## Alexander the Great Rode a Centipede

Long, long ago, in the morning of the world, I sat in a lecture hall listening to Gene Kleinberg talk about elementary calculus. The hall was, for its day, rather well equipped. The chalkboards (remember those?) consisted of a number of panels, arranged in several layers. At the start of the lecture all the panels would be at the bottom of the board, superimposed on each other, at an easy height for writing on. However, only the frontmost panel was visible at that moment (this is an important point; keep it in mind). The lecturer would write until the panel in front was filled, at which point he or she would push a button. Hidden machinery would spring into action, and the first panel – call it Panel 1 – would rise, majestically, to a spot well over the lecturer’s head but still in clear view of the students, while the clean surface of Panel 2 would be exposed for the lecturer to continue his or her writing. Between classes, physical plant people normally came in and washed (and lowered) all the panels.

On this particular morning, Professor Kleinberg filled the first panel with something no doubt important, though what it was I have nevertheless long since forgotten, and pushed the button. Panel 1 rose, as it was supposed to do, but Professor Kleinberg, to judge by his expression, was not expecting his next discovery. For the surface of Panel 2 which was exposed was not clean, not pristine, not ready to be written on.

Rather, the exposed surface of Panel 2 contained the following remarkable text.

### Proof that Alexander the Great Rode a Centipede

Before proceeding with the main proof, we shall need a Lemma:

#### Lemma 1: Alexander the Great’s Horse had Six Legs

Alexander the Great’s horse was a horse. Therefore, at the front, it had forelegs, and at the back it had two more legs. But four legs plus two more legs make six legs. Therefore, clearly, Alexander the Great’s horse had six legs, as was to be shown.

And from Lemma 1, we shall need to derive an Easy Corollary:

#### Corollary 1 to Lemma 1: Alexander the Great’s Horse had an Infinite Number of Legs

By Lemma 1, we know that Alexander the Great’s horse had six legs.
Six is an extremely odd number of legs for a horse to have.

But six is an even number.  Therefore by lemma 1 we see that Alexander the Great’s horse also had an even number of legs.

No number smaller than infinity can be both odd and even. Therefore Alexander the Great’s horse must have had an infinite number of legs, as was to be shown.

And now, from the Corollary, the theorem readily falls.

For we realize at once that an infinite number of legs is a larger number of legs than that possessed by any living mammal, or any living reptile, or indeed any living insect or arachnid. In fact, if we consider any animal other than the Centipede, it is at once obvious that such an animal possesses fewer legs than Alexander’s horse.

From this we can easily see our way clear to the only possible conclusion:

Alexander the Great’s “horse” was no horse at all, but was, rather, a CENTIPEDE.

Q.E.D.

Professor Kleinberg looked at the proof, slowly, thoughtfully, taking time to read it carefully. And then, silently, with no comment, he erased it, and continued with the lecture.
But it stuck in my memory. I’m not sure it was stated exactly as I have written it here, but it was certainly very much like the proof given here. I also have no idea where it originated, nor who it was who crept into the classroom before the lecture and placed the proof upon the second panel.

Page created 8/16/05