Hi, Folks. A student of Ken Ono just sent me a very nice item related to my stuff, where he shows GRH implies everything in my list of probable widgets actually is a widget. About three times a page he says something is "associated to" something else, which grates on my nerves a bit. However, i can see that this might be standard usage in the modular forms industry. The difference, I guess, is that the first item is being assigned to the second item. Here's one,

"We say that a ternary quadratic form Q is associated to an elliptic curve E/Q if the cuspidal part of its theta function is a Hecke eigenform which lifts, under the Shimura correspondence, to the cusp form associated to E."

So, two associations in one sentence.

Just hoping for feedback here. I don't see this as a successful MO question. Also, I am not obligated to comment on the language. But I could...

Thanks, Todd. I am sending the comment. as he has already submitted the preprint it probably does not matter. I do remember Harry Gindi going on and on about that when I began looking here in early 2010.

Alberto, that's interesting. Good to have someone to blame.

Ben, it appears I had correctly guessed the attractions of this usage.

As a former sub-ed of sorts: I find myself agreeing with Ben, as long as usage is consistent within the paper or book being considered. However, I don't have the same problems that Ben does with "assigned to".

Following on from Todd's suggestion: I see that Milne recommends "attached to", which might not work in the cases which Ben has in mind. Perhaps "corresponding to" is a workable compromise?

Will, I refuse to trust any program which names itself after British slang for "someone with mental disorder" :)

The language is evolving. I doubt I speak the modern Russian anymore. I can put it as "Few people are capable of speaking proper Russian in the today's Russia", of course, but it doesn't change the facts. "Associated with" is a norm that comes from the primary meaning which puts the verb in the active mode even if it is used in the passive voice. "He is associated with a local gang" means that he made his free (or partially free) choice at some point and became a member. Under no circumstances will one say "I associate John with a blue car" in the meaning "I attach John to this car" (i.e., physically chain him to it). Such sentence can be understood only metaphorically and still it is the car and John that force you to connect them in your mind, not the other way around. However, in mathematics the word "associate" is a synonym of "assign", "relate", "tie", "connect", and a dozen of other verbs that either require "to" for the indirect object, or allow both "to" and "with". Of course, the temptation to use the same preposition for the words that mean the same is strong enough to induce a slip of tongue that transfers into a habit, a custom, and, finally, a norm. So, I guess you are formally perfectly right but you are fighting an already lost battle...

Thanks, fedja. I did send the student a second email directing him to this discussion and saying that there seemed to be a predominant usage for which I had never had any need. I did figure out part of what that engineer on MSE wanted, the Smith chart is simply the result of taking the upper half plane and mapping it to the unit disc by a linear fractional transformation. The lines of constant real part and constant imaginary part are copied over into the disc, becoming geodesics that meet at 1 and horocycles that are tangent at 1. I put a pdf there from some website. It is anyone's guess what else he was talking about. http://math.stackexchange.com/questions/244728/uniqueness-of-shortest-distance-between-the-center-of-two-circles-and-in-higher/244800#244800

@KConrad Of course not. My English is terrible and I know of it (sigh!)... I fancy I get the general feeling of the language and can, in principle, figure things out in finite time using a few props on the way but speaking fluently and effortlessly without making stupid mistakes now and then is well beyond my abilities. Anyway, what I'm saying is that the math. usage is different from the colloquial one. My adviser told me once that some overzealous technical editor changed "в угле" (in the angle) to "в углу" (in the corner) ("угол" means both in Russian) in one of his papers. You never say "в угле" when talking about physical reality (except, perhaps, in the radar detection business) but you also never say "в углу ABC". Both would sound equally incongruous. I can give you many more examples of such discrepancies. It is hard to believe that there is nothing similar in the English language and this "associate" example seems to be very similar in nature to the "в углу" story.

As to what native English speakers do to their language sometimes, read this: http://english.stackexchange.com/questions/10206/should-anymore-only-be-used-in-a-negative-statement-or-question. I lived in WI for a few years. Yep, they do speak this way despite it may strike the ear much more than "associated to".

My point is simply that the grammatical forms follow the changes in meaning and usage, not vice versa. If you want an English example, almost everybody says "a function supported on a set" nowadays despite the verb "to support" normally requires "by" in such constructions. Moreover, despite I know authors who still use "by" in mathematical texts, the modern consensus is that "by" is just incorrect there. However if you try to look up "supported on" on Webster, it is not listed as an option there anywhere...

We are about to conclude that Will is THE MAN.

I was joking!

(I have no problems with prescriptive-yet-open-to-changing-prescriptions-if-appropriate people, Will: that one aspect of my personality I do not have any problem with :-) )