Ciro Santilli @cirosantilli 35

This was the pre-Internet precursor of wikis. This program was likely venerable, shame it predates Ciro Santilli's era.

But the thing was much more bloated it seems, and also included visual programming elements, and WYSISYG UI creation.

square, cube. 4D case known as tesseract.

Convex hull of all $\{-1,1{\}}^D$ (Cartesian product power) D-tuples, e.g. in 3D:

From this we see that there are $2^D$ vertices.

Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.

Ciro Santilli distinctly remembers being taught that at basic electrical engineering school during Ciro Santilli's undergrad studies at the University of São Paulo.

It really allows you to do alternating current calculations much as you'd do DC calculations with resistors, quite poweful. It must have been all the rage in the 1950s.

This was the first major commercial computer hit. Stlil vacuum tube-based.

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

Ice is the name of one of the solid phases of water.

In informal contexts, it usually refers to the phase of ice observed in atmospheric pressure, Ice I_h.

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.

Split in the spectral line when a magnetic field is applied.

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?

Anomalous: evidence of spin.

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.

p splits into 3, d into 5, f into 7 and so on, i.e. one for each possible azimuthal quantum number.

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)".

From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis $C$ modifies the matrix representation of a bilinear form as:

So, by taking $S=C^T$, we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.

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):

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.

Some related ideas:

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:

SGML predecessor.

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.