[gradschoolfail]

Yes 2020.

Does <<the galois theory of algorithms>> throw any light on vNuC? (von Neumann universal constructors, aka(?) the orthographically suggestive “geon”)

P4: >…we have to construct a Hamiltonian whose ground-state energy is dependent on the outcome of a (quantum) computation. This is possible thanks to Feynman and Kitaev’s history state construction used ubiquitously throughout quantum complexity proofs

[Escape hatches of substance, steadfast in starstorms, abstracting into infinity…]

[aebtebeten]

Defo. I should skim vN's book today, but a priori I'd say it's a mechanical instance of generators and structures; the more universal the universe of structures, the larger the class of generators. (and on the flip side, all members of the empty set are universal constructors, capable of making any other member)

To make a uC you need a quine and some generators; the galois connexion above ought to pick out the fixpoints/closed sets. (in particular, we're usually interested in cases where the latter are infinite but the former are finite — the XX continuation of angels* dancing on medieval pinheads)

Lagniappe: https://www.xkcd.com/974/

* I guess now we would say they expended a great deal of intellectual energy on attempting to discern if angels had 0, finite, or infinite measure?

EDIT: if you haven't already, consider that quinoids don't have to exactly self-reproduce, don't have to be quines: one can program "objects" that, upon receiving a message, reproduce themselves and all their response methods (essence) — but with a new state (accident).

[082349872349872]

https://archive.org/details/theoryofselfrepr00vonn_0/page/10... has a shout out (bottom of page) to one of my favourite papers: https://www.rand.org/content/dam/rand/pubs/research_memorand...

Having missed its 64th anniversary, I guess I should plan to get a working implementation of my kleene algebra (quantale) in shape for its 75th?