Of course the Earth is at the center of the universe. Just look at the evidence. The sun, moon, stars, and planets all wheel around us in the great celestial dance; how are we possibly to make sense of that if we're not at the focal point? And have you seen the Earth? It's large and solid and made of rock—are you seriously suggesting it moves?

Look up in the sky. Birds. Clouds. The wind. All moving effortlessly, right? They are well removed from this immobile rock on which we stand, so it stands to reason that movement comes even more naturally to the stars and planets, even further removed from us.

Besides, things up there are just so different. Our lives here on Earth are dirty, chaotic, even sinful. But the graceful movements of the heavenly realm are something else. Motions so precise we can use them to set our calendars. Unfailing, the same stars appear on the horizon at the precise time they did last year, and the year before, and so on into the unwritten time of our ancestors.

Surely the laws of nature that we understand here on Earth don't apply up there. They have their own rules, their own sets of laws that govern their behavior. The heavens surround us but are separate from us.

Oh, what about those comets and meteors? Surely they're just strange atmospheric phenomena. Don't worry too much about those.

Can we really blame our forebears for thinking we are at the center? Up until a few hundred years ago, it was the simplest and most natural explanation of the available data. Not only that, it was supported by rational, coherent arguments. Our ancestors, as we do, used multiple paths to understand the world around them—evidence-based, faith-based, reason-based, math-based—all of which pointed in the same direction: out.

Our ancestors were no dummies. They were just as smart as we are today and perfectly capable of understanding the world around them. And astronomy was vitally important to their daily lives: when to plant crops, when to reap the harvest, when to start preparing for campaigns, when to celebrate holidays. Humans have been using calendars for millennia (at least!), and the natural, regular, repeatable, predictable movements of the heavens provided the perfect device.

I suppose I should mention that ancient peoples thought that the stars influenced our daily lives too—not just by proxy through the effects of the seasons, but literally determined our fate. It's a unique perspective that's missing from modern scientific perspectives (with good reason, and I'll get to that in a bit). But again, I have to stress that your extremely-great-grandparents regarded their horoscope with as much seriousness as they could muster.

The motions of the stars and planets were connected to the seasons. So even though the celestial realm obeys its own set of laws, it must surely be connected—somehow—to events here on Earth. And despite the messiness and chaotic nature of our home, there's a sense of some sort of hidden order and regularity behind our lives. There are obvious patterns in nature, so perhaps there are unobvious patterns as well, patterns that can only be teased out by careful observation and interpretation.

Thus, the astrologer: someone who carefully studied the great wheel of heavenly motions and inferred their implications for the Earthbound. Born during a particular month? That must be linked to your personality. Solar eclipse during your reign as emperor? Yikes, better clean up your act. Comet appears as you prepare for battle? The gods disfavor your enemy, and the time is right for attack.

One of our earliest records of the profession of astrologer (or, if you prefer, astronomer; the two terms weren't cleanly separated until relatively recently) comes to us from ancient China, right as they were at the edge of developing a writing system. The story goes that the two court astrologers of the emperor Chung K'ang failed to predict a solar eclipse in 2137 BCE. They were immediately beheaded.1

Yes, our ancestors took this sky-watching stuff seriously.

So it's no surprise that as the centuries progressed, more data from observations accumulated, and astronomers were able to make ever-more-sophisticated models of those motions so they could make better astrological predictions. What better way to accurately tell your fortunes, an entrepreneurial young astrologer might say to a prospective royal client, than with the most precise measurements and predictions available?

And the Ptolemaic system, developed by Ptolemy (hence the name) in the second century CE and fully established as everyone's favorite cosmological model by the sixteenth century in Europe, provided the most detailed astrological calculations possible. This model of the universe put the Earth at the center (of course!), with each celestial body assigned to its own crystal sphere. These spheres nested within each other like a set of heavenly matryoshka dolls, gliding effortlessly against each other in their cosmic dance.

The moon's sphere came first, followed by one carrying the sun and one for each of the planets (except Uranus and Neptune, which were too dim to be known), with the outermost layer carrying the sphere of stars. Beyond that was probably heaven itself, or something like it.

It's a little difficult for our modern minds to wrap themselves around prescientific cosmologies. Individual statements or expressions sound perfectly normal in isolation. Even today you could hear someone talking about, say, the time of the next lunar eclipse, or someone lecturing about the nature of the divine. But today these kinds of statements tend to be widely separated. Nobody (who wants to be taken seriously) claims that the pattern of lunar eclipses gives us a window into Holy Wisdom and a clue about what we ought to have for dinner this week.

It's not that modern scientists are incapable of religious thought, but they usually don't think about both subjects at the same time, and it's rare for a scientific treatise to use religious texts to bolster its argument (and vice versa).

This compartmentalization of inquiry into the world around us is a relatively recent invention. For almost all of human history, people who were curious about the universe were simply that: curious about the universe. And one could inquire about the universe in many different ways: using evidence, using divine revelation, using rational arguments, using mathematical proofs, and so on.

So the highly sophisticated cosmological Ptolemaic model wasn't just a physical model of the order of the universe—it was fully incorporated into the religious, philosophical, and mathematical views of the time and place.2

I'm highlighting this blending of modes of inquiry into the natural world because I think there's something missing from the usual story of the birth of the scientific revolution. That story, put very simply, goes like this: we used to think the Earth was at the center of the universe, but that model was flawed. Copernicus proposed that the sun was at the center, Kepler refined this theory, and Galileo got in a big argument with the Catholic Church about it. Lots of fighting and a good amount of burning at the stake ensued, but eventually science prevailed, and now we know better.

I don't think that gives the right flavor of what went down at the turn of the 1600s. Don't get me wrong: Galileo fought with the church (a lot), people got burned (a lot), and a sun-centered model was adopted (eventually). But the impression that I, at least, got as I was taught this way back in grade school was that the arrogant know-it-alls thought the Earth was at the center, taking pride of place, and refused to accept the new view.

To be fair, most people of historic eras simply didn't think about this at all. They were too busy dying of plague, dying from starvation, or dying in battle to wonder about the precise mathematical formula that would unlock the inner workings of the celestial spheres. The arguments that have passed down to us are from the intelligentsia of the age: those who could read and write (usually in Latin), who had access to the books written by their intellectual ancestors, who had enough time to make precise measurements of the objects in the sky, and who had the ear of a king or pope or other wealthy dude to fund their studies.

So I can't tell you what Mathias or Marta Everyman thought about the universe, but I can tell you what Nicolaus Copernicus, Tycho Brahe, Johannes Kepler, and Galileo Galilei thought.

By the late 1500s, folks pretty much knew there were some issues with the Ptolemaic model of cosmology. The trouble, as is usually the trouble when theories begin to crumble, was data. Assuming that the planets move in perfect circles doesn't quite fit the observations. Sometimes the planets appear to move backward in their orbits, which just shouldn't happen.

The easiest solution is to add a so-called epicycle, a circle-within-a-circle to account for the extra motion. OK, fair enough. Circles are nice and elegant, and a series of nested circles within each orbit is only one step away from a series of nested spheres to explain the orbits themselves. There's a certain appealing symmetry there.

But in the centuries leading up to 1600, astronomers started making more accurate observations, and they noted deviations from the circles-within-circles approach. To explain this, they added ever more epicycles, each one tacked onto a particular planet to match all the observations.

It was a bit complicated, but it worked: it fit the data and was able to make predictions. You could tell your fortunes with the epicycle Earth-centered system. Maybe it was a bit cumbersome, so naturally you would need a few years of training before you could become an adept astrologer. But there's nothing wrong with baking a little job security into the system, right?

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 source 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.

Kepler was right—it is more accurate to think of the solar system as just that, solar—but for all the wrong reasons. And his legacy survived not on its scientific merits but on its astrological usefulness. Scholarly discourse slowly abandoned the concept of heavenly crystal spheres in the decades following Kepler's input. There simply wasn't a need: it was much easier to talk about the universe as if the sun hung at the center and the planets zoomed along on their little elliptical racetracks.

But his story serves as an object lesson for this book. The universe is far, far messier than we would prefer it to be. Wouldn't it be great if a few simple circles (and heck, let's be generous and toss in a few epicycles too) were enough to completely describe the cosmos?

Unfortunately, Mother Nature isn't that kind to us. Ellipses are more complicated than circles, for sure, but to Kepler that was a boon rather than a curse. With this much more rich information, he had enough clues to perceive an orderly pattern. He didn't fully understand the causes or physical implications of his third law, but he did discern it.

And that's why Kepler, as nutty as he was, even in the eyes of his peers, was onto something good.

Oh, right, Galileo. He was kind of a big deal, operating at the same time as Kepler, living in Italy in the shadow of his frenemy the Catholic Church. He was the astronomer's astronomer and the curmudgeon's curmudgeon. A rude dude who straight up called his boss an idiot (pro tip for the Renaissance scientist: don't tick off the pope, who also happens to wield supreme temporal power over your land). I'm not saying the church was in the right putting him under house arrest for arguing against the orthodoxy, but Galileo didn't exactly do himself any favors. The full story of Galileo is wonderful and convoluted and wonderfully convoluted, and also the subject of another book.13

Instead, I want to focus on what Galileo saw with his newfangled telescope. The instrument itself is deceptively simple. On paper it looks so easy a kindergartener could assemble it: a couple of curved lenses and a tube. The physics of optics does all the rest. And while Galileo didn't invent the telescope per se, he certainly invented the astronomical telescope, which is what we usually think of when we use the word “telescope.”

The device had been developed within Galileo's lifetime, and, people being people, I'm sure somebody somewhere pointed it up at the night sky to see what he could see. Unfortunately, that person couldn't see much; the trick to telescopes isn't in their construction but in their finishing. You have to polish the lens to an extremely high level of precision so the path of light gets bent in just the right way, or you get a smudgy mess on the other end.

A telescope does two things. First, it's just a bucket for light. Your pupil can only cram so much light into it at a time, and that sets a limit to the dimmest thing you can see (I'm, uh, glossing over some biological details here, but you get the idea). A wider telescope is like a wider eyeball: it can soak up photons that would normally just hit the rest of your face.

The second thing a telescope does is magnify. It takes all that collected light and focuses it down to a smaller area so that it can fit in your eye. That operation turns small separations into big separations, so a minuscule dot on the horizon can be recognized as, say, a ship.

“Hey, guys, there's a ship on the horizon…I think” was the current gold standard for telescopes until Galileo took a crack at it. With uncommon dedication, he made a lens so smooth, so flawless, that the celestial realm completely changed its character.¹⁴

The moon, thought to be a smooth globe of marble, was instead a loose collection of jagged rocks. Jupiter was not alone—it was joined by four small moons that were obviously orbiting it. Saturn had two lumps on either side of it that, over the course of Galileo's repeated observations, shrank to thin slivers and disappeared—before reappearing again.

The sun had spots that, after a little geometrical legwork, were shown to be attached to its surface. And that surface was spinning. Fast.

Venus had phases. Phases. Like the moon. Since phases are a trick of perspective—the light from the sun illuminates only one side of an object at a time, and that side can be different from the one we view—the only way to make that work was for the sun to be at the center of the solar system.

The universe that Galileo revealed was frightfully messy. With this joining Brahe's earlier discovery of a new star appearing and his demonstration that comets were not confined to our atmosphere,15 scholars (at this early stage, I hesitate to call them scientists in the sense we're used to) were quickly realizing that our home is a strange place indeed.

What got Galileo into trouble (well, one of the things) was his insistence on circular orbits. He saw, right through the lens of his telescope, direct evidence for a sun-centered cosmos. He must have been aware of Kepler's work—Johannes wrote to him like an eager fanboy—but he either missed the memo on elliptical orbits or outright ignored it because it was caught up in mystic mumbo jumbo.

It's interesting that Kepler and Galileo were tackling the same problem (the structure and contents of the universe) using different techniques (Kepler digging deep into mathematics and Galileo producing literal volumes of observations) and arriving at conclusions that seem at odds. But on closer inspection, their results were two sides of the same coin.

Galileo saw firsthand a messy universe but insisted on simple, orderly circles to explain the orbits of the planets. Kepler found elegant geometric order in the chaos but argued that the universe was directly connected to our everyday lives. I can't think of better prototypical experimentalists and theorists.

Put them together and you have the picture that modern cosmology—the study of the cosmos—brings us: we live in a simple universe that is connected to our daily lives.

Wait, no, that's not right. It's the other combination: we live in a messy universe that doesn't care about us.

That's it.