On Sat, Jul 20, 2019 at 5:21 AM Telmo Menezes <[email protected]> wrote:
>> 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.* > You could if you wanted to because unlike Lambda calculus Turing Machines, von Neumann Machines, and GPUs can all be implemented physically; but if you're only interested in philosophy then you wouldn't want to because you would just be inserting in tons of additional engineering details needed to make computers economically viable. Only?! If X is Turing Complete then a Turing Machine can emulate X and X >> can emulate a Turing Machine. > > > > Y > *es, but the Turing Machine has no special status in relation to any other > Turing complete system.* > It is the simplest Turing complete system. > >> 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?* The amount of information needed to describe its most basic operation. *> I can think of physical implementations of computers that simpler in the > sense that they do not require some sort of writing device,* > Any computer is going to need memory to store the program and usually there will be data too, and memory involves reading and writing. > > *motors to move the tape,* > Any computer with more than one bit of memory is going to need to move the place where it reads and writes. *> some sort of sensor to read the state,* > Any computer is going to have to have internal states that change, and that change can't be random, the change must depend on its current state and the next bit of information it reads. > *> 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.* > The position of the billiard balls are the memory and determine the state of the machine, however the 2D position of a billiard ball can't be described by just one bit of information as a square on Turing's tape can be. So a 2D billiard ball computer is considerably more complicated than a 1D paper tape, but if you like the billiard balls that's fine because unlike Lambda Calculus it can be implemented physically. *> I'm sure it is possible to create computational surfaces made of > lattices of very simple molecules. * I'm sure of that too but there is nothing simple about molecules or the 2D surface of 3D lattices *> The Turing Machine is not the simplest implementation of a physical > computer, * > You haven't told me about a simpler one. > *it is (perhaps?) the simplest implementation that uses explicit memory > and sequential computations.* > If it has no memory and can't make sequential computations then you might have a calculator but you don't have a computer. > *> These two things make it easier for us to reason about its > computations, and that is all. It is not the "fundamental" computer.* > If its the easiest for us to understand then it is the simplest, if it can't be made any simpler, any more elementary, without loosing important properties then it is fundamental because that's what the word means. 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/CAJPayv0PqqyFTnTt00%2B%2BgEcCqcYN893ac1RZi%3Dnq5pQbzN7LgA%40mail.gmail.com.
