[gradschoolfail]

Thanks for the ref!

Not sure when i’ll get there praying for a serendipitous intersection of cargoculting nonsssociativity and diagram spelunking (aided by your hints, half-remember’d)

Although… i confess to doing the trivial thing of drawing the “cayley graph” of {rock,paper,scissors} and observing that it looks like a loopfree 3-vertex term (1 outgoing)

https://en.wikipedia.com/wiki/Commutative_magma

[082349872349872]

Rock-paper-scissors also gives rise to scenes that are bad for naive sorting (for graphics or CAD), where you have three objects such that any two can be sorted in occlusion order, but not all three.

Can we triage our ikigai such that I (sympathising with my machinery) take all your overly-associative structures and you (communing with the universe?) take all my insufficiently-associative structures?

(there are many in maths: eg topologies, being families of sets, can be represented by a particular magma)

Lagniappe: https://www.georgehart.com/triad.html

[gsf_emergency]

Well ring me when you've a way of categorizing some of the nonrepresentable topologies, I do love any chance to juxtapose those ikigais

https://news.ycombinator.com/item?id=42106477

[082349872349872]

Categorically, while different algebraic structures may not be isomorphic, they're likely all capable (under decoration) of carrying the same information.

For instance, in the Boom Hierarchy* (sets,bags,lists,trees) we can represent the information carried by any of the structures by any of the others (exercise!) despite the fact that operations on that information may be made easier or more difficult by the presence or lack of laws (idempotency,commutativity,associativity) that are the linear delta-edges between those types-as-vertices themselves.

[IIRC, magmas would be mobiles, and I'd bet we can extend the above to them as well.]

* I know I repeat these often, but hey, I'm not alone: gopher-the-language was inspired by a "go" lemma-function in someone's sol'n to samefringe.

[gsf_emergency]

How much work is "likely" doing..

I'd been at peace if you mentioned the triples, but it's too late now..

[082349872349872]

"likely" is not doing much work for the domain I was thinking of: structures which are suitable for making into collection data structures, in that their carrier sets are infinite because their ops don't lose information about the values (the hyle if not the morphe) given by their arguments.

Of course, absent those restrictions, it's doing way more work than it can possibly handle.

[gsf_emergency]

wasn't it our own Carl Sagan who suggested looking into \pi for alien messages (but/and he was perhaps under the influence)

But not the references inside apple boxen