Ciro Santilli @cirosantilli 37

For a quick and dirty introduction to the format, see: ELF Hello World Tutorial.

Formal name: "fungi".

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: