1. A Baker’s Dozen 5

Throughout his life, he would remain convinced that stars were im-

bued with magical powers. So, just like a student trying to make

sense out of a series of numbers in an IQ test, Kepler sought to detect

regularities in the data he was provided with. He added, subtracted,

multiplied, and divided numbers to, from, with, and by each other;

he used factors and constants and postulated invisible planets. It was

to no avail; all his efforts were in vain. “I lost a lot of time playing

around with these numbers,” he would later state regretfully.

The epiphany occurred in 1595. Kepler, who had in the mean-

time advanced to the position of school teacher, was drawing a geo-

metric figure on the blackboard when he suddenly had a brain wave:

the planets’ orbits ran along spheres that circumscribed interleaved

Platonic solids. Checking his flash of enlightenment with sober calcu-

lations, Kepler saw his intuition confirmed. Remarkably, the margin

of error was less than 10 percent and this lay within the accuracy of

then available astronomical observations. A year later he published

his insight in Mysterium Cosmographicum (Cosmic Mystery), a book

that was greeted with enthusiasm by the professional world. After all,

the harmonious interplay of the heavenly bodies was a brilliant con-

firmation of the Pythagorean world view. There was just one minor

problem: his insight was totally and utterly false.

The moment of truth came several years later. One of Kepler’s

bitter rivals, the imperial mathematician to Emperor Rudolph II,

Tycho Brahe, took issue with Kepler’s interpretation. But without

access to Brahe’s significantly more accurate data, Kepler had no way

of addressing the issue. Only after Brahe died and Kepler was ap-

pointed his successor, did he gain access to the observations. Then, at

long last, Kepler was in a position to analyze Brahe’s planetary obser-

vations and to complete his own tables. Finally he realized that the

orbits of the planets are not perfect circles, but ellipses. Hence, they

could not run around spheres. In Kepler’s favor it must be said that

he was honest and brave enough to own up to his previous mistake.

In 1609 and 1619 he published A New Astronomy and Harmony of

the Worlds in which he proposed three theses. These, for once, were

correct and would henceforth carry his name: Kepler’s Laws.