Ah, waht is mathematics?
I suspect humans could spend their life-times pondering this profound
question and never fully understand.
I'm a mathematical realist in the sense that I think mathematical
entities are real objective properties of reality and not just human
inventions, but I've come to seriously doubt the Platonist idea that
mathematics is static and timeless. Rather I now favor the idea that
mathematical truth can evolve with time. See Greg Chaitin for some
ideas about this.
As some of you may, know, I've suggested some radical ideas about time
on this list: namely the idea that there may be more than one time
dimension, in the sense that there may be more than one valid way to
define cause and effect relations.
My big big idea is that mathematics could be a sort of 'higher order
causality' ,or, if you like a 'higher dimensional time'. This is
possible if some mathematical truths are not static, but can evolve
Suppose that causality itself had a two-level structure, with
'mathematical time' on the top level, and what we think of as physical
time on the bottom level. This two level time structure is compatible
with David Bohm's interpretation of QM where reality indeed has a
two-level structure - both the wave function and the particle are
equally real but correspond to different levels of reality.
The two-level time structure could also explain the difference between
the 1st person and 3rd person perspectives and resolve the puzzle of
flowing time versus platonic timelessness.
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