3 ms·
That's an interesting question. Firstly, we can note that there are no Turing machines for computing uncomputable numbers in the temporal world, either. There a
by mannykannot 5y ago
That's an interesting question. Firstly, we can note that there are no Turing machines for computing uncomputable numbers in the temporal world, either. There are Turing machines which will not halt (and therefore not compute any number), and their graphs will either form cycles or extend indefinitely like the number line itself, but in neither case will these graphs contain a reachable halt state.
(Having said that, I cannot wrap my mind around Babour's concept of an atemporal universe, either.)
- User23 5y agoThere are no Turing machines in the “temporal world” at all. We compute using devices much closer to some kind of bounded automata. An arbitrarily large, even growable, tape has more limited computational power than an infinite tape.
- mannykannot 5y agoCan you elabrate on why a growable tape has more limited computational power than an infinite tape (is the growth you have in mind constrained in some way?) Not that we could have the latter, or an unconstrained version of the former, in our temporal world, of course!
- User23 5y agohttps://cs.stackexchange.com/questions/127810/difference-between-linear-bound-automata-and-a-turing-machine https://cs.stackexchange.com/questions/127810/difference-bet...
- mannykannot 5y agoI see, so by 'growable' you don't mean arbitrarily growable or growable-as-needed without restriction. That would have overturned my intuitions in these matters.
- User23 5y agoI’m not confident in my ability to explain it more clearly. However I highly recommend reading Sipser[1] because his treatment of the subject, and many others, is as clear as can be. [1] https://www.goodreads.com/book/show/400716.Introduction_to_the_Theory_of_Computation https://www.goodreads.com/book/show/400716.Introduction_to_t...
- mannykannot 5y agoThanks - this is new to me.