Elements of the orthogonal group have determinant plus or minus one by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
All groups are isomorphic to a subgroup of the symmetric group by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Or in other words: symmetric groups are boring, because they are basically everything already!
State initialization (quantum computing) by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
I like relativistic quantum mechanics.
Best mathematical explanation: Section "Spin comes naturally when adding relativity to quantum mechanics".
Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles" has an amazing summary of the preceding chapters the spin value has a relation to the representations of the Lorentz group, which encodes the spacetime symmetry that each particle observes. These symmetries can be characterized by small integer numbers:
- spin 0: representation
- spin half: representation
- spin 1: representationAs usual, we don't know why there aren't elementary particles with other spins, as we could construct them.
Basically a synonym for doing a large chunk of de novo DNA synthesis.
Schrödinger equation for a free one dimensional particle by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Schrödinger equation for a one dimensional particle with . The first step is to calculate the time-independent Schrödinger equation for a free one dimensional particle
Then, for each energy , from the discussion at Section "Solving the Schrodinger equation with the time-independent Schrödinger equation", the solution is:Therefore, we see that the solution is made up of infinitely many plane wave functions.
Solutions for the Schrodinger equation with multiple particles by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Bibliography:
- Quantum Mechanics for Engineers by Leon van Dommelen (2011) "5. Multiple-Particle Systems"
The correlation between software engineers and Buddhism by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli believes that there is a positive correlation between being a software engineer and liking Buddhist-like things.
Maybe it is linked to minimalism and DRY, which software engineers value so greatly.
Even Ciro had to try an unoriginal Buddhist joke intro in one of this Stack Overflow answers.
Ciro also feels that his "minimal reproducible example" scientific language/concept learning method obsession of breaking things into tiny sub-problems has a strong link with Koans.
Some notable Buddhism/programmer examples:
- www.catb.org/~esr/writings/unix-koans/ "The Unix Koans of Master Foo - Rootless Root (无根的根)" by the legendary Eric Steven Raymond is notable
- thecodelesscode.com/ "The Codeless Code" by anonymous Qi.
- canonical.org/~kragen/tao-of-programming.html
- wiki.c2.com/?MysticalProgrammingKoans
- rubykoans.com/ even evil programming languages adopt them!
- The Zen of Python
Another thing that points the correlation out is the existence of wattsalan.github.io/ on a
github.io
about Alan Watts.Reuploaded into the blockchain itself: bitcoin.stackexchange.com/questions/35959/how-is-the-whitepaper-decoded-from-the-blockchain-tx-with-1000x-m-of-n-multisi/105574#105574 by using the Satoshi uploader.
More conveniently available on bitcoin.org: bitcoin.org/bitcoin.pdf nowadays, except when it was down for a few years due to our master Craig Steven Wright.
Romantic Warrior by Return to Forever (1976) by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
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