiriLab food, chemistry, architecture, and beauty in general. Trigger warning: strong opinions.
@VKValev bit of history of Physics + chiral media
@DrBrianPatton social justice in science
@alisonmartin57 weaving and bamboo structures
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#PhysicsFactlet (299)
Fractional derivatives: a brief tutorial/🧵. If you know some calculus you should be able to follow. If you are a Mathematician (or you like to see things done properly) I advise "Fractional Differential Equations" by I. Podlubny instead 😉
1/ The history of fractional derivatives begins together with the history of the much more common integer-order derivatives, and a number of big names in mathematics worked on it over the centuries.
Afaik, the first to work on the problem was Leibniz himself.
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#PhysicsFactlet (283)
Lorentz transformations pre-date Special Relativity. How is that even possible?
A thread.

Trigger warning for typos (hopefully just in the text and not in the equations) and carefree manipulations of equations 😉
1/ The historical route is interesting but complicated, so I will leave that story for someone more qualified to write it. What I want to look at is: how do we get the Lorentz transformations without knowing anything about special relativity?
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#PhysicsFactlet (273)
A brief introduction to the calculus of variations.
Trigger warning: lots of formulas manipulated the way experimental physicists do 🙂
🧵 1/ The simplest introduction to the calculus of variations is to solve in a slightly roundabout way a very easy geometrical problem: what is the shortest path between 2 points on a plane?
(spoiler: it's a straight line)
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A few days ago I was asked by some last year students advice on how to decide whether doing a PhD is the right thing to do. I will put here a summary of what I told them, just in case it can be useful for someone else.
🧵 1/ [Disclaimer: What follows are personal opinions based on STEM disciplines in Europe. So this is a partial and (by definition) incomplete picture.
Also, I am assuming you like the subject you want to do a PhD in, and that you can find a supervisor who is not a sociopath.]
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I am experimenting with recording lectures for the coming term.
Here I will make a summary of how it went in (semi)real-time. Wish me luck 😰 First experiment was (as expected) a disaster.
What was supposed to be a 10min video was over 20min long, with me mumbling, mispronouncing half of the words, and in general being too worried about recording to remember to explain anything. 😭

Moving all the old Physics factlects to the same hashtag to make easier to find them. As Twitter does not allow me to edit my tweets, I need to repost all of them. Apologies if this floods your timeline. #Physicsfactlet (1)
The uncertainty principle is not a principle, it is a theorem. Just like the Pauli exclusion principle and many others. It was a principle when it was first formulated, but we have since realised that it can be derived from first principles.