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

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

I admit I don't recall abutment but abutting has a long history in spec sequence jargon the idea I think was that the spectral sequence runs to/ buts up against the E\infty term or is it to the object of which E\infty is the associated graded? sorry it's been so long... jim

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

On Wednesday 20 August 2008 2:13 pm, Michael Barr wrote:

I am NOT about to change a word that has apparently existed for over 50 years just because it is not particularly meaningful.

I am going to risk putting my two cents here and perhaps being rejected by the moderator. One of the reasons why a word may need to be changed even if it has existed for 50 years is to avoid confusion. For example in the book "Categories for Software Engineering" the author talks about the "social life" of a set being the other sets it talks to. For a long while this puzzled me, until it dawned on me that the idea that the author was using was that the origins of modern Object-Orientated Programming (ie C++, Java) started with SmallTalk. In SmallTalk, objects communicated with one another by sending messages; and so making an analogy with familiar concepts that programmers use "sets have a social life" because SW objects "talk" to each other by sending messages. Stated another way it is difficult to see how a (Mathematical) object is the same as a (Software) object. The latter gets created and destroyed as the object comes in and out of scope. Hence what does one do? When stated generically, does the word object mean a mathematical one (around 60 years old) or a software one (more widely used)? Nim.

To add to the chatter on this topic I'll point to the bilingual Grothendieck-Serre Correspondence (Pierre Colmez, Jean-Pierre Serre, eds., Catriona Maclean, tranlater. AMS/SMF, 2004). The first appearance of "abutment" of a spectral sequence appears on p. 21 as the translation of Serre's "au bout" (quotation marks in the text.) On p. 26 Grothendieck uses "l'aboutissement" (in quotation marks) which is also translated as "abutment". Aboutissement and the translation abutment, without quotation marks, then appear on occasion throughout the remainder of the text. -- Bob -- Robert L. Knighten RLK@knighten.org

Thaks, Vaughan That reraises a question I implied earlier limit for the E_\infty term is appropriate but that is the graded of what I dimly recall the SS abuts to - the ungraded, e.g. H^(E) in the Serre-Leray SS anyone confirm that? jim Pratt wrote:

Meanwhile I count eight occurrences of "abut" and "abutment" in the (36 kilobyte!) main Wikipedia article on spectral sequences (there are a dozen separate much shorter articles on particular spectral sequences, along with a 15 kB article on derived categories).

On the other hand the algebra and geometry articles of the 1987 Britannica Macropaedia both prefer the term "limit" for what a spectral sequence converges to, in respectively Peter Hilton's contribution "Other aspects of homological algebra" to the algebra article, and the geometry article's section on algebraic topology.

Since Wikipedia seems to be trumping Britannica these days, and no one here has objected to established usage in mathematics trumping linguistic suitability, the precise distance of "abutment" from the optimal English cognate for "aboutissement" would appear to be academic, an epithet reflecting the outside world's perception that raising moot points is in our job description.

Vaughan

...

...

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.

Fred

[ Note from moderator: It is time to close this thread. Further discussion of the linguistic part of Michael's query should happen away from the list. Thanks to contributors. ] Michael Barr wrote:

I am NOT about to change a word that has apparently existed for over 50 years just because it is not particularly meaningful.

"aboutissement" existed for over 50 years of course, but the translation "abutment" is, (at least in the references given in these postings, including the translation of the grothendieck-serre correspondence) much more recent, it seem that all of its occurrences are from the second millennium, or very close. On the other hand, we have learned in these postings that in the 1980's and before, the word "limit" (and not "abutment') was used for what a spectral sequence converges to. An authority as Peter Hilton used "limit". There are a lot of well established words in mathematics which are not particularly meaningful, but the difference with "abutment" is precisely that they are well established.