[Haskell-cafe] Category Theory woes

Daniel Fischer daniel.is.fischer at web.de
Thu Feb 18 11:54:50 EST 2010

Am Donnerstag 18 Februar 2010 17:10:08 schrieb Nick Rudnick:
> Hi Daniel,
> ;-)) agreed, but is the word «Ring» itself in use?

Of course, many people wear rings on their fingers.

Oh - you meant "in the sense of gang/group"?

It still appears as part of the name of some groups as a word of its own, 
otherwise, I can at the moment only recall its use in compounds.

> The same about the
> English language...  de.wikipedia says:
> « Die Namensgebung /Ring/ bezieht sich nicht auf etwas anschaulich
> Ringförmiges, sondern auf einen organisierten Zusammenschluss von
> Elementen zu einem Ganzen.

I don't know whether that's correct.
It may be, but then the french "anneau" is a horrible mistranslation.

> Diese Wortbedeutung ist in der deutschen
> Sprache ansonsten weitgehend verloren gegangen. Einige
> ältereVereinsbezeichnungen </wiki/Verein> (wie z. B. Deutscher Ring
> </wiki/Deutscher_Ring>, Weißer Ring </wiki/Wei%C3%9Fer_Ring_e._V.>) oder
> Ausdrücke wie „Verbrecherring“ weisen noch auf diese Bedeutung hin. Das
> Konzept des Ringes geht auf Richard Dedekind
> </wiki/Richard_Dedekind> zurück; die Bezeichnung /Ring/ wurde allerdings
> von David Hilbert </wiki/David_Hilbert> eingeführt.»
> (http://de.wikipedia.org/wiki/Ringtheorie)
> How many students are wondering confused about what is «the hollow» in a
> ring every year worlwide, since Hilbert made this unreflected wording,

You know, a "field" is a "Körper" in german, ("corps" in french), a "Ring" 
is a "Körper" with a hole in it (no division in general).

> by just picking another term around «collection»? Although not a
> mathematician, I've visited several maths lectures, for interest, having
> the same problem. Then I began asking everybody I could reach -- and
> even maths professors could not tell me why this thing is called a
> «ring».

That's often a problem with things that were named by Germans in the 
nineteenth or early twentieth century. They had pretty undecipherable ways 
of choosing metaphors and coming up with weird associations.

> Thanks for your examples: A «gang» {of smugglers|car thieves} shows even
> the original meaning -- once knowed -- does not reflect the
> characteristics of the mathematical structure.
> Cheers,
>     Nick
> Daniel Fischer wrote:
> > Am Donnerstag 18 Februar 2010 14:48:08 schrieb Nick Rudnick:
> >> even in Germany, where the
> >> term «ring» seems to originate from, since at least a century nowbody
> >> has the least idea it once had an alternative meaning
> >> «gang,band,group»,
> >
> > Wrong. The term "Ring" is still in use with that meaning in composites
> > like Schmugglerring, Autoschieberring, ...

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