That makes much more sense than my flash, which had been following a spark in the other direction:
Delimited continuations are functions, and as such (in a world of algebraic types where we can take sums and products of types) exponentials of types, ran^dom.
[in particular, with the substitution of isomorphism for equality they follow the normal K-12 rules: C^(A+B) ~= C^A * C^B, etc.]
I'd just been glancing at https://en.wikipedia.org/wiki/Convex_conjugate#Examples and the pattern by which single-branched f(x) seems to often become a multibranch f(x) reminded me of how logic-reversing functions in general and logical implication in particular "adds branching": if we wish to establish x'<=5 then if x is already <= 5 we may `skip` but otherwise we must calculate x-5 (and then subtract it off); similarly an implication x->y may be satisfied on one branch by not x but on the other requires y.
[and on the general topic: I like to think of temperature as tying together energy and entropy, where positive temperatures yield the familiar relationships but negative temperatures "unintuitive" ones]
This reverse flash might be what could motivate me to make the connection useful.. an exercise in geometric vengeance (and intuition building) for me to use backtracking DCs in optimization problems (engineering => SDP/IPs)? now to find a plug-and-chug example..
Besides negative T occuring in situations where the arrow of t appears reversed..., PG13 "exponentials turn products into sums"
There is also the pun where S stands for both "action" and "entropy" so that's another direction in which to hunt for the Lagrange multiplier/Lagrangian-Hamiltonian connecting unicorn e.g. picking the "most representative", not necessarily the most optimal path.
I don't know if this counts as an indecent flash, because.. well it is a half-formed opinion (malformed intuition?) born of recent experience..
It's hard to describe this personal experience succinctly, nevertheless I can relate it to wizened physicists often marvelling at having terms miraculously cancel when they engage in the voudou popularly known as path integration
Delimited continuations are functions, and as such (in a world of algebraic types where we can take sums and products of types) exponentials of types, ran^dom.
[in particular, with the substitution of isomorphism for equality they follow the normal K-12 rules: C^(A+B) ~= C^A * C^B, etc.]
I'd just been glancing at https://en.wikipedia.org/wiki/Convex_conjugate#Examples and the pattern by which single-branched f(x) seems to often become a multibranch f(x) reminded me of how logic-reversing functions in general and logical implication in particular "adds branching": if we wish to establish x'<=5 then if x is already <= 5 we may `skip` but otherwise we must calculate x-5 (and then subtract it off); similarly an implication x->y may be satisfied on one branch by not x but on the other requires y.
[and on the general topic: I like to think of temperature as tying together energy and entropy, where positive temperatures yield the familiar relationships but negative temperatures "unintuitive" ones]