Can knots be described mathematically?

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Clinton Huxley
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Re: Can knots be described mathematically?

Post by Clinton Huxley » Thu Dec 15, 2011 1:28 pm

Gawdzilla wrote:
Clinton Huxley wrote:I believe that Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces, but I'm no expert.
Spoiler that shit! :kids:
Trigger Warning!!!1! :
The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.
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Re: Can knots be described mathematically?

Post by Gawdzilla Sama » Thu Dec 15, 2011 1:31 pm

Disgusting little boy! :nono:
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Re: Can knots be described mathematically?

Post by Bella Fortuna » Thu Dec 15, 2011 1:59 pm

Clinton Huxley wrote:
Bella Fortuna wrote:
Clinton Huxley wrote:
Bella Fortuna wrote:
Clinton Huxley wrote:There are knot the answers Rum was hoping for
A-Gordian to you he should be getting something different?
A cutting remark.
I can't beweave you would say such a thing.
Don't get your knickers in a twist
Don't make me loathe you with every fibre of my being.
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Re: Can knots be described mathematically?

Post by Clinton Huxley » Thu Dec 15, 2011 2:12 pm

Well, this thread is going without a hitch.
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AND MERRY XMAS TO ONE AND All!

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Re: Can knots be described mathematically?

Post by Gawdzilla Sama » Thu Dec 15, 2011 2:16 pm

Clinton Huxley wrote:Well, this thread is going without a hitch.
Send me a cable if it gets past two pages. :coffee:
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Re: Can knots be described mathematically?

Post by Clinton Huxley » Thu Dec 15, 2011 2:18 pm

Gawdzilla wrote:
Clinton Huxley wrote:Well, this thread is going without a hitch.
Send me a cable if it gets past two pages. :coffee:
Who noose how many pages it will run to?
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Re: Can knots be described mathematically?

Post by Bella Fortuna » Thu Dec 15, 2011 2:19 pm

You've all gone loopy.
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Re: Can knots be described mathematically?

Post by Tyrannical » Thu Dec 15, 2011 2:21 pm

So much for an actually interesting topic.
A rational skeptic should be able to discuss and debate anything, no matter how much they may personally disagree with that point of view. Discussing a subject is not agreeing with it, but understanding it.
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Re: Can knots be described mathematically?

Post by Bella Fortuna » Thu Dec 15, 2011 2:22 pm

Keep hanging on for the bitter end... :coffee:
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Re: Can knots be described mathematically?

Post by Ronja » Thu Dec 15, 2011 2:31 pm

OK, OK, Grampy, spoilering it then for possibly later (like on Newton's Birthday) attempting to translate it into something more alike the English vernacular.
Clinton Huxley wrote:
Gawdzilla wrote:
Clinton Huxley wrote:
Trigger Warning!!!1! :
I believe that Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces, but I'm no expert.
Spoiler that shit! :kids:
Trigger Warning!!!1! :
The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.
You see, I claim I understood those spoilered bits, but only if I manage to rewrite them in something that is somewhat more understandable will I really believe that claim.

BTW, it's not my own doing, but the result of repeated exposure: one of our math teachers in college was nutty about knots and used to bring a different mind-benders into each weekly meeting, with prizes for those who could solve the puzzle, either topologically / theoretically or in practice. The puzzles were alike the simpler wooden and metal ones on this page http://www.mrpuzzle.com.au/webcontent33.htm and he also used to do rope tricks (knots that were not knots etc) and then ask us to explain them. It was fun in an embarrassing sort of way, 'cause I never managed to be the first to solve anything, and gave plenty of wrong answers. :oops:
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Re: Can knots be described mathematically?

Post by FBM » Thu Dec 15, 2011 2:35 pm

More puns. Now I'm really torqued. :nono:
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Re: Can knots be described mathematically?

Post by Gawdzilla Sama » Thu Dec 15, 2011 2:36 pm

FBM wrote:More puns. Now I'm really torqued. :nono:
Don't get roped into this. :mod:
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Re: Can knots be described mathematically?

Post by Ronja » Thu Dec 15, 2011 2:58 pm

Rum, I'm not sure if you will like this, but swiftly browsing through it the text appeared sympathetic. It's about the history of mathematical knot theory, told in a somewhat rambling manner:
Scottish Physics and Knot Theory’s Odd Origins by Daniel S. Silver
http://www.southalabama.edu/mathstat/pe ... ottish.pdf
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Re: Can knots be described mathematically?

Post by Rum » Thu Dec 15, 2011 4:52 pm

The answer is no then. What a tangled web etc..
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Re: Can knots be described mathematically?

Post by FBM » Thu Dec 15, 2011 4:56 pm

Gawdzilla wrote:
FBM wrote:More puns. Now I'm really torqued. :nono:
Don't get roped into this. :mod:
Aglet it go on for as long as I could.
"A philosopher is a blind man in a dark room looking for a black cat that isn't there. A theologian is the man who finds it." ~ H. L. Mencken

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