Yesterday’s Zippy strip manages to combine abstract algebra (in the notion of idempotence) with linguistic behavior (in the notion of onomatomania):
The behavior. Zippy is notoriously given to onomatomania (aka phrase repetition disorder / repetitive phrase disorder and mantric repetition), an obsessive repetition of certain expressions for pleasure (see the Page on this blog about my postings on chants, cheers, mantras, and onomatomania).
I am not entirely immune to mantric repetition. I have been seduced by Chichicastenango, by Shadrach, Meshach, and Abednego, by Midas has asses’ ears, even by peri-ictal schizophreniform psychosis. All of them invitations to the dance. Carmen Miranda sings I’m Chiquita Banana and I’m here to say / Bananas have to ripen in a certain way in my ear and I’m repeating it, in her extravagant Spanish accent, over and over, and would cha-cha across the floor if I could.
The algebraic property. Griffy’s definition is grievously inadequate; after multiplication by itself is what he should have said, and that leaves some significant concepts floating in the ether. The NOAD definition is much better; and it gives the origin:
adj. idempotent: denoting an element of a set which is unchanged in value when multiplied or otherwise operated on by itself. ORIGIN late 19th century: from Latin idem ‘same’ + potent ‘powerful’.
The origin tells us that potent in the word is, well, potent in it; which in turn tells us that the word is pronounced
/ˌajdɛmˈpotǝnt/ idemPOtent
/ˌajˈdɛmpǝtǝnt/ iDEMpotent
(which is the pronunciation I’ve heard several mathematicians who were not native speakers of English use consistently in public lectures — heard enough times that I’m kind of attracted to it myself).
[Digression. One result of learning some technical field through texts printed in English is that you can guess at how the technical terms are pronounced, but you could be wrong; English spelling is a fickle companion. When a technical term is in fact exotic, as with idempotent, absolutely anyone could get it wrong — frankly, I’d really prefer iDEMpotent — and you should be excused for your error, but even so, you should learn the pronunciation that’s current in the field.
Alas for non-native speakers, a large number of technical terms, in various fields, are taken from ordinary English. So that mispronunciations of everday English get carried over into the technical context, where they will sound especially risible. Speakers of many languages would prefer to avoid the English word sheet entirely, for fear of producing what English speakers will hear as shit, but if you’re a specialist in printing, philately, or topology, you’ve got to struggle with it.
And so I get to report on an occasion many years ago, when I was in the audience for an Italian computer scientist delivering a paper on approaches to mental categories — a technical term from psychology / philosophy — in natural language processing. Well, he was aiming for
/ˈkætǝˌgori/ CATegory (granted, with an Italian accent)
/kǝˈtɛgǝri/ caTEGory
A more careful definition would make explicit the idea that idempotence is relative to some set S (like the whole numbers {0, 1, 2, …}) and an operation O (like multiplication ×) defined on the elements of S. Then an element e is, by definition, idempotent with respect to O, if
e O e = e
For the whole numbers with respect to ×, that means that an idempotent number n would have to satisfy
n × n = n
There are then exactly two idempotent whole numbers, 0 and 1, since 0 × 0 = 0 and 1 × 1 = 1 and these are the only whole numbers for which n × n = n.
[Digression. Mathematicians twist themselves up in these ways because they’re looking for patterns in things that recur in different ways in different contexts; they then abstract these patterns and study them on their own. In this case, the idempotence pattern recurs in many different ways in different contexts.
For example, consider a bunch of buttons you can press, and think about the set of effects a button might have (maybe it turns on a light, maybe it summons an elevator, whatever), and also think about the effect of pushing two buttons in sequence: pusheff1 … pusheff2; what’s the effect of this composite action? This composition of button-push effects is the operation here, on the set of such effects, and we can now ask what happens when you push the same button twice, in sequence; maybe the effect is reversed (such buttons are very common), maybe the effect is amplified (such buttons are common too), and so on, including the possibility that pushing the button a second time has no effect —
pusheff1 … pusheff1 = pusheff1
Ah, that’s idempotence! Ordinary elevator-summoning buttons have idempotent effect.]
The combination. The mantrically repeated technical term from abstract algebra. The puzzle here is how Zippy the Pinhead, from Dingburg, came across a technical term from abstract algebra. I don’t recall previous excursions into math in the strip, but maybe I’m just a neglectful reader.
Clearly, Griffy somehow came across the term, admired it, and taught it to Zippy, who then performed it for pleasure. There are, apparently, sides of Bill Griffith I hadn’t previously appreciated.
Bonus. The title of this posting is a labored pun on the song title “Oh, Dem Golden Slippers”. From Wikipedia:
“Oh, Dem Golden Slippers” is a minstrel song penned by African-American James A. Bland in 1879, [and] is particularly well known as a bluegrass instrumental standard.
… The song is well-known today as the unofficial theme song of the Philadelphia Mummers Parade [on New Year’s Day].
And now I’ve given myself an earworm. Played by a big string band.
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