Democracy Updated 2025-07-16
Tax Updated 2025-07-16
Good video game to watch Updated 2025-07-16
This is a list of video games that are good to watch other people playing, even if you don't play yourself. And often they are better to watch than to play as you don't have to waste your time as much!
Cool person Updated 2025-07-16
While Ciro Santilli is a big fan of having "one global country" (and language), which is somewhat approximated by globalization, he has come to believe that there is one serious downside to globalization as it stands in 2020: it allows companies to pressure governments to reduce taxes, and thus reduces the power of government, which in turn increases social inequality. This idea is very well highlighted in Can't get you out of my head by Adam Curtis (2021).
The only solution seems to be for governments to get together, and make deals to have fair taxation across each other. Which might never happen.
Cayley graph Updated 2025-07-16
You select a generating set of a group, and then you name every node with them, and you specify:
  • each node by a product of generators
  • each edge by what happens when you apply a generator to each element
Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the
Cycle of an element of a group Updated 2025-07-16
Take the element and apply it to itself. Then again. And so on.
In the case of a finite group, you have to eventually reach the identity element again sooner or later, giving you the order of an element of a group.
The continuous analogue for the cycle of a group are the one parameter subgroups. In the continuous case, you sometimes reach identity again and to around infinitely many times (which always happens in the finite case), but sometimes you don't.
A Mathematician's Apology Updated 2025-07-16
With major mathematicians holding ideas such as:
Exposition, criticism, appreciation, is work for second-rate minds. [...] It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.
it is not surprise that the state of STEM education is so shit as of 2020, especially at the the missing link between basic and advanced! This also implies that the number of people that can appreciate any advanced mathematics research is tiny, and consequently so is the funding.
Multidimensional Fourier transform Updated 2025-07-16
Lecture notes:
Video 1.
How the 2D FFT works by Mike X Cohen (2017)
Source. Animations showing how the 2D Fourier transform looks like for simple inpuf functions.
Fourier inversion theorem Updated 2025-07-16
A set of theorems that prove under different conditions that the Fourier transform has an inverse for a given space, examples:
Laplace transform Updated 2025-07-16
Video 1.
The Laplace Transform: A Generalized Fourier Transform by Steve Brunton (2020)
Source. Explains how the Laplace transform works for functions that do not go to zero on infinity, which is a requirement for the Fourier transform. No applications in that video yet unfortunately.
Zermelo-Fraenkel set theory Updated 2025-10-14
One of the first formal proof systems. This is actually understandable!
This is Ciro Santilli-2020 definition of the foundation of mathematics (and the only one he had any patience to study at all).
TODO what are its limitations? Why were other systems created?
Calysta Updated 2025-07-16
Sea shanty Updated 2025-07-16

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