Ciro Santilli @cirosantilli  40

First proper nearest galaxy to the Milky Way. Everything in the middle in the Local group is either a satellite of the Milky Way or Andromeda.

Many Andromeda satellite galaxies are simply numbered Andromeda II, Andromeda III and so on.

As described on Wikipedia, the observational history of Andromeda is fascinating. Little by little, people noticed that it had a different nature to many other objects observed on the sky, and the hypothesis that there are other galaxies like ours grew in force.

Part of our fascination with Andromeda is due to how similar in size and shape and close it is to the Milky Way.

It is clearly the only thing so large and so close.

Andromeda is, without a doubt, our sister galaxy.

One can't help but wonder if there is some alien looking back at us when we are looking at them through our telescope.

Andromeda is also the furthest object from Earth that can be seen with the naked eye.^[ref] Not surprising, as it literally shines with the strength of a trillion suns!

Once again, relies on superconductivity to reach insane magnetic fields. Superconductivity is just so important.

Ciro Santilli saw a good presentation about it once circa 2020, it seems that the main difficulty of the time was turbulence messing things up. They have some nice simulations with cross section pictures e.g. at: www.eurekalert.org/news-releases/937941.

There is a Turing machine that halts for every member of the language with the answer yes, but does not necessarily halt for non-members.

Non-examples: cs.stackexchange.com/questions/52503/non-recursively-enumerable-languages

Subset of recursively enumerable language as explained at: difference between recursive language and recursively enumerable language.

This is the classic result of formal language theory, but there is too much slack between context free and context sensitive, which is PSPACE (larger than NP!).

By Noam Chomsky.

A good summary table that opens up each category much more can be seen e.g. at the bottom of en.wikipedia.org/wiki/Automata_theory under the summary thingy at the bottom entitled "Automata theory: formal languages and formal grammars".

The opposite of from first principles.