On Sat, Jul 20, 2019 at 4:18 AM Bruno Marchal <[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. > > > *> That works for a lambda expression to. * > No it does not work because machines have inputs and outputs but "lambda expressions" have neither and are just a sequence of squiggles that never change and mean nothing unless a brain made of matter that obeys the laws of physics is added into the mix. > You confuse the mathematical notion of Turing machine, with its general > sense, > You confuse the fact that a "general sense" can't *do* anything but a machine can. And a paper tape and read/write head doesn't know or need to know anything about mathematical notation other than 1 and 0. It just knows it can print one of those two symbols and then either halt or move right or left; and that's all it needs. *>All universal machine/formalisme can emulate all universal > machine/formalism.* > What in the world is machine/formalism?! It sounds to me like big/little or possible/impossible or "this statement is false". >> 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. > > > *> Yes, combinators are simpler, and lambda expression too. It is just > simple substation. Can you imagine something simpler that * > > *K x y = x* > *S x y z = x z (y z)* > *?* > Yes, I can indeed imagine something simpler than that, seventeen times simpler to be exact, it is this: * I only used one ASCII character while you used 17; my character can't calculate anything but neither can your 17. 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/CAJPayv1n194GASiq-EADHXmesrx9sj8N-TcafeLpmeappyiueg%40mail.gmail.com.
