5 ms·
Infinite precision is just analog's version of an infinitely-long tape.
by couchand 3y ago
Infinite precision is just analog's version of an infinitely-long tape.
- lisper 3y agoBut even with infinite precision, how do you build a universal analog computer? And how do you program it?
- progval 3y agoAny Turing machine is a (computable) function; and https://www.sciencedirect.com/science/article/pii/S0885064X07000246 https://www.sciencedirect.com/science/article/pii/S0885064X0... shows any computable function can be computed by a GPAC. Therefore, if you take any universal Turing machine, there exists a GPAC that computes that Turing machine; and it is programmable because you can change the input it would give to the emulated Turing machine. Sure it's inefficient due to the two layers of emulation, but it shows it's possible.
- lisper 3y agoAh. TIL. Thanks!
- fanf2 3y agoRight :-) I prefer to say a Turing machine’s tape is “unbounded” rather than “infinite” because it supports calculations of arbitrarily large but finite size. So in the analogue case, I would say unbounded precision and unbounded waiting time.
- Dylan16807 3y agoInfinite precision is exponentially more difficult. It's very easy to have unbounded tape, with a big buffer of tape and some kind of "factory" that makes more tape when you get near the edge. Unbounded precision? Not going to happen in a real machine. You get to have several digits and no more.