Cirism Updated +Created
Welcome to the wonderful world of Cirism!
Followers of Cirism call themselves Cirists, and their primary goal in life is to obtain Cirocoins.
Enlightened Cirists donate money to the cause at: Section "Sponsor Ciro Santilli's work on OurBigBook.com". It is totally optional of course, your soul will just be eternally damned if you don't.
Ciro Santilli once proclaimed:
Thou shalt eat thy watermelon in the morning, and thy melon in the evening. Thou shalt not eat thy watermelon in the evening, nor shalt thou eat thy melon in the morning.
Sylvester's law of inertia Updated +Created
The theorem states that the number of 0, 1 and -1 in the metric signature is the same for two symmetric matrices that are congruent matrices.
For example, consider:
The eigenvalues of are and , and the associated eigenvectors are:
symPy code:
A = Matrix([[2, sqrt(2)], [sqrt(2), 3]])
A.eigenvects()
and from the eigendecomposition of a real symmetric matrix we know that:
Now, instead of , we could use , where is an arbitrary diagonal matrix of type:
With this, would reach a new matrix :
Therefore, with this congruence, we are able to multiply the eigenvalues of by any positive number and . Since we are multiplying by two arbitrary positive numbers, we cannot change the signs of the original eigenvalues, and so the metric signature is maintained, but respecting that any value can be reached.
Note that the matrix congruence relation looks a bit like the eigendecomposition of a matrix:
but note that does not have to contain eigenvalues, unlike the eigendecomposition of a matrix. This is because here is not fixed to having eigenvectors in its columns.
But because the matrix is symmetric however, we could always choose to actually diagonalize as mentioned at eigendecomposition of a real symmetric matrix. Therefore, the metric signature can be seen directly from eigenvalues.
Also, because is a diagonal matrix, and thus symmetric, it must be that:
What this does represent, is a general change of basis that maintains the matrix a symmetric matrix.
Modem router Updated +Created
Solutions of the Schrodinger equation Updated +Created
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.
Uncertainty principle Updated +Created
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.
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 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:
  • to localize the wave in space at position 0 to reduce the space uncertainty, we have to reduce the support. However, doing so makes the momentum variation on the edges more and more important, as the slope will go up and down faster (higher top, and less x space for descent), leading to a larger variance (note that average momentum is still 0, due to to symmetry of the bump function)
  • to localize the momentum as much as possible at 0, we can make the support wider and wider. This makes the bumps at the edges smaller and smaller. However, this also obviously delocalises the wave function more and more, increasing the variance of x
Numerical software Updated +Created
The Dropout Updated +Created
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?
SpaceX Updated +Created
Video 1.
What Elon Musk's 42,000 Satellites Could Do To Earth by Tech Insider (2020)
Source. Good primer. The main difference from older systems is that they fly closer to Earth, and are not geostationary. As a result, you have better latency. But you also need a bunc of them to have continuous coverage of an area.
Generating set of a group Updated +Created
Crime Updated +Created
Video 1.
FBI vs Un-Defuseable Bomb by Qxir (2021)
Source. Tells the story of Harvey's Resort Hotel bombing (1980)
Molecular biology Updated +Created
Bibliography:
It's Popular Now It Sucks Updated +Created
Classical mechanics Updated +Created
University entry exam Updated +Created
These are the most evil examinations society has.
They mean that until you are 18, you have to study a bunch of generic crap you hate just to get into university. Rather than studying whatever it is that you truly love to become a God at it as fast as possible and have any chance of advancing the field.
And then, if you decide that you want to change, which is not unlikely since you haven't really try to study what you signed up for before then, it can be very hard and time consuming, leading to a bunch of adults with useless degress they will never use at work.
With the invention of the Internet, all teaching material can be free and open source. Only laboratory space has any cost (besides the opportunity cost of participation in actual projects in a research team).
Per-country list: en.wikipedia.org/wiki/List_of_admission_tests_to_colleges_and_universities
Post-nominal letters Updated +Created
Cobalt bomb Updated +Created
Mahayana Updated +Created
Mahayana adds a bunch of stuff on top of the Pali Canon. Most of it appears to be random mysticism. Maybe there is something good in it... maybe.
Topological quantum computer Updated +Created
Video 1.
Topological Quantum Computer by Professor John Preskill
. Source.
Video 2.
Topological Quantum Computation by Jason Alicea (2021)
Source.
Video 3.
Anyons by Yuly Billig (2022)
Source.
tig (git UI) Updated +Created
This is good. But it misses some key operations, so much so that makes Ciro not want to learn/use it daily.

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