Pinned post

Okay, mastodon.cloud seems to be beyond repair. So I will be slowly migrating to my accounts @RefurioAnachro@mathstodon.xyz for maths stuff, which should be the lot of it, and to @RefurioAnachro@toot.cat for other, mostly unix and programming related posts, and possibly some goofing around. Feel free to follow me there, according to your preferences. I'll keep this one for the foreseeable future, but I might not be bothering checking it very often, not only because the server may be down again.

The following ultra-short intro to (co)homology is a reaction to this recent article which appeared on quantamagazine here:

https://www.quantamagazine.org/how-mathematicians-use-homology-to-make-sense-of-topology-20210511/

Thanks to John Wehrle for sharing, and to Andreas Geisler for making me think about it:

Gentile blubbering Steve Reich-y electronic space.

#listening to

Patch Notes: Hélène Vogelsinger -

https://www.youtube.com/watch?v=kYxheEGl2oM

.

I've been wrestling with Cohen's forcing again. And I have questions. Here's what got me restarted into this topic, and much of the following is inspired by it: Scott Aaronson: The Complete Idiot’s Guide to the [...] Continuum Hypothesis: Part 1 https://scottaaronson.com/blog/?p=4974

Follow @mathemensch, he's a nice person, #newhere, and also a model theorist and aspiring algebraic geometer!

I really wish I could pin individual threads in Mastodon (or #glitch) for when I'm following a (or several) interesting conversations.

Folks, get Siobhan Roberts' book "Genius At Play" to learn more about his life, and about his many other results, in game theory, and his work with Martin Gardner, Elwyn Berlekamp and Richard Guy... Invented notations for polyhedra, worked on octonions and number theory, and even published on free will. As he had to, I must end somewhere, but his work lives on! Farewell!

*Programming in 2D text*

This evening I'm thinking of two ideas I've thought about several times before, but never together.

The first: Arjun Nair's https://github.com/batman-nair/IRCIS, an esoteric language (art for art's sake) that comes with a cool visualizer. Maybe all languages should.

The second is Dave Ackley's https://movablefeastmachine.org, a tiled processor for very finely grained distributed computation. Programming it is like playing with a cellular automaton.

Category theory is a very high level tool. Take, for example, the idea of 'universal constructions'. I'd link Wikipedia, but its article comes up with a cat-theoretic description of the idea, which needlessly complicates things. It's a basic technique: Given some constraints, find the most general object (algebra, ...) that satisfies them. It's about interpreting things. It's nonconstructive. Commutative diagrams aren' programs, they're more like equations to be solved.

This is the second time I read about a problem becoming easier in hyperbolic space. I forgot the other one, I'll have to hunt for it! I can see what's happening with TSP here - there must be more problems like this! Thanks for inspiring!

Square packing: http://www.adamponting.com/square-packing/

Adam Ponting found a way to cover arbitrarily large (e.g. as measured by inradius) contiguous patches of the plane by distinct squares of sizes from \(1\) to \((2n+1)^2\), for any \(n\). Via https://demonstrations.wolfram.com/PontingSquarePacking/ and http://www.mathpuzzle.com/

@freemo \ x_{n+1} = r x_n(1 - x_n) \ is a simple enough population model. Lets try simulating it! Oh no...

new blog post summarizing the recent stuff on mating Julia sets that I've been playing with

https://mathr.co.uk/blog/2020-01-16_slow_mating_of_quadratic_julia_sets.html

- g+ blog archive
- https://refurioanachro.github.io/g-viewer/

Higher maths is cool – come and see invisible worlds with me!

Joined Apr 2017