6 1. A Baker’s Dozen

In his third law, Kepler drew a parallel between the time it takes

for a planet to orbit the sun and the length of the axis of its el-

lipses. He had the vision that there must be a mathematical link

between the planets’ distances from the Sun and their velocities. But

what was that link? Another IQ test was to be solved. What was

the relationship between the sequence of numbers 58, 108, 150, 228,

778, 1430 (semi-axes of the planets’ ellipses, measured in millions of

kilometers) and the sequence 88, 225, 365, 687, 4392, 10753 (orbital

periods, measured in days)? Kepler solved the problem with supreme

ease. He determined that the square of the orbital period, divided by

the third power of the semi-axis, is nearly exactly equal to 0.04 for all

six planets. This time his intuition, again without the faintest trace

of a justification, led to one of the most fundamental laws of nature.

Both Kepler’s correct and incorrect insights originated from his

deeply seated conviction that God had created the world based on

numerical laws. The idea of nesting platonic solids, each encased

in a sphere, within one another, seemed just as plausible to natural

scientists during the Age of Enlightenment as that the square of one

variable should be proportional to the cube of another. While the first

hypothesis proved to be a figment of Kepler’s fertile imagination, the

second would go down in the annals as a path breaking discovery.

For many years, Kepler’s three laws remained nothing but a nu-

merical curiosity. The natural philosophers of the time, all of them

men of faith, were convinced that the reason for the laws, if there

was one, would surely remain a mystery within God’s eternal wis-

dom forever. It was only in 1687 with Isaac Newton’s monumen-

tal Philosophiæ Naturalis Principia Mathematica (The Mathemati-

cal Principles of Natural Philosophy) that Kepler’s laws were put on

firm theoretical footing. The English physicist provided mathemat-

ical proof that the motion of planets does not just obey divine rule

but that the ellipses are an absolute necessity.

Newton’s contemporaries did not take readily to his law of gravi-

tation. While everyone understands that a cart moves once it is pulled

by the towing bar, it requires much imagination to accept that the

cart can be moved from a distance without even so much as touching

the bar. Nevertheless, Newton’s model still required a divine force