Kepler and The Shape of Water
"Those laws [of nature] are within the grasp of the human mind; God wanted us to recognize them by creating us after his own image so that we could share in his own thoughts."
When Isaac Newton said, “If I have seen further, it is by standing on the shoulders of giants,” he was in no small part talking about Johannes Kepler. Kepler’s three laws of planetary motion couldn’t have been far from Newton’s mind when the apple dropped. Newtonian laws of motion and gravity derive from the consequential discovery of our heliocentric solar system. Our solar system is populated not only with seen, but also unseen objects. Small comets are an unseen aggregate of innumerable water-ice objects whose discovery by Professor Louis A Frank and his team at the University of Iowa that is at least as consequential as Kepler’s discovery of the planets’ elliptical motion around our Sun. This essay, like all my essays I suppose, takes a dim view of forgetfulness. I’m writing to help us remember.
I have wanted to write on substack a biographical essay on Johannes Kepler. In trying, I find I am not up to it. In short, I don’t dare take the time and space from my readers, or myself. The end result would be unsatisfactory for all of us. Let me recommend instead, Max Casper, Kepler’s chief biographer and dean of his mathematical and literary works. Before I get on with telling you why I was going to write about Kepler, let me share what Kepler wrote in one of his Almanacks:
I may say with truth that whenever I consider in my thoughts the beautiful order, how one thing issues out of and is derived from another, then it is as though I had read a divine text, written into the world itself, not with letters but rather with essential objects, saying: Man, stretch thy reason hither, so that thou mayest comprehend these things. KEPLER, in his calendar for the year 1604
Kepler was after the truth. The truth about essential objects and their movements. He was Tycho Brahe's helper, friend and peer. Tycho Brahe was a fanatic about accuracy. In his observatory he dug to bedrock for foundations to make his observations as accurate as possible. Brahe was the last consequential astronomer to work without a telescope too. Kepler was every bit as fanatical as his friend when it came to accurate measurements. Both men spent a good part of their lives gazing into the night sky and taking measurements. Kepler is sometimes called the father of modern astronomy. Maybe Brahe is Kepler’s metaphorical stepdad? As usual with fraternal orders, it's complicated.
This is why I abandoned writing a biographical essay about Kepler. It gets too tangled up in other biographies. In the late 16th, 17th and early 18th century the experimental method of inquiry got firmly established. The experimental method prevailed because it works so well at discovering truth about matter and how it moves and changes. The experimental method is not the result of a single man. But I sense Kepler is the most prototypical member of the fraternity. Brahe hated the margin of error so much he would fabricate accuracy into his tables. Was he taking astronomical mulligans? Kepler instead slogged it out. He was a bulldog. He got it right. He was the first one. He cleaned up the errors in the heliocentric system with a hypothesis that the planetary orbits are ellipses. The preciseness of his observations is breathtaking. Repeatability was his reward. Fifty years after his death, virtually everyone had accepted his discoveries about the planets and his three laws of planetary motion. Kepler had changed the world. Kepler’s experiments were accepted because they could be repeated. In his spare time, he calculated ideal dimensions for a wine cask and invented integral calculus - and other odds and ends, like defending his mother in her witchcraft trial. Mostly he wrote almanacs and cast horoscopes. Why else would a ruler pay a Royal Mathematician?
My point is these math guys were indeed giants. Their faith: they were all believers, seemed to embolden them in inquiry. As Kepler wrote, “it is as though I had read a divine text, written into the world itself.” Kepler did work on snowflakes that’s still foundational to our understanding of crystal formation. He wrote in De nive sexangula, “There must be a cause why snow has the shape of a six-cornered starlet, it cannot be chance. Why always six?” He was indebted to the English mathematician Thomas Harriot, who had been asked by Sir Walter Raleigh to figure out the best way to stack cannonballs. Kepler calculated that hexagonal packing “will be the tightest possible, so that in no other arrangement could more pellets be stuffed into the same container.” It’s called Kepler’s Conjecture and it wasn’t proven computationally until 1998. In the end, of course, Kepler can’t figure out the snowflake. To this day, nobody has figured out the snowflake. “As I write it has again begun to snow, and more thickly than a moment ago. I have been busily examining the little flakes,” is how our man concludes his treatise. Can we call Kepler’s math, enchanted math?
Why did the experimental method emerge when it did? Where it did? Can we divine an answer? Start with the proverb, ‘two heads are better than one.’ Guttenberg's moveable type was almost two-hundred years old when Kepler died in 1630. Nicolaus Copernicus, who had a big hand in starting all this mathematical inquiry had the advantage of the printing press. His book, De Revolutionibus, was published in 1543, just a few months before his death. Copernicus is said to have died clutching a copy of De Revolutionibus.
The Protestant Reformation had enlivened imaginations - men could and ought to read and listen directly to God’s word. Moveable type made the making of books exponentially faster. Any new idea could be disseminated widely and quickly. Some people insist we should think of mathematics as a language. For my purposes that idea works, even though I can’t speak the lingo. Kepler imagined the same God who revealed himself in scripture was also revealing his mind, geometrically and mathematically, to men through the creation.
All those printed seeds brought forth collaborative fruit, and not surprisingly, on occasion, competition and recriminations. Kepler and Galileo were not always on the best of terms, but they were definitely collaborating. Kepler sent two copies of his book, Mysterium Cosmographicum to Galileo, who wrote back; “I think, my Kepler, we will laugh at the extraordinary stupidity of the multitude. What do you say to the leading philosophers of the faculty here, to whom I have offered a thousand times of my own accord to show my studies, but who with the lazy obstinacy of a serpent who has eaten his fill have never consented to look at planets, nor moon, nor telescope? Verily, just as serpents close their ears, so do these men close their eyes to the light of truth.” Another time, later, Kepler sent something to Galileo and Galileo republished it without acknowledgement. Galileo never did accept Kepler’s discovery that the planets’ orbits are ellipses.
My long-time readers know my preoccupation with Professor Louis A Frank’s discovery of small comets. The cover of his book, Cosmic Rain, uses the subtitle, The Controversial Discovery of Small Comets. I wish the ‘controversial’ part were true. Perhaps a better subtitle would be, The Forgotten Discovery of Small Comets. One of the reasons I am writing about Kepler and those first modern astronomers is because Frank’s discovery of the small comets is every bit as consequential as the discovery of our heliocentric solar system.
There was nothing enchanted about Professor Louis A Frank’s discovery of small comets. Frank was as hard-headed about science and its peer-review process as they come. The process of testing experiments through peer review was probably the only religion Frank would claim - it’s what he meant when he wrote, “Science is my life.” Frank’s discovery came about because he had to have the true answer to his question, “what are those spots in our images? “Why are they crashing our program?” Our lifework sometimes chooses us. We choose how we will work.
Frank discovered small comets, but no one, including Frank, has ever seen one intact. Frank saw in Earth’s atmosphere what he called, “plummeting pistons of water vapor.” He saw the small comet debris field, at least part of it. The water vapor clouds blocking the Earth’s UV dayglow were creating ‘atmospheric holes’ in their images. Frank postulated the small comets had a carbon shell for two reasons. One, graphite explained how they were held together on their long and increasingly hot journey towards the sun. Two, graphite also explained why they were never seen. Nobody in the world had a better handle on imaging objects from outer space than Lou Frank. Inorganic carbon, graphite, exotic graphene, (the stuff of nuclear reactors, stealth bombers and exotically strong composites) would absorb all the electromagnetic spectrum our imaging equipment can see. Frank didn’t know the small comet mantles were carbon. He knew it could only be a carbon mantle that could so completely hide them. The small comets are like kamikaze stealth bombers carrying a payload of stealth snow, cloaked with something that uniquely absorbs light and the full spectrum of electromagnetic energy.
Frank’s trust in the peer-review process betrayed him. It’s a false God for sure. Peer-review has always been more about protecting scientists’ interests than it has been about testing an experiment’s truth. In the peculiar case of Louis A Frank, it has erased his discovery of small comets. It has erased him. Peer-review canceled Professor Frank and his experiments. Newton, Kepler, Copernicus, and all those earlier fellows spoke Frank’s μαθηματικός language. In Greek, ‘mathematician’ means, one fond of learning. Kepler and Newton would have believed in Frank’s small comets. They were fluent in Math. They weren’t afraid of the truth. Truth was their best friend. A dark veil has been draped over what we call science. Who would have thought it would be the scientists themselves throwing the blanket party!
Churchill wrote in his 1931 essay, Fifty Years Hence:
[Science’s] once feeble vanguards, often trampled down, often perishing in isolation, have now become a vast organized united class-conscious army marching forward upon all fronts towards objectives none may measure or define. It is a proud, ambitious army which cares nothing at all for the laws that men have made; nothing for their most time-honoured customs, or most dearly-cherished beliefs, or deepest instincts.