Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Moonshine, intentionally with capital M as most people do follow this convention for the Monster and (Monstrous) Moonshine VOA.
From the way you write, it sounds as if this is the first time you’ve heard of monstrous moonshine, but the term has been around since the eighties. And of course no one here had anything to do with it; the coinage is due to the ever-whimsical John H. Conway, who apparently found a certain numerical “coincidence” so off the wall that he called it “moonshine” (lunacy, more or less), “monstrous” because it involved the Monster Group which is the largest of the so-called sporadic finite simple groups. You can read about it at the wikipedia article.
John Conway is British; perhaps the (American?) meaning of illegal hooch didn’t immediately suggest itself to him. There’s a famous bit of lore though about a second piece of moonshine or coincidence which relates the prime factorization of the cardinality of the Monster to the properties of certain modular groups. The American mathematician Andrew Ogg was struck by the coincidence, and offered a reward of Jack Daniels to the first who could explain it, thus adding another layer of significance to the term.
All this is well-worn history, and “moonshine” has become such an old joke that the joke is all but forgotten, and the term “moonshine” has become a more or less neutral piece of terminology. As one might expect.
I’m not sure what needs to be discussed though. Jargon is hardly unique to mathematics, and the etymology of this particular bit of jargon seems not very remarkable to me or hard to understand, even if the phenomenon it refers to is.
Added Monster group. Also sporadic finite simple group and classification of finite simple groups. Both a bit stubby.
My own guess, Ian, is that there is jargon in direct proportion to the range of concepts in the science (let’s not argue over whether math is a science; that’s not really relevant). I mean no disrespect at all to chemistry and biology in saying that currently, mathematics is of far greater intellectual depth than either of these, for reasons not hard to understand: it’s had an enormous head start, but perhaps more importantly the very nature of mathematics naturally entails much greater creative scope. We can set up any axiom system we jolly well please in mathematics, subject only to the constraint of abiding by logic, whereas sciences closely tied to empirical data are naturally under far greater constraints.
I don’t think there’s anything to be done about jargon; it’s the nature of the beast. Speculating a little beyond my ken, my sense is that chemistry and biology may be more amenable to exposition for non-specialists because there are still many simply-stated questions whose answers are unknown, whereas in mathematics, most of the simply-stated questions were answered long ago and the current research necessarily ventures into waters where even the questions require a specialized training.
I second Ian in disliking (somewhat vague) concept and even more the word “evil” in category theory. Instead of a word I prefer to quote a (variant of the) principle (and there are undoubtfully various well-defined versions of what people may intend calling evil in different categorical or higher categorical contexts).
Of course, there are good reasons for condensing quotations of principles to single words: flows more easily off the tongue (or fingertips), easy embeddability in sentences, etc. I guess one could question the wisdom of the word ’evil’, though.
I agree, of course.
It is true that often mathematicians are surprisingly careless with naming concepts that they hold in high esteem.
Apart from jokes, a recurring problem is that important concepts are named after minor or less-than-minor aspects of them. Examples include “triple” or “bar complex”. The trouble is that there is a constant competition in understandability of the established versus the self-explanatory.
I agree with both of these last two points. In this regard, “Moonshine” was not one of Conway’s most shining moments – he is often much more thoughtful in his word choice even when being whimsical or playfully inventive. “Monster” is not good either; I would have preferred the other moniker “Friendly Giant”, since “monster” suggests pathology or teratology which is quite inapt here.
So what’s the story behind “Friendly Giant”? Who made that up?
since “monster” suggests pathology or teratology which is quite inapt here.
I always envision the Monster group as being blue and eating cookies.
I am guessing “Friendly Giant” is due to Bob Griess, who was one of the principal actors in the discovery of this group. The initials FG could also refer to Fischer-Griess; whether that’s coincidental is hard to say. See the references in the WP article.
Thanks. I added that to Monster group. Maybe you can further expand there.
This is one of those irregular verbs, isn’t it:
I completely agree that we should use simple language. Let’s call a monoid in the category of co-V-algebra objects in the category of models of V-algebras a monoid in the category of co-V-algebra objects in the category of models of V-algebras.
Except that then I’d have to give up my simply amazing triple pun in the title of a forthcoming paper (assuming I can convince my coauthor to let it see the light of day).
Once the entry grows in content widely and wildly it will be a delight to split it into the appropriate pieces. :) Volunteers for breeding toward a wild growth are lurking around I hope…
Regarding nomenclature: there are “vertex algebras” and “vertex operator algebras”, and they are apparently not the same (VOA’s include a structure of Virasoro element satisfying certain axioms). If I’m not mistaken, the moonshine module is a VOA (hence by forgetfulness a VA, but the Virasoro element structure is important, if my memory is correct). Isn’t “moonshine module” what people usually call it? I’m thinking that would be the better page title, and that it ought to be described as a VOA, not a VA. (I’m not an expert, and my memories are based on rather old memories of discussions with Lepowsky and Huang at Rutgers when I was a graduate student.)
Maarten: by all means add comments directly to the Lab page, and let us know here.
Added link to Monster group and sporadic finite simple groups to subquotient, and a little more history on Monster group. It is interesting how the Monster was predicted to exist with various properties and even its order could be estimated without even knowing it existed. Classification of finite simple groups is black magic to me.
I thought I had read even more dramatic things – that not only did they know the order, they knew the full character table before proving it actually existed! I’ll see whether I can track that down.
As I said elsewhere, I was a graduate student at Rutgers where several of the leading finite group theorists were: Daniel Gorenstein, Michael O’Nan, Charles Sims, Richard Lyons – Gorenstein was the ring leader of the classification project and the other three have groups named after them. Also Lepowsky, one of the architects of the moonshine module, was there. The model theorists at Rutgers, for example Gregory Cherlin, are also au courant with the classification, as they use it directly in their work.
Alas, I never learned any of that stuff. Finite group theory is not an easy field to get into.
Edit: what I thought I remembered about the character table is right there in the WP article.
Surely vertex algebras are not as specific as VOAs with Virasoro. There is also a notion of conformal algebra. Thus one has to be careful with hasty identifications like the statement that all these are just FQFTs or alike. It will take a time to have separate entries for each class.
There is a potential blunder at wikipedia. The conformal Lie algebra has two meanings: one is the Lie algebra of the conformal group (old meaning) and another is a Lie analogue of conformal algebras of Victor Kac. Wikipedia redirects “conformal algebra” to the entry “conformal group” just because they have a section on the Lie algebra of conformal group, which they call conformal (Lie) algebra and sometimes forget “Lie” what was here and there a habit in old times. This is very misleading.
1 to 25 of 25