Notes for AKT-170110-1/0:48:55 - Revision history

Rolandvdv at 12:20, 11 January 2017

2017-01-11T12:20:53Z

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	{{Dror}}: Thanks for the comment, Roland! Do you have a link to the Jaeger result?		{{Dror}}: Thanks for the comment, Roland! Do you have a link to the Jaeger result?
			{{Roland}}: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0305004100068936

	No, I mean that I can write a short program that ''does the job well'', in practice even if not in theory. So even though the Jones polynomial is in-theory complicated, in practice it can be computed for knots with about 200 crossings.		No, I mean that I can write a short program that ''does the job well'', in practice even if not in theory. So even though the Jones polynomial is in-theory complicated, in practice it can be computed for knots with about 200 crossings.

Drorbn at 11:58, 11 January 2017

2017-01-11T11:58:34Z

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	Roland		Roland

			{{Dror}}: Thanks for the comment, Roland! Do you have a link to the Jaeger result?
⚫	~~{{Dror}}:~~ No, I mean that I can write a short program that ''does the job well'', in practice even if not in theory. So even though the Jones polynomial is in-theory complicated, in practice it can be computed for knots with about 200 crossings.

		⚫	No, I mean that I can write a short program that ''does the job well'', in practice even if not in theory. So even though the Jones polynomial is in-theory complicated, in practice it can be computed for knots with about 200 crossings.

	Aside. Jones once claimed to me (in person) that the Jones polynomial can be computed with knots with up to 200 crossings, but I've never verified it with my directly. Yet I've seen Khovanov homology computed (using my algorithm!) on knots with about 70 crossings, and in the light of that, 200 for Jones seems reasonable.		Aside. Jones once claimed to me (in person) that the Jones polynomial can be computed with knots with up to 200 crossings, but I've never verified it with my directly. Yet I've seen Khovanov homology computed (using my algorithm!) on knots with about 70 crossings, and in the light of that, 200 for Jones seems reasonable.

Drorbn: Created page with "Roland van der Veen wrote {{Dror}}: Dear Dror, I enjoyed watching your first hour of AKT and had a minor gripe about your sentence at around 48:55 Your statement "Relative t..."

2017-01-11T11:55:57Z

Created page with "Roland van der Veen wrote {{Dror}}: Dear Dror, I enjoyed watching your first hour of AKT and had a minor gripe about your sentence at around 48:55 Your statement "Relative t..."

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Roland van der Veen wrote {{Dror}}:

Dear Dror,

I enjoyed watching your first hour of AKT and had a minor gripe about your sentence at around 48:55
Your statement
"Relative to difficult to compute things, the Jones polynomial is in fact surprisingly easy to compute"
is in some sense very wrong as it ignores the fact that computing Jones is #P-hard, shown by Jaeger. Toda's theorem implies that using an oracle computing Jones one can obtain a polynomial time algorithm to solve all NP problems and even much more difficult problems
https://en.wikipedia.org/wiki/Toda's_theorem

I suppose what you mean is you can write a short program to do the job.

Best,
Roland

{{Dror}}: No, I mean that I can write a short program that ''does the job well'', in practice even if not in theory. So even though the Jones polynomial is in-theory complicated, in practice it can be computed for knots with about 200 crossings.

Aside. Jones once claimed to me (in person) that the Jones polynomial can be computed with knots with up to 200 crossings, but I've never verified it with my directly. Yet I've seen Khovanov homology computed (using my algorithm!) on knots with about 70 crossings, and in the light of that, 200 for Jones seems reasonable.

--[[User:Drorbn|Drorbn]] ([[User talk:Drorbn|talk]]) 06:55, 11 January 2017 (EST)