Fred Linton has in this mail enlighten us all about the meaning in french of the words "aboutissement" and "aboutement". Quite different meanings. (*) It seems that "aboutir" means more or less "to arrive" or "to finish" "come to the end" etc, while "abuter" means 'to join end to end', thus ""abuter" a path" would mean "to make it into a loop" while ""aboutir" a path" would mean "to arrive to the end point" if "abutment" translates "aboutement", it certaily does not translate "aboutissement" Having in mind (*) above, somebody knowledgeable in both mathematics (in particular spectral sequences) and english should be able to come up with a correct english version of what Grothendieck meant by "aboutissement", which was certainly not "abutment". Fred E.J. Linton wrote:
Greetings.
Way back on Monday, in an email direct to Mike, I had asked,
Think 'abut' for aboutir or 'abutment' for aboutissement are unusable false cognates?
The more I read the comments here, and the more I consult dictionaries and phrase books, the more I come to think the answer, alas, is YES.
Without, for the moment, examining the roles of "aboutir" and "aboutissement" in the setting of spectral sequences, let me expound for a bit on plain French philology.
French "bout" is a masculine noun whose meaning tends to be along the lines of 'end', 'tip', 'extremity', as in the idiomatic expressions:
"aux bouts du monde" = 'to the ends of the earth' ; "d'un bout à l'autre" = 'from beginning to end' (literally: 'from one end to the other') ; "sur le bout des doigts" = 'at [one's] finger tips' ; "au bout d'une heure" = 'after (lit.: at the end of) an hour' ; "le bout de la langue" = 'the tip (extremity) of the tongue' ; "au bout de la rue" = 'at the end of the street' .
Not to be confused with French "but" = 'end' in the rather different sense of 'goal', 'aim', 'target', 'purpose', etc.
French "abouter" is a verb, derived from "bout", whose meaning is 'to join (or to place) end to end'; its past participle "abouté" thus serves as the adjective 'placed (or joined) end to end', whence the carpenterial nouns "about", for 'end' or 'butt-end' and "aboutement", 'butt-junction' or 'abutment'.
The French verb "aboutir" develops 'end' rather differently: its meanings are rather 'to come to an end at (or with)', 'to join', 'to meet', 'to border upon', 'to end in', 'to tend to', as with:
"N'aboutir à rien" = 'to come to nothing' ; "Ce champ aboutit à un marais" = 'this field borders upon a swamp' ; the long, winding road that may quite possibly "aboutit" in a cul-de-sac ; "N'aboutir à rien" = 'to come to nothing' ; and even "Faire aboutir un abscè" = 'to bring an abscess to a head' (literally: 'to cause an abscess to come to an end') .
The French noun "aboutissement", being derived from "aboutir" rather than from "abouter", thus differs from "aboutement" in signifying rather the end (or border or new state or condition) at or to which something may "aboutit"; or, the act of achieving that end, border, state, or condition. In particular, for a context where "aboutir" has the meaning 'to tend to', the sense of "aboutissement" may well be 'that which is tended to', which is very nearly 'limit'. This nearly suggests that "aboutir" might even, at times, be capable of expressing the sense 'to converge to'.
That said, how does this all fit with spectral sequences?
Certainly there is well-established usage involving the terms of a spectral sequence converging to something-or-other. Only in the full context of the French text around "aboutir" or "aboutissement", though, would I be able to hazard any guess whether 'convergence' or 'limit' would be the right counterparts. Quite possibly they are *not*.
Still, I'm hesitant to withdraw my warning that 'abut' and 'abutment' are probably false cognates, no matter that several mathematical authors have chosen to use them to render these terms.
Is there any hope, perhaps, of getting input from some francophone spectral sequence experts -- best of all, from AG himself?
Thanks to Eduardo D and Vaughan P and Michel H for their misgivings, which encouraged me to compose the above, despite the assurances of Jim S that the 'abut*' usage is by now well entrenched.
Cheers,
-- Fred
------ Original Message ------ Received: Wed, 20 Aug 2008 07:27:05 AM EDT From: edubuc@dm.uba.ar To: "categories" <categories@mta.ca> Subject: Re: categories: Re: Re: abutment = aboutement?
I agree with Vaughan.
Further, I have the feeling that "abutment" is not the appropriate way of rendering into mathematical english the meaning of the word "aboutissement" as it was used by Grothendieck.
I repeat, we should analyse the whole french sentence to come up with a good translation.
Is it not possible that somebody (not very versant in either french or english) had first the need to translate Grothendieck's "aboutissement", and unlike Michael Barr who asked advise, just came up with "abutment" (out of some dictionary).
and then, other people (also not very good at either french or english) in the same area just keep copying him and each other?
and generated the whole cascade coming out of google . . .
who is to blame for the first use of "abutment" for Grothendieck's "aboutissement" in mathematical english ? ja !!!
are we all going to follow ?
I will be the first to use "abutment" if the word has a long tradition, and some prestigious mathematicians have used it.
I finish with a question: Is it the case here ?
Eduardo Dubuc
I'm with Michel on this one:
Just a remark about "abutment": it translates the French "aboutement", with a rather different meaning than "aboutissement". The latter is closer to the "ending" (of some process; with possibly a little shade of "fatality" in it).
The two words are related, and I don't know whether the mathematical idea behind makes "abutment" good, or even better, but I just wanted to mention the difference.
Not a single abutment in any of the following YouTube videos posted by their proud aboutisseurs.
http://www.youtube.com/results?search_query=aboutissement&search_type=
Evidently G needed a word with the sense of "limit" or "completion" that didn't overload terms that already had technical meanings in that context while itself having a technical ring to it, which "aboutissement" seems to do nicely in French. Something like "terminus" might serve this purpose in English.
An abutment is an engineering construct for butting two things together, often in the context of bridges, whether over a river or between teeth, and seems quite unsuitable for this purpose.
Vaughan