>From: Brent Meeker <[EMAIL PROTECTED]>
>On 01-Sep-01, Jacques Mallah wrote:
> >    There is more than that in mathematics. Structures, for example.
> > Anything that could be described mathematically, such as geometries,
> > computations, and anything that could be a model of a (hypothetical)
> > world. There's plenty of room for implementations there.

>Even structures in mathematics, e.g. an isocolese triangle, or a set of
>partial differential equations with boundary conditions are either
>different or they are identical (and hence indistinguishable).  I don't
>see how they can be regarded as different implementations of the same
>structures or theorems.  We only speak of different implementations
>because we can run the same program on two different computers, we can
>write down the same theorems on two different pieces of paper.  In the
>Platonic realm two things that are mathematically identical are
>absolutely identical and hence are the same thing.

    There is plenty of room in Plato's kitchen, though.  For example the 
structure that physicists think best describes our universe is in there.  
Different parts of that structure are not identical, but they can implement 
the same (type of) computation as other parts.

                         - - - - - - -
               Jacques Mallah ([EMAIL PROTECTED])
         Physicist  /  Many Worlder  /  Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
         My URL: http://hammer.prohosting.com/~mathmind/

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