Ciro Santilli @cirosantilli 37

The Busy beaver scale allows us to gauge the difficulty of proving certain (yet unproven!) mathematical conjectures!

To to this, people have reduced certain mathematical problems to deciding the halting problem of a specific Turing machine.

A good example is perhaps the Goldbach's conjecture. We just make a Turing machine that successively checks for each even number of it is a sum of two primes by naively looping down and trying every possible pair. Let the machine halt if the check fails. So this machine halts iff the Goldbach's conjecture is false! See also Conjecture reduction to a halting problem.

Therefore, if we were able to compute $BB(n)$, we would be able to prove those conjectures automatically, by letting the machine run up to $BB(n)$, and if it hadn't halted by then, we would know that it would never halt.

Of course, in practice, $BB$ is generally uncomputable, so we will never know it. And furthermore, even if it were computable, it would take a lot longer than the age of the universe to compute any of it, so it would be useless.

However, philosophically speaking at least, the number of states of the equivalent Turing machine gives us a philosophical idea of the complexity of the problem.

The busy beaver scale is likely mostly useless, since we are able to prove that many non-trivial Turing machines do halt, often by reducing problems to simpler known cases. But still, it is cute.

But maybe, just maybe, reduction to Turing machine form could be useful. E.g. The Busy Beaver Challenge and other attempts to solve BB(5) have come up with large number of automated (usually parametrized up to a certain threshold) Turing machine decider programs that automatically determine if certain (often large numbers of) Turing machines run forever.

So it it not impossible that after some reduction to a standard Turing machine form, some conjecture just gets automatically brute-forced by one of the deciders, this is a path to

Ultimate explanation by Ciro Santilli: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426

Links group homomorphism and the quotient group via normal subgroups.

Almost always too short superficial where it matters unfortunately, as usual.

Most important application: produce X-rays for X-ray crystallography.

Note however that the big experiments at CERN, like the Large Hadron Collider, are also synchrotrons.

List of facilities: en.wikipedia.org/wiki/List_of_synchrotron_radiation_facilities

Uses the frequency of the hyperfine structure of caesium-133 ground state, i.e spin up vs spin down of its valence electron $6s^1$, to define the second.

International System of Units definition of the second since 1967, because this is what atomic clocks use.

TODO why does this have more energy than the hyperfine split of the hydrogen line given that it is further from the nucleus?

Why caesium hyperfine structure is used:

A function that maps two sets to a third set.

You select a generating set of a group, and then you name every node with them, and you specify:

Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the

It is a bit hard to decide if those people are serious or not. Sometimes it feels scammy, but sometimes it feels fun and right!

Particularly concerning is the fact that they are not a not-for-profit entity, and it is hard to understand how they might make money.

Charles Simon, the founder, is pretty focused in how natural neurons work vs artificial neural network models. He has some good explanations of that, and one major focus of the project is their semi open source spiking neuron simulator BrainSimII. While Ciro Santilli believes that there might be insight in that, he also has doubts if certain modules of the brain wouldn't be more suitable coded directly in regular programming languages with greater ease and performance.

FutureAI appears to be Charles' retirement for fun project, he is likely independently wealthy. Well done.

Most commonly known as a byproduct radioactive decay.

Their energy is very high compared example to more common radiation such as visible spectrum, and there is a neat reason for that: it's because the strong force that binds nuclei is strong so transitions lead to large energy changes.

A decay scheme such as Figure "caesium-137 decay scheme" illustrates well how gamma radiation happens as a byproduct of radioactive decay due to the existence of nuclear isomer.

Gamma rays are pretty cool as they give us insight into the energy levels/different configurations of the nucleus.

They have also been used as early sources of high energy particles for particle physics experiments before the development of particle accelerators, serving a similar purpose to cosmic rays in those early days.

But gamma rays they were more convenient in some cases because you could more easily manage them inside a laboratory rather than have to go climb some bloody mountain or a balloon.

The positron for example was first observed on cosmic rays, but better confirmed in gamma ray experiments by Carl David Anderson.

This one strikes the right balance between restriction and permissions. NC and ND are simply too restrictive.

TODO where does the SA boundary end? E.g.:

Does source code need to be redistributed: opensource.stackexchange.com/questions/1849/does-the-cc-by-sa-license-require-that-source-code-of-derivative-works-be-shared

Case law list on the CC wiki: wiki.creativecommons.org/wiki/Category:Case_Law

See: Video "Your Life is Your life by Charles Bukowski".

Examples: square, octahedron.

Take $(0,0,0,\dots ,0)$ and flip one of 0's to $\pm 1$. Therefore has $2\times D$ vertices.

Each edge E is linked to every other edge, except it's opposite -E.

On Baidu Baike: baike.baidu.com/item/扇画/8486689