Book: "Dark Integers"
Story: "Luminous"

(The story "Dark Integers" is actually a sequel)

Premise: In reality, mathematical truths are undecided until embodied in a 
physical system, until a physical system's state is different depending on 
the truth of the system. Fermat's Last Theorem was neither true nor false 
until someone actually proved it, thereby modifying the state of their brain 
based on the result. Premise: Mathematical truth is restricted to the speed 
of light, and hence different parts of the universe might have different 
mathematical proofs that are true.  Conclusion: Current theories about 
integers might or might not be consistent, and mathematical statements might 
or might not be true depending on the order in which you try to prove 
things.  Invent the discovery of such a state in the real world, and discuss 
possible ramifications. :-)

A delightful short story, if only for the premise.

-- 
   Darren New, San Diego CA, USA (PST)
   Understanding the structure of the universe
    via religion is like understanding the
     structure of computers via Tron.

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On 08/23/09 20:42, Darren New wrote:
> Book: "Dark Integers"
> Story: "Luminous"
>
> (The story "Dark Integers" is actually a sequel)

	Was Greg Egan the author you've touted frequently in the past? I only 
recently read some of his stuff. Dark Integers (the story - not the 
anthology) was quite good. Perhaps I got it from a link you posted? It's 
free to read on Asimov's (magazine) site.

	Just about a week ago I read Diaspora (the only book of his that I've 
read). It was interesting. Not great, but good enough for me to read 
more later. I've heard Permutation City is the one to read.

-- 
How do frogs die? Ker-mit suicide.

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Neeum Zawan wrote:
> On 08/23/09 20:42, Darren New wrote:
>> Book: "Dark Integers"
>> Story: "Luminous"
>>
>> (The story "Dark Integers" is actually a sequel)
> 
>     Was Greg Egan the author you've touted frequently in the past? 

Yes. I love 99% of his stuff.

>     Just about a week ago I read Diaspora (the only book of his that 
> I've read). It was interesting. Not great, but good enough for me to 
> read more later. I've heard Permutation City is the one to read.

Yes. I liked the first chapter of Diaspora best, wherein he describes the 
evolution of self-awareness.

-- 
   Darren New, San Diego CA, USA (PST)
   Understanding the structure of the universe
    via religion is like understanding the
     structure of computers via Tron.

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Darren New wrote:
> Book: "Dark Integers"
> Story: "Luminous"
> 
> (The story "Dark Integers" is actually a sequel)
> 
> Premise: In reality, mathematical truths are undecided until embodied in 
> a physical system, until a physical system's state is different 
> depending on the truth of the system. Fermat's Last Theorem was neither 
> true nor false until someone actually proved it, thereby modifying the 
> state of their brain based on the result. Premise: Mathematical truth is 
> restricted to the speed of light, and hence different parts of the 
> universe might have different mathematical proofs that are true.  
> Conclusion: Current theories about integers might or might not be 
> consistent, and mathematical statements might or might not be true 
> depending on the order in which you try to prove things.  Invent the 
> discovery of such a state in the real world, and discuss possible 
> ramifications. :-)
> 
> A delightful short story, if only for the premise.
> 

A similar SF premise but I can't remember whose it was or the story - 
perhaps Asimov ?

That the physical properties of the universe are set by God (or a god ?) 
but only when some pesky scientist bothers to go looking at them.  The 
first time a property is measured there is a large margin of error which 
allows time for the deity to determine what the more precise value 
should be.

Like Pi - Well its about 3.  You know, give or take about 20%  That 
should keep them busy while I work out the real value.

Then I think it went on that by measuring how quickly the precision of a 
measurement could be improved by successive measurements and assuming 
that this all works at the speed of light, you could calculate the 
distance to heaven.  Do this from different locations and you could 
triangulate.

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Paul Fuller wrote:
> Like Pi - Well its about 3.  You know, give or take about 20%  That 
> should keep them busy while I work out the real value.

LOL!  Delightful!  Please let me know if you figure out what story this is.

-- 
   Darren New, San Diego CA, USA (PST)
   Understanding the structure of the universe
    via religion is like understanding the
     structure of computers via Tron.

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Paul Fuller schrieb:
> That the physical properties of the universe are set by God (or a god ?) 
> but only when some pesky scientist bothers to go looking at them.  The 
> first time a property is measured there is a large margin of error which 
> allows time for the deity to determine what the more precise value 
> should be.

That was me :-) (No, seriously: I love this idea, and have been toying 
around with it occasionally for one or two decades by now, and I'm sure 
I didn't pick it up anywhere (*). Though I must confess I never wrote 
about it :-P)

(* Well, maybe it was inspired by Douglas Adams, and that quote along 
the lines of "there's a theory that if anyone ever manages to fully 
understand the universe, it will instantaneously be replaced by 
something even more bizarre. There's another theory that this has 
happened already.")

I find it actually remarkably consistent with quantum mechanics: As long 
as you don't look at a particle, it is not at any particular location, 
i.e. the answer is undecided. As long as you don't look at how big pi 
is, or the charge of an electron, or what atomic nuclei are composed of, 
the answer is undecided...

> Then I think it went on that by measuring how quickly the precision of a 
> measurement could be improved by successive measurements and assuming 
> that this all works at the speed of light, you could calculate the 
> distance to heaven.  Do this from different locations and you could 
> triangulate.

LOL, that's great!

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Darren New wrote:
> Premise: In reality, mathematical truths are undecided until embodied in 
> a physical system, 

Pretty cool. An example of an actually unprovable truth that isn't 
completely contrived:

http://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem

Ramsey's Theorem in almost english at the start, that might explain why you 
might care:

http://en.wikipedia.org/wiki/Ramsey%27s_theorem


-- 
   Darren New, San Diego CA, USA (PST)
   Understanding the structure of the universe
    via religion is like understanding the
     structure of computers via Tron.

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Darren New schrieb:
> Ramsey's Theorem in almost english at the start, that might explain why 
> you might care:

Well, I think the emphasis here should be on /might/ :-P

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clipka wrote:
> Darren New schrieb:
>> Ramsey's Theorem in almost english at the start, that might explain 
>> why you might care:
> 
> Well, I think the emphasis here should be on /might/ :-P

Well, my intent was the take-away that there's actually things like graph 
problems where you color the edges of something, that trigger godel, rather 
than just a big long artificially-constructed string that nobody otherwise 
cares about.

Sort of the difference between the halting problem and some of the actual 
useful stuff (like the printing problem, etc) that falls out of it.

I can imagine there's a use for solutions of colored graphs. I can't imagine 
there's a use for a Godel string outside of Godel proofs.

-- 
   Darren New, San Diego CA, USA (PST)
   Understanding the structure of the universe
    via religion is like understanding the
     structure of computers via Tron.

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