## NNN: Order! Order!

(2 July 2000)

Being a collection of miscellaneous items.

First up, a puzzle. A couple of years back, someone named Puzzlerkin posted this cute little item to the rec.puzzles newsgroup:

Consider the following word series:

aid
guess
degree
estate
avenue
sense

Now suggest a word that could correctly continue the sequence. (See answer.)

On a vaguely related topic, there's an interesting mathematical paradox that I gather is known as Richardson's Paradox. The idea is that, to express a given number in English, it takes a certain minimum number of words. For example, the number 5984 could be expressed as "five thousand nine hundred eighty-four" (five or six words, depending on how you count it), or perhaps as "six thousand minus sixteen," which is only four words. But four is probably a minimum for that number; 5984 probably can't be expressed in three English words or fewer. (Unless it happens to be your house number, in which case I suppose "my address" would work.) Similarly, there are (large) numbers which can't be expressed in ten English words or fewer; there are even larger numbers that can't be expressed in thirteen English words or fewer.

Now, by a mathematical principle the name of which escapes me, if you examine the set of such numbers, there must be a least member of that set—that is, a smallest number in that class of numbers. And that number could be referred to as:

The smallest number which cannot be expressed in thirteen English words or fewer.

Which is thirteen English words; which is a contradiction.

(I suspect that the resolution to the paradox is that the set of numbers which cannot be expressed in thirteen English words or fewer is not a well-defined set. But I'm not sure what the traditional solution to this conundrum is.)

That paradox reminds me roundaboutly of something I encountered in a Raymond Smullyan book: a proof that all horses have thirteen legs. (I'm probably mangling some of the details here; bear with me.) The idea is that you go around finding horses, and any that have thirteen legs, you paint red. Any that don't have thirteen legs, you paint blue. Now go around again, looking at all the horses; if all of them are red, then you've proved that all horses have thirteen legs, Q.E.D. But what if you find a blue one? Well, that would be a horse of a different color!

Ahem. Okay, so it was more of a joke than a proof. Moving right along:

If "horse of another color" weren't a fixed phrase (he said, attempting a segue), I could have said that it would be a horse of a whole nother color. I'm fascinated by the "whole nother" phenomenon: MW10 says that "nother" in that context appeared in print as early as 1909, but I've only noticed it coming into widespread (informal) use in the past decade or so. It's become so common that people don't stop to comment on it any more.

I thought for a while that that phrase was a perfect example of tmesis, as I noted in an earlier column, but it was pointed out to me that tmesis is supposed to apply to insertion into a compound, as in far fucking out! So a whole nother, like fan-fucking-tastic and abso-blooming-lutely and kanga-bloody-roo, may be more an example of infix than of tmesis, alas. Though The Oxford Companion to the English Language indicates that tmesis doesn't require a compound, so I'm not sure. Incidentally, the Oxford Companion also suggests that Ubbi Dubbi and other such languages can be seen as another form of infixation (insertion of an element into a word).

N is a slippery letter. It leaps across the spacing gap between words without regard to sense or derivation. The word newt, for instance, was originally Middle English ewte (whence also the modern word eft), but someone mis-analyzed an ewte as a newt, and the new form stuck. Similarly, Middle English a naddre became an addre and then an adder (as in snake), a napron became an apron, a noumpere became an oumpere and then an umpire, an ekename became a nekename and then a nickname, and then anes became the nanes and then the nonce. Seems to me that instead of minding our Ps and Qs, we ought to be minding our Ns. Though I suppose it's too late, since most of those mis-analyses happened way back in Middle English...

At any rate, that's all I have time for, at least for then anes.

Jed Hartman <logophilia@kith.org>