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. 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? Stathis Papaioannou _________________________________________________________________ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.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 -~----------~----~----~----~------~----~------~--~---
