In informal contexts, it usually refers to the phase of ice observed in atmospheric pressure, Ice Ih.
Most notable example: gallium arsenide, see also: gallium arsenide vs silicon.
An important class of semiconductors, e.g. there is a dedicated III-V lab at: École Polytechnique: www.3-5lab.fr/contactus.php
Non-anomalous: number of splits matches predictions of the Schrödinger equation about the number of possible states with a given angular momentum. TODO does it make numerical predictions?
www.pas.rochester.edu/~blackman/ast104/zeeman-split.html contains the hello world that everyone should know: 2p splits into 3 energy levels, so you see 3 spectral lines from 1s to 2p rather than just one.
It also mentions that polarization effects become visible from this: each line is polarized in a different way. TODO more details as in an experiment to observe this.
Well explained at: Video "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)".
Experimental physics - IV: 22 - Zeeman effect by Lehrportal Uni Gottingen (2020)
Source. This one is decent. Uses a cadmium lamp and an etalon on an optical table. They see a more or less clear 3-split in a circular interference pattern,
They filter out all but the transition of interest.
- youtu.be/ZmObNFAqkBE?t=165 passes the lines through a polarizer, which shows how orbital angular momentum is carried by photon polarization
- youtu.be/ZmObNFAqkBE?t=370 says they are looking at 1D2 to 1P1 changes.
Ciro once read that there are two types of mathematicians/scientists (he thinks it was comparing Einstein to some Jack of all trades polymath who didn't do any new discoveries):
- high flying birds, who know a bit of everything, feel the beauty of each field, but never dig deep in any of them
- gophers, who dig all the way down, on a single subject, until they either get the Nobel Prize, or work on the wrong problem and waste their lives
TODO long after Ciro forgot where he had read this from originally, someone later pointed him to: www.ams.org/notices/200902/rtx090200212p.pdf Birds and Frogs by Freeman Dyson (2009), which is analogous but about Birds and Frogs. So did Ciro's memory play a trick on him, or is there also a variant; of this metaphor with a gopher?
Ciro is without a doubt the bird type. Perhaps the ultimate scientist is the one who can combine both aspects in the right amount?
Ciro gets bored of things very quickly.
Once he understands the general principles, if the thing is not the next big thing, Ciro considers himself satisfied without all the nitty gritty detail, and moves on to the next attempt.
In the field of mathematics for example, Ciro is generally content with understanding cool theorem statements. More generally, one of Ciro's desires is for example to understand the significance of each physics Nobel Prize.
This is also very clear for example after Ciro achieved Linux Kernel Module Cheat: he now had the perfect setup to learn all the Linux kernel shady details but at the same time after all those years he finally felt that "he could do it, so that was enough", and soon moved to other projects.
If Ciro had become a scientist, he would write the best review papers ever, just like in the current reality he writes amazing programming tutorials on Stack Overflow.
Ciro has in his mind an overly large list of subjects that "he feels he should know the basics of", and whenever he finds something in one of those topics that he does not know enough about, he uncontrollably learns it, even if it is not the most urgent thing to be done. Or at least he puts a mention on his "list of sources" about the subject. Maybe everyone is like that. But Ciro feels that he feels this urge particularly strongly. Correspondingly, if a subject is not in that list, Ciro ignores it without thinking twice.
Ciro believes that high flying birds are the type of people better suited for venture capital investment management: you know a bit of what is hot on several fields to enough depth to decide where to place your bets and how to guide them. But you don't have the patience to actually go deeply into any one of them and deal with each individual shit that comes up.
Cosmos: A Personal Voyage (1980) episode 1 mentions as quoted by the Wikipedia page for Eratosthenes:That's Ciro.
According to an entry in the Suda (a 10th-century encyclopedia), his critics scorned him, calling him beta (the second letter of the Greek alphabet) because he always came in second in all his endeavours.
Matrix congruence can be seen as the change of basis of a bilinear form Updated 2025-04-24 +Created 1970-01-01
From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis modifies the matrix representation of a bilinear form as:
So, by taking , we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.
visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) is a good quick visual non-mathematical introduction is to it.
One of the Millennium Prize Problems and Hilbert's problems.
What is the Riemann hypothesis REALLY about? by HexagonVideos (2022)
Source. SGML predecessor.
Subset generators:
- github.com/mf1024/ImageNet-datasets-downloader generates on download, very good. As per github.com/mf1024/ImageNet-Datasets-Downloader/issues/14 counts go over the limit due to bad multithreading. Also unfortunately it does not start with a subset of 1k.
- github.com/BenediktAlkin/ImageNetSubsetGenerator
Unfortunately, since ImageNet is a closed standard no one can upload such pre-made subsets, forcing everybody to download the full dataset, in ImageNet1k, which is huge!
Implosion-type fission weapons are more complicated than gun-type fission weapon because you have to precisely coordinate the detonation of a bunch of explosives.
Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.
And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!
Bibliography:
- www.youtube.com/watch?v=EK_6OzZAh5k How Electron Spin Makes Matter Possible by PBS Space Time (2021)
The scale where human brain simulation becomes possible according to some estimates.
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