FOM: Jurassic pebbles (more on Davis/Hersh)
peter at galois.geg.mot.com
Tue Mar 17 11:07:55 EST 1998
> Now, coming to the temporal arguments concerning the Jurassic beach.
> Isn't it clear that in drawing the conclusion that the rearrangement
> and counting can be done *in principle* on a Jurassic beach, Davis is
> making a claim about the relationship between the practices of
> formulating and proving mathematical theorems and some very particular
> human practices of rearrangement and counting, and their relationship
> with the situation as we understand it pertaining in Jurassic times.
Suppose the human process is replaced with a "natural" one. For example,
what if there is a crystaline structure that prefers deposition of new
atoms in a square arrangement of atoms, thus given a positive integer
number of new atoms, the new atoms are *more likely* to be arranged in
four squares as given by Lagrange's theorem, and *less likely* to be
arranged in some other way. Now there is no human component to the
argument. The question is: Does the lack of a requirement for a
human (or otherwise competent) observer affect your arguments
concerning the objective/subjective nature of mathematics?
The construction I suggested is based upon Lagrange's theorem. If this
is stretching the physics too much, then some other mathematical
statement can be substituted. For example, there must be mathematical
laws that apply to the formation of DNA, and this DNA is in fact read
and interpreted in the process of reproduction of cells, and this
process goes along without any human intervention, and it is commonly
thought that this process was around long before there were any
Other examples are, to be an *observer* of gravity, it is sufficient
to have a non zero mass, so one could say that anything with mass is
an observer of gravity and its inverse square law. To be an observer
of the electric field, it is sufficient to have a non zero charge,
thus an electron qualifies.
Peter White, Motorola
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