Ciro Santilli @cirosantilli 37

A function that maps two sets to a third set.

This is perhaps slightly worse than the Tinker Tailor Soldier Spy, but still amazing.

Some difficult points:

And do 5 big queries instead of hundreds of smaller ones.

For example, a README.ciro document that references another document saying:needs to fetch "speed-of-light" from the ID database (previously populated e.g. by preparsing light.ciro:to decide that it should display as "Speed of light" (the title rather than the ID).

Previously, I was doing a separate fetch for each \x[] as they were needed, leading to hundreds of them at different times.

Now I refactored things so that I do very few database queries, but large ones that fetch everything during parsing. And then at render time they are all ready in cache.

This will be fundamental for the live preview on the browser, where the roundtrip to server would make it impossible

Examples: square, octahedron.

Take $(0,0,0,\dots ,0)$ and flip one of 0's to $\pm 1$. Therefore has $2\times D$ vertices.

Each edge E is linked to every other edge, except it's opposite -E.

On Baidu Baike: baike.baidu.com/item/扇画/8486689

A superstar security researcher with some major exploits from in the 2000's.

Analogous problem to the secondary structure of proteins. Likely a bit simpler due to the strong tendency for complementary pairs to bind.

The $U(1)$ unitary group is one very over-generalized way of looking at it :-)

As always, the best way to get some intuition about an equation is to solve it for some simple cases, so let's give that a try with different fixed potentials.

I've finally had enough of Nvidia breaking my Ubuntu 21.10 suspend, so I investigated some more and found a workaround on the NVIDIA forums: stackoverflow.com/questions/58233482/next-js-setting-up-eslint-for-nextjs/70519682#70519682.

Thanks enormously to heroic user humblebee, and once again, Nvidia, fuck you.

It is good to watch the Out For blood in Silicon Valley (2019) documentary after this to see how the characters look like in real life. Many feel amazingly cast, very close to the original. The only great exception is the Indian dude, who is completely different. Was it that hard to find some indian dude who looked and felt a little more like the real one?

The wave equation contains the entire state of a particle.

From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.

And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.

More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.

When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.

This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".

Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in $L^2$ due to Carleson's theorem.

Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle

In precise terms, the uncertainty principle talks about the standard deviation of two measures.

We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:

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