[ExI] Egan free
Bryan Bishop
kanzure at gmail.com
Sun Apr 13 04:18:01 UTC 2008
On Saturday 12 April 2008, Damien Broderick wrote:
> Greg Egan's "Dark Integers," a sequel to "Luminous," is available for
> free download at the ASIMOV'S website:
>
> http://www.asimovs.com/_issue_0805/DarkINtegers.shtml
>
> It's up for a Hugo, is why.
Luminous is on my shelf, in a treasured spot.
It all started out as a joke. Argument for argument's sake. Alison and
her infuriating heresies.
"A mathematical theorem," she'd proclaimed, "only becomes true when a
physical system tests it out: when the system's behaviour depends in
some way on the theorem being true or false.
It was June 1994. We were sitting in a small paved courtyard, having
just emerged from the final lecture in a one-semester course on the
philosophy of mathematics - a bit of light relief from the hard grind
of the real stuff. We had fifteen minutes to to kill before meeting
some friends for lunch. It was a social conversation - verging on mild
flirtation - nothing more. Maybe there were demented academics, lurking
in dark crypts somewhere, who held views on the nature of mathematical
truth which they were willing to die for. But were were twenty years
old, and we knew it was all angels on the head of a pin.
I said, "Physical systems don't create mathematics. Nothing creates
mathematics - it's timeless. All of number theory would still be
exactly the same, even if the universe contained nothing but a single
electron."
Alison snorted. "Yes, because even one electron, plus a space-time to
put it in, needs all of quantum mechanics and all of general
relativity - and all the mathematical infrastructure they entail. One
particle floating in a quantum vacuum needs half the major results of
group theory, functional analysis, differential geometry - "
"OK, OK! I get the point. But if that's the case... the events in the
first picosecond after the Big Bang would have `constructed' every last
mathematical truth required by any physical system, all the way to the
Big Cruch. Once you've got the mathematics which underpins the Theory
of Everything... that's it, that's all you ever need. End of story."
"But it's not. To apply the Theory of Everything to a particular system,
you still need all the mathematics for dealing with that system - which
could include results far beyond the mathematics the TOE itself
requires. I mean, fifteen billion years after the Big Bang, someone can
still come along and prove, say... Fermat's Last Theorem." Andrew Wiles
at Princeton had recently announced a proof of the famous conjecture,
although his work was still being scrutinised by his colleagues, and
the final verdict wasn't yet in. "Physics never needed that before."
I protested, "What do you mean, `before'? Fermat's Last Theorem never
has - and never will - have anything to do with any branch of physics."
Alison smiled sneakily. "No branch, no. But only because the class of
physical systems whose behaviour depend on it is so ludicrously
specific: the brains of mathematicians who are trying to validate the
Wiles proof."
"Think about it. Once you start trying to prove a theorem, then even if
the mathematics is so `pure' that it has no relevance to any other
object in the universe... you've just made it relevant to yourself. You
have to choose some physical process to test the theorem - whether you
use a computer, or a pen and paper... or just close your eyes and
shuffle neurotransmitters. There's no such thing as a proof which
doesn't rely on physical events, and whether they're inside or outside
your skull doesn't make them any less real."
Found originally at:
http://math.ucr.edu/home/baez/week123.html
- Bryan
________________________________________
http://heybryan.org/
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