(for Xφ, I prefer to define it as relative to a given frame: φ holds the next time any of the frame variables change, which allows both continuous<->discrete translation and for Lamport's stuttering [to allow abstraction!])
Next up: GC via creation and annihilation operators? (in my algebraic view of informatics, one is often either structuring by cleaving two parts to make a whole, or destructuring by cleaving a whole into two parts)
EDIT: and by past-oriented I mean using "was ever" for "eventually" and in the past for "globally", as well as "since" for "until". rotate t by i^2. Eg
dirty := F{edit} U ({save} ∨ {load})
says the local buffer differs from the cloud if there was ever an edit since a save or load.
EDIT 2: ...and I'm pretty sure I can autogenerate code that turns these kinds of def'ns into an imperative event-driven state machine; one can of course come up in theory with formulae that require an arbitrarily complex implementation, but I think in practice most def'ns (especially if we provide backpressure by signalling the complexity of the resulting imp) would be satisfied with simple ones.
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)
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)
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.
"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.
Could be, although I could also imagine the BHA was intending that as a smoke test: if we were to find a putative alien message, we'd want to make sure the same procedure doesn't find other messages in the first N digits of \pi or related constants.
(shouldn't all messages be in \pi sooner or [much, much...] later?)
[does the def'n of "message" include finite length?]
I'd imagine, though, the KST-patched protocol would be to look at how the certain later digits of \pi vary "in realtime" based on where certain earlier digits (of \hbar) tell us to look.. that'd indicate sophisticated control of remote curvature :)
>Sagan's friend physicist Kip Thorne gave Sagan ideas on the nature of wormholes when Sagan was developing the outline of the novel.
(for Xφ, I prefer to define it as relative to a given frame: φ holds the next time any of the frame variables change, which allows both continuous<->discrete translation and for Lamport's stuttering [to allow abstraction!])
Next up: GC via creation and annihilation operators? (in my algebraic view of informatics, one is often either structuring by cleaving two parts to make a whole, or destructuring by cleaving a whole into two parts)
EDIT: and by past-oriented I mean using "was ever" for "eventually" and in the past for "globally", as well as "since" for "until". rotate t by i^2. Eg
says the local buffer differs from the cloud if there was ever an edit since a save or load.EDIT 2: ...and I'm pretty sure I can autogenerate code that turns these kinds of def'ns into an imperative event-driven state machine; one can of course come up in theory with formulae that require an arbitrarily complex implementation, but I think in practice most def'ns (especially if we provide backpressure by signalling the complexity of the resulting imp) would be satisfied with simple ones.