The right to define

There are many things that have no natural cause: many things that are the way they are because people have agreed to have them that way. Nowhere is this more true than among mathematicians.

For example, the average height of a population is a simple mathematical calculation, once the population is well defined. (Over time it is a function; at least logarithmically Hölder continuous, and possibly smooth.) But the “normal height” for a population? Why, that is whatever the relevant authority decides a “normal height” to be.

Thus in mathematics the meaning of “an important discovery” is largely dependent on the person using the term; see “Important discovery in the fridge”, dept. mailing list, last week — versus “Important discovery: Destruction of Earth imminent”, math-phys. mailing list, this week.

Among mathematicians, this “right to define” has been restricted, as otherwise the results would not be pleasant. Thus only the departmental head has the right to redefine the zero hour: that is, she gets to define midnight. This is not as sexy as it sounds; merely that if she chooses midnight to be 2 pm outside time (“on the rube clock”), then 8 o’clock is 10 pm outside time, and that’s when the workday starts.

Others are not allowed to mess with the official departmental time; this has been so ever since an adjunct professor redefined his workday into a singularity and retired five minutes later.

A particularly haunting case of redefining time is the sad life of the graduate student who, due to circumstances entirely his own fault, is set to graduate in February of 1993, as soon as that comes around. Opinion is divided on whether the intransigence of his professor is admirable or abominable; the main lesson of the case is thought to be this: never let Microsoft Word’s autocomplete anywhere close to your study plan, and always proofread everything before signing.

Fields laureates, that is, those that get awarded the Fields Medal, the Nobel of mathematics, customarily have the added privilege of defining category boundaries. For an example why this is a privilege best restricted to a small set of sophisticated, sensible people, see von Sturmleben’s paper, “All penii larger than mine are ‘wangi’; by definition I have the largest penis”, Acta Math., 185 (2000) no. 2, 287–290.

As for a more mundane case of time, borderline on the departmental-head powers, who hasn’t heard a math professor exclaim, “Just a minute! I redefine a minute to be fifteen minutes.”?

And who hasn’t heard the inevitable adjunct, popping out of thin air, sneering: “So ya define x to be 15x? Solve for x, and a minute is nothing! Ya have no time! Come on now pops we gots no time!

Or the assistant, similarly appearing, crowing: “So a minute is a zero unit? Then so are all other measures of time! All of time appears in this one and same instant then! Let’s go see Shakespeare, born living and dead, right now!”

Or the lowly lecturer, shuffling to view, moaning with his hands thrust forwards: “Ah truly then this job not only feels like centuries, but is centuries — millennia — endless spans of futile, frustrating toil!”

Ah, such is the playful nature of mathematicians, for certain definitions of “playful”.

One may wonder why mathematics departments all over the world — for they all are like this — have not descended into utter anarchy as the result of the right to define. This is a question whose answer is trivial; mathematicians like their definitions to be well-defined, with nice analogues to the definitions of other people (read: mathematicians), and as the result any department exists in a slowly fluctuating state of collaborative insanity, shared by the inmates (read: faculty), and as is well known, this is but the Earth in microcosm.

After all, to offer one final example, money is a ludicrously fictional concept, made even sillier by the antics of loans and trading in futures and so on; and yet the vast majority of humanity treats money as something which makes sense! Mathematicians have long since seen through this madness, and thus require in salary only enough for basic needs plus writing implements; which the ever at least slightly puzzled administration is happy to give.

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