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I would argue that no actually searchable solution space is really infinite (if only because infinite turing machines can't exist). Finite solution spaces can g
by shkkmo 2y ago
I would argue that no actually searchable solution space is really infinite (if only because infinite turing machines can't exist). Finite solution spaces can get more than large enough to be intractable.
- smokel 2y agoWhat about ℕ? Seems pretty infinite to me, unless with "actually" you mean finite in time and space, which would make your argument a tautology. Or am I missing something?
- shkkmo 2y agoSearches happen in finite time an space and, more importantly, systems performing those searches have practical finite limits on parameters that determine size of the space within which that search can take place (such as available memory). Even within fairly modest finite limits, you can produce a solution space that cannot be significantly searched with the available finite matter and time available in the observable universe. Thus, the problem with using search isn't that solution spaces can be infinite, but that finite solution spaces can be unimaginably large.
- lupire 2y agoAlmost every "number" "in" N doesn't actually exist. In the search for numbers that exist, we will most likely only ever find a finite set of numbers before the Universe or humanity dies. ("Scare quotes")