Ciro Santilli @cirosantilli 35

Originally by Keyhole Inc., which the nbecame Google Maps, but the format seems standardized and has non-Google support, so should be OK.

The busy beaver game consists in finding, for a given $n$, the turing machine with $n$ states that writes the largest possible number of 1's on a tape initially filled with 0's. In other words, computing the busy beaver function for a given $n$.

There are only finitely many Turing machines with $n$ states, so we are certain that there exists such a maximum. Computing the Busy beaver function for a given $n$ then comes down to solving the halting problem for every single machine with $n$ states.

Some variant definitions define it as the number of time steps taken by the machine instead. Wikipedia talks about their relationship, but no patience right now.

The Busy Beaver problem is cool because it puts the halting problem in a more precise numerical light, e.g.:

Bibliography:

This is the one where French Nobel Prizes come from: en.wikipedia.org/wiki/List_of_École_normale_supérieure_people#Nobel_laureates

They are actually inheritable! But alleles are rare: www.ncbi.nlm.nih.gov/pmc/articles/PMC5559844

A single line in the emission spectrum.

So precise, so discrete, which makes no sense in classical mechanics!

Has been the leading motivation of the development of quantum mechanics, all the way from the:

Initially there were mathematical reasons why people suspected that all boson needed to have 0 mass as is the case for photons a gluons, see Goldstone's theorem.

However, experiments showed that the W boson and the Z boson both has large non-zero masses.

So people started theorizing some hack that would fix up the equations, and they came up with the higgs mechanism.