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 
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 
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 
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 
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
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