Ciro Santilli @cirosantilli 37

Kind of extends the complex numbers.

Some facts that make them stand out:

For super-resolution microscopy.

This could have been a Nobel Prize in Physics as well!

TODO how to calculate

Since DNA is the centerpiece of life, Ciro Santilli is extremely excited about DNA-related technologies, see also: molecular biology technologies.

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: