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
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Received on Tue Aug 01 2006 - 09:18:40 PDT