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? Just an intution/hunch... not a defensible claim.
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