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Can we stop with this stuff? It is a 100% useless distinction, Turing machines can only ever use a fixed amount of memory, so we can run any Turing machine for
by kaba0 3y ago
Can we stop with this stuff? It is a 100% useless distinction, Turing machines can only ever use a fixed amount of memory, so we can run any Turing machine for as long as we want to, we can just pause it, “change the tape” to a bigger one, and continue.
- lanstin 3y agoWell, it's not useless mathematically. The Turing machine cannot run on all inputs with a bounded tape size. The quickly growing functions show pretty strongly that no physically incarnateable device can compute easy to specify functions on inputs less than 1000. "Turing machine" or Turing equivalence are pretty precisely defined mathematical concepts, so using them in different senses is a bit perverse; in my mind, more perverse than using literally to mean figuratively. Also, how does one change the tape in ones brain? I'd love a pensieve but those also are not physical, at least not yet. The thing I'd really like is a Turing machine where the nth transition took 1/2^n seconds, so we could run them to infinity in just two seconds.