Mathematical Metaphor of the Month

From Hugo Schuchardt’s essay, “Sachen und Wörter” (1912):

Ein Fortschritt im allgemeinen Sinn  wird nur dadurch erzielt, daß  Sachforschung und Wortforschung  nicht bloß … nebeneinander stehen,  sondern daß sie sich durchdringen,  sich miteinander verflechten  und zu Ergebnissen zweifacher Art führen.   Kurz, das  und  in “Sachen und Wörter”  verwandele sich  aus einem Additionszeichen  in ein Multiplikationszeichen:  es entwickle sich  eine Sach-wort-geschichte.

A sort of “tensor product” of vocabulary and reality, alors.

[Update]  Someone whose behest I would not dream of discounting, just emailed me saying “Translation please!”, saying he disdains to resort to Google.

Surprised that anyone would dare to diss the Godlike Google, I checked on Google Translate.  This is what it came up with:

A progress in the general sense is only achieved in that kind of research and research not just word ... next to each other, but that they penetrate each other, intertwine with each other and lead to results of two kinds. Short, and in "things and words" Can you turn off an addition sign in a multiplication sign: it was developing a kind-word-history.

Umm … hmmm …. Not quite ready for prime-time, actually.  In fact -- not even ready for Cable.

(As a professional translator, I feel rather schadenfroh over such MT mishaps!)

OK, so I’ll try my hand at it:

True progress [for the philologer] can be achieved only when the depiction of Things  and the depiction of Words   do not simply coexist side-by-side, but rather -- interpenetrate,  nay -- interweave,  the warp of one  through the other’s woof, and thus yield a self-dual result.   That is to say:  the “and” and “Words and Things” must sublate the addition-sign into a (so to speak) multiplication-sign [of interanimated implication, inseparably intertwined]: thus then is born a [Janus-observing] ‘Word-cum-Thing-complexus’.

(Hey, I never promised I’d translate it into Easy English!)

Note:  That “warp and woof” business was a bit of Dragoman’s License ™, but Schuchardt himself avails himself of the same metaphor, a bit later in the same essay:

Treten Sachen und Wörter … zueinander in Beziehung, so müssen wir sie uns unter dem Bilde  nicht paralleler, sonder sich kreuzender Linien vorstellen,  etwa die Sache als Ketten-  und die Wörter als Einschußfäden.

-- Hugo Schuchardt, in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 129

Schuchardt is referring to the Wörter-und-Sachen movement, which stepped out of the close air of the philological closet, to consider Realia (“Sachen”), and the evolution of language in concert with that.   Schuchardt seems to be striving towards a more dialectical conception of that initially empiricist program:  the ‘tensor product’ of the two von Hause aus quite separate enterprises (as, dendrology and onomastics -- cf. the classic Indo-European Trees) being necessarily mediated by the ideational:  in the words of the scholastics:  Voces significant res  mediantibus conceptibus.

http://www.liveinternet.ru/journalshowcomments.php?jpostid=150171859&journalid=762167&go=next&categ=0

It was exactly such a progress that I undertook in my (alas unpublished) monograph, Linguistic Life on the Left (dating back to Berkeley days), which was written, not in the spirit of a lepidopterist, but from within the Zeitgeist.