FOM: lagrangian pebbles
rhersh at math.unm.edu
Thu Mar 19 04:24:17 EST 1998
On Wed, 18 Mar 1998, Martin Davis wrote:
Hersh wrote:> >
> >But the mathematical subject of potential theory (the 3 dimensional
> >gravitational potential) as existing apart from, independently of
> >physical phenomena, was created by Newton and his successors. It
> >did not exist even in Neanderthal times, let alone in the Jurassic.
>Davis wrote: But then how can we justify the mathematics that derives the
rules of > planetary motion from Newton's laws applying to jurassic times?
The delusion that ideas or theories or theorems exist "on their own"
apart from knowers and thinkers permits one to say that the theory
of the Newtonian potential (or any other math theory) always "was
true," which is incoherent without carrying along "always existed,"
even if you choose to label the latter a "nonproblem."
Nowadays astronomical calculations are done by machine. But
the machine didn't always exist, neither did its software,
neither did C or C++, neither did the theories of computing
of Turing, v. Neumann et al. We created all that, recently.
The Newtonian potential was created a few decades ago.
The planets don't know a thing about Turing or von Neumann or
whoever. They just move as they move. We create theories to
help us predict or postdict their movement. The theories aren't
there in interplanetary space. They're in our books, our programs,
and our conversation. We use them now to figure out how the planets
move, moved and will move. When we die away, the planets will go
on as before, but our hardware, software, C, C++ , and theories
of potentials and differential equations will vanish with us.
What if a future intelligent race goes to study our solar system,
or their own? Won't they need the same intellectual machinery
as us? Possible, but I don't see it as a sure thing. There's
more than one way to skin a cat, or to model a physical system,
or to use a model to study the system.
Since we don't know anything about the existence, let alone
the properties, of extraterrestrials, except that it seems certain
that if there are any we'll never know it, it
seems to me a rather shaky basis for argument.
Artists sometimes make pictures of the night sky. Such a picture
might be made carefully, scientifically, even to the best of our
knowledge without error. It would still be only something we made.
It might be generated by, or stored in, your favorite computer, and
that computer representation of the picture might be printed out and
published in a journal, and read and discussed and accepted and
put on library shelves. None of that would make it eternal or
timeless or independent of human thought. It would always be
a mode of communication among human beings.
Horrors! Relativism, postmodernism, call the police!
Just kidding, Martin.
More information about the FOM