4 ms·

Thanks, all this looks helpful, will let my subconscious meditate on "desingularization(-singularization)" with regards to what I just read. https://en.wikiped

Thanks, all this looks helpful, will let my subconscious meditate on "desingularization(-singularization)" with regards to what I just read. https://en.wikipedia.org/wiki/Graph_C*-algebra#Desingularization https://en.wikipedia.org/wiki/Graph_C*-algebra#Desingulariza... Especially enjoyed the mention of the Ycombinator, my barbaric nonintuition would have been that nothing so activated could arise from 2 (or just the 1!?! beta-reduction) seemingly trivial constructs, but this punches me in the face like Mike Tyson says (and continuously, in the gut) (I admit I am not in the pareidolic flow ATM, but promise to take a long look at these passages when I am) Scott=Aaronson? Do you have a link?

vinnyvichy 2y ago
EDIT: My barbaric/peasant state of intuition says that K is more like a differential equation (Maxwell's equations) but S is more akin to the "integral form" (Jefimenko's) Note how the People feel like they understand M but for J they feel at least a bit of wariness.. And thanks for the JCS quote, it does feel relevant to the struggle to even design useful quantum computers Going back to mulling the Lagrange multipliers now :) Pace Darwin, the anglo geniuses seem generally trigger happy -- not good for HN idolatry (up to and including the manPG) (Grassmann vs Hamilton, if you want to visit that general topic) (JM Keynes vs..?)
- 082349872349872 2y ago
  > the struggle to even design useful quantum computers My knee-jerk question for the last few decades (which I probably st^Wliberated from MGM?) is "given that we succeed in decoupling the system enough to accomplish some quantum computation, how do we expect to be coupling it enough to feed the problem in and write the results out?"
  - vinnyvichy 2y ago
    As usual the childlike questions are the hardest ..
082349872349872 2y ago
Dana Scott; I found https://www.cs.ox.ac.uk/files/298/handbook.pdf https://www.cs.ox.ac.uk/files/298/handbook.pdf helpful before reading him directly. (he started off trying to formalise denotational semantics with powersets, and only after failing there fell back to dcpo's; recently I was reading something about the one-to-one correspondence between finite posets and finite topologies which implied that for the infinite case he should've expected to wind up with dcpo's in general when the particular nice cases are lattices, but now I'm blanking on what [and where] it was. Slogan: computer scientists prefer their models topless.) https://github.com/CMU-HoTT/scott/ https://github.com/CMU-HoTT/scott/ looks like a nice collection! I also liked Scott & Rabin 1958, but HN didn't. https://hn.algolia.com/?q=Finite+Automata+and+Their+Decision+Problems https://hn.algolia.com/?q=Finite+Automata+and+Their+Decision...
082349872349872 2y ago
Huh, I'm extremely ignorant of C*-algebras (yet another area where JvN seems to have already been stomping around!) but the expansion between https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:Desingularization-1.jpg https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:D... and https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:Desingularization-2.jpg https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:D... really reminds me of Kleene-star expansion from A* to 1|A|AA|AAA|... `*` is an involution in C*, however, and in Kleene `*` is idempotent. Funnily enough, I've written a codegen with an involutive `*`: if one has Dijkstra-style IF...FI and DO...OD constructs in the intermediate language, it's possible to generate reasonable code in such a manner that (merely by patching all the jumps appropriately) one can round trip both IF->DO->IF and DO->IF->DO, with IF->DO corresponding to "star" and DO->IF corresponding to what Conway(?) called the "starth-root". (Just as LISP got LABEL very early and LABELS relatively late, I think a great deal of harm has been done because data processing, from the card era up through early micros, had harsh pragmatic reasons to analyse A* as 1|AA*, yet many things simplify by multiplying cases in the pursuit of symmetry, and instead analysing A* as 1|A|A*A*)
- vinnyvichy 2y ago
  To productive puns! And as Gr might have said, ignorance is the mother of discovery (and other beasts) Glancing at Scott-Rabin I couldn't find any mention of powersets but on p7 his count of "between indices" sounds like he was enumerating a power set. Or did you have some other passages in mind?
  - 082349872349872 2y ago
    Not that far back... Try around 1970? In PRG-2* he's still thinking along the lines of "AXIOM 3. A data type is a complete lattice under its partial ordering." (p9) https://www.cs.ox.ac.uk/files/3222/PRG02.pdf https://www.cs.ox.ac.uk/files/3222/PRG02.pdf * I loved FJD's mention of '[Maxwell] gave a presidential address ... which was published in volume 2 of the recently founded journal "Nature".'

vinnyvichy 2y ago

EDIT: My barbaric/peasant state of intuition says that K is more like a differential equation (Maxwell's equations) but S is more akin to the "integral form" (Jefimenko's) Note how the People feel like they understand M but for J they feel at least a bit of wariness.. And thanks for the JCS quote, it does feel relevant to the struggle to even design useful quantum computers Going back to mulling the Lagrange multipliers now :) Pace Darwin, the anglo geniuses seem generally trigger happy -- not good for HN idolatry (up to and including the manPG) (Grassmann vs Hamilton, if you want to visit that general topic) (JM Keynes vs..?)

082349872349872 2y ago
> the struggle to even design useful quantum computers My knee-jerk question for the last few decades (which I probably st^Wliberated from MGM?) is "given that we succeed in decoupling the system enough to accomplish some quantum computation, how do we expect to be coupling it enough to feed the problem in and write the results out?"
- vinnyvichy 2y ago
  As usual the childlike questions are the hardest ..

082349872349872 2y ago

Dana Scott; I found https://www.cs.ox.ac.uk/files/298/handbook.pdf https://www.cs.ox.ac.uk/files/298/handbook.pdf helpful before reading him directly. (he started off trying to formalise denotational semantics with powersets, and only after failing there fell back to dcpo's; recently I was reading something about the one-to-one correspondence between finite posets and finite topologies which implied that for the infinite case he should've expected to wind up with dcpo's in general when the particular nice cases are lattices, but now I'm blanking on what [and where] it was. Slogan: computer scientists prefer their models topless.) https://github.com/CMU-HoTT/scott/ https://github.com/CMU-HoTT/scott/ looks like a nice collection! I also liked Scott & Rabin 1958, but HN didn't. https://hn.algolia.com/?q=Finite+Automata+and+Their+Decision+Problems https://hn.algolia.com/?q=Finite+Automata+and+Their+Decision...

082349872349872 2y ago

Huh, I'm extremely ignorant of C*-algebras (yet another area where JvN seems to have already been stomping around!) but the expansion between https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:Desingularization-1.jpg https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:D... and https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:Desingularization-2.jpg https://en.wikipedia.org/wiki/Graph_C*-algebra#/media/File:D... really reminds me of Kleene-star expansion from A* to 1|A|AA|AAA|... `*` is an involution in C*, however, and in Kleene `*` is idempotent. Funnily enough, I've written a codegen with an involutive `*`: if one has Dijkstra-style IF...FI and DO...OD constructs in the intermediate language, it's possible to generate reasonable code in such a manner that (merely by patching all the jumps appropriately) one can round trip both IF->DO->IF and DO->IF->DO, with IF->DO corresponding to "star" and DO->IF corresponding to what Conway(?) called the "starth-root". (Just as LISP got LABEL very early and LABELS relatively late, I think a great deal of harm has been done because data processing, from the card era up through early micros, had harsh pragmatic reasons to analyse A* as 1|AA*, yet many things simplify by multiplying cases in the pursuit of symmetry, and instead analysing A* as 1|A|A*A*)

vinnyvichy 2y ago
To productive puns! And as Gr might have said, ignorance is the mother of discovery (and other beasts) Glancing at Scott-Rabin I couldn't find any mention of powersets but on p7 his count of "between indices" sounds like he was enumerating a power set. Or did you have some other passages in mind?
- 082349872349872 2y ago
  Not that far back... Try around 1970? In PRG-2* he's still thinking along the lines of "AXIOM 3. A data type is a complete lattice under its partial ordering." (p9) https://www.cs.ox.ac.uk/files/3222/PRG02.pdf https://www.cs.ox.ac.uk/files/3222/PRG02.pdf * I loved FJD's mention of '[Maxwell] gave a presidential address ... which was published in volume 2 of the recently founded journal "Nature".'