Ivar Ekeland’s *Mathematics and the Unexpected* has a beautiful quote from the scientist Johannes Kepler, referring to his discovery of the laws governing planetary orbits:

I am now enlightened, in the midst of a most desirable contemplation, eighteen months ago by the first glimmering of dawn, three months ago by clear daylight, and just a few days ago by the sun itself… The die is cast; I will write my book, and little does it matter whether it is read now or has to await posterity. It may well wait a hundred years for a reader, since God Himself has waited six thousand years for someone to behold His work.

I like this quote for so many reasons. It is known that Kepler was greatly disconcerted when he had to abandon the idea that planets revolve in “perfect” circles. He wanted very much to believe in the harmony of the spheres. In fact, the planetary orbits are so nearly circular, that Kepler found his predicted planetary positions to deviate from his mentor Tycho Brahe’s observations by only 8 minutes of an arc, about 1/8th of a degree. It is entirely possible that a scientist would persist with the circular orbits theory and ascribe the deviation to experimental error, especially a scientist who wanted very badly to believe in circular orbits. But Kepler persisted with investigating the error, and eventually discovered that the orbits were in fact elliptical with the sun located at one of the foci. In this context, it is wonderful to read, “I will write my book…” and to note the tone of finality in Kepler’s words, that the job was done, and the conclusion was indisputable.

Second, Kepler was, in a way, being prophetic when he wondered whether his work would wait a hundred years for a reader. For 80 years would pass before Isaac Newton used calculus and his laws of gravitation to derive and confirm Kepler’ s laws. In moving from circular to elliptical orbits Kepler peeled away at one layer of celestial mechanics. But, the most charming quality of this quote is that it contains another layer waiting to be peeled, obvious to us today, but not to Kepler five hundred years ago. Surely, Kepler echoed the dominant belief of his time when he said that God had waited six thousand years for someone to read his work, his design of the cosmos. Now of course, we know that the wait – if, at all, anybody was waiting – was much *much* longer: about 13 trillion years (edit:Nils pointed out my unfortunate gaffe here: 13 x 10^{9} = 13 billion years, not trillion!). The tolerance in estimating the age of the universe is so large that the figure 6000 cannot even qualify as an approximation error. Crystallized in Kepler’s words is a fine example of how science progresses, and how our understanding of Nature proceeds by peeling away at its infinite layers.

From the first two chapters, in which we encounter the leap of Kepler’s imagination and the arrogance of Laplace’s determinism, this book promises to be fun.

A beautiful observation turned into a wonderful post. I love this idea of peeling away layers, in our knowledge, in how we explore our world, and universe. We go wider and deeper every day. But, in my humble opinion, thirteen

trillionyears is surely a bit on the steep side, even in astronomical terms, no?Right you are, Nils. 13 Giga years of course, so it should be 13 billion. Thanks for pointing this out. And while we’re at it, we might as well clarify that it is American billion, not British billion ðŸ˜‰ .

Ekeland’s book sounds interesting; I’d love to read and know more about mathematics.

I am disappointed at Kepler’s handling of approximations as a scientist. Had he been a true rational mind, he’d have said ‘at least five thousand years’, and he’d have been right.

Maybe he sucked at approximations and orders of magnitude, hence his quest for total accuracy, leading to ellipses instead of approximate circles;-)

LOL @ madarine: This reminds me of a certain experiment we did many years ago, in order to determine the efficiency of an age old Babcock-Wilcox boiler. Our calculations gave something like 3%. Students who had carried out the same experiment in the past years were known to advise their juniors, that if they fudged the denominators in the fractions, it was possible for the efficiency to go up to 7 or 8%, which was the answer that generations of lab instructors had in mind ;-).

I bet a clever approximation method could have come up with 5% [+/- 3%] and everybody would have been happy.