rhersh at math.unm.edu
Mon Mar 23 00:23:46 EST 1998
Again hoping not to add to the flood of irrelevant postings,
I find myself called upon to deal with the Lagrangian pebbles.
Recall that the issue is Lagrange's theorem (LT) that every natural
number is the sum of at most four squares.
This was proposed as a counterexample to my claim that there is
no math, including no theorems, except as an activity of people
It was proposed that the theorem is applicable
to any piles of pebbles that might have collected on a Jurassic or
Cretaceous beach, long before the arrival of homo sapiens.
q.e.d.- "LT was true before there were humans."
Fine. Suppose that for the moment I agree, "LT was true whenever there were
piles of pebbles." There were not always pebbles.
The history of the cosmos as now told by cosmologists has
a considerable period (I forget if it was hundreds of thousands,
millions or billions of years) when its physical
state did not allow matter in
the solid state such as rocks or pebbles to exist.
But I don't think the upholders of the antiquity of LT would agree
that LT came to be true only at a certain maturity of the cosmos.
I expect that they hold it was true ever since the big bang, and
even before. Or perhaps to put it more acceptably, it is simply
timeless, and makes no sense to put a "when?" to it.
So the pebbles on a Jurassic beach are a diversion.
But saying LT or any other math fact is timeless amounts to
saying it is abstract, independent of physical, mental or social
So we are back to the main issue.
We are back to the classical objection to
Platonism. "This view generally labeled "platonist" ...leaves it
unintelligible how the denizens of this atemporal, supra-sensible realm
could have any connection with, or bearing upon, conditions in the
temporal, sensible realm that we inhabit." (M. Dummett, p.
12, Mathematics and Mind, ed. A. George, Oxford 1994.)
Back to the piles of pebbles and postdicting eclipses:
When physicists or geologists or cosmologists study aspects of
nature before the advent of people, they use mathematics.
The mathematics they use didn't exist before there were people.
People created it. Scientists using man-made mathematics to study
pre-human reality doesn't imply that the mathematics was
pre-human. It does presuppose that the pre-human reality was
capable of being described with some degree of accuracy
by our mathematical concepts.
I use the English language
to talk about pre-human physical reality (for instance,
above in talking about pebbles on a Jurassic beach.) That
doesn't mean the word "pebbles" or "beach" is pre-human. I
use my language and my concepts now to talk about pebbles back then.
Similarly I use N or the elements of N to talk about
those pebbles. That doesn't mean N was around back there
in the Jurassic. Still less were any theorems, conjectures,
or other statments about N present before people had created N.
I hope I have been polite, I have no desire to offend most
members of this list.
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