rhersh at math.unm.edu
Mon Mar 23 15:17:38 EST 1998
On Mon, 23 Mar 1998, Martin Davis wrote:
> At 10:23 PM 3/22/98 -0700, Reuben Hersh wrote:
> >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.
> I can just imagine what you would say to a student who produced such a non
> sequitor. It seems to me that you're just evading.
> The question is (as you surely must know by now): how could LT have been
> applicable to jurassic pebbles if the theorem only makes sense in the
> context of human activity?
Thanks for your prompt reply.
Don't you think LT is timeless? If so, it would always be true,
pebbles or no pebbles?
But if you want to stick to the pebbles, fine.
I see the question as not being essentially different for present,
past, or future pebbles. How is a human construct applicable
to non-human (physical) reality?
Answer: how can any representation represent anything? A painting,
a verbal description, a mathematical formula are different from the
thing they represent (say the Moon, as Frege liked to say) but still
while different they represent it. Of course, they are different from
the thing they represent; that's essential to the notion of representing.
To say a painting or a verbal description is a representation of the
moon doesn't gainsay that they are human creations, and perishable.
Even Shakespeare's "so long lives this, and this gives life to thee"
only ran "while men have mouths to speak and eyes to see" (or was
it "ears to hear"?). Shakespeare will vanish, and so will Newton,
in geologic and astronomic time.
Is this all too evasive, metaphorical, sophomoric?
When mathematics is applied to physical reality, it is a representation
of physical reality. A formula can be a good representation of the
moon 100 million years ago, and in a different way so can a picture--in
fact, it is possible for the formula and the picture to be equivalent.
We have our notion of the moon 100 million years ago, and we have
various ways of communicating that notion to each other. Whether
that notion and that communication are faithful to the physical reality
is a question of physical science and of a model (mathematical, verbal,
or visual) of the given physical model. Pebbles in the Jurassic
are not essentially different from conditions in the Earth's core,
or anywhere else not accessible to direct observation. We use
our physical theory, what relevant observations we have, and
mathematics (whether theoretical or computational) to draw some
conclusions, which may seem more ore less compelling.
That doesn't make our methods of thinking about the problem
superhuman or eternal. They are just the best we have got.
About the pebbles, by "pebbles" I take it you mean discrete
interchangeable non-interacting reasonably long-lasting
objects. The natural numbers are our standard mathematical
model for such. To tbe extent that the Jurassic pebbles are
can be thought of as "pebbles" in this idealized sense, we
can draw conclusions about them from elementary number theory.
But elementary number theory is a human creation, as is N.
Part of the motivation for our creating it was of course that
it could be applied to certain physical situations. That
doesn't make it eternal, it is our tool for (among other things)
describing physical situations which may well be unobservable
to us directly, whether for reasons of time or space.
Sorry to be so wordy! I am trying hard to be understood!
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