Re: "The map is not the Territory"...
From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 08/02/04
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Date: Mon, 02 Aug 2004 05:26:00 GMT
"Robert J. Kolker" <robert_kolker@hotmail.com> wrote in message
news:zx7Pc.209112$JR4.177214@attbi_s54...
>
>
> Bill Hobba wrote:
>
> >
> >
> > Hmmm. Some rather knowledgeable people like Penrose might disagree with
you
> > there - they believe (as do I) that the equations pertain to world
beyond
> > our normal senses and it is that world that determines how the world of
our
> > normal senses operates. Take for example a Turing machine - I think it
> > would be rather naive to believe such a devise is not fundamentally
> > described by the mathematics - the issue that it is not possible to
> > construct one with, for example, an infinite tape, would not seem a
> > fundamental issue - that it captures something basic about how a real
> > physical one would operate seems beyond question. It would be a rather
> > amazing thing if such a machine did not function how the mathematics
says it
> > should eg it was able to actually solve the halting problem.
>
> How about a finite state machine with a lot of states that gets busted
> somewhere along the line. Turing machines (as a class) are abstractions
> and they do not have a counterpart in physical reality. In short Turing
> Machines do not exist in the same sense as bricks, trees and stones.
Whoa there Bob. Except for the infinite tape requirement is it technically
a trivial matter to physically contract a Turing machine. My point is that
the mathematics that describes how such a real physical device would operate
captures in an essential way how it would behave. The only out I see is my
statement 'captured in an essential way' - one could argue that it is just a
model and a real machine would not act quite in the same way - eg its tape
would not be infinite or it will occasionally make errors, the tape may
break etc. To me that is the essential issue - if we have in our
mathematics captured the essence of what is happening - I believe we have.
That being the case if the mathematics that describes the physical situation
does not mesh quite right (eg requires constants to be put in by hand) then
it is an indication a better description is lurking about - just like if a
real Turing machine did something inexplicable like solve the halting
problem.
Thanks
Bob
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