Stathis Papaioannou wrote: > John M writes: > > > Peter Jones writes: > > > > > > > > Hmm. Including limitations in time? > > > > Yes, if an infinite number of finite computations are run simultaneously on > > a system with a finite number of physical states. > > > > Stathis Papaioannou > > ------------------------------------- > > So if I have a system with finite number of physical states, it will take a > > matching finite number of (base)-computations leaving an infinite number > > untreated. Out of them I can take a deduction for muiltiplying the finite > > number of physical states by the finite number of the base-states to get to > > the total number of computability on that system in parallel - still a > > finite number. I still have an infinite number of unbtreated cases left. > > Damn that infinite! Cantor's curse. > > > > John M > > Suppose there is a very simple physical system that goes through two states, > "on" and "off". You wish to map these states onto a binary sequence which at > first glance seems too long: 10110100... You write down the following: on the > first run, on->1 and off->0; on the second run, on->1 and off->1; on the > third run, on->0 and off->1; and so on, for as long as you like. It is not > common > practice to change the code from run to run when designing a computer, but > that is just a matter of convenience. If you specify exactly how the code > changes the meaning is unambiguous, and in principle the two physical states > can encode any number of binary states, or even more complex computations.
A computation is not a series of states. A computation is an implementation of an algorithm, and algorithms include conditional statements which must be modelled by something with counterfactual behaviour -- by something which *could have* execute the other branch. > The above probably seems silly to most people reading this, because the burden > of the computation falls on the specification of the code, the physical > processes > being essentially irrelevant. Nevertheless, we may have the situation where > the > code specification is documented in a big book while the computer (such as it > is) > carries out the physical processes which, if we to refer to the book, performs > perfectly legitimate computations. We could even design a driver for a > monitor to > display the computations, again using the book. Now, suppose the last copy of > the book is destroyed. The computer would still do its business, but it may as > well be a random number generator for all the good it does us without the code > specification. But what if, by the book, the computer is actually carrying out > *conscious* computations? Would it suddenly cease being conscious as the book > is burned in a fire, or gradually lose consciousness as the book's pages are > ripped out one by one? No amount or arbitrary mapping can transofrm a situation without counterfactuals into one with them --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---