6 ms·

The S part makes sense as does https://en.wikipedia.org/wiki/Exponential_object#Examples https://en.wikipedia.org/wiki/Exponential_object#Examples (I am guess

The S part makes sense as does https://en.wikipedia.org/wiki/Exponential_object#Examples https://en.wikipedia.org/wiki/Exponential_object#Examples (I am guessing their eval is your `apply`) Your explanation of K doesn't make sense ATM but I get the vague sense that K is "dual" to S, so maybe I should start with that?

082349872349872 2y ago
while meditating on K (but not the KKK of the Kataastaasan Kagalangalangang Katipunan): > (I am guessing their eval is your `apply`) Almost: their eval is the result of evaluating my `apply`, so "fac `apply` 6" expands to "1 if 6<=1 else 6 * fac `apply` (6-1)" which can then be evaluated to "720"; the evaluation of the application is their `eval`, for which fac:ℕ^ℕ * 6:ℕ -> 720:ℕ. (I guess my `apply`, being B^A * A -> B^1, is still isomorphic to their eval, so it does depend upon what "is" is) > And are the SKI uphill or downhill derivatives :)? With that in mind, `I` is obviously a flat derivative, that just walks along contour lines... Assuming we're following Lee's injunction to "be like water" (the path of the 10'000 things?), then `K` would be downhill, for it's always easy to throw away/project out/forget the inessential. `S` would then be uphill, but in a special way: unless we're doing something special, like S(K(SII))(S(S(KS)K)(K(SII))), we want to go "uphill", but towards a pass; we're trying to use the application to build an "activated complex"* which will then spontaneously (via evaluation) ultimately reach a value, downhill from where we started. What is `∇` in this model? * https://en.wikipedia.org/wiki/Activated_complex https://en.wikipedia.org/wiki/Activated_complex ; you don't see it in the typical 1-D slice pictured, but that transition state is a saddle point in the full parameter space.
- 082349872349872 2y ago
  ... and thinking about how their `eval` is continuous: Turing's argument for building his machine to work on an infinite tape of squares holding a finite number of symbols: https://news.ycombinator.com/item?id=41048777 https://news.ycombinator.com/item?id=41048777 , makes sense for human (and machine) computers, but presumably gods (and angels, and therefore demons and devils?) can make infinitely fine distinctions "at a glance", so they could build a machine with a single square and an infinite number of symbols instead. However, angelic lambda calculus fails to have any models, for there'd be an infinite regress in the cardinality of higher order functions. If my understanding of Scott is correct, it's the continuity of the exponential and its `eval` which keep higher order functions from "blowing up", and so (although they could presumably do everything in O(1) with infinite lookup tables) if they actually wish to compute in Heaven they'd have to do it pretty much like we do. As below, so above... > It did not last: the Devil howling 'Ho, Let Einstein be,' restored the status quo. —JCS
  - vinnyvichy 2y ago
    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 ..
    - 2y ago
082349872349872 2y ago
a tangent on K (that's been a dead end for me for 3 decades now, so maybe you'll have better luck?): - K takes one argument and throws it away. - S takes one argument and duplicates it. Pareidoliacally, this is reminiscent of how in simplices: - face maps forget and go down, eg face to edge. - degeneracy maps "duplicate" and go up, eg from edge to degenerate "face". Is there a way we could come up with a computational equivalent of Stoke's theorem? https://wikimedia.org/api/rest_v1/media/math/render/svg/7e32dee0e809fa85b6ad7475e4b4c14c9bc17242 https://wikimedia.org/api/rest_v1/media/math/render/svg/7e32... restating those integrals in braket notation because HN isn't so ∳ friendly: <∂o|x> = <o|dx> Squiggol and origami programming seems like it ought to lead there, but maybe I've been following Leibniz too much and instead ought to have used some Newtonian astrology? (that said, the residuation operator in semigroups, and hence quantales, does seem to have a liminal ability to move between bras and kets, at least for certain well-defined substructures: those for which moving between all possible suffixes and all possible prefixes, double time-reversal, is a round trip)
- vinnyvichy 2y ago
  Thanks, I fancy myself an expert pareidoliac! Trying to keep the sarcasm productive, I see:) well at least you seem to enjoy it. I'm surprised you didn't critique Sussman's (& Felleisen?)'s conflation with E&M further, didn't they try this angle already? Actually, seems like they didn't take it far enough so that video is going into the queue.. If the obstinate shall both delve and spin, who then will.. (Isayevicha blagoslovi!) Okay, the quantales seem to be another useful generator of examples
  - 082349872349872 2y ago
    Yaakov Isayevich or Isav Isayevich? (I didn't get the impression SICM attempted to go beyond simple coding? Please let me know if I should delve into it...) Aha! TIL the reference behind the reference in "tripping like birthright": https://www.youtube.com/watch?v=-TQmo5TvZQY&t=116s https://www.youtube.com/watch?v=-TQmo5TvZQY&t=116s > Tēnei te tangata pūhuruhuru / Nāna nei i tiki mai whakawhiti te rā —TR Nā ka mea a Hākopa ki a Rīpeka, ki tōna whaea, Na ko Ehau, ko tōku tuakana, he tangata pūhuruhuru, ko ahau ia he kiri maheni

082349872349872 2y ago

while meditating on K (but not the KKK of the Kataastaasan Kagalangalangang Katipunan): > (I am guessing their eval is your `apply`) Almost: their eval is the result of evaluating my `apply`, so "fac `apply` 6" expands to "1 if 6<=1 else 6 * fac `apply` (6-1)" which can then be evaluated to "720"; the evaluation of the application is their `eval`, for which fac:ℕ^ℕ * 6:ℕ -> 720:ℕ. (I guess my `apply`, being B^A * A -> B^1, is still isomorphic to their eval, so it does depend upon what "is" is) > And are the SKI uphill or downhill derivatives :)? With that in mind, `I` is obviously a flat derivative, that just walks along contour lines... Assuming we're following Lee's injunction to "be like water" (the path of the 10'000 things?), then `K` would be downhill, for it's always easy to throw away/project out/forget the inessential. `S` would then be uphill, but in a special way: unless we're doing something special, like S(K(SII))(S(S(KS)K)(K(SII))), we want to go "uphill", but towards a pass; we're trying to use the application to build an "activated complex"* which will then spontaneously (via evaluation) ultimately reach a value, downhill from where we started. What is `∇` in this model? * https://en.wikipedia.org/wiki/Activated_complex https://en.wikipedia.org/wiki/Activated_complex ; you don't see it in the typical 1-D slice pictured, but that transition state is a saddle point in the full parameter space.

082349872349872 2y ago
... and thinking about how their `eval` is continuous: Turing's argument for building his machine to work on an infinite tape of squares holding a finite number of symbols: https://news.ycombinator.com/item?id=41048777 https://news.ycombinator.com/item?id=41048777 , makes sense for human (and machine) computers, but presumably gods (and angels, and therefore demons and devils?) can make infinitely fine distinctions "at a glance", so they could build a machine with a single square and an infinite number of symbols instead. However, angelic lambda calculus fails to have any models, for there'd be an infinite regress in the cardinality of higher order functions. If my understanding of Scott is correct, it's the continuity of the exponential and its `eval` which keep higher order functions from "blowing up", and so (although they could presumably do everything in O(1) with infinite lookup tables) if they actually wish to compute in Heaven they'd have to do it pretty much like we do. As below, so above... > It did not last: the Devil howling 'Ho, Let Einstein be,' restored the status quo. —JCS
- vinnyvichy 2y ago
  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 ..
  - 2y ago

082349872349872 2y ago

a tangent on K (that's been a dead end for me for 3 decades now, so maybe you'll have better luck?): - K takes one argument and throws it away. - S takes one argument and duplicates it. Pareidoliacally, this is reminiscent of how in simplices: - face maps forget and go down, eg face to edge. - degeneracy maps "duplicate" and go up, eg from edge to degenerate "face". Is there a way we could come up with a computational equivalent of Stoke's theorem? https://wikimedia.org/api/rest_v1/media/math/render/svg/7e32dee0e809fa85b6ad7475e4b4c14c9bc17242 https://wikimedia.org/api/rest_v1/media/math/render/svg/7e32... restating those integrals in braket notation because HN isn't so ∳ friendly: <∂o|x> = <o|dx> Squiggol and origami programming seems like it ought to lead there, but maybe I've been following Leibniz too much and instead ought to have used some Newtonian astrology? (that said, the residuation operator in semigroups, and hence quantales, does seem to have a liminal ability to move between bras and kets, at least for certain well-defined substructures: those for which moving between all possible suffixes and all possible prefixes, double time-reversal, is a round trip)

vinnyvichy 2y ago
Thanks, I fancy myself an expert pareidoliac! Trying to keep the sarcasm productive, I see:) well at least you seem to enjoy it. I'm surprised you didn't critique Sussman's (& Felleisen?)'s conflation with E&M further, didn't they try this angle already? Actually, seems like they didn't take it far enough so that video is going into the queue.. If the obstinate shall both delve and spin, who then will.. (Isayevicha blagoslovi!) Okay, the quantales seem to be another useful generator of examples
- 082349872349872 2y ago
  Yaakov Isayevich or Isav Isayevich? (I didn't get the impression SICM attempted to go beyond simple coding? Please let me know if I should delve into it...) Aha! TIL the reference behind the reference in "tripping like birthright": https://www.youtube.com/watch?v=-TQmo5TvZQY&t=116s https://www.youtube.com/watch?v=-TQmo5TvZQY&t=116s > Tēnei te tangata pūhuruhuru / Nāna nei i tiki mai whakawhiti te rā —TR Nā ka mea a Hākopa ki a Rīpeka, ki tōna whaea, Na ko Ehau, ko tōku tuakana, he tangata pūhuruhuru, ko ahau ia he kiri maheni