February 24, 2004

Counting poles

There's been some commentary recently about William Safire's column on multipolar, mostly focusing on the oxymoronic phrase "common elitist usage". I was struck by a different part of Safire's piece, his discussion of the etymology of pole

A pole, from the Greek polos, ''axis,'' is ''one of two ends of an axis going through a sphere.''

from which he concludes that multipolar is incoherent, because

An axis has two ends -- no more, no fewer -- and so polar can refer to one end and bipolar to two ends, like a magnet or a couple of superpowers. But since the prefix multi- means ''more than two,'' a multiple prefix was tacked on the stem word that didn't deserve that treatment.

My first reaction was "Sez who?"

I'm no expert in the history of English, but the OED gives two different nouns spelled "pole", and for pole1 says that the etymology is from OE. pál via ME. pôl, with the meaning

1. a. In early use, A stake, without reference to length or thickness; now, a long, slender, and more or less cylindrical and tapering piece of wood (rarely metal), as the straight stem of a slender tree stripped of its branches; used as a support for a tent, hops or other climbing plants, telegraph or telephone wires, etc., for scaffolding, and for other purposes.

The root is the same as for palisade, which certainly covers a multitude of poles. It's pretty rare for an application to rely on a single stake; and most tents and all hops fields have more than one pole. According to the American Heritage Dictionary's Appendix I, the Indo-European root is *pag-, which meant "To fasten", with other derivatives including "fang, peace, pact, palisade, and travel".

The OED does trace pole2 back through Latin polus to Greek polos, with the meaning

1. Each of the two points in the celestial sphere (north pole and south pole) about which as fixed points the stars appear to revolve; being the points at which the earth's axis produced meets the celestial sphere.

Liddell & Scott give a variety of meanings to the Greek source word, in addition to "axis of the celestial sphere" : "centre of the circular threshing-floor", "dowel", "windlass, capstan" among others. Since the Indo-European root is *kwel- meaning "To revolve, move around, sojourn, dwell", with derivatives including "colony, cult, wheel, cyclone, pulley, and bucolic", it seems clear that the "axis of a turning sphere" sense is a specialization of a much less constrained meaning, hardly limited to one thing with two ends.

So we seem to have Safire coming and going, so to speak. However, he is dealing not with pole but with polar, and the -ar suffix in question is (I guess) the one that comes from Latin -aris, and occurs in words like lunar, globular, scholar. It would be unexpected to see this suffix added to a Germanic word like the OED's pole1 -- so Safire's etymology is correct. And so is his metaphorical analysis, I have to grant, since pole2 has clearly gone through a long bipolar phase since its early bronze age days as a word for "wandering around".

This affixal selection -- -ar permitting only pole2 -- is too bad, because pole1 has its share of scientific applications as well. These come via the poles (as opposed to zeros) of a transfer function, namely the complex frequencies for which the overall gain of the system is infinite. Although I don't know the history of this term, I've always assumed that it's related to the shape of a plot of the transfer function gain around the pole, which looks like the fabric of a tent approaching a tent pole. It's normal for systems to have multiple poles -- as many as you like -- without causing any problems as long as they stay out of the right half-plane (in the Laplace domain, because this would make the system unstable). So there's no reason that "multi-polar" couldn't refer to the multiple poles of a circus tent or a resonant system -- this would be a great source of metaphors -- if only Old English poles could be polar, or resonance poles were Greek poles rather than Anglo-Saxon ones.

But maybe it's just as well. There are already lots of bad electrical-engineering puns about flights from Warsaw with Poles in the right half-plane, and a smaller number of references to "bipolar bears" in the mental health area. If resonance frequencies could be polar, then some really vile (if mercifully obscure) jokes about instabilities of arbitrage schemes would be inevitable.

Anyhow, it's interesting that two plausibly related senses for the same phonemic string -- English pole as "the axis of a turning sphere" or "a long, slender cylindrical rod" -- turn out to come from completely different historical sources, here the IE roots kwel- (originally meaning "wander around") and pag- (originally meaning "fasten").

[Update: Douglas Davidson writes:

There are many related and unrelated uses of "pole" in science and mathematics, from polar coordinates to polarized light to the singularities of analytic functions that you mention. (If they are in fact derived from 'polos', then the polhode and herpolhode of Poinsot would have to be the strangest.) The one that scotches Safire, however, is the standard multipole expansion, whereby functions are analyzed into their monopole, dipole, quadrupole, etc. components according to their angular distribution. (The odd assortment of numerical prefixes is another topic entirely.)

If "polar" could be a form of the Anglo-Saxon "pole", then any field of hops or three-ring circus tent would refute Safire. Given that it can't, Davidson (and others like Language Hat & Semantic Compositions) are right to brandish quadrupoles and the like in his direction.

The question of the "poles" of analytic functions is a sideshow, but I'm still curious about which kind of pole word they are. I guess I don't have much real evidence for my intuition that they are Anglo-Saxon poles rather than Greco-Latin poles. My first impulse is just based on the tent-pole image, which may be personal and irrelevant. I don't think you can talk about "polar bandwidth" or "polar frequency" in this sense, which might be evidence, but there could be other reasons for that. If the term was (for example) originally French, then it must be the Greco-Latin version after all, but I don't know the history. And I have to confess that polhode and herpolhode are new to me...]

Posted by Mark Liberman at February 24, 2004 12:29 AM