Ciro Santilli @cirosantilli 37

Since a matrix $M$ can be seen as a linear map $f_M(\vec{x})$, the product of two matrices $MN$ can be seen as the composition of two linear maps:One cool thing about linear functions is that we can easily pre-calculate this product only once to obtain a new matrix, and so we don't have to do both multiplications separately each time.

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:As usual, we don't know why there aren't elementary particles with other spins, as we could construct them.

Bibliography:

TODO understand a bit more intuitively.

Video "The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)" at youtu.be/dQWn9NzvX4s?t=3707 says that no one has ever been able to come up with an intuitive reason for the proof.

A detailed list of all transactions is kept at: ../sponsor/budget.js.

Ciro Santilli use the following accounting for this sponsorship calculations.

For significant one time donations, he takes the final money received in one of his cash GBP accounts, then he checks how much that is in dollars on Google at the time of cash out, and then writes that amount down as the final dollar value which is what ultimately counts. This exposes Ciro to USD/GBP fluctuations, but it simplifies accounting for donors which is more important, so it is likely worth it.

For small regular donations, Ciro just tallies it all up in GBP from time to time and converts it all to dollars in one go as it is not worth spending too much time updating those too often.

If you pass parallel light.

For a biconvex spherical lens, it is given by:where:

Football is a synonym for association football, can we be done with that! The word "soccer" is an aberration.

See also Ciro Santilli's critique of rooting for sport teams.

Important 4D spaces:

The for loop is a subcase of the while loop.

One theoretical motivation for its existence is that it has the fundamental property that we are immediately certain it will terminate, unlike while loops with arbitrary conditions.

Primitive recursive functions are the complexity class that divides those two.

Atoms exist and last for a long time, while in classical electromagnetic theory punctual orbiting electrons should emit radiation quickly and fall into the nucleus: physics.stackexchange.com/questions/20003/why-dont-electrons-crash-into-the-nuclei-they-orbit

In other sections:

Bibliography:

It should be illegal to give someone money to advertise your product.

We should just use tags and upvote-based algorithms.

Advertisement is a form of brainwashing.

TODO find Sergey Brin quote bout advertising being a form of perverting search engine ranking neutrality. In other words, there are neutral metrics to what people find good, like links and upvotes. And then advertising is a way to pervert that to someone's profit.

Sometimes Ciro Santilli thinks advertising should be on-subscription only, but that is too restrictive, e.g. imagine the local business owner who wears a t-shirt of their business.

The IETF was a notable one: www.nytimes.com/2021/04/13/technology/racist-computer-engineering-terms-ietf.html