FOM: Reals and reality /imaginaries and reality

[Robert S Tragesser]

        There are traces of a debate in
physics about the reality of the complex
numbers,  as between Robert Mills and
Roger Penrose.
        While saying that "the algebra
of complex numbers is more complete
and elegant than the algebra of 
real numbers,  and the calculus is
also richer and tighter than the
calculus of real numbers",  Robert
Mills goes on to say that i = sqr
root of minus 1, "does not occur in
the laboratory", that the complex
psi is really a vector in 2-dim.
vector space with two real components;
that "complex analysis is just two copies
of real analysis."
        Roger Penrose asserts that complex
#'s are a fundamental ingredient in 
physical reality.  This is in the
context of remarks like, "the most
fundamental of symmetry groups in
physics is just the symmetry of
a simple complex closed curve."That
complex geometry is fundamental to 
reality."
        What are the issues here?
        Are we here in the foundationally
unilluminated domain where it makes
sense to say, "functions are in general
irreducible to sets of ordered pairs;
and just as functions are irreducible
to sets of ordered pairs,  so,  too,
are the complex numbers irreducible
to pairs of real numbers."

rbrt tragesser
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