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And are the SKI uphill or downhill derivatives :)? To help you listen more productively to 孝德公 https://lirias.kuleuven.be/retrieve/678705 https://lirias.kuleu

And are the SKI uphill or downhill derivatives :)? To help you listen more productively to 孝德公 https://lirias.kuleuven.be/retrieve/678705 https://lirias.kuleuven.be/retrieve/678705 So that you can start thinking about the (full) SpeKtrum of gumi(←♦→)ity Btw, looking for a starting point to engage in patrocinium I discovered again your comment on patrocinium https://news.ycombinator.com/item?id=40691384 https://news.ycombinator.com/item?id=40691384 And to iterate: we need more than dichotomy (maybe three combinators?) I mean, why are you so sure that the ingredient necessary to break the "generalized (cognitive) prisoners dilemma" is not "an epsilon of payout (up to sign)"? Seems like undue arrogance to act or not act on your certainty? >We cannot rule out the possibility that this ambivalence may have been intentional on Philodemus’s part Boy someone needs to formalize this G

vinnyvichy 2y ago
(c'mon bro, admit it, you have empathy for the housecats) It's more crucial to have empathy for the pigeons
- 082349872349872 2y ago
  To show the proper peristophilia (would this be the peristophilandum?): `K` forgets an argument; `eval` forgets the differences between all the syntaxes that share a semantic denotation; eg, "1*1" and "1" are very different (even their lengths are different) as strings, but they both evaluate to 1. (I believe this before-and-after-evaluation is what drives the utility of intuitionist logic in informatics; it's difficult for pre-eval `not` to be crisp) `S` grafts an argument into multiple places in an expression tree; `apply` does the same (in a lazy* language it even avoids the gratuitous eval of args); eg "fac `apply` 6" reduces directly to "1 if 6<=1 else 6 * fac `apply` (6-1)", in which the 6 has been grafted in triplicate. Does that make sense? * I guess the sage would always write code such that it doesn't matter if evaluation be eager or lazy or even somewhere in between (cf https://news.ycombinator.com/item?id=40947303 https://news.ycombinator.com/item?id=40947303 ), but I have yet to figure out how to manage that... EDIT: [pedantry] FI salonkikelpoinen started with LA sella resulting in IT sala, salone going through FR salon by way of DE salonfähig
  - vinnyvichy 2y ago
    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

(c'mon bro, admit it, you have empathy for the housecats) It's more crucial to have empathy for the pigeons

082349872349872 2y ago
To show the proper peristophilia (would this be the peristophilandum?): `K` forgets an argument; `eval` forgets the differences between all the syntaxes that share a semantic denotation; eg, "1*1" and "1" are very different (even their lengths are different) as strings, but they both evaluate to 1. (I believe this before-and-after-evaluation is what drives the utility of intuitionist logic in informatics; it's difficult for pre-eval `not` to be crisp) `S` grafts an argument into multiple places in an expression tree; `apply` does the same (in a lazy* language it even avoids the gratuitous eval of args); eg "fac `apply` 6" reduces directly to "1 if 6<=1 else 6 * fac `apply` (6-1)", in which the 6 has been grafted in triplicate. Does that make sense? * I guess the sage would always write code such that it doesn't matter if evaluation be eager or lazy or even somewhere in between (cf https://news.ycombinator.com/item?id=40947303 https://news.ycombinator.com/item?id=40947303 ), but I have yet to figure out how to manage that... EDIT: [pedantry] FI salonkikelpoinen started with LA sella resulting in IT sala, salone going through FR salon by way of DE salonfähig
- vinnyvichy 2y ago
  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