Peter:
As I recall all "I" wrote (and the post marked it as >>> was:
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
*
I wanted to point to the 'flipside of it' which was not addressed in your
reply: mixing finite and infinite. Those >>>>> marks drive me crazy. too.
John
----- Original Message -----
From: "1Z" <peterdjones.domain.name.hidden>
To: "Everything List" <everything-list.domain.name.hidden>
Sent: Tuesday, August 01, 2006 9:17 AM
Subject: Re: Bruno's argument
>
>
> 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 - 16:45:25 PDT