Wikipedia:Articles for deletion/Anti-knot
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[edit] Anti-knot
Other editors and I discussed the problems with this article long ago, but none of us got around to AFD'ing it the first time. In summary, 1) the term "anti-knot" appears to be a neologism, not used in any of the references, and I couldn't find a suitable reference using Google Scholar. 2) the content appears to be partly bogus, partly vague/speculative. The first proof assumes what it is trying to prove. The second uses a magical "knot energy" that does exactly what is needed. It's fair to say that the property needed of this knot energy is nontrivial and most likely an open problem. The "proof" given seems to be OR synthesized from the three references. 3) the purpose of this page is to explain that "anti-knots" in fact do not exist. This is in fact a well-known basic result (as explained in knot sum), so there isn't anything more to be said about the topic. C S (talk) 11:19, 30 May 2008 (UTC)
- Redirect/Merge to knot theory, or a more suitable page? A brief mention of the result should be sufficient. For a ref., perhaps: Cromwell, Peter R. (2004). Knots and Links. Cambridge University Press, p. 90. ISBN 0521548314. Theorem 4.6.1. Given a non-trivial knot K there is no 'anti-knot' K-1 such that the product K # K-1 is the trivial knot.—RJH (talk) 19:49, 30 May 2008 (UTC)
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- I guess I could have just redirected to knot sum where the information is already there, as I said. The only problem I have with that is that "anti-knot" is a neologism. It is in Cromwell, true (the very last hit on Google Scholar, which I overlooked), but his use of it is not meant to indicate it is a standard term. So I would not want to propagate a neologism by mentioning the term in knot sum. --C S (talk) 22:55, 30 May 2008 (UTC)
- Redir per RJH. M1ss1ontomars2k4 (talk) 22:59, 30 May 2008 (UTC)
- Note: This debate has been included in the list of Science-related deletion discussions. -- Fabrictramp | talk to me 23:47, 30 May 2008 (UTC)
- Merge to connected sum. I think the amount of text needed to be added to complete the merge would be very small, on the order of adding "That is, no knot can have an anti-knot that is its inverse element in the connected sum monoid." after the existing sentence "In three dimensions, the unknot cannot be written as the sum of two non-trivial knots." This is an important fact about knots that is already covered in connected sum and does not need a separate article but that could stand to be made a little more prominent there. The two supposed "proofs" in the anti-knot article, though, look worthless and should not be merged. If not merged, it should be deleted; it does not stand alone as a separate article in its current state. —David Eppstein (talk) 05:54, 31 May 2008 (UTC)
- Comment I've seen this non-existence of "anti-knots" mentioned somewhere in Wikipedia before. Maybe this should redirect to that. But at the moment I don't know where that is. Michael Hardy (talk) 06:17, 31 May 2008 (UTC)
- PS: I don't see how the first proof works. It seems to be circular (pun not entirely intended). Michael Hardy (talk) 06:18, 31 May 2008 (UTC)
Delete. Nothing in here worth saving.Redir/Merge. Connected sum does a much better job of explaining the non-existence of "anti-knots", and the "application" to string theory is entirely bogus (because the "strings" in string theory exist in spaces with more dimensions and much more complex toplogy than 3D Euclidean space). Gandalf61 (talk) 10:23, 31 May 2008 (UTC)
- Connected sum asserts that anti-knots do exist in higher dimensions; that makes the polemic against knot physics largely fallacious as well as inappropriate. Take it out. If we need to link this somewhere, <span id> now permits redirects to arbitrary points in text. Septentrionalis PMAnderson 16:00, 31 May 2008 (UTC)
- Redirect? One place where I find a valid proof of the non-existence of anti-knots is Eilenberg–Mazur swindle. Since this is a valid concept, but perhaps of interest only for proving the non-existence result, it should get redirected if it's deleted. I'm not sure where. Michael Hardy (talk) 00:58, 2 June 2008 (UTC)
- Michael, I'm starting to get very puzzled by your comments. You don't appear to have read any of the remarks above. For example, you commented on R.E.B.'s talk page that you would have had no idea to look at Mazur swindle for a proof of the theorem. But several people (including me in my nomination) have already pointed out that the valid content is in knot sum/ connected sum, which states that the Mazur swindle gives a proof. It is also stated that knot genus gives a proof, although the details are not included. You commented about the "valid concept" of anti-knot, but I have no idea what this means. There is a theorem that no "anti-knots" exist, but nobody except Cromwell states it that way. The concept of "anti-knot" is about as "valid" a concept as the concept of natural numbers without a prime decomposition. There is, of course, a theorem that every natural number has a prime (even unique) decomposition. Nonetheless I would find it strange that if one author were to state that theorem as "No 'unbreakable' natural numbers, i.e. not having a prime decomposition, exist" , and then people were to start calling "unbreakable natural numbers" a valid concept. --C S (talk) 01:37, 2 June 2008 (UTC)
- It has to be a valid concept if there's a theorem saying it can't exist. Certainly the concept of natural number without a prime decomposition is a valid concept. Otherwise there could be no theorem saying no such thing exists. If the concept were not valid, the theorem would have no content. The difference between that and the concept of anti-knot is that the existence of prime factorizations can be stated without introducing a concept such as the one you propose. On the other hand, the theorem saying there is no anti-knot is essentially negative: you can't state it without the concept. Michael Hardy (talk) 03:47, 3 June 2008 (UTC)
- Sure you can: every sum of nontrivial knots is itself nontrivial. No mention of antiknots. —David Eppstein (talk) 03:56, 3 June 2008 (UTC)
- It has to be a valid concept if there's a theorem saying it can't exist. Certainly the concept of natural number without a prime decomposition is a valid concept. Otherwise there could be no theorem saying no such thing exists. If the concept were not valid, the theorem would have no content. The difference between that and the concept of anti-knot is that the existence of prime factorizations can be stated without introducing a concept such as the one you propose. On the other hand, the theorem saying there is no anti-knot is essentially negative: you can't state it without the concept. Michael Hardy (talk) 03:47, 3 June 2008 (UTC)
- Michael, I'm starting to get very puzzled by your comments. You don't appear to have read any of the remarks above. For example, you commented on R.E.B.'s talk page that you would have had no idea to look at Mazur swindle for a proof of the theorem. But several people (including me in my nomination) have already pointed out that the valid content is in knot sum/ connected sum, which states that the Mazur swindle gives a proof. It is also stated that knot genus gives a proof, although the details are not included. You commented about the "valid concept" of anti-knot, but I have no idea what this means. There is a theorem that no "anti-knots" exist, but nobody except Cromwell states it that way. The concept of "anti-knot" is about as "valid" a concept as the concept of natural numbers without a prime decomposition. There is, of course, a theorem that every natural number has a prime (even unique) decomposition. Nonetheless I would find it strange that if one author were to state that theorem as "No 'unbreakable' natural numbers, i.e. not having a prime decomposition, exist" , and then people were to start calling "unbreakable natural numbers" a valid concept. --C S (talk) 01:37, 2 June 2008 (UTC)
- Relisted to generate a more thorough discussion so that consensus may be reached.
Please add new comments below this notice. Thanks, jonny-mt 05:34, 9 June 2008 (UTC)- I am the only delete !vote other than the nomination, and I would join a consensus to redirect, probably to a section of Connected sum. Michael Hardy is the only keep argument, and he hasn't actually !voted. Please close. Septentrionalis PMAnderson 20:17, 9 June 2008 (UTC)
- Yeah, just Redirect to connected sum. Jkasd 03:05, 10 June 2008 (UTC)
