[ExI] Egan free

[Bryan Bishop]

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/