Ciro Santilli @cirosantilli 37

Example: sqlite/ip.c, adapted from www.sqlite.org/loadext.html, also mentioned explained at: stackoverflow.com/questions/7638238/sqlite-ip-address-storage/76520885#76520885.

Sample usage in the test program: sqlite/test.sh.

Docs: www.sqlite.org/loadext.html

Example where this level is sufficient: nodejs/sequelize/raw/parallel_update_async.js.

If session autosave was finally mainlined, this would be Nirvana.

In Physics, in order to test a theory, you must be able to extract a number from it.

It does not matter how, if it is exact, or numerical, or a message from God: a number has to come out of the formulas in the end, and you have to compare it with the experimental data.

Many theoretical physicists seem to forget this in their lectures, see also: Section "How to teach and learn physics".

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:

Project trying to compute BB(5) once and for all. Notably it has better presentation and organization than any other previous effort, and appears to have grouped everyone who cares about the topic as of the early 2020s.

Very cool initiative!

By 2023, they had basically decided every machine: discuss.bbchallenge.org/t/the-30-to-34-ctl-holdouts-from-bb-5/141

In June 2024 they felt that they had verified the result after a full Coq proof was published: So now onto BB(6) I guess.

Just like for the finite general linear group, the definition of special also works for finite fields, where 1 is the multiplicative identity!

Note that the definition of orthogonal group may not have such a clear finite analogue on the other hand.

Survey by Ciro Santilli: math.stackexchange.com/questions/1985/software-for-drawing-geometry-diagrams/3938216#3938216

Many plotting software can be used to create mathematics illustrations. They just tend to have more data-oriented rather than explanatory-oriented output.

In 2019, a paper proved that MTG is Turing complete with a legacy legal deck. Live demo with some hand waving: Video "I Built a COMPUTER in Magic: The Gathering by Because Science (2019)". As Ciro Santilli comments at: github.com/cirosantilli/cirosantilli.github.io/issues/42 this was an interest addition to the previous "indefinite infinite loop" e.g. as found in a Four Horsemen combo deck

Open source ones: