On Fri, Jul 19, 2019, at 18:37, John Clark wrote: > On Fri, Jul 19, 2019 at 1:33 PM Telmo Menezes <[email protected]> wrote: > >> >* **How do you decide if something is a Turing Machine or not? * > > X is a Turing Machine if and only if for any given input to X there exists a > Turing Machine that will produce the same output as X does with the same > input.
Ok, but then you can replace "Turing Machine" above with "von Neumann Machine" or "GPU" and it still works. > >> *> Is Domino a Turing Machine? * > > A Domino computer is. > >> *> What about my brain?* > > It's a Turing Machine. > >> > ***What about the billiard ball computer?* > > It's a Turing Machine. > >> *> The only equivalence used in Computer Science is in completeness: Van >> Neumann Machines and GPUs are Turing Complete, in the sense that they are as >> general a computational device as a Turing Machine.* > > Only?! If X is Turing Complete then a Turing Machine can emulate X and X can > emulate a Turing Machine. Yes, but the Turing Machine has no special status in relation to any other Turing complete system. > >> *> I never heard or read anyone before claiming that Turing Machines are >> physically more fundamental,* > > Do you know of anything simpler that can make calculations than read a > square, erase what you read and then print either a 0 or a 1 on it depending > on your state, then change into another state depending on what you read, > then either halt or move right or left and read another square. Simple in what sense? I can think of physical implementations of computers that simpler in the sense that they do not require some sort of writing device, motors to move the tape, some sort of sensor to read the state, then some mechanism to make the decision on how to activate the motors and writing device. I gave you one: Domino. It only requires objects falling over other objects. Or the billiard ball computer, which only requires the physical collision of balls inside tubes. I'm sure it is possible to create computational surfaces made of lattices of very simple molecules. A network of thershold-activated units that allows for backward links is Turing complete. The Turing Machine is not the simplest implementation of a physical computer, it is (perhaps?) the simplest implementation that uses explicit memory and sequential computations. These two things make it easier for us to reason about its computations, and that is all. It is not the "fundamental" computer. Telmo. > > John K Clark > >> > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv2HL22OknRKijRMMjfFS5hBvq7r0eWpyEAhK1QuOC3jgA%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv2HL22OknRKijRMMjfFS5hBvq7r0eWpyEAhK1QuOC3jgA%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/dfd88967-91dc-4273-838a-0c1595727c94%40www.fastmail.com.
