Sunday, January 1, 2012

Orthoëpy of “monotony” (Word-of-the-Day)

Please turn to page  58 of Paul Halmos, Introduction to Hilbert Space (1951, 2nd edn. 1957) -- or, if you happen not to have your copy handy, here is the relevant quote:

Theorem.  If E is a finitely-additive, projection-valued set-function on the class of all measurable subsets of a measurable space, then E is monotone and subtractive.
Proof.  That E is subtractive is trivial;  monotony follows from 29.3.

Now of course -- you already knew that.   But the point here is rather the status of this interesting word monotony -- in particular, how to pronounce it in this case.

Familiar to everyone is monotony, the noun of monotonous, pronounced respectively and in parallel, mon-OT-on-ee and mon-OT-on-us.  But the adjective here, though cognate, is quite different:  monotone, pronounced MON-o-tone :  meaning:  increasing (bzw. decreasing) and never decreasing (bzw. increasing).  Alles klar?

The question then is:  How do we pronounce its associated noun? 
Now, I have never actually heard the term in speech, despite having sat through many a math-class.  The adjective is more usual than the noun, and the noun, when it does come up, is usually monotonicity  (mon-o-tone-ISS-it-ee) -- though strictly, this is the noun of monotonic (mon-o-TON-ik), not of monotone.  So how to pronounce this technical term “monotony” we have never heard in this meaning?    Every fibre of my being cries out, that we must pronounce it  MON-o-tone-ee.
The word is, thus, a homograph, with different pronunciations for its two (related) senses.

Compare and contrast  the situation with the words homology, pronounced ho-MOL-o-jee  in both the mathematical and the general sense;  versus homotopy, which has only a mathematical sense, and which is always pronounced HO-mo-top-ee.  Linguistically, this is an odd situation, since, semantically, homology and homotopy are very closely related, and one would expect their pronunciation-patterns  to march in step.

(See what you’ve been missing, by not majoring in math?  Don’t let your children make the same mistake !)

[Update, Juli 2012]  Someone just accessed this post with the searchstring
          alles klar pronunciation

Geht in Ordnung!
AH-less KLAHR.

The sense meant  is something between "Is that clear?"  and "Any questions?"
Intended  as gently  ironic...

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