The following is an archived discussion of a featured article nomination. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.

The article was not promoted by SandyGeorgia 03:34, 28 March 2009 [1].

Knot theory[edit]

Nominator(s): C S (talk)

Substantial editing of this article over the last couple years by me and some other editors have resulted in what I believe to be a well-written and sourced article on knot theory accessible to the "intelligent layman". I think all the FA criteria are satisfied, but I've never nominated an article for FA before, so please be gentle :-) C S (talk) 10:42, 15 March 2009 (UTC)[reply]

Comments by Sasata

Cool! Knot theory. Something I can relate to, having used shoelaces since childhood.

I hope you've been using the right knot to tie them. Even famous knot theorists have been known to make that mistake.
  • I expanded and revised the lede. How's it now?
  • Better. But see more comments below. Sasata (talk) 02:08, 16 March 2009 (UTC)[reply]
  • I tried to make it flow more, and at least there are no single sentence paragraphs anymore. How's it now?
  • Done. Actually I didn't like how that sentence read so I redid it by importing some examples instead from the history article.
  • Doesn't seem that implausible to me (topology didn't exist as a subject until then) :-). I made a correction though. Gauss had studied knots earlier in the 1830s, but this was something of an isolated event, and his discoveries were rediscovered later by Maxwell, etc. So I put that in. Good catch -- somehow I had put it in the more fuller history of knot theory article but omitted it here.
  • Sure. It's a basic topological object and knot theory is topological.
  • Done. query: Should all the references in the reference section have ndashes too?
  • The Flapan book ref given a sentence later suffices. But I've added an early journal reference to Jon Simon.
  • Source is given in the history of knot theory article (and any source for topological quantum computation would suffice too), but I've added it to this article.
  • Ok, added. The papers are spread out over a time period so I just said late 1960s.
  • They just are. Asking why is like asking why factoring numbers is hard, Nobody knows why! Some algorithms are partially implemented on computers, but only partially because the algorithms can be complicated. Theoretically it is already clear some algorithms will not work in practice (with the limits on computing resources). In the case of unknotting, some algorithms are fully implemented. In the case of general knot recognition, no full implementation of Haken's algorithm exists. Yes, sitting around the table arguing is a perhaps too accurate picture. It's the same as in any subject where there are many unresolved basic questions.
  • I'm thinking it would be funny to feed a topologist spaghetti with the ends tied together. There's a joke in there somewhere. Sasata (talk) 02:08, 16 March 2009 (UTC)[reply]
  • what do you mean "spaghetti with the ends"? Isn't spaghetti just a blob? :-) (so the topologist says while drinking his doughnut and trying to bite a coffee mug...)--C S (talk) 07:56, 16 March 2009 (UTC)[reply]
  • If you think it would be helpful to include any of this, I can. But to take the "factoring numbers" example, this is something that is actually not understood at all with lots of investigative work being done and much unpublished info. I tried to summarize things as best I could.
  • It's just a particularly appealing simple case. Is a loop knotted or not? That's a basic question, and given the complexity of the general question, one can hope to make progress on the easier situation. The Hass ref suffices for this statement, but I added another ref anyway to get a bit of variety (since this statement is more reflective of opinion and sociology).
  • Ok.
  • an alternating knot by definition has an alternating diagram, but not every knot has such a diagram, e.g. there are non-alternating knots. In any case, this is something of a digression (originally added by a random passer-by), so I removed it.
  • This is a bit of repetition from the lede. Do you prefer the wording from the lede? It talks about the "quantity" being the same for different descriptions of the knot. I added an example to make it clearer. Does that help?

*I'm going to stop here and register an oppose vote. Will check back later to see if its more comprehensible to me. Sasata (talk) 15:39, 15 March 2009 (UTC)[reply]

I'm striking out the oppose vote (want to stay neutral), and will come back again with another read and more comments after the nom has had time to deal with Jakob.scholbach's comments below. Sasata (talk) 21:17, 16 March 2009 (UTC)[reply]

Ok fresh comments, from the beginning. Sasata (talk) 02:08, 16 March 2009 (UTC)[reply]


  • No, but quantity is not referring to knots. It's referring to knot invariants, which are quantities assigned to knots. More below.
  • Practical advantage? Mathematicians generalize. This is what they do! I guess I can throw in a sentence like "...to gain further insight, mathematicians generalize..."
  • This seems based on the misconception about quantity above. Since knot invariants are used to distinguish knots, "powerful" here just means they are very effective at distinguishing knots.
  • Ok. Done.
  • This linguistic contortion is actually being used for a particular reason. Knots themselves do not show up in topological quantum computation, but the mathematical techniques used and developed by knot theorists do. This may be anal-retentive though...I'll just change it to "knot theory".
  • good point.
  • No, again, "quantity" was referring to knot invariant. When reading the article again, I'm very puzzled how it is possible to conclude that "knot invariant" is another term for "knot". I'm wondering whether you simply misread some passages, or whether the misunderstanding is due to the writing being horrible. You realize that I've modified the descriptions of knot invariant in the lede and introduction to the section "knot invariant" since the first time you looked? I'm not sure if you've read them. --C S (talk) 06:59, 16 March 2009 (UTC)[reply]
  • Also, the term embedding was used in the lede, but probably it is not really necessary in this section, so I just removed the term and rewrote the sentence. --C S (talk) 07:54, 16 March 2009 (UTC)[reply]
  • Fixed.

((double image|right|unknots.svg|200|Ochiai unknot.svg|200|(Left) The unknot, and a knot equivalent to it. (Right) It is more difficult to determine whether complex knots such as this are equivalent to the unknot.))


  • Good points. All that is meant is that changing the direction of the projection slightly will give you a knot diagram. So I just said that instead :-)
  • Isolated is referring to the fact that these times are discrete. This paragraph is really a very intuitive description of something considerably more technical. There might be a whole interval of time where events happen, but the point is that you can arrange it so it doesn't happen that way Actually, it suffices to just say "finitely many times"...I hope the new wording is clear.
  • The Reidemeister moves can be thought of as three types of events: 1) straightening a kink 2) two strands becoming tangent at a point as they pass each other 3) three strands coming together at a point and then moving away. More complicated events would be anything that can happen as you project the knot to a plane but don't have a diagram. So, for example, if more than three strands comes together at a point. Or if three strands become tangent at a point. Etc. I'll try and reword this.
  • Also, to clarify: if two diagrams are connected by Reidemeister moves, then they represent the same knot (because the Reidemeister moves clearly give a movement of the knot that gives the equivalence). It's not as clear that if two diagrams represent the same knot that there are these moves that connect them. That's the point of this analysis.
  • It doesn't sound like that to me....is this related to the misconception from above that an invariant is a knot?


  • Thanks for all the comments! I hope you get a lot of rest and come back :-) --C S (talk) 06:59, 16 March 2009 (UTC)[reply]
  • Dabs are not up to speed (based on the checker tool in the toolbox)
    • They need fixing.
Fixed.
  • External links (based on the checker tool) and ref formatting (based on the WP:REFTOOLS script) is found up to speed.--Best, ₮RUCӨ 15:51, 15 March 2009 (UTC)[reply]
  • It's been cleaned up. The few items left, I believe, are appropriate see also items. --C S (talk) 21:05, 15 March 2009 (UTC)[reply]

Comment

  • I see there are many references already, but some parts still miss them. Anyway, if you would have used the footnotes, you could display also the concrete pages, which would make it much more transparent :) --  LYKANTROP  ✉ 13:15, 18 March 2009 (UTC)[reply]
Otherwise, sources look okay, links checked out with the link checker tool. Ealdgyth - Talk 16:11, 16 March 2009 (UTC)[reply]

Comments Jakob.scholbach (talk) 20:25, 16 March 2009 (UTC)[reply]

I think this is a pretty nice article, well-written in many places, with good emphasis on explanations of "standard" facts etc. However, I have a number of problems: in many places the parlance is not really encyclopedic, which should be easy to fix. Perhaps find a copyeditor? Also, the organization of the article as a whole could use a clearer structure. I feel it would be good to have a section simply called "Knots [and links]", which introduces a couple of basic notions such as knots, links, ambiant space, isotopy, knot complement etc., and also serves as an introductory section. (Notice also that "Knot diagrams" mostly talks about Reidemeister moves. I suggest putting the diagrams part into the intro section). My main concern is comprehensiveness, an FA criterion. As far as I can see, there are quite a bit of applications of k.th., both in mathematics and outside, which deserve a proper treatment. (History section briefly touches upon, but that's not enough). Also, I have the awkward feeling that modern developments get fairly short shrift. (Actually you acknowledge this yourself.) The article does not achieve a clear picture of what modern knot theory is, what are its leading questions, open problems, main techniques etc.

In addition to the above, a couple of more concrete points ('til hyperbolic invariants):

(I will not be able to respond to progress before next Monday.) Jakob.scholbach (talk) 23:02, 17 March 2009 (UTC)[reply]

Oppose The history section lists several applications of the theory (statistical physics, chirality, DNA) but the body of this article does not tell a word about it. I think it is very missing and am therefore opposing on the basis of comprehensiveness. I would also like to suggest the authors to merge this article with Knot (mathematics). Vb 11:56, 18 March 2009 (UTC) —Preceding unsigned comment added by 79.233.248.217 (talk) [reply]

I think you don't have to do anything special, just state that you withdraw. SandyGeorgia will then archive the nomination at some point. Jakob.scholbach (talk) 08:20, 26 March 2009 (UTC)[reply]
Please reconsider. This is better than most FAs as it stands, and many of the objections are unimportant MoScruft. Expanions are always welcome, but 4-dimensional invariants should probably be a subarticle anyway. Septentrionalis PMAnderson 22:48, 26 March 2009 (UTC)[reply]
Probably, as I said above, only a few paragraphs are needed, which I could whip up in a few days work, but I would have to dig out some sources and get into the zone. Right now, I'm dealing with other matters, so I can't say when I would be able to get around to working on the article.
The above discussion is preserved as an archive. Please do not modify it. No further edits should be made to this page.
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