Ciro Santilli @cirosantilli 35

en.wikipedia.org/w/index.php?title=Nutrient&oldid=1075972831#Essential gives somewhat of an overview:

math.stackexchange.com/questions/41706/practical-uses-of-matrix-multiplication/4647422#4647422 highlights deep learning applications.

Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.

Deterministic, but non-local.

A little suspicious that it bears the name of Lorentz, who is famous for special relativity, isn't it? See: Maxwell's equations require special relativity.

Formal name: "plantae".

Measured particle speeds with a rotation barrel! OMG, pre electromagnetism equipment?

Like everything else in Lie group theory, you should first look at the matrix version of this operation: the matrix exponential.

The exponential map links small transformations around the origin (infinitely small) back to larger finite transformations, and small transformations around the origin are something we can deal with a Lie algebra, so this map links the two worlds.

The idea is that we can decompose a finite transformation into infinitely arbitrarily small around the origin, and proceed just like the product definition of the exponential function.

The definition of the exponential map is simply the same as that of the regular exponential function as given at Taylor expansion definition of the exponential function, except that the argument $x$ can now be an operator instead of just a number.

Examples:

Awesome tool to view quick stuff quickly without generating files. Unfortunately it doesn't support all options that the ffmpeg CLI supports, e.g. ffplay multiple input files. One day, one day.

TODO it would be awesome if we could de-generalize the equations in 2D and do a JavaScript demo of it!

Not sure it is possible though because the curl appears in the equations:

An efficient algorithm to calculate the discrete Fourier transform.

Ciro Santilli is just too old to understand what the point of that website is compared to Twitter. There must be one, right?

Also, it is impossible to use it on the browser without a cell phone, similar critique as Section "Messaging software that force you to have a mobile phone" but a bit more aggravating, because, well, you would expect creators want people to see their stuff on a browser unlike private messages?

Published as "Fine Structure of the Hydrogen Atom by a Microwave Method" by Willis Lamb and Robert Retherford (1947) on Physical Review. This one actually has open accesses as of 2021, miracle! journals.aps.org/pr/pdf/10.1103/PhysRev.72.241

Microwave technology was developed in World War II for radar, notably at the MIT Radiation Laboratory. Before that, people were using much higher frequencies such as the visible spectrum. But to detect small energy differences, you need to look into longer wavelengths.

This experiment was fundamental to the development of quantum electrodynamics. As mentioned at Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Shrinking the infinities", before the experiment, people already knew that trying to add electromagnetism to the Dirac equation led to infinities using previous methods, and something needed to change urgently. However for the first time now the theorists had one precise number to try and hack their formulas to reach, not just a philosophical debate about infinities, and this led to major breakthroughs. The same book also describes the experiment briefly as:

It is two pages and a half long.

They were at Columbia University in the Columbia Radiation Laboratory. Robert was Willis' graduate student.

Previous less experiments had already hinted at this effect, but they were too imprecise to be sure.