|WikiProject Mathematics||(Rated Start-class, Low-importance)|
|This page was nominated for deletion on 16 September 2008. The result of the discussion was nomination withdrawn.|
This is a wonderful little article. JonathanFeinberg 14:16, 6 October 2006 (UTC)
Origin of the term
The first paragraph about the origen of the expression is confusing and even contradictory: was it N. Steenrod or S. Maclane that coined the term? I thought I gave a reference citing Steenrod, but someone else put the statement by Maclane which seems to suggest something else. Whatever it is, we need to straighten this out. --CSTAR (talk) 18:08, 14 December 2007 (UTC)
- When Mac Lane writes (in his 1997 retrospective) that the subject was then [i.e., in 1942 or thereabouts] called "general abstract nonsense", he is clearly, almost emphatically, not claiming that he was the originator. This quote establishes, though, that the coinage predates category theory itself as a subject, which codified the abstract and economical form of reasoning already developed and fruitfully applied in homological algebra. I've tried to make this clearer in the article. --Lambiam 00:30, 15 December 2007 (UTC)
Is this article a hoax? It does not seem to be since many people have put a lot of time into editing it but I don't recall category theory every being called abstract nonsense.
- No, it is not a hoax. See e.g. Serge Lang's Algebra, which has an entry for "Abstract nonsense" in its index. — Tobias Bergemann (talk) 06:57, 28 August 2008 (UTC)
- As the article now says the term is (usually at least, I know of no exception) used non-pejoratively. It is a "self-deprecating", term used "jokingly" and affectionately by practitioners of category theory. Used in this way, It does not mean that category theory is in fact "nonsense", nor is it an insult. Paul August ☎ 15:25, 19 September 2008 (UTC)
- Keep in mind we have articles on ethnic slurs on Wikipedia. Whether or not the term or article's existence is insulting to category theory (or more properly, to category theorists) is really irrelevant. --C S (talk) 15:48, 19 September 2008 (UTC)
- I know of many cases where this term is used in a derogatory fashion. Sometimes it is used by mathematicians who are intimidated by an abstract argument, in an attempt to make themselves feel better by calling it "nonsense". Sometimes it is used against Category Theorists to trivialise their work. It is certainly not standard terminology among all mathematicians, and it causes controversy among Category Theorists, so I have slightly modified the article to reflect the fact that only some mathematicians use this term. Some of us think it is misleading and insulting to describe a whole field of mathematics as "nonsense" even if you don't actually mean that it is nonsense. Eugenia Cheng (talk) 08:36, 11 February 2011 (UTC)
I am not worried about the references to the article; this article is well sourced. However, I do not see any specific point in creating this article and nor do I see its purpose. In my opinion, this article is degrading category theory. If you have any opinions, could you please post them?
- I think you have got the wrong end of the stick here. The term is not derogatory - instead, it is used in an affectionate and humorous fashion. And I don't agree that every article on Wikipedia has to have a "purpose" or a "point" either. Gandalf61 (talk) 13:21, 16 September 2008 (UTC)
- Whether an article has derogatory references is, on Wikipedia, not relevant to whether an article should be deleted; it is to do with whether an article/topic has notable significance—see WP:NOTABLE for more details. Under those criteria, this article should certainly stay (I've had at least five professors refer to category theory as abstract nonsense, and have read the reference in Lang as well). As far as I'm concerned, this article should definitely stay. Xantharius (talk) 01:29, 17 September 2008 (UTC)
The article seems to be about this particular whimsical terminology. Per WP:DICDEF, we should not maintain articles purely to document word usage (that is the role of Wiktionary). It seems that we should therefore merge this article into Category theory as this seems to be the substantive topic. Colonel Warden (talk) 16:29, 17 September 2008 (UTC)
- It has been mentioned at the deletion page discussion that this particular stable expression transcends category theory. For instance it is used routinely in topology and algebra. I don't think it reduces merely to "word usage" but rather describes a certain type of mathematical argument. Perhaps we can agree to call it metamathematics. Katzmik (talk) 16:33, 17 September 2008 (UTC)
- These sources indicate that the phrase is a synonym or nickname for homological algebra. Perhaps that should be the merge target. That article could use a light introduction. Colonel Warden (talk) 16:49, 17 September 2008 (UTC)
- I have long viewed "abstract nonsense" as simply a playful synonym for category-theoretic methods. Perhaps this is because I'm in a different area of mathematics. As an aside, this article is certainly not "metamathematics" as it is understood by the mathematical logic community. — Carl (CBM · talk) 17:00, 17 September 2008 (UTC)
- There is not necessarily a contradiction between these two positions. "abstract nonsense" started out as a nickname for homological algebra, but, as the article itself makes clear, it has been used in a wider sense than its original meaning. As per my comment above, I have to modify my position. While talking to a colleague yesterday I caught myself using the expression "by a general nonsense argument". This is what I had in mind all along. It could be that the two expressions "abstract nonsense" and "general nonsense" are used somewhat differently. Perhaps a redirect page should be created for "general nonsense" as well, so we can see how much traffic it gets at article traffic statistics site. Katzmik (talk) 12:13, 18 September 2008 (UTC)
History and meaning of the term
In a post titled: "FOM: affectionate jokes, reply to Simpson" to the FOM mailing list, in reference to the term "abstract nonsense", Colin Mclarty has the following to say:
- Friedman brought the same term up in an earlier post, but he noted that it is usually used jokingly by people who like category theory. The story ought to be well known by now.
- Norman Steenrod first hung this tag on category theory. He had spent years trying to axiomatize homology, encouraged by Solomon Lefschetz. Lefschetz had also backed the young topologist Sammy Eilenberg, and encouraged Eilenberg's collaboration with the algebraist Mac Lane explicating certain calculations in homology. When Eilenberg and Mac Lane created category theory, Steenrod saw he could use their way of emphasizing morphisms at least as much as objects. He happily said this "abstract nonsense" was the key to solving his problem.
- The phrase was popularized by Lang's ALGEBRA, which had an index entry under "abstract nonsense". The page numbers sent you to various one line proofs such as "By abstract nonsense, tensor products are unique up to isomorphism when they exist". The joke got old and survives only vestigially in the latest edition.
- I think some of the above, particularly some reference to Lang's influential book ought to be incorporated into the article. Paul August ☎ 16:11, 18 September 2008 (UTC)
- I've removed the copyvio. As C S says we can't copy text from another source verbatim — any direct quotes we decide to use need to be quoted and cited. If no one else does first, I will try get to this eventually, but I am inconvenienced at the moment by being able to type only with one hand. By the way I think the passages I cited from Lang are more authoritative. Paul August ☎ 13:21, 19 September 2008 (UTC)
Is 'The Usual Yoga' a synonym? =
- Related? Yes. Synonymous? No. "The usual yoga" is the means by which the nonsense is understood. By indicating general nonsense, you're indicating that there is a certain usual exercise ("yoga", get it?) which is sufficiently trivial as to be left un-explicit in the discussion. "Nonsense" may be seen as analogous to "absurdum" in that popular Latin phrase about a certain kind of proof, as "yoga" is to "reductio". --126.96.36.199 (talk) 02:52, 27 July 2010 (UTC)
First reference: attribute to Wiktor Macura
I don't know how to edit the references section, but I wanted to point out that the reference to the MathWorld article should probably cite Wiktor Macura.
There's a note at the bottom of this page: http://mathworld.wolfram.com/AbstractNonsense.html
Saying it should be cited as:
Macura, Wiktor K. "Abstract Nonsense." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/AbstractNonsense.html
So while MathWorld is created by Eric Weisstein, the individual entry is attributed to Wiktor Macura.
I'm pretty sure the example only works if we assume is nontrivial (originally it said "positive Betti number" with no reference to which Betti number was positive), which I think detracts pretty heavily from the result (for example, it misses the Hopf fibration). Please tell me if I'm missing something! Algebra123230 (talk) 00:24, 4 June 2013 (UTC)
The article claims, "category theory is the study of the general form of mathematical theories, without regard to their content."
How does this distinguish CT from, e.g., Zermelo-Fraenkel set theory?
How about this?
Category theory is a mathematical foundation which offers an alternative to set theory. Whereas set theory is founded on a language with only one binary relation symbol, namely membership, interpreted as holding between sets, category theory is founded on a language with only one binary operation symbol, namely composition, interpreted as an abstraction of composition of functions. Vaughan Pratt (talk) 05:21, 10 July 2014 (UTC)