Coincidence is often thought to have no place in science, but in fact the tenets of statistics tell us that coincidental events, even seemingly of amazing proportions, can and must happen from time to time.

So it was that on July 22, 1995, two amateur astronomers, Alan Hale in New Mexico and Thomas Bopp in Arizona, were observing exactly the same part of the sky, at exactly the same time, just as a previously unknown comet was becoming bright enough to be noticed by Earth-based telescopes. Hale and Bopp both reported their find to the astronomical authorities, and within a day the Internation Astronomical Union had announced the discovery of comet Hale-Bopp, named in the traditional manner after the last names of those who had discovered it.

Astronomers around the world turned their telescopes on the new comet. Because it was still quite far from the Sun but...