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Okay, mastodon.cloud seems to be beyond repair. So I will be slowly migrating to my accounts @RefurioAnachro for maths stuff, which should be the lot of it, and to @RefurioAnachro 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:

quantamagazine.org/how-mathema

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

pluspora.com/posts/6169256

@visitar is #newhere, let's give a warm welcome to a great supporter of local culture and a good friend!

Gentile blubbering Steve Reich-y electronic space.

#listening to
Patch Notes: Hélène Vogelsinger -
youtube.com/watch?v=kYxheEGl2o
.

Okay, mastodon.cloud seems to be beyond repair. So I will be slowly migrating to my accounts @RefurioAnachro for maths stuff, which should be the lot of it, and to @RefurioAnachro 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.

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 scottaaronson.com/blog/?p=4974

Last time I had asked for intuitions about associativity, @JasonHise64 suggested that associativity is commutativity squared. In retrospect, his suggestion seems much clearer than I had initially been able to see. But I think I got it now. Let's take a look together... (thread)

My 7yo just got quarantined, because someone in his class was tested positive. Apparently, I'm not included. That feels... wrong?

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.

Trying to get my nextcloud's @rf@cloud.digital-gecko.net to follow me. They say my follow would only show up when there's a status update. It certainly feels buggy. And how does one 'look at the protocol'?!?

Don't bother, this is basically just a rather chatty test post.

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!

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John Horton Conway changed the meaning of Life for many of us. He invented surreal numbers, found simple groups - important missing pieces in their classification, wrote a captivating book about quadratic forms, and traded many more cool discoveries for small bits of his hygiene. Thanks to him I'll never forget about the bricks of princeton! I'm sorry that he couldn't live to see the full uncovering of the meaning of the monster group, which will probably take many more decades, if we're lucky.

An enjoyable problem (104.B) from the latest Mathematical Gazette: A regular 7-gon is inscribed in the unit circle, with one vertex at (1,0). Find the equations of the two parabolas, symmetric across the x-axis, which pass through the vertices of the heptagon as shown.

Estimating untested infections. Now there's a publication in Nature about an idea I first learned from @ColinTheMathmo.

nature.com/articles/d41586-020

@dredmorbius

*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 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 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!

@11011110

Square packing: 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 demonstrations.wolfram.com/Pon and 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

mathr.co.uk/blog/2020-01-16_sl

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