Your Place in the Universe

by Paul M. Sutter

  Besides, in some academic circles (ha!) the argument went that the epicycles were just added to account for observations. There was a deeper, more hidden “truth” in the universe, and cosmological models were just that: models to explain the data—nothing more, nothing less. A tool, if you will, that could be wielded to give better astrological predictions.

  So when Nicolaus Copernicus on his deathbed in 1543 allowed his book detailing a sun-centered cosmology to be published, the reaction was pretty mild. “Hmmm” seems to have been the collective response of the leading figures. Some thought it was kind of nifty, others were violently opposed, but most folks simply didn't care. As the decades passed, however, the debates grew more complex, more heated, and overall more fun for us in the present day to read. And to be perfectly honest, the debates were, well, honest. Sure, some so-called enlightened figures had reflexive knee-jerk reactions, but most scholars armed themselves with the tools of the thinking trade—evidence, reason, philosophy, mathematics, divinity—and went to work trying to devastate their opponents. If you go to a typical scientific conference today, you'll see that some things never change. The weapons may be different, of course, but the modes of delivery are the same.3

  Copernicus's fancy new model wasn't immediately compelling. He argued that—hey, guys, check this out, I know it's a crazy idea but work with me—the sun is the center of the universe, not the Earth. Look at the problems it solves! Sometimes planets move backward in their orbits? It's because we're catching up in their orbit. And you know some of those awkward pain-in-the-neck mathematical contrivances in the geocentric model, like epicycles? Well, you can safely chuck most of them if the sun is at the center. And—well, those are the big ones.

  What, you're not convinced?

  You're not alone. To account for the day/night cycle, we now have to claim that the Earth is spinning. Are you crazy? Have you seen the Earth? Wouldn't we be blasted by bajillion-mile-per-hour winds and/or spun off the planet? And Copernicus still insisted on circular orbits because circles are really beautiful, and so he still had to add epicycles to account for the detailed motions. (Although, to be fair to Copernicus, his system was mathematically simpler.)

  And let's really think about this, OK? Let's assume, for the sake of argument so I can later prove you wrong, that the Earth orbits the sun. Wouldn't the stars wobble a little bit between summer and winter, based on our different observing positions, the same way our view off a distant object can wobble if we switch eyes? They don't, at least as far as we can tell. So either (a) the stars are unfathomably far away and our universe is way too large to comfortably think about, or (b) the Earth is at the center.

  We're going to reject option (a) because it's immediately eye-rollingly wrong, so we're left with an Earth-centered universe.

  That was the argument made by Tycho Brahe, the Danish astronomer who was really fond of making arguments: he lost his nose during a duel with his third cousin. Its brass replacement served as a useful warning to every other academic later in his life: don't flipping mess with Brahe.4

  It also didn't hurt that Brahe was perhaps the foremost astronomer to ever appear on our planet. Working from Uraniborg, his own private fortress of science, his observations practically defined exquisite. He spotted a supernova. He figured out that comets were not, after all, merely some atmospheric phenomena. He crafted his very own personal cosmological model, with the Earth at the center, the sun orbiting the Earth, and everything else orbiting the orbiting sun (it wasn't very popular—I get the image of that one loud drunk guy at the party telling everyone his take on, say, the JFK assassination). And he collected the most detailed observations that had ever been made of the positions of the planets. All of this was done without the aid of a telescope—just looking and measuring, measuring and looking, night after night. He jealously guarded his tables of astronomical insights, allowing his assistants access only in heavily supervised scenarios.

  Now I'm not saying that one of his assistants, Johannes Kepler, murdered him to gain unrestricted access to those tables. But it is awfully convenient that Kepler, who fervently believed (and I'm using “believe” here in a rather faith-based sense) that the sun was the center of the universe, was working with Brahe and desperately wanted unchaperoned access to those tables to prove his ideas right.

  The story goes that Brahe was drinking heavily at a banquet and had to use the little astronomers’ room but didn't want to get up for fear of insulting his host. In the ensuring days, he ended up very slowly and painfully dying, likely from a ruptured bladder.5

  We'll leave that as the official line, but I'm keeping my eye on you, Kepler.

  Johannes was a pretty clever dude, but saying he was eccentric is to only scratch the surface. He was the court astrologer (yes, you read that right) to Emperor Rudolph II of the Holy Roman Empire. That's not too surprising, but he was also a numerologist of the highest order.6

  Kepler fervently—and perhaps fanatically—believed that mathematical and geometrical coincidences found in nature were anything but mere bits of chance. No. There was hidden order and deeper meaning within the motions of heavenly bodies. What's more, that order and meaning didn't just have consequences in the celestial realm but directly affected, influenced, and informed our daily lives. Right here on dirty, muddy, sinful Earth.

  Perhaps there was a reason that although Kepler and Galileo wrote to each other, Galileo never really referenced any of Kepler's astronomical work in his arguments with the church.7 You can kind of see why. To employ one of the arguments of Kepler would immediately open Galileo to accusations of being a—shudder—mystic.

  But Kepler opened up that can of worms with relish and dug right in with the nearest fork he could find, drooling the whole time. He figured the sun was at the center of the solar system. Why? Because as the most prominent, fiery denizen of the solar system, it was obviously the focal point. Just like God the Father was the focal point of the Christian faith, the source of everything else.

  His words, not mine.8

  As nutty as Kepler was to us, he was no dummy either. He fully knew the weaknesses of Copernicus's solar system, but he thought he could do better. No—he knew he could do better.

  And he had the data to do it. Table after repetitive table of positions of planets and stars, measured with as much accuracy as the human eye could muster. All his, now that Brahe was conveniently out of the picture.

  Kepler was convinced that buried within those tables of numbers was a hidden order, and if he sought long enough he would recognize a pattern. This is, of course, before computerized pattern-matching algorithms, before computers themselves. A fancy mathematical tool called logarithms had just been invented, which was pretty handy, but otherwise Kepler had to brute-force the whole thing.

  In his searching he found dozens of what we (and, to be frank, pretty much any rational person) would call coincidences. But to Kepler they weren't just random chance alignments or interesting repetitions of numbers. No, they were the voice of the divine, calling out through the cosmos, instructing us on how to operate our lives.

  Kepler wrote a few books on the subject, and the vast majority of his ideas are nowadays ignored. What survives are what we know as Kepler's laws of planetary motion, which he discovered pretty much from trial and error, hoping to find something that stuck and unified the complex, interwoven motions of heavenly objects.9

  The first law is that planets move in ellipses. Perfect circles for the motions of the planets just weren't cutting it anymore, even with a sun-centered universe. And besides, epicycles upon epicycles made horoscopes way too difficult to calculate—just where exactly is Mercury supposed to be on the day of the princess's wedding? Sheesh!

  Kepler went about trying every geometric pattern he could think of, trying to find a common unifying theme to the planetary orbits. Apparently he initially skipped over the humble ellipse (which would be the first thing you would think of if you wanted to upgrade from a circle), assuming someone
in the past millennium would have tried it already. He was wrong, and when he finally gave ellipses a shot, everything snapped together.

  There it was, the voice of God himself speaking not through circles, but through ellipses. A simple geometric expression, combined with the placement of the sun at the center, put all the planets in their correct places. Nested epicycles with their complicated, convoluted mathematical machinery could be tossed into the garbage.

  But circles are so beautiful! Surely the creator of the universe, in all his divine wisdom, wouldn't make a mistake like placing planets on elliptical orbits, right?

  Kepler was ready for the criticism (I told you he was smart). You see, circles are a little too simple. A circle is a circle is a circle. You just need a single number, the radius, and you've completely defined it. But with ellipses you need two numbers: the major and minor radii, meaning the lengths of the long and short sides Two numbers means there's more bandwidth for God to tell us interesting things about the cosmos—and us.

  And here's where Kepler's second law comes into play: the planets, as they swing around in their orbits, carve out equal areas in equal time. Think about trying to divvy up an odd-shaped pizza. You want everyone to get the same amount of pizza, so some folks will get a long and skinny slice, while others will get a short and wide slice. We don't need to get into the crust debate for the purposes of this analogy.

  Understanding and confusion I: At the top, a short excerpt from the wild ride of Kepler's multivolume Harmonices Mundi, where he discovers Deep and Important truths about the celestial realm and uses those to link the motions of the planets to musical notes and scales and then to the fortunes of our daily lives. That last bit is arguable. Below, his contemporary Galileo Galilei scans the same heavens not with math but with a telescope and stares in blubbering wonder at what his polished glass reveals. In this case, in Sidereus Nuncius he sketches the rough-and-tumble surface of the moon, a far cry from the smooth marble finish it appears to be from afar.

  An ellipse has two centers, called foci, and the sun is placed at one of those foci for each planetary orbit. When that planet is closest to the sun, in a given amount of time it will carve out a short and wide slice of orbit. Likewise, when it's farther away, it gets long and skinny pieces in the same timeframe. To accomplish this, the planet must move faster when it's closer to the sun, and slower when it's farther away.

  Now for Kepler's big trick: the speeds of the planets in their orbit are telling us something. Or rather, they are singing us something. Kepler saw in the heavens the “music of the spheres,” a celestial symphony singing their notes. And since the planets were closer to heaven, their song was truly a holy hymn.

  Again, his words. Not mine.10

  Kepler was particularly interested in the ratios of the slowest to fastest speeds, because to his eyes they looked very much like the ratios of notes used to make musical tones. But he didn't stop at the “Hey, that's neat” stage; instead he went all the way for the astrological touchdown and argued that the qualities of the notes played by the celestial denizens determined their character.

  Most important, the ratio of the Earth's own speed was nearly 16:15 (and hey, if we have to fudge the numbers a bit to get a nice ratio, I'm sure nobody will notice), which was the same ratio as between the notes mi and fa. This was obviously right to Kepler, since “in this our home misery and famine hold sway.”

  This is seriously Kepler's line of thinking, and what motivated him to develop what we consider fundamental truths of our solar system. God created a perfect, harmonious universe, but we screwed it up with our sinful ways. So now only a few pockets of that primordial majesty remain: The planets, of course, since they're untouched by human affairs (ahem, at the time). Here on Earth we still have music, mathematics, and geometry, which, given the perfect relationships found within them, ought to have some glimmer of the divine.

  To Kepler, the universe was permeated with a divine orderliness that was largely masked in our world but could be viewed in the heavens. So here was his easy-peasy divination horoscope-making plan: (1) Study the heavens. (2) Discover a hidden sacred geometry. (3) Relate it to a similar geometry on Earth. (4) Use that to tell the future.

  Kepler went on for pages and pages of this kind of stuff, but there's only so much I can relate to you without going nuts, so we'll stop there.

  Thus, Kepler saw the universe as messier than we had thought (having to jump from circles to spheres), but for a good reason: the sacred geometry of the sky was informing us of divine plans. But for several years one crucial element eluded him: something to unify the divine motions of the planets.

  Finding this sacred geometry in the celestial realm wasn't enough. There had to be something deeper, even more fundamental. The elliptical orbits were useful, yes, but they only hinted at the heavenly. Kepler was hunting for a sort of universality in the laws that govern our universe, not just faint glimmers of connection. And it was by digging deeper into the details of planetary motions that he was able to uncover something truly astounding—to him, and to us even today.

  Take Mercury, for example. It sits at a particular distance from the sun (or, I should say, particular distances, since its orbit is an ellipse), and it takes a certain amount of time to complete one of its orbits. The Earth has another distance and another amount of time, unique to this planet. And again, Jupiter, or Mars, or any planet, has its very own special pair of numbers assigned to it: some measure of its distance from the sun and some measure of how long it takes to complete one orbit.

  These are all blindingly obvious and bland statements about our solar system that anyone could make. But have you ever wondered why? Why does Mercury have that number assigned to it, but not any other? Why does Jupiter take this long to orbit the sun, instead of slightly more or less time? It can't just be random coincidence, can it?

  After years of searching through those tables of numbers, hand calculation after tedious hand calculation, Kepler found a formula that stuck. Today we know it as his third law, and I'm sure he considered it among his greatest achievements. The positions and speeds of the planets were not pulled out of some cosmic hat; there was indeed a deeper order.

  Kepler discovered that the motions and positions of the planets obey a simple, harmonious relationship, and it goes like this: Pick a planet, any planet. Measure the amount of time it takes to go around the sun once. That's called the period, and you'll need to square that number. Next, draw the ellipse the planet makes in its orbit. Find the longest distance from the center of that ellipse to the edge. In math terms, that's called the semi-major axis. Cube that number.

  The square of the period divided by the cube of the semi-major axis gives you a particular value. Repeat this exercise for all the planets and write down all their numbers—a tedious but pretty straightforward exercise.

  And now for the voilà: that number is identical for all the planets, from tiny, fast Mercury to distant, slow Saturn. Across the solar system, this quantity is the same. It's an almost bizarrely simple formula unifying the motions of every planet. To us, this result seems almost pedestrian, but we're separated from this discovery by more than four hundred years of finding common elements among the stars. This was practically the philosopher's stone of astronomy. A holy grail of mathematical insight.

  And almost nobody cared. Kepler was an eccentric mystic who buried this profound insight within volumes of—well, there aren't a lot of polite words to describe it. Still, as the decades wore on, scholars recognized the importance of Kepler's work, preserving it for future generations to ponder.

  After all, his analysis only moved the goalposts; it didn't end the game. Sure, he could now handily explain the particular positions and speed of the planets. But why the period squared? Why the semi-major axis cubed? And this division thing, what's up with that? Kepler himself wasn't too concerned—the fact that he found any relationship at all was something to celebrate. As to what divine wisdom could be unlocked by understanding the s
ource of the equation: well, it's hard to be employed as a mystic without some mystery in the universe, right?

  Not that Kepler was entirely ignored—far from it. His head-scratching leaps of faith and logic were regarded with a sort of quaint curiosity, but behind the ramblings was the mind of a precise mathematician. He deftly employed his newfound organization of the cosmos—the elliptical orbits, the sun at a focal point, the underlying relationship among the planets—to great effect, publishing a set of tables that cataloged more than 1,500 star positions and predicted the positions of the planets to unheard-of accuracy, along with sets of calculation tools for handy do-it-yourself astronomy.11

  That book, called The Rudolphine Tables in honor of his patron, was a smash hit (as much anything could be back then).12 It was read, copied, and used, partly for navigation—accurate star positions are rather useful, after all—but mostly for astrology. Knowing which planet was precisely within which constellation was essential for understanding the present and divining the future.

  It was that book, based on a more sun-centered model of the universe, that made all the difference. With the addition of elliptical orbits, everything was just so much easier. If making the sun the focal point of the cosmos made you uncomfortable, at least you could console yourself that it was only a model. The universe does what the universe does (and we can still think we're at the center); what Kepler did was introduce a handy trick of mathematics to make your astrological life so much easier.

  So it's a bit ironic that Kepler is often included as some sort of patron saint of science. Sure, his achievements were remarkable. But so were Tycho Brahe's (and arguably, depending whether you lean more toward theory or experiment, Brahe's were superior), but unfortunately for old Brass Nose, he ended up on the wrong side of the argument. He did apparently have superhuman bladder control, but that didn't seem to help his scientific legacy.