Isaac Newton

The success of known physical laws to explain the world around us has consistently bred some confident and cocky attitudes toward the state of human knowledge, especially when the holes in our knowledge of objects and phenomena are perceived to be small and insignificant. Nobel laureates and other esteemed scientists are not immune from this stance, and in some cases have made especially embarrassing proclamations about the end of science.

A famous end-of-science prediction came in 1894, during the speech given by the soon-to-be Nobel laureate Albert A. Michelson on the dedication of the Ryerson Physics Lab, at the University of Chicago.

The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote....Future discoveries must be looked for in the sixth place of decimals.

One of the most brilliant astronomers of the time, Simon Newcomb, who was also co-founder of the American Astronomical Society, shared Michelson's views in 1888 when he noted, We are probably nearing the limit of all we can know about astronomy. Even the great physicist Lord Kelvin, who had the absolute temperature scale named after him, fell victim to his own confidence in 1900 with the claim, There is nothing new to be discovered in physics now. All that remains is more and more precise measurement. These comments were expressed at a time when the luminiferous ether was still the presumed medium in which light propagated through space, and when the slight difference between the observed and predicted path of Mercury around the Sun was real and unsolved. These unsolved problems were perceived at the time to be small, requiring perhaps only small adjustments to the known physical laws to account for them.

Fortunately, Max Planck, one of the founders of quantum mechanics, had more foresight than his academic advisor. Here, in a 1924 lecture, he reflects on the advice given to him in 1874, when he began his studies in physics.

When I began my physical studies and sought advice from my venerable teacher Philipp von Jolly...he portrayed to me physics as a highly developed, almost fully matured science...Possibly in one or another nook there would perhaps be a dust particle or a small bubble to be examined and classified, but the system as a whole stood there fairly secured, and theoretical physics approached visibly that degree of perfection which, for example, geometry has had already for centuries.

Initially Planck had no reason to doubt his teacher's views. But when our classical understanding of how matter radiates energy could not be reconciled with experiment, Planck became a reluctant revolutionary in 1900 by suggesting the existence of the quantum, an indivisible unit of energy that heralded an era of new physics. The next thirty years would see the discovery of the special and general theories of relativity, quantum mechanics, and the expanding universe.

With all this myopic precedence you would think that the brilliant and prolific physicist Richard Feynman would have known better. In his 1965 book The Character of Physical Law he declares,

We are very lucky to be living in an age in which we are still making discoveries....The age in which we live is the age in which we are discovering the fundamental laws of nature, and that day will never come again. It is very exciting, it is marvelous, but this excitement will have to go.

I claim no special knowledge of when the end of science will come, or where the end might be found, or whether an end exists at all. What I do know is that our species is dumber than we normally admit to ourselves. This limit of our mental faculties, and not necessarily of science itself, ensures to me that we have only just begun to figure out the universe.

Let's assume, for the moment, that human beings are the smartest species on Earth. If, for the sake of discussion, we define smart as the capacity of a species to do abstract mathematics then one might further assume that human beings are the only smart species to have ever lived.

What are the chances that this first and only smart species in the history of life on Earth has enough smarts to completely figure out how the universe works? Chimpanzees are an evolutionary hair's-width from us yet I think we can agree that no amount of tutelage will ever leave a chimp fluent in trigonometry. Now imagine a species on Earth, or anywhere else, as smart compared with humans as humans are compared with chimpanzees. How much of the universe might they figure out?

Tic-tac-toe fans know that the game's rules are sufficiently simple that it's possible to win or tie every game—if you know which first-moves to make. But young children play the game as though the outcome were remote and unknowable. The rules of engagement are also clear and simple for the game of chess, but the challenge of predicting your opponent's upcoming sequence of moves grows exponentially as the game proceeds. So adults—even smart and talented ones—are challenged by the game and play it as though the end were a mystery.

Let's go to Isaac Newton, who leads my list of the smartest people who ever lived. (I am not alone here. A memorial inscription on a bust of him in Trinity College, England, proclaims Qui genus humanum ingenio superavit, which loosely translates from the Latin, of all humans, there is no greater intellect.) What did Newton observe about his state of knowledge?

I do not know what I appear to the world; but to myself I seem to have been only like a boy playing on a seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay undiscovered before me.

The chessboard that is our universe has revealed some of its rules, but much of the cosmos still behaves mysteriously—as though there remain secret, hidden regulations to which it abides. These would be rules not found in the rulebook we have thus far written.

The distinction between knowledge of objects and phenomena, which operate within the parameters of known physical laws, and knowledge of the physical laws themselves is central to any perception that science might be coming to an end. The discovery of life on the planet Mars, or beneath the floating ice sheets of Jupiter's moon Europa, would be the greatest discovery of any kind ever. You can bet, however, that the physics and chemistry of its atoms will be the same as the physics and chemistry of atoms here on Earth. No new laws necessary.

But let's peek at a few unsolved problems from the underbelly of modern astrophysics and expose the breadth and depth of our contemporary ignorance, the solutions of which, for all we know, await the discovery of entirely new branches of physics.

While our confidence in the big bang description of the origin of the universe is very high, we can only speculate what lies beyond our cosmic horizon, 13 billion light years from us. We can only guess what happened before the big bang or why there should have been a big bang in the first place. Some predictions, from the limits of quantum mechanics, allow our expanding universe to be the result of just one fluctuation from a primordial space-time foam, with countless other fluctuations spawning countless other universes.

Shortly after the big bang, when we try to get our computers to make the universe's hundred billion galaxies, we have trouble simultaneously matching the observational data from early and late times in the universe. A coherent description of the formation and evolution of the large-scale structure of the universe continues to elude us. We seem to be missing some important pieces of the puzzle.

Newton's laws of motion and gravity looked good for hundreds of years, until they needed to be modified by Einstein's theories of motion and gravity—the relativity theories. Relativity now reigns supreme. Quantum mechanics, the description atomic and nuclear universe, also reigns supreme, except that, as conceived, it is irreconcilable with Einstein's theory of gravity. They each predict different phenomena for the domain in which they might overlap. Something's got to surrender. Either there's a missing part of Einstein's gravity that enables it to accept the tenets of quantum mechanics, or there's a missing part of quantum mechanics that enables it to accept Einstein's gravity.

Perhaps there's a third option: the need for a larger, inclusive theory that supplants them both. Indeed, string theory has been invented and called upon to do just that. It attempts to reduce the existence of all matter, energy, and their interactions to the simple existence of higher dimensional vibrating strings of energy. Different modes of vibration would reveal themselves in our measly dimensions of space and time as different particles and forces. Although string theory has had its adherents for more than twenty years, its claims continue to lie outside our current experimental capacity to verify its formalisms. Skepticism is rampant, but many are nonetheless hopeful.

We still do not know what forces enabled inanimate matter to assemble into life as we know it. Is there some mechanism or law of chemical self-organization that escapes our awareness because we have nothing with which to compare our Earth-based biology, and so we cannot evaluate what is essential and what is irrelevant to the formation of life?

We've known since Edwin Hubble's seminal work during the 1920s that the universe is expanding, but we've only just learned that the universe is also accelerating, by some anti-gravity pressure dubbed dark energy for which we have no working theory to understand.

At the end of the day, no matter how confident we are in our observations, our experiments, our data, or our theories, we must go home knowing that ninety percent of all the gravity in the cosmos comes from some unknown, mysterious source. This source remains completely undetected by all means we have ever devised to observe the universe. As far as we can tell, it's not made of ordinary stuff such as electrons, protons, and neutrons, or any form of matter or energy that interacts with them. We call this offending substance, dark matter, which remains the greatest enigma of modern times.

Does any of this sound like the end of science? Does any of this sound like we are on top of the situation? Does any of this sound like it's time to congratulate ourselves? To me it sounds like we are all stupid helpless idiots, not unlike like our kissing cousin, the chimpanzee, trying to learn the Pythagorean theorem.

Maybe I'm being a little hard on Homo sapiens and have carried the chimpanzee analogy a little too far. Perhaps the question is not how smart is an individual of a species, but how smart is the collective brain-power of the entire species. Among humans, discoveries made by some are routinely shared with others through conferences, books, other media, and of course the Internet. While natural selection drives Darwinian evolution, the growth of human culture is largely Lamarckian, where new generations of humans inherit the acquired discoveries of generations past, allowing cosmic insight to accumulate without limit.

Each discovery of science therefore adds a rung to a ladder of knowledge whose end is not in sight because we are building the ladder as we go along. As far as I can tell, as we assemble and ascend this ladder, we will forever uncover the secrets of the universe—one by one.

Whenever cartoonists draw biologists, chemists, or engineers, the characters typically wear protective white lab coats that have assorted pens and pencils poking out of the breast pocket. Astrophysicists use plenty of pens and pencils, but we never wear lab coats unless we are building something to launch into space. Our primary laboratory is the cosmos, and unless you have bad luck and get hit by a meteorite, you are not at risk of getting your clothes singed or otherwise sullied by caustic liquids spilling from the sky. Therein lies the challenge. How do you study something that cannot possibly get your clothes dirty? How do astrophysicists know anything about either the universe or its contents if all the objects to be studied are light-years away?

Fortunately, the light emanating from a star reveals much more to us than its position in the sky or how bright it is. The atoms of objects that glow lead busy lives. Their little electrons continually absorb and emit light. And if the environment is hot enough, energetic collisions between atoms can jar loose some or all of their electrons, allowing them to scatter light to and fro. All told, atoms leave their fingerprint on the light being studied, which uniquely implicates which chemical elements or molecules are responsible.

As early as 1666, Isaac Newton passed white light through a prism to produce the now-familiar spectrum of seven colors: red, orange, yellow, green, blue, indigo, and violet, which he personally named. (Feel free to call them Roy G. Biv.) Others had played with prisms before. What Newton did next, however, had no precedent. He passed the emergent spectrum of colors back through a second prism and recovered the pure white he started with, demonstrating a remarkable property of light that has no counterpart on the artist's palette' these same colors of paint, when mixed, would leave you with a color resembling that of sludge. Newton also tried to disperse the colors themselves but found them to be pure. And in spite of the seven names spectral colors change smoothly and continuously from one to the next. The human eye has no capacity to do what prisms do—another window to the universe lay undiscovered before us.

A careful inspection of the Sun's spectrum, using precision optics and techniques unavailable in Newton's day, reveals not only Roy G. Biv, but narrow segments within the spectrum where the colors are absent. These "lines" through the light were discovered in 1802 by the English medical chemist William Hyde Wollaston, who naively (though sensibly) suggested that they were naturally occurring boundaries between the colors. A more complete discussion and interpretation followed with the efforts of the German physicist and optician Joseph von Fraunhofer (1787–1826), who devoted his professional career to the quantitative analysis of spectra and to the construction of optical devices that generate them. Fraunhofer is often referred to as the father of modern spectroscopy, but I might further make the claim that he was the father of astrophysics. Between 1814 and 1817, he discovered that when he passed the light of certain flames through a prism, the pattern of lines resembled what he found in the Sun's spectrum, which further resembled lines found in the spectra of many stars, including Capella, one of the brightest in the nighttime sky. By the mid-1800s the chemists Gustav Kirchhoff and Robert Bunsen (of "Bunsen-burner" fame from your chemistry class) were making a cottage industry of passing the light of burning substances through a prism. They mapped the patterns made by known elements and discovered a host of new elements, including rubidium and caesium. Each element left its own pattern of lines—its own calling card—in the spectrum being studied. So fertile was this enterprise that the second most abundant element in the universe, helium, was discovered in the spectrum of the Sun before it was discovered on Earth. The element's name's bears this history with its prefix derived from "Helios" the Sun.

A detailed and accurate explanation of the role of atoms and their electrons in how spectral lines are formed would not emerge until the era of quantum mechanics a half-century later, but the conceptual leap already been made: Just as Newton's equations of gravity connected the realm of laboratory physics to the solar system, Fraunhofer connected the realm of laboratory chemistry to the cosmos. The stage was set to identify, for the first time, what chemical elements filled the universe, and under what conditions of temperature and pressure their patterns revealed themselves to the spectroscopist.

Among the more bone-headed statements made by armchair philosophers, we find the following 1835 proclamation:

On the subject of stars, all investigations which are not ultimately reducible to simple visual observations are...necessarily denied to us.... We shall never be able by any means to study their chemical composition...I regard any notion concerning the true mean temperature of the various stars as forever denied to us...

Auguste Compte, French Natural Philosopher

Quotes like that can make you afraid to say anything in print.

Just seven years later, in 1842, the Austrian physicist Christian Doppler proposed what became known as the Doppler effect, which is the change in frequency of a wave being emitted by an object in motion. One can think of the moving object as stretching the waves behind it (reducing their frequency) and compressing the waves in front of it (increasing their frequency). The faster the object moves, the more the light is both compressed in front of it and stretched behind it. This simple relationship between speed and frequency has profound implications. If you know what frequency was emitted, but you measure it to have a different value, the difference between the two is a direct indication of the object's speed toward or away from you. In an 1842 paper, Doppler makes the prescient statement:

It is almost to be accepted with certainty that this [Doppler effect] will in the not too distant future offer astronomers a welcome means to determine the movements... of such stars which... until this moment hardly presented the hope of such measurements and determinations.

The idea works for sound waves, for light waves, and in fact, waves off any origin. (I'd bet Doppler would be surprised to learn that his discovery would one day be used in microwave-based "radar guns" wielded by police officers to extract money from people who drive automobiles above a speed limit set by law.) By 1845, Doppler was conducting experiments with musicians playing tunes on flatbed railway trains, while people with perfect pitch wrote down the changing notes they heard as the train approached and then receded.

During the late 1800s, with the widespread use of spectrographs in astronomy, coupled with the new science of photography, the field of astronomy was re-born as the discipline of astrophysics. One of the preeminent research publications in my field, the Astrophysical Journal, was founded in 1895, and, until 1962, bore the subtitle: An International Review of Spectroscopy and Astronomical Physics. Even today, nearly every paper reporting observations of the universe gives either an analysis of spectra or is heavily influenced by spectroscopic data obtained by others. Since it takes much more light to generate of spectrum of object than it does to takes to snapshot of it, the biggest telescopes in the world, such as the 10-meter Keck telescopes in Hawaii, are tasked primarily with getting spectra. In short, were it not for science's ability to analyze light by breaking it up into its component colors, we would know next-to-nothing about the universe.

Astrophysics educators surely face a pedagogical challenge of the highest rank. We deduce nearly all of our scientific information about the structure, formation and evolution of things in the universe from the study of spectra, but the analysis of spectra is removed by several levels of inference from the things being studied. Analogies and metaphors help, by linking a complex, somewhat abstract idea to a simpler, more tangible one. The biologist might describe the shape of the DNA molecule as two coils, connected to each other the way rungs on a ladder connect its sides. I can picture a coil. I can picture two coils. I can picture rungs on a ladder. I can therefore picture the molecule's shape. Each part of the description sits only one level of inference removed from the molecule itself. And they came together nicely to make a tangible image in the mind. However easy or hard it is, one can now talk about the science of the molecule. To explain how we know the speed of a receding star from us requires five nested levels of abstraction:

• Level 0: Star
• Level 1: Picture of a star
• Level 2: Light from the picture of a star.
• Level 3: Spectrum from the light from the picture of a star.
• Level 4: Patterns of lines lacing the spectrum from the light from the picture of a star.
• Level 5: Shifts in the patterns of lines in the spectrum from the light from the picture of the star.

Going from Level 0 to Level 1 is a trivial step that we take every day when we get our pictures back from the photo processor. But by the time your explanation reaches level five, your audience is befuddled or just fast sleep. Therein is why the public hardly ever hears about the role of spectra in cosmic discovery—it's just too far removed from the objects themselves to explain efficiently or with ease. In the design of exhibits for a natural history museum, or for any museum where real things matter, what you typically seek are artifacts for display cases—rocks, bones, tools, fossils, memorabilia, and so forth. All these are "Level 0" specimens require little or no cognitive investment before you give the explanation of what the object is. For astrophysics displays, however, we cannot place stars or quasars on display because they would vaporize the Museum.

Most astrophysics exhibits are therefore conceived in Level 1, leading principally to displays of pictures—some quite striking and beautiful. The most famous telescope in modern times, the Hubble Space telescope, is known to the public primarily through the beautiful, full-color, high-resolution images it has acquired of objects in the universe. The problem here is that after you view such exhibits, you leave waxing poetic about the beauty of the universe yet you are no closer than before to understanding how it all works. To really know universe requires forays into Levels 3, 4, and 5. While much good science has come from the Hubble Telescope (including the most reliable measure to-date for the expansion rate of the universe) you would never know it from media accounts that the foundation of our cosmic knowledge continues to flow primarily from the analysis of spectra and not from looking at pretty pictures. I want people to wax poetic not only from exposure to Levels 0 and 1, but also from exposure to Level 5, which admittedly requires a greater intellectual investment on the part of the student, but also (and perhaps especially) on the part of the educator.

It's one thing to see a beautiful color picture, taken in visible light, of a nebula in our own Milky Way galaxy. But it's another thing to know from its radio wave spectrum that it also harbors newly formed stars of very high mass within its cloud layers. This gas cloud is a stellar nursery, regenerating the light of the universe.

It's one thing to know that every now and again, high-mass stars explode. Photographs can show you this. But x-ray and visible light spectra of these dying stars reveal cache of heavy elements that enrich the galaxy and are directly traceable to the constituent elements of life on earth. Not only do we live among the stars, the stars live within us.

It's one thing to look at a poster of a pretty spiral galaxy. But it's another thing to know from Doppler shifts in its spectral features that the galaxy is rotating at 200 kilometers per second, from which we infer the presence of 100 billion stars using Newton's laws of gravity. And by the way, the galaxy is receding from us a 1/10 the speed of light as part of the expansion of the universe.

It's one thing to look at nearby stars that resemble the Sun in luminosity and temperature. But it's another thing to use hyper-sensitive Doppler measurements of the star's motion to infer the existence of planets in orbit around them. At press time, our catalog is rising though a hundred such planets outside the familiar ones in our own solar system.

Fortunately, for the magnetohydrodynamicists among us, atomic structure changes slightly under the influence of a magnetic field. This change can be seen in the slightly altered spectral pattern caused by these magnetically afflicted atoms.

It's one thing to observe the light from a quasar at the edge of the universe. But its another thing entirely to analyze the quasar's spectrum and deduce the structure of the invisible universe, laid along the quasar's path of light as gas clouds and other obstructions take their bite our of the quasar spectra.

And armed with Einstein's relativistic version of the Doppler formula, we deduce the expansion rate of the entire universe from the spectra of countless galaxies near and far, and thus infer the age and fate of the universe.

One could make a compelling argument that we know more about the universe than marine biologist knows about the bottom of the ocean or the geologist knows about the center of the Earth. Far from an existence as powerless stargazers, modern astrophysicists are armed to the teeth with the tools and techniques of spectroscopy, enabling us all to stay firmly planted on Earth, yet finally touch the stars without burning our fingers, and claim to know them as never before.

In nearly all sports that use balls, the balls go ballistic at one time or another. Whether you're playing baseball, cricket, football, golf, jai alai, soccer, tennis, or water polo, a ball gets thrown, smacked, or kicked and then briefly becomes airborne before returning to Earth.

Air resistance affects the trajectory of all these balls, but regardless of what set them in motion or where they might land, their basic paths are described by a simple equation found in Newton's Principia, his seminal 1687 book on motion and gravity. Several years later, Newton interpreted his discoveries for the Latin-literate lay reader in The System of the World, which includes a description of what would happen if you hurled stones horizontally at higher and higher speeds. Newton first notes the obvious: the stones would hit the ground farther and farther away from the release point, eventually landing beyond the horizon. He then reasons that if the speed were high enough, a stone would travel the Earth's entire circumference, never hit the ground, and return to smack you in the back of the head. If you ducked at that instant, the object would continue forever in what is commonly called an orbit. You can't get more ballistic than that.

The speed needed to achieve Low Earth Orbit (affectionately called LEO) is a little less than 18,000 miles per hour sideways, making the round trip about an hour and a half. Had Sputnik 1, the first artificial satellite, or Yury Gagarin, the first human to travel beyond Earth's atmosphere, not reached that speed after being launched, they would never have made it into orbit.

Newton also showed that the gravity exerted by any spherical object acts as though all the object's mass were concentrated at its center. Indeed, anything tossed between two people on the Earth's surface is also in orbit, except that the trajectory happens to intersect the ground. This was as true for Alan B. Shepard's fifteen-minute ride aboard the Mercury spacecraft Freedom 7, in 1961, as it is for a golf drive by Tiger Woods, a home run by Sammy Sosa, or a ball tossed by a child: they have executed what are sensibly called suborbital trajectories. Were the Earth's surface not in the way, all these objects would execute perfect, albeit elongated, orbits around Earth's center. And though the law of gravity doesn't distinguish among these trajectories, NASA does. Shepard's journey was mostly free of air resistance, because it reached an altitude where there's hardly any atmosphere. For that reason alone, the media promptly crowned him America's first space traveler.

Suborbital paths are the trajectories of choice for ballistic missiles. Like a hand grenade that arcs ballistically toward its target after being hurled, a ballistic missile flies only under the action of gravity after being launched. These weapons of mass destruction travel hypersonically, fast enough to traverse half of the Earth's circumference in forty-five minutes before plunging back to the surface at thousands of miles an hour. If a ballistic missile is heavy enough, the thing can do more damage just by falling out of the sky than can the explosion of the conventional bomb it carries on board.

The world's first ballistic missile was the V-2 rocket, designed by a team of German scientists under the leadership of Wernher von Braun and used by the Nazis during the Second World War, primarily against England. As the first object to be launched above Earth's atmosphere, the bullet-shaped, large-finned V-2 (the V stands for Vergeltungswaffen, or Vengeance Weapon) inspired an entire generation of spaceship illustrations. After surrendering to the Allied forces, von Braun was brought to the United States, where in 1958 he directed the launch of Explorer 1, the first U.S. satellite. Shortly thereafter, he was transferred to the newly created National Aeronautics and Space Administration. There he developed the Saturn V, the most powerful rocket ever created, making it possible to fulfill the American dream of landing on the Moon.

While hundreds of artificial satellites orbit Earth, the Earth itself orbits the Sun. In his 1543 magnum opus, De Revolutionibus, Nicolaus Copernicus placed the Sun in the center of the universe and asserted that Earth plus the five known planets—Mercury, Venus, Mars, Jupiter, and Saturn—executed perfect circular orbits around it. Unknown to Copernicus, a circle is an extremely rare shape for an orbit and does not describe the path of any planet in our solar system. The actual shape was deduced by the German mathematician and astronomer Johannes Kepler, who published his calculations in 1609. The first of his laws of planetary motion asserts that planets orbit the Sun in ellipses. An ellipse is a flattened circle, and the degree of flatness is indicated by a numerical quantity called eccentricity, abbreviated e. If e is zero, you get a perfect circle. As e increases from zero to one, your ellipse gets more and more elongated. Of course, the greater your eccentricity, the more likely you are to cross somebody else's orbit. Comets that plunge in from the outer solar system have highly eccentric orbits, whereas the orbits of Earth and Venus closely resemble circles, with very low eccentricities. The most eccentric planet is Pluto, and sure enough, every time it goes around the Sun, it crosses the orbit of Neptune, acting suspiciously like a comet (see my column Pluto's Honor, February 1999).

The most extreme example of an elongated orbit is the famous case of the hole dug all the way to China. Contrary to the expectations of our geographically challenged fellow citizens, China is not opposite the United States on the globe. The Indian Ocean is. To avoid emerging under two miles of water, we should dig from Shelby, Montana, to the isolated Kerguelen Islands.

Now comes the fun part. Jump in. You now accelerate continuously in a weightless, free-fall state until you reach Earth's center—where you vaporize in the fierce heat of the iron core. But let's ignore that complication. You zoom past the center, where the force of gravity is zero, and steadily decelerate until you just reach the other side, at which time you have slowed to zero. Unless a Kerguelian grabs you, though, you will fall back down the hole and repeat the journey indefinitely. Besides making bungee jumpers jealous, you have executed a genuine orbit, taking about an hour and a half—just like that of the space shuttle.

Some orbits are so eccentric that they never loop back around again. At an eccentricity of exactly one you have a parabola, and for eccentricities greater than one the orbit traces a hyperbola. To picture these shapes, aim a flashlight at a nearby wall. The emergent cone of light will form a circle. Now gradually angle the flashlight upward, and you create ellipses of higher and higher eccentricities. When your cone points straight up, the light that still falls on the nearby wall takes the exact shape of a parabola. Tip the flashlight a bit more, and you have made a hyperbola. (Now you have something different to do when you go camping.) Any object with a parabolic or hyperbolic trajectory moves so fast that it will never return. If astronomers ever discover a comet with such an orbit, we will know that it has emerged from the depths of interstellar space and is on a one-time tour through the inner solar system.

Newtonian gravity describes the force of attraction between any two objects anywhere in the universe, no matter where they are found, what they are made of, or how large or small they may be. For example, you can use Newton's law to calculate the past and future behavior of the Earth-Moon system. But add a third object—a third source of gravity—and you severely complicate the system's motions. More generally known as the three-body problem, this ménage à trois yields richly varied trajectories whose tracking generally requires a computer.

Some clever solutions to this problem deserve attention. In one case, called the restricted three-body problem, you simplify things by assuming the third body has so little mass compared with the other two that you can ignore its presence in the equations. With this approximation, you can reliably follow the motions of all three objects in the system. And we're not cheating: many cases like this exist in the real universe. Take the Sun, Jupiter, and one of Jupiter's itty-bitty moons. In another example drawn from the solar system, an entire family of rocks move in stable orbits around the Sun, a half-billion miles ahead of and behind Jupiter. These are the Trojan asteroids, each one locked (as if by sci-fi tractor beams) by the gravity of Jupiter and the Sun.

Another special case of the three-body problem was discovered in recent years. Take three objects of identical mass and have them follow each other in tandem, tracing a figure eight in space. Unlike those automobile racetracks where people go to watch cars smashing into each other at the intersection of two ovals, this setup takes better care of its participants. The forces of gravity require that for all times the system balances at the point of intersection, and, unlike the complicated general three-body problem, all motion occurs in one plane. Alas, this special case is so odd and so rare that there is probably not a single example of it among the hundred billion stars in our galaxy, and perhaps only a few examples in the entire universe, making the figure-eight three-body orbit an astrophysically irrelevant mathematical curiosity.

Beyond one or two other well-behaved cases, the gravitational interaction of three or more objects eventually makes their trajectories go bananas. To see how this happens, simulate Newton's laws of motion and gravity on your computer. Now nudge every object according to the force of attraction between it and every other object in the simulation. Recalculate all forces and repeat. The exercise is not simply academic. The entire solar system is a many-body problem, with asteroids, moons, planets, and the Sun in a state of continuous mutual attraction. Newton worried greatly about this problem, which he could not solve with pen and paper. Fearing the entire solar system was unstable and would eventually crash its planets into the Sun or fling them into interstellar space, he postulated that God might step in every now and then to set things right.

Pierre-Simon de Laplace presented a solution to the many-body problem of the solar system more than a century later, in his magnum opus, Méchanique Céleste. But to do so, he had to invent a new form of mathematics known as perturbation theory. The analysis begins by assuming that there is only one major source of gravity and that all the other forces are minor, though persistent—exactly the situation in our solar system. Laplace then demonstrated analytically that the solar system is indeed stable, and that you don't need new laws of physics to show it.

Or is it? Modern analysis demonstrates that on timescales of hundreds of millions of years—periods much longer than the ones considered by Laplace—planetary orbits are chaotic. That leaves Mercury vulnerable to falling into the Sun, and Pluto vulnerable to getting flung out of the solar system altogether. Worse yet, the solar system might have been born with dozens of other planets, most of them now long lost to interstellar space. And it all started with Copernicus's simple circles.

If you imagine yourself rising above the plane of the solar system, you would see each star in our Sun's neighborhood moving about at relative speeds between ten and twenty kilometers a second. But collectively those stars all orbit the galaxy in wide, nearly circular paths, at speeds in excess of 200 kilometers a second. Most of the hundred billion stars of the Milky Way lie within a broad, flat disk, and, like the orbiting objects in all other spiral galaxies, the clouds, stars, and other constituents of the Milky Way thrive on big, round orbits.

Elliptical galaxies are rounded rather than disk-like, yet the orbits of their constituents are anything but round. Many of their stars follow highly elliptical trajectories, plunging swiftly toward the center from all directions and rising steeply back out, the way comets in our solar system do. Elliptical galaxies take the collective shape of all their stars' orbits, just as a swarm of bees takes the collective shape of all its bees' paths.

If you continue rising now, above the plane of the entire Milky Way, you would see the beautiful Andromeda galaxy, a mere 2.5 million light-years away. It's the spiral galaxy closest to us, and all the currently available data suggest we're on a collision course. As we plunge ever deeper into each other's gravitational embrace, we will become a twisted wreck of strewn stars and colliding gas clouds. Just wait about six or seven billion years. With better measurements of our relative motions, however, astronomers may discover a strong sideways component in addition to the motion that brings us together. If so, the Milky Way and Andromeda will instead swing past each other in an elongated orbital dance.

Whenever you go ballistic, you are in free fall. All of Newton's stones were in free fall toward Earth. The one that achieved orbit was also in free fall toward Earth, but our planet's surface curved out from under it at exactly the same rate as it fell—a consequence of the stone's extraordinary sideways motion. The International Space Station is also in free fall toward Earth. So is the Moon. And, like Newton's stones, they are all maintaining a prodigious sideways motion that prevents them from crashing to the ground. For those objects, as well as for the space shuttle, the wayward wrenches of spacewalking astronauts, and other hardware in LEO, one trip around the planet takes about ninety minutes.

The higher you go, however, the longer the orbital period. At about 22,300 miles up, the orbital period is the same as the Earth's rotation rate. Satellites launched into this orbit are said to be geostationary; they hover over a single spot on the planet, enabling rapid, sustained communication between continents as well as satellite TV. Much higher still, at an altitude of 240,000 miles, is the Moon, which takes 27.3 days to complete its orbit.

A fascinating feature of free fall is the persistent state of weightlessness aboard any craft with such a trajectory. In free fall you and everything around you fall at exactly the same rate. A scale placed between your feet and the floor would also be in free fall. Because nothing is squeezing the scale, it would read zero. For this reason, and no other, astronauts are weightless in space.

But the moment the spacecraft speeds up or begins to rotate or undergoes resistance from the Earth's atmosphere, the free-fall state ends and the astronauts weigh something again. Every science-fiction fan knows that if you rotate your spacecraft at just the right speed, or accelerate your spaceship at the same rate as an object falls to Earth, you will weigh exactly what you weigh on your doctor's scale. You can always simulate Earth gravity during those long, boring space journeys.

Another clever application of Newton's orbital mechanics is the slingshot effect. Space agencies often launch probes from Earth that have too little energy to reach their planetary destinations. Instead the orbital wizards aim the probes along cunning trajectories that swing near a hefty, moving source of gravity, such as Jupiter. By falling toward Jupiter in the same direction as Jupiter moves, a probe can steal some Jovial orbital energy during its flyby and then sling forward like a jai alai ball. If the planetary alignments are right, the probe can perform the same trick as it swings by Saturn, Uranus, or Neptune in turn, stealing more energy with each close encounter. A one-time shot at Jupiter can double a probe's speed through the solar system.

The fastest-moving stars of the galaxy, the ones that give colloquial meaning to going ballistic, are the stars that fly past the supermassive black hole in the center of the Milky Way. A descent towards this black hole (or any black hole) can accelerate a star up to speeds approaching that of light. No other object has the power to do this. If a star's trajectory swings slightly to the side of the hole, executing a near miss, it will avoid getting eaten, but its speed will dramatically increase. Now imagine a few hundred or a few thousand stars engaged in this frenetic activity. Astrophysicists view such stellar gymnastics—detectable in most galaxy centers—as conclusive evidence for the existence of black holes: the black hole's smoking gun.

I've always wanted to live where gravity is so weak that you could throw baseballs into orbit. And it wouldn't be hard. No matter how slow you pitch, there's an asteroid somewhere in the solar system with just the right gravity for you to accomplish this feat. Throw with caution, though. If you throw too fast, e could reach one, and you'd lose the ball for good.

Writing in centuries past, many scientists felt compelled to wax poetic about cosmic mysteries and God's handiwork. Perhaps one should not be surprised at this: most scientists back then, as well as many scientists today, identify themselves as spiritually devout.

But a careful reading of older texts, particularly those concerned with the universe itself, shows that the authors invoke divinity only when they reach the boundaries of their understanding. They appeal to a higher power only when staring into the ocean of their own ignorance. They call on God only from the lonely and precarious edge of incomprehension. Where they feel certain about their explanations, however, God gets hardly a mention.

Let's start at the top. Isaac Newton was one of the greatest intellects the world has ever seen. His laws of motion and his universal law of gravitation, conceived in the mid-seventeenth century, account for cosmic phenomena that had eluded philosophers for millennia. Through those laws, one could understand the gravitational attraction of bodies in a system, and thus come to understand orbits.

Newton's law of gravity enables you to calculate the force of attraction between any two objects. If you introduce a third object, then each one attracts the other two, and the orbits they trace become much harder to compute. Add another object, and another, and another, and soon you have the planets in our solar system. Earth and the Sun pull on each other, but Jupiter also pulls on Earth, Saturn pulls on Earth, Mars pulls on Earth, Jupiter pulls on Saturn, Saturn pulls on Mars, and on and on.

Newton feared that all this pulling would render the orbits in the solar system unstable. His equations indicated that the planets should long ago have either fallen into the Sun or flown the coop—leaving the Sun, in either case, devoid of planets. Yet the solar system, as well as the larger cosmos, appeared to be the very model of order and durability. So Newton, in his greatest work, the Principia, concludes that God must occasionally step in and make things right:

The six primary Planets are revolv'd about the Sun, in circles concentric with the Sun, and with motions directed towards the same parts, and almost in the same plane. . . . But it is not to be conceived that mere mechanical causes could give birth to so many regular motions. . . . This most beautiful System of the Sun,

Planets, and Comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.

In the Principia, Newton distinguishes between hypotheses and experimental philosophy, and declares, Hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. What he wants is data, inferr'd from the phænomena. But in the absence of data, at the border between what he could explain and what he could only honor—the causes he could identify and those he could not—Newton rapturously invokes God:

Eternal and Infinite, Omnipotent and Omniscient; . . . he governs all things, and knows all things that are or can be done. . . . We know him only by his most wise and excellent contrivances of things, and final causes; we admire him for his perfections; but we reverence and adore him on account of his dominion.

A century later, the French astronomer and mathematician Pierre-Simon de Laplace confronted Newton's dilemma of unstable orbits head-on. Rather than view the mysterious stability of the solar system as the unknowable work of God, Laplace declared it a scientific challenge. In his multipart masterpiece, Mécanique Céleste, the first volume of which appeared in 1798, Laplace demonstrates that the solar system is stable over periods of time longer than Newton could predict. To do so, Laplace pioneered a new kind of mathematics called perturbation theory, which enabled him to examine the cumulative effects of many small forces. According to an oft-repeated but probably embellished account, when Laplace gave a copy of Mécanique Céleste to his physics-literate friend Napoleon Bonaparte, Napoleon asked him what role God played in the construction and regulation of the heavens. Sire, Laplace replied, I have no need of that hypothesis.

Laplace notwithstanding, plenty of scientists besides Newton have called on God—or the gods—wherever their comprehension fades to ignorance. Consider the second-century a.d. Alexandrian astronomer Ptolemy. Armed with a description, but no real understanding, of what the planets were doing up there, he could not contain his religious fervor:

I know that I am mortal by nature, and ephemeral; but when I trace, at my pleasure, the windings to and fro of the heavenly bodies, I no longer touch Earth with my feet: I stand in the presence of Zeus himself and take my fill of ambrosia.

Or consider the seventeenth-century Dutch astronomer Christiaan Huygens, whose achievements include constructing the first working pendulum clock and discovering the rings of Saturn. In his charming book The Celestial Worlds Discover'd, posthumously published in 1696, most of the opening chapter celebrates all that was then known of planetary orbits, shapes, and sizes, as well as the planets' relative brightness and presumed rockiness. The book even includes foldout charts illustrating the structure of the solar system. God is absent from this discussion—even though a mere century earlier, before Newton's achievements, planetary orbits were supreme mysteries.

Celestial Worlds also brims with speculations about life in the solar system, and that's where Huygens raises questions to which he has no answer. That's where he mentions the biological conundrums of the day, such as the origin of life's complexity. And sure enough, because seventeenth-century physics was more advanced than seventeenth-century biology, Huygens invokes the hand of God only when he talks about biology:

I suppose no body will deny but that there's somewhat more of Contrivance, somewhat more of Miracle in the production and growth of Plants and Animals than in lifeless heaps of inanimate Bodies. . . . For the finger of God, and the Wisdom of Divine Providence, is in them much more clearly manifested than in the other.

Today secular philosophers call that kind of divine invocation God of the gaps—which comes in handy, because there has never been a shortage of gaps in people's knowledge.

As reverent as Newton, Huygens, and other great scientists of earlier centuries may have been, they were also empiricists. They did not retreat from the conclusions their evidence forced them to draw, and when their discoveries conflicted with prevailing articles of faith, they upheld the discoveries. That doesn't mean it was easy: sometimes they met fierce opposition, as did Galileo, who had to defend his telescopic evidence against formidable objections drawn from both scripture and common sense.

Galileo clearly distinguished the role of religion from the role of science. To him, religion was the service of God and the salvation of souls, whereas science was the source of exact observations and demonstrated truths. In a long, famous, bristly letter written in the summer of 1615 to the Grand Duchess Christina of Tuscany (but, like so many epistles of the day, circulated among the literati), he quotes, in his own defense, an unnamed yet sympathetic church official saying that the Bible tells you how to go to heaven, not how the heavens go.

The letter to the duchess leaves no doubt about where Galileo stood on the literal word of the Holy Writ:

In expounding the Bible if one were always to confine oneself to the unadorned grammatical meaning, one might fall into error. . . .

Nothing physical which . . . . demonstrations prove to us, ought to be called in question much less condemned) upon the testimony of biblical passages which may have some different meaning beneath their words. . . .

I do not feel obliged to believe that the same God who has endowed us with senses, reason and intellect has intended us to forgo their use.

A rare exception among scientists, Galileo saw the unknown as a place to explore rather than as an eternal mystery controlled by the hand of God.

As long as the celestial sphere was generally regarded as the domain of the divine, the fact that mere mortals could not explain its workings could safely be cited as proof of the higher wisdom and power of God. But beginning in the sixteenth century, the work of Copernicus, Kepler, Galileo, and Newton—not to mention Maxwell, Heisenberg, Einstein, and everybody else who discovered fundamental laws of physics—provided rational explanations for an increasing range of phenomena. Little by little, the universe was subjected to the methods and tools of science, and became a demonstrably knowable place.

Then, in what amounts to a stunning yet unheralded philosophical inversion, throngs of ecclesiastics and scholars began to declare that it was the laws of physics themselves that served as proof of the wisdom and power of God.

One popular theme of the seventeenth and eighteenth centuries was the clockwork universe—an ordered, rational, predictable mechanism fashioned and run by God and his physical laws. The early telescopes, which all relied on visible light, did little to undercut that image of an ordered system. The Moon revolved around Earth. Earth and other planets rotated on their axes and revolved around the Sun. The stars shone. The nebulae floated freely in space.

Not until the nineteenth century was it evident that visible light is just one band of a broad spectrum of electromagnetic radiation—the band that human beings just happen to see. Infrared was discovered in 1800, ultraviolet in 1801, radio waves in 1888, X rays in 1895, and gamma rays in 1900. Decade by decade in the following century, new kinds of telescopes came into use, fitted with detectors that could see these formerly invisible parts of the electromagnetic spectrum. Now astrophysicists began to unmask the true character of the universe.

Turns out that some celestial bodies give off more light in the invisible bands of the spectrum than in the visible. And the invisible light picked up by the new telescopes showed that mayhem abounds in the cosmos: monstrous gamma-ray bursts, deadly pulsars, matter-crushing gravitational fields, matter-hungry black holes that flay their bloated stellar neighbors, newborn stars igniting within pockets of collapsing gas. And as our ordinary, optical telescopes got bigger and better, more mayhem emerged: galaxies that collide and cannibalize each other, explosions of supermassive stars, chaotic stellar and planetary orbits. Our own cosmic neighborhood—the inner solar system—turned out to be a shooting gallery, full of rogue asteroids and comets that collide with planets from time to time. Occasionally they've even wiped out stupendous masses of Earth's flora and fauna. The evidence all points to the fact that we occupy not a well-mannered clockwork universe, but a destructive, violent, and hostile zoo.

Of course, Earth can be bad for your health too. On land, grizzly bears want to maul you; in the oceans, sharks want to eat you. Snowdrifts can freeze you, deserts dehydrate you, earthquakes bury you, volcanoes incinerate you. Viruses can infect you, parasites suck your vital fluids, cancers take over your body, congenital diseases force an early death. And even if you have the good luck to be healthy, a swarm of locusts could devour your crops, a tsunami could wash away your family, or a hurricane could blow apart your town.

So the universe wants to kill us all. But let's ignore that complication for the moment.

Many, perhaps countless, questions hover at the front lines of science. In some cases, answers have eluded the best minds of our species for decades or even centuries. And in contemporary America, the notion that a higher intelligence is the single answer to all enigmas has been enjoying a resurgence. This present-day version of God of the gaps goes by a fresh name: "intelligent design." The term suggests that some entity, endowed with a mental capacity far greater than the human mind can muster, created or enabled all the things in the physical world that we cannot explain through scientific methods.

An interesting hypothesis.

But why confine ourselves to things too wondrous or intricate for us to understand, whose existence and attributes we then credit to a superintelligence? Instead, why not tally all those things whose design is so clunky, goofy, impractical, or unworkable that they reflect the absence of intelligence?

Take the human form. We eat, drink, and breathe through the same hole in the head, and so, despite Henry J. Heimlich's eponymous maneuver, choking is the fourth leading cause of unintentional injury death in the United States. How about drowning, the fifth leading cause? Water covers almost three-quarters of Earth's surface, yet we are land creatures—submerge your head for just a few minutes, and you die.

Or take our collection of useless body parts. What good is the pinky toenail? How about the appendix, which stops functioning after childhood and thereafter serves only as the source of appendicitis? Useful parts, too, can be problematic. I happen to like my knees, but nobody ever accused them of being well protected from bumps and bangs. These days, people with problem knees can get them surgically replaced. As for our pain-prone spine, it may be a while before someone finds a way to swap that out.

How about the silent killers? High blood pressure, colon cancer, and diabetes each cause tens of thousands of deaths in the U.S. every year, but it's possible not to know you're afflicted until your coroner tells you so. Wouldn't it be nice if we had built-in biogauges to warn us of such dangers well in advance? Even cheap cars, after all, have engine gauges.

And what comedian designer configured the region between our legs—an entertainment complex built around a sewage system?

The eye is often held up as a marvel of biological engineering. To the astrophysicist, though, it's only a so-so detector. A better one would be much more sensitive to dark things in the sky and to all the invisible parts of the spectrum. How much more breathtaking sunsets would be if we could see ultraviolet and infrared. How useful it would be if, at a glance, we could see every source of microwaves in the environment, or know which radio station transmitters were active. How helpful it would be if we could spot police radar detectors at night.

Think how easy it would be to navigate an unfamiliar city if we, like birds, could always tell which way was north because of the magnetite in our heads. Think how much better off we'd be if we had gills as well as lungs, how much more productive if we had six arms instead of two. And if we had eight, we could safely drive a car while simultaneously talking on a cell phone, changing the radio station, applying makeup, sipping a drink, and scratching our left ear.

Stupid design could fuel a movement unto itself. It may not be nature's default, but it's ubiquitous. Yet people seem to enjoy thinking that our bodies, our minds, and even our universe represent pinnacles of form and reason. Maybe it's a good antidepressant to think so. But it's not science—not now, not in the past, not ever.

Another practice that isn't science is embracing ignorance. Yet it's fundamental to the philosophy of intelligent design: I don't know what this is. I don't know how it works. It's too complicated for me to figure out. It's too complicated for any human being to figure out. So it must be the product of a higher intelligence.

What do you do with that line of reasoning? Do you just cede the solving of problems to someone smarter than you, someone who's not even human? Do you tell students to pursue only questions with easy answers?

There may be a limit to what the human mind can figure out about our universe. But how presumptuous it would be for me to claim that if I can't solve a problem, neither can any other person who has ever lived or who will ever be born. Suppose Galileo and Laplace had felt that way? Better yet, what if Newton had not? He might then have solved Laplace's problem a century earlier, making it possible for Laplace to cross the next frontier of ignorance.

Science is a philosophy of discovery. Intelligent design is a philosophy of ignorance. You cannot build a program of discovery on the assumption that nobody is smart enough to figure out the answer to a problem. Once upon a time, people identified the god Neptune as the source of storms at sea. Today we call these storms hurricanes. We know when and where they start. We know what drives them. We know what mitigates their destructive power. And anyone who has studied global warming can tell you what makes them worse. The only people who still call hurricanes acts of God are the people who write insurance forms.

To deny or erase the rich, colorful history of scientists and other thinkers who have invoked divinity in their work would be intellectually dishonest. Surely there's an appropriate place for intelligent design to live in the academic landscape. How about the history of religion? How about philosophy or psychology? The one place it doesn't belong is the science classroom.

If you're not swayed by academic arguments, consider the financial consequences. Allow intelligent design into science textbooks, lecture halls, and laboratories, and the cost to the frontier of scientific discovery—the frontier that drives the economies of the future—would be incalculable. I don't want students who could make the next major breakthrough in renewable energy sources or space travel to have been taught that anything they don't understand, and that nobody yet understands, is divinely constructed and therefore beyond their intellectual capacity. The day that happens, Americans will just sit in awe of what we don't understand, while we watch the rest of the world boldly go where no mortal has gone before.