Death by Black Hole: And Other Cosmic Quandaries - Neil deGrasse Tyson (2014)
SECTION 1. THE NATURE OF KNOWLEDGE
Chapter 4. THE INFORMATION TRAP
Most people assume that the more information you have about something, the better you understand it.
Up to a point, that’s usually true. When you look at this page from across the room, you can see it’s in a book, but you probably can’t make out the words. Get close enough, and you’ll be able to read the chapter. If you put your nose right up against the page, though, your understanding of the chapter’s contents does not improve. You may see more detail, but you’ll sacrifice crucial information—whole words, entire sentences, complete paragraphs. The old story about the blind men and the elephant makes the same point: if you stand a few inches away and fixate on the hard, pointed projections, or the long rubbery hose, or the thick, wrinkled posts, or the dangling rope with a tassel on the end that you quickly learn not to pull, you won’t be able to tell much about the animal as a whole.
One of the challenges of scientific inquiry is knowing when to step back—and how far back to step—and when to move in close. In some contexts, approximation brings clarity; in others it leads to oversimplification. A raft of complications sometimes points to true complexity and sometimes just clutters up the picture. If you want to know the overall properties of an ensemble of molecules under various states of pressure and temperature, for instance, it’s irrelevant and sometimes downright misleading to pay attention to what individual molecules are doing. As we will see in Section 3, a single particle cannot have a temperature, because the very concept of temperature addresses the average motion of all the molecules in the group. In biochemistry, by contrast, you understand next to nothing unless you pay attention to how one molecule interacts with another.
So, when does a measurement, an observation, or simply a map have the right amount of detail?
IN 1967 BENOIT B. MANDELBROT, a mathematician now at IBM’s Thomas J. Watson Research Center in Yorktown Heights, New York, and also at Yale University, posed a question in the journal Science: “How long is the coast of Britain?” A simple question with a simple answer, you might expect. But the answer is deeper than anyone had imagined.
Explorers and cartographers have been mapping coastlines for centuries. The earliest drawings depict the continents as having crude, funny-looking boundaries; today’s high-resolution maps, enabled by satellites, are worlds away in precision. To begin to answer Mandelbrot’s question, however, all you need is a handy world atlas and a spool of string. Unwind the string along the perimeter of Britain, from Dunnet Head down to Lizard Point, making sure you go into all the bays and headlands. Then unfurl the string, compare its length to the scale on the map, and voilà! you’ve measured the island’s coastline.
Wanting to spot-check your work, you get hold of a more detailed ordnance survey map, scaled at, say, 2.5 inches to the mile, as opposed to the kind of map that shows all of Britain on a single panel. Now there are inlets and spits and promontories that you’ll have to trace with your string; the variations are small, but there are lots of them. You find that the survey map shows the coastline to be longer than the atlas did.
So which measurement is correct? Surely it’s the one based on the more detailed map. Yet you could have chosen a map that has even more detail—one that shows every boulder that sits at the base of every cliff. But cartographers usually ignore rocks on a map, unless they’re the size of Gibraltar. So, I guess you’ll just have to walk the coastline of Britain yourself if you really want to measure it accurately—and you’d better carry a very long string so that you can run it around every nook and cranny. But you’ll still be leaving out some pebbles, not to mention the rivulets of water trickling among the grains of sand.
Where does all this end? Each time you measure it, the coastline gets longer and longer. If you take into account the boundaries of molecules, atoms, subatomic particles, will the coastline prove to be infinitely long? Not exactly. Mandelbrot would say “indefinable.” Maybe we need the help of another dimension to rethink the problem. Perhaps the concept of one-dimensional length is simply ill-suited for convoluted coastlines.
Playing out Mandelbrot’s mental exercise involved a newly synthesized field of mathematics, based on fractional—or fractal (from the Latin fractus, “broken”)—dimensions rather than the one, two, and three dimensions of classic Euclidean geometry. The ordinary concepts of dimension, Mandelbrot argued, are just too simplistic to characterize the complexity of coastlines. Turns out, fractals are ideal for describing “self-similar” patterns, which look much the same at different scales. Broccoli, ferns, and snowflakes are good examples from the natural world, but only certain computer-generated, indefinitely repeating structures can produce the ideal fractal, in which the shape of the macro object is made up of smaller versions of the same shape or pattern, which are in turn formed from even more miniature versions of the very same thing, and so on indefinitely.
As you descend into a pure fractal, however, even though its components multiply, no new information comes your way—because the pattern continues to look the same. By contrast, if you look deeper and deeper into the human body, you eventually encounter a cell, an enormously complex structure endowed with different attributes and operating under different rules than the ones that hold sway at the macro levels of the body. Crossing the boundary into the cell reveals a new universe of information.
HOW ABOUT EARTH itself? One of the earliest representations of the world, preserved on a 2,600-year-old Babylonian clay tablet, depicts it as a disk encircled by oceans. Fact is, when you stand in the middle of a broad plain (the valley of the Tigris and Euphrates rivers, for instance) and check out the view in every direction, Earth does look like a flat disk.
Noticing a few problems with the concept of a flat Earth, the ancient Greeks—including such thinkers as Pythagoras and Herodotus—pondered the possibility that Earth might be a sphere. In the fourth century B.C., Aristotle, the great systematizer of knowledge, summarized several arguments in support of that view. One of them was based on lunar eclipses. Every now and then, the Moon, as it orbits Earth, intercepts the cone-shaped shadow that Earth casts in space. Across decades of these spectacles, Aristotle noted, Earth’s shadow on the Moon was always circular. For that to be true, Earth had to be a sphere, because only spheres cast circular shadows via all light sources, from all angles, and at all times. If Earth were a flat disk, the shadow would sometimes be oval. And some other times, when Earth’s edge faced the Sun, the shadow would be a thin line. Only when Earth was face-on to the Sun would its shadow cast a circle.
Given the strength of that one argument, you might think cartographers would have made a spherical model of Earth within the next few centuries. But no. The earliest known terrestrial globe would wait until 1490-92, on the eve of the European ocean voyages of discovery and colonization.
SO, YES, EARTH is a sphere. But the devil, as always, lurks in the details. In Newton’s 1687 Principia, he proposed that, because spinning spherical objects thrust their substance outward as they rotate, our planet (and the others as well) will be a bit flattened at the poles and a bit bulgy at the equator—a shape known as an oblate spheroid. To test Newton’s hypothesis, half a century later, the French Academy of Sciences in Paris sent mathematicians on two expeditions—one to the Arctic Circle and one to the equator—both assigned to measure the length of one degree of latitude on Earth’s surface along the same line of longitude. The degree was slightly longer at the Arctic Circle, which could only be true if Earth were a bit flattened. Newton was right.
The faster a planet spins, the greater we expect its equatorial bulge to be. A single day on fast-spinning Jupiter, the most massive planet in the solar system, lasts 10 Earth-hours; Jupiter is 7 percent wider at its equator than at its poles. Our much smaller Earth, with its 24-hour day, is just 0.3 percent wider at the equator—27 miles on a diameter of just under 8,000 miles. That’s hardly anything.
One fascinating consequence of this mild oblateness is that if you stand at sea level anywhere on the equator, you’ll be farther from Earth’s center than you’d be nearly anywhere else on Earth. And if you really want to do things right, climb Mount Chimborazo in central Ecuador, close to the equator. Chimborazo’s summit is four miles above sea level, but more important, it sits 1.33 miles farther from Earth’s center than does the summit of Mount Everest.
SATELLITES HAVE MANAGED to complicate matters further. In 1958 the small Earth orbiter Vanguard 1 sent back the news that the equatorial bulge south of the equator was slightly bulgier than the bulge north of the equator. Not only that, sea level at the South Pole turned out to be a tad closer to the center of Earth than sea level at the North Pole. In other words, the planet’s a pear.
Next up is the disconcerting fact that Earth is not rigid. Its surface rises and falls daily as the oceans slosh in and out of the continental shelves, pulled by the Moon and, to a lesser extent, by the Sun. Tidal forces distort the waters of the world, making their surface oval. A well-known phenomenon. But tidal forces stretch the solid earth as well, and so the equatorial radius fluctuates daily and monthly, in tandem with the oceanic tides and the phases of the Moon.
So Earth’s a pearlike, oblate-spheroidal hula hoop.
Will the refinements never end? Perhaps not. Fast forward to 2002. A U.S.-German space mission named GRACE (Gravity Recovery and Climate Experiment) sent up a pair of satellites to map Earth’s geoid, which is the shape Earth would have if sea level were unaffected by ocean currents, tides, or weather—in other words, a hypothetical surface where the force of gravity is perpendicular to every mapped point. Thus, the geoid embodies the truly horizontal, fully accounting for all the variations in Earth shape and subsurface density of matter. Carpenters, land surveyors, and aqueduct engineers will have no choice but to obey.
ORBITS ARE ANOTHER category of problematic shape. They’re not one-dimensional, nor merely two-or three-dimensional. Orbits are multidimensional, unfolding in both space and time. Aristotle advanced the idea that Earth, the Sun, and the stars were locked in place, attached to crystalline spheres. It was the spheres that rotated, and their orbits traced—what else?—perfect circles. To Aristotle and nearly all the ancients, Earth lay at the center of all this activity.
Nicolaus Copernicus disagreed. In his 1543 magnum opus, De Revolutionibus, he placed the Sun in the middle of the cosmos. Copernicus nonetheless maintained perfect circular orbits, unaware of their mismatch with reality. Half a century later, Johannes Kepler put matters right with his three laws of planetary motion—the first predictive equations in the history of science—one of which showed that the orbits are not circles but ovals of varying elongation.
We have only just begun.
Consider the Earth-Moon system. The two bodies orbit their common center of mass, their barycenter, which lies roughly 1,000 miles below the spot on Earth’s surface closest to the Moon at any given moment. So instead of the planets themselves, it’s actually their planet-moon barycenters that trace the Keplerian elliptical orbits around the Sun. So now what’s Earth’s trajectory? A series of loop-the-loops—thirteen of them in a year, one for each cycle of lunar phases—rolled together with an ellipse.
Meanwhile, not only do the Moon and Earth tug on each other, but all the other planets (and their moons) tug on them too. Everybody’s tugging on everybody else. As you might suspect, it’s a complicated mess, and will be described further in Section 3. Plus, each time the Earth-Moon system takes a trip around the Sun, the orientation of the ellipse shifts slightly, not to mention that the Moon is spiraling away from Earth at a rate of one or two inches per year and that some orbits in the solar system are chaotic.
All told, this ballet of the solar system, choreographed by the forces of gravity, is a performance only a computer can know and love. We’ve come a long way from single, isolated bodies tracing pure circles in space.
THE COURSE OF a scientific discipline gets shaped in different ways, depending on whether theories lead data or data lead theories. A theory tells you what to look for, and you either find it or you don’t. If you find it, you move on to the next open question. If you have no theory but you wield tools of measurement, you’ll start collecting as much data as you can and hope that patterns emerge. But until you arrive at an overview, you’re mostly poking around in the dark.
Nevertheless, one would be misguided to declare that Copernicus was wrong simply because his orbits were the wrong shape. His deeper concept—that planets orbit the Sun—is what mattered most. From then on, astrophysicists have continually refined the model by looking closer and closer. Copernicus may not have been in the right ballpark, but he was surely on the right side of town. So, perhaps, the question still remains: When do you move closer and when do you take a step back?
NOW IMAGINE YOU’RE strolling along a boulevard on a crisp autumn day. A block ahead of you is a silver-haired gentleman wearing a dark blue suit. It’s unlikely you’ll be able to see the jewelry on his left hand. If you quicken your pace and get within 30 feet of him, you might notice he’s wearing a ring, but you won’t see its crimson stone or the designs on its surface. Sidle up close with a magnifying glass and—if he doesn’t alert the authorities—you’ll learn the name of the school, the degree he earned, the year he graduated, and possibly the school emblem. In this case, you’ve correctly assumed that a closer look would tell you more.
Next, imagine you’re gazing at a late-nineteenth-century French pointillist painting. If you stand 10 feet away, you might see men in tophats, women in long skirts and bustles, children, pets, shimmering water. Up close, you’ll just see tens of thousands of dashes, dots, and streaks of color. With your nose on the canvas you’ll be able to appreciate the complexity and obsessiveness of the technique, but only from afar will the painting resolve into the representation of a scene. It’s the opposite of your experience with the ringed gentleman on the boulevard: the closer you look at a pointillist masterpiece, the more the details disintegrate, leaving you wishing you had kept your distance.
Which way best captures how nature reveals itself to us? Both, really. Almost every time scientists look more closely at a phenomenon, or at some inhabitant of the cosmos, whether animal, vegetable, or star, they must assess whether the broad picture—the one you get when you step back a few feet—is more useful or less useful than the close-up. But there’s a third way, a kind of hybrid of the two, in which looking closer gives you more data, but the extra data leave you extra baffled. The urge to pull back is strong, but so, too, is the urge to push ahead. For every hypothesis that gets confirmed by more detailed data, ten others will have to be modified or discarded altogether because they no longer fit the model. And years or decades may pass before the half-dozen new insights based on those data are even formulated. Case in point: the multitudinous rings and ringlets of the planet Saturn.
EARTH IS A FASCINATING PLACE to live and work. But before Galileo first looked up with a telescope in 1609, nobody had any awareness or understanding of the surface, composition, or climate of any other place in the cosmos. In 1610 Galileo noticed something odd about Saturn; because the resolution of his telescope was poor, however, the planet looked to him as if it had two companions, one to its left and one to its right. Galileo formulated his observation in an anagram,
designed to ensure that no one else could snatch prior credit for his radical and as-yet-unpublished discovery. When sorted out and translated from the Latin, the anagram becomes: “I have observed the highest planet to be triple-bodied.” As the years went by, Galileo continued to monitor Saturn’s companions. At one stage they looked like ears; at another stage they vanished completely.
In 1656 the Dutch physicist Christiaan Huygens viewed Saturn through a telescope of much higher resolution than Galileo’s, built for the express purpose of scrutinizing the planet. He became the first to interpret Saturn’s earlike companions as a simple, flat ring. As Galileo had done half a century earlier, Huygens wrote down his groundbreaking but still preliminary finding in the form of an anagram. Within three years, in his book Systema Saturnium, Huygens went public with his proposal.
Twenty years later Giovanni Cassini, the director of the Paris Observatory, pointed out that there were two rings, separated by a gap that came to be known as the Cassini division. And nearly two centuries later, the Scottish physicist James Clerk Maxwell won a prestigious prize for showing that Saturn’s rings are not solid, but made up instead of numerous small particles in their own orbits.
By the end of the twentieth century, observers had identified seven distinct rings, lettered A through G. Not only that, the rings themselves turn out to be made up of thousands upon thousands of bands and ringlets.
So much for the “ear theory” of Saturn’s rings.
SEVERAL SATURN FLYBYS took place in the twentieth century: Pioneer 11 in 1979, Voyager 1 in 1980, and Voyager 2 in 1981. Those relatively close inspections all yielded evidence that the ring system is more complex and more puzzling than anyone had imagined. For one thing, the particles in some of the rings corral into narrow bands by the so-called shepherd moons: teeny satellites that orbit near and within the rings. The gravitational forces of the shepherd moons tug the ring particles in different directions, sustaining numerous gaps among the rings.
Density waves, orbital resonances, and other quirks of gravitation in multiple-particle systems give rise to passing features within and among the rings. Ghostly, shifting “spokes” in Saturn’s B ring, for instance—recorded by the Voyager space probes and presumed to be caused by the planet’s magnetic field—have mysteriously vanished from close-up views supplied by the Cassini spacecraft, sending images from Saturnian orbit.
What kind of stuff are Saturn’s rings made of? Water ice, for the most part—though there’s also some dirt mixed in, whose chemical makeup is similar to one of the planet’s larger moons. The cosmo-chemistry of the environment suggests that Saturn might once have had several such moons. Those that went AWOL may have orbited too close for comfort to the giant planet and gotten ripped apart by Saturn’s tidal forces.
Saturn, by the way, is not the only planet with a ring system. Close-up views of Jupiter, Uranus, and Neptune—the rest of the big four gas giants in our solar system—show that each planet bears a ring system of its own. The Jovian, Uranian, and Neptunian rings weren’t discovered until the late 1970s and early 1980s, because, unlike Saturn’s majestic ring system, they’re made largely of dark, unreflective substances such as rocks or dust grains.
THE SPACE NEAR a planet can be dangerous if you’re not a dense, rigid object. As we will see in Section 2, many comets and some asteroids, for instance, resemble piles of rubble, and they swing near planets at their peril. The magic distance, within which a planet’s tidal force exceeds the gravity holding together that kind of vagabond, is called the Roche limit—discovered by the nineteenth-century French astronomer Édouard Albert Roche. Wander inside the Roche limit, and you’ll get torn apart; your disassembled bits and pieces will then scatter into their own orbits and eventually spread out into a broad, flat, circular ring.
I recently received some upsetting news about Saturn from a colleague who studies ring systems. He noted with sadness that the orbits of their constituent particles are unstable, and so the particles will all be gone in an astrophysical blink of an eye: 100 million years or so. My favorite planet, shorn of what makes it my favorite planet! Turns out, fortunately, that the steady and essentially unending accretion of interplanetary and intermoon particles may replenish the rings. The ring system—like the skin on your face—may persist, even if its constituent particles do not.
Other news has come to Earth via Cassini’s close-up pictures of Saturn’s rings. What kind of news? “Mind-boggling” and “startling,” to quote Carolyn C. Porco, the leader of the mission’s imaging team and a specialist in planetary rings at the Space Science Institute in Boulder, Colorado. Here and there in all those rings are features neither expected nor, at present, explainable: scalloped ringlets with extremely sharp edges, particles coalescing in clumps, the pristine iciness of the A and B rings compared with the dirtiness of the Cassini division between them. All these new data will keep Porco and her colleagues busy for years to come, perhaps wistfully recalling the clearer, simpler view from afar.