Talk:Fuzzy sphere

Does the "fuzzy sphere" have anything to do with the "fuzzy logic" proposed by L.Zadeh in 1965? The article should be placed in a more general context, like which branch of physics is the fuzzy sphere used in?

No, the fuzzy sphere is not related to 'fuzzy logic'. The fuzzy sphere is an example of a Noncommutative geometry. Noncommutative geometries are an active area of research in theoretical physics, as these provide a means for regularising quantum field theories. Effectively, the noncommutativity generates an uncertainty relation (akin to heisenberg's uncertainty relationship) that creates a 'fuzziness' of the geometry which 'smears out' divergences. Proponents like Alain Connes claim that a quantum spacetime based on noncommutative geometries will be at the heart of a (still to be developed) all-encompassing theory of quantum gravity.

And yes, the article falls short of placing this abstract mathematical concept in context. JocK (talk) 02:52, 8 December 2008 (UTC)[reply]

Are people who write like this article completely unaware of how bad their writing is?

I am seriously curious. Because I really hate it when I come to a Wikipedia article only to find that whoever wrote it has no idea how to explain what something is in an introductory sentence or paragraph. So instead they just rattle off whatever unintelligible technical gobbledegook comes into their heads. I'm not saying any of it is wrong. (How could I; I don't understand any of it.) But suppose it true. Does that even matter if almost nobody understands what you are talking about?

For instance: In the first mention of an algebra of functions that is noncommutative, this seems impossible: If functions from a sphere (a 2-sphere? an n-sphere?) go to the reals or complexes as codomain — and if the algebra operations are the usual ones applying to functions of addition, multiplication and scalar multiplication — then the algebra will certainly be commutative. So why is this most obvious reasoning wrong? The writer never bothers to explain.

What are these "spherical harmonics" spoken of? No explanation, because the author thinks that letting readers click in order to figure out what the author means is a manner of writing. (It is not writing at all.)

Then "...whose spin l is equal to some j". What is this trying to say?

Like most authors who think the way to explain something is to assume the reader already knows what they are talking about, this author is badly mistaken.

I hope someone who is a) knowledgeable on the subject, and b) willing to take the trouble to write clearly, will please rewrite the first section intelligibly.2600:1700:E1C0:F340:25EB:BFCF:6103:3A10 (talk) 07:59, 22 February 2019 (UTC)[reply]

Well, assuming a knowledge of spherical harmonics is reasonable if the subject is noncommutative geometry. The problem is that truncating a graded commutative algebra can't make it noncommutative, so that can't be what's happening. Hopefully I can read Madore and figure out what's happening. (No, I wasn't the original writer.) 81.224.188.19 (talk) 18:23, 5 January 2021 (UTC) jk[reply]