1Z wrote: > > 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.
I think this "something" is an interaction with something outside the computer, i.e. a different input or a real-time sensor input. I could also be a random variable generated internally - but I'm not clear on whether that satisfies lz's idea - it doesn't satisfy mine. Brent Meeker --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
