bbchallenge.org/story#what-is-known-about-bb lists some (all?) cool examples,

wiki.bbchallenge.org/wiki/Cryptids contains a larger list. In June 2024 it was discovered that BB(6) is hard.

Stopped 2019 apparently. Shame. We need something to be upstreamed!

ECDH has smaller keys. youtu.be/gAtBM06xwaw?t=634 mentions some interesting downsides:

If you can reduce a mathematical problem to the Halting problem of a specific turing machine, as in the case of a few machines of the Busy beaver scale, then using Turing machine deciders could serve as a method of automated theorem proving.

That feels like it could be an elegant proof method, as you reduce your problem to one of the most well studied representations that exists: a Turing machine.

However it also appears that certain problems cannot be reduced to a halting problem... OMG life sucks (or is awesome?): Section "Turing machine that halts if and only if Collatz conjecture is false".

The following things come to mind when you look into research in this area, especially the search for BB(5) which was hard but doable:

Bibliography:

Described at: www.sligocki.com/2022/06/10/ctl.html

Bibliography: discuss.bbchallenge.org/t/decider-translated-cyclers/34

Like a cycler, but the cycle starts at an offset.

To see infinity, we check that if the machine only goes left N squares until reaching the repetition, then repetition must only be N squares long.

Bibliography: discuss.bbchallenge.org/t/decider-cyclers/33

Example: bbchallenge.org/279081.

These are very simple, they just check for exact state repetitions, which obviously imply that they will run forever.

Unfortunately, cyclers may need to run through an initial setup phase before reaching the initial cycle point, which is not very elegant.

Also, we have no way of knowing the initial setup length of the actual cycle length, so we just need an arbitrary cutoff value.

And unfortunately, this can lead to misses, e.g. Skelet machine #1, a 5 state machine, has a (translated) cycle that starts at around 50-200M steps, and takes 8 trillion steps to repeat.

They are pioneers in making superconducting magnets, physicist from the university taking obsolete equipment from the uni to his garage and making a startup kind of situation. This was particularly notable for this time and place.

They became a major supplier for magnetic resonance imaging applications.

Cute synonym for second brain, sample usage: beepb00p.xyz/exobrain/#cntnt

In this solution of the Schrödinger equation, by the uncertainty principle, position is completely unknown (the particle could be anywhere in space), and momentum (and therefore, energy) is perfectly known.

The plane wave function appears for example in the solution of the Schrödinger equation for a free one dimensional particle. This makes sense, because when solving with the time-independent Schrödinger equation, we do separation of variable on fixed energy levels explicitly, and the plane wave solutions are exactly fixed energy level ones.

This is especially interesting for user mode emulation.

User mode emulation refers to the ability of certain emulators to emulate userland code running on top of a specific operating system, usually Linux.

For example, QEMU allows you to run a variety of userland ELF programs directly on it, without an underlying Linux kernel running.

User mode emulation is achieved by implementing system calls and special filesystems such as /dev manually on the emulator one by one.

The general tradeoff is that simulation is less acurate as it may lack certain highly advanced kernel functionality you haven't implemented yet. But it is much easier to run executables with it, and you don't have to wait for boot to finish before running, you just run executables directly from the command line.

Said to be the 5th Google employee, and Eileen Gu's father: gossipnextdoor.com/meet-ray-sidney-eileen-guus-alleged-dad/