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From: RichD on 14 Nov 2009 16:57
On Nov 14, rich burge <r3...(a)aol.com> wrote:
>http://www.nytimes.com/2009/10/08/science/Wpolynom.html?_r=1
>
> > >How would algebraic geometry contribute
> > >to resolving this question?
>
> From:http://people.cs.uchicago.edu/~fortnow/papers/pnp-cacm.pdf
>
> "In essence, they define a family of high-dimension poly-
> gons Pn based on group representations on certain
> algebraic varieties. Roughly speaking, for each n,
> if Pn contains an integral point, then any circuit
> family for the Hamiltonian
> path problem must have size at least nlog n on inputs
> of size n, which implies P != NP. Thus, to show that
> P != NP it suffices to show that Pn contains an
> integral point for all n."

Cool.

What does it mean?

--
Rich
From: zzbunker on 14 Nov 2009 19:45
On Nov 14, 4:45 pm, RichD <r_delaney2...(a)yahoo.com> wrote:
> On Nov 14, "zzbun...(a)netscape.net" <zzbun...(a)netscape.net> wrote:
>
> >    It's why they invented Microwave Cooling,
>
> Microwave cooling?

Well, nobody excpets idiots that don't understand
anything other than Dark Matter to understand science.



>
> --
> Rich

From: Gerry Myerson on 15 Nov 2009 17:30
In article
<dc176955-b8f6-4688-a475-d6cac684357b(a)f18g2000prf.googlegroups.com>,
rich burge <r3769(a)aol.com> wrote:

> On Nov 13, 8:24�pm, Gerry <ge...(a)math.mq.edu.au> wrote:
> > On Nov 14, 1:13�pm, RichD <r delaney2...(a)yahoo.com> wrote:
> >
> > >http://www.nytimes.com/2009/10/08/science/Wpolynom.html? r=1
> >
> > > How would algebraic geometry contribute to resolving this question?
> >
> > I don't know. Have you tried reading the article in CACM
> > that is referenced in the Times?
> > --
> > GM
>
> From: http://people.cs.uchicago.edu/~fortnow/papers/pnp-cacm.pdf
>
> "In essence, they define a family of high-dimension poly-
> gons Pn based on group representations on certain algebraic
> varieties. Roughly speaking, for each n, if Pn contains an
> integral point, then any circuit family for the Hamiltonian
> path problem must have size at least nlog n on inputs of size
> n, which implies P != NP. Thus, to show that P != NP it
> suffices to show that Pn contains an integral point for all n."

Thanks. What might a "high-dimension polygon" be?

--
Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: Robert Israel on 15 Nov 2009 18:54
Gerry Myerson <gerry(a)maths.mq.edi.ai.i2u4email> writes:

> In article
> <dc176955-b8f6-4688-a475-d6cac684357b(a)f18g2000prf.googlegroups.com>,
> rich burge <r3769(a)aol.com> wrote:
>
> > On Nov 13, 8:24�pm, Gerry <ge...(a)math.mq.edu.au> wrote:
> > > On Nov 14, 1:13�pm, RichD <r delaney2...(a)yahoo.com> wrote:
> > >
> > > >http://www.nytimes.com/2009/10/08/science/Wpolynom.html? r=1
> > >
> > > > How would algebraic geometry contribute to resolving this question?
> > >
> > > I don't know. Have you tried reading the article in CACM
> > > that is referenced in the Times?
> > > --
> > > GM
> >
> > From: http://people.cs.uchicago.edu/~fortnow/papers/pnp-cacm.pdf
> >
> > "In essence, they define a family of high-dimension poly-
> > gons Pn based on group representations on certain algebraic
> > varieties. Roughly speaking, for each n, if Pn contains an
> > integral point, then any circuit family for the Hamiltonian
> > path problem must have size at least nlog n on inputs of size
> > n, which implies P != NP. Thus, to show that P != NP it
> > suffices to show that Pn contains an integral point for all n."
>
> Thanks. What might a "high-dimension polygon" be?

I presume he meant polytope.
--
Robert Israel israel(a)math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
From: spudnik on 16 Nov 2009 15:38
didn't Einstein and a buddy invent acoustical cooling?... like,
he wasn't such a dummy, after all!

> > Microwave cooling?
>
>   Well, nobody excpets idiots that don't understand
>   anything other than Dark Matter to understand science.

thus:
did you check that on a symbolic processor?... neat.

> (2a)^2 + (2b)^2 + (2c)^2 + (2d)^2 =
> (a+b-c-d)^2 + (a+b-c-d)^2 + (a-b)^2 + (c-d)^2 + (a-b)^2 + (c-d)^2 ,

thus:
the English useage of "maths," emphasizing the plurality
of "mathematics" or *mathematica* -- not MathematicaTM
of the Wolframites -- is the four subjects of the quadrivium;
the trivium, you've obviously acquired in spite of school.
check-out Fermat's reconstruction of Euclid's porisms,
as a model of proving theorems in (planar) geometry e.g..

thus:
apparently the only factor that effects the decay
of a given atomic state (a-hem) is that of proximity
to other decaying states, as in critical mass;
sort of a bosonic aspect of fermions?
sure wish, someone'd bury that stinky cat of Schroedinger
('s joke .-)

> > > I've got some radium that behaves very oddly.")
> > >http://en.wikipedia.org/wiki/Bell%27s_theorem#Importance_of_the_theorem
> > The idea of a hidden variable is a grammatical consequence of any
> > quantum theory, as I argued.

thus:
saw the latest rendition of Rubik's Hexahedron at a store;
it is just a vari-colored light in the center of each face,
which apparently uses an acceleraometer to orient itself
(with respect to thee .-)

thus:
nice, constructive analysis;
wouldn't an approach via the Fermat point
of a trigon, be useful?
(L'Ouvre: http://wlym.com .-)
> In terms of convex hulls we are finding the largest line segment contained
> in it and then finding the midpoint of the line segment perpendicular to the
> largest line segment that runs through the largest line segment's midpoint.

--Cap'n Trade & Warren Buffet, together again?
Rep. Waxman's God-am bill, doesn't institute a tarrif, instead !?!
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