Back to the first post, reversible computing, there is an interesting youtube video on this subject "New Computer Breakthrough is Defying the Laws of Physics", https://www.youtube.com/watch?v=2CijJaNEh_Q&t=34s
On Sat, 18 Jan 2025 at 13:00, Santafe <desm...@santafe.edu> wrote: > Yes, Glen’s final para (and the one before) were the only interpretation I > meant. > > I wasn’t trying to be imaginative at all in the short thing I wrote about > costs in relation to reversibility. Just the plain-vanilla stuff, for the > sake of maybe articulating a theorem within the usual assumptions. > > So, for a classical computer, if I used the expression “well-formed”, I > just meant “computable” in the usual Church-Turing sense, and written in a > representation that does execute on whatever computer one is working with. > So, generates an answer and stops. > > For quantum computers, also deterministic, but in the sense of unitary > evolution of a state. I haven’t spent time learning how this works, so I > just guess at what it must be. If I recall, for Schor’s algorithm to > factor products of primes, one starts with some representation for the > product, then evolves for a while, and at some definite time later, > probability concentrates on a subset of the qubits that indicate what the > factors are, with some probability of ambiguity. Since all this is > unitary, there must be a conserved volume of state space, so I have > supposed that this unitary evolution shouldn’t asymptotically converge > forever on a best-estimator for the factors; rather it should pass through > some best estimator at a finite time and then diverge again into things > that are not easy to interpret. Something like a Poincare cycle. If I am > not wrong in my imagination of how this works, then the thing that would > take the place of halting in the classical computer would be whatever tells > you how long you should evolve before trying to interpret the output, or > else a criterion that the output is as well-concentrated (locally in time) > as it is going to get. Since unitary evolution is reversible (in > idealization), I suppose one could even look for a minimum of wave-function > support, and if one has passed that, back up the computation to get close > to the minimizer state. > > Whereas the notion of “all the computable programs” is believed (as I > understand it) to be defined for a classical Turing machine (even if > uncomputable to enumerate), I have never heard anyone talk about, and > haven’t tried to imagine myself, what all the interpretable inputs to a > quantum computer might be, as some kind of cellularization of the > multi-qubit input state. So I tried to stay away from more than mentioning > quantum computing. > > To try to use these formal models as metaphors for reasoning with > ambiguous methods is of course interesting to do. But I didn’t mean to do > that. To say anything that might have content would require arguing for > some method for using metaphors from the formal world, to the unavailable > world of “reasoning”, and I don’t claim to have anything to offer toward > that. > > Eric > > > > On Jan 14, 2025, at 14:10, glen <geprope...@gmail.com> wrote: > > > > Thanks. I get your answer to (1). I'm still unclear on (2). Yours is > more useful than Frank's because his leaves open what it means in relation > to computation. Both your clause "answer becomes obvious/self-evident" and > Eric's original sense of tautology (with excess) give me some hints at > what's required beyond Frank's. That sense has something to do with the > successive iteration ... like "effectiveness" I guess. If you have a state > and there's no ambiguity in the *next* state, then that sentence has an > inevitable, deterministic successor. I guess it need not even be > deterministic. But a sampling strategy has to be also be well-formed such > that the computation can move along without supervision by a daemon like us > or some outside agent. I.e. well-formed means has a unique inference. I > don't see how it can be a computation without this inevitable chunking > along. > > > > In whatever my poor conception of normal logic is, whatever > transformations/inferences you make on a sentence takes you to another > (true) sentence. But your choice of transformation can take it further from > whatever final form you want, as well as closer to that final form. But > there's a sense of the word "computation" that implies it's completely > mechanical. No logician is needed for the transformations to occur. > > > > Do y'all intend to say such things? I mean, for reversibility to obtain, > it kinda has to be that way, right? You can't have arbitrary branches in > the inferences if you want to restore the initial state from the final > state. Unless, perhaps, you can ensure that the logic, itself, is somehow > convex ... so that every sentence is derivable from every other sentence. > Is that what we're talking about? Sorry for my confusion and thanks for > having the conversation in public! > > > > On 1/13/25 16:49, steve smith wrote: > >> glen asked > >>> Question 2: What does "well-formed" mean in this concept of > computation? > >> 2) I suppose this is EricS's question, but here is my answer. I think > of "well formed questions" being the province of "science" more than > "engineering" or "computation" but am not prepared to say that either are > fundamentally different than "science". In Science I intuit a maxim that > "if the question is well enough crafted, the answer becomes > obvious/self-evident"... some kind of Willem du Occam corollary? 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