CHAPTER 2
CAN WE KNOW THE
UNIVERSE?
REFLECTIONS ON A
GRAIN OF SALT
Nothing is rich but the inexhaustible wealth
of nature. She shows us only surfaces,
but she is a million fathoms deep.
RALPH WALDO EMERSON
SCIENCE IS A WAY of thinking much more than it is a body of knowledge. Its goal is to find out how the world works, to seek what regularities there may be, to penetrate to the connections of things—from subnuclear particles, which may be the constituents of all matter, to living organisms, the human social community, and thence to the cosmos as a whole. Our intuition is by no means an infallible guide. Our perceptions may be distorted by training and prejudice or merely because of the limitations of our sense organs, which, of course, perceive directly but a small fraction of the phenomena of the world. Even so straightforward a question as whether in the absence of friction a pound of lead falls faster than a gram of fluff was answered incorrectly by Aristotle and almost everyone else before the time of Galileo. Science is based on experiment, on a willingness to challenge old dogma, on an openness to see the universe as it really is. Accordingly, science sometimes requires courage—at the very least the courage to question the conventional wisdom.
Beyond this the main trick of science is to really think of something: the shape of clouds and their occasional sharp bottom edges at the same altitude everywhere in the sky; the formation of a dewdrop on a leaf; the origin of a name or a word—Shakespeare, say, or “philanthropic”; the reason for human social customs—the incest taboo, for example; how it is that a lens in sunlight can make paper burn; how a “walking stick” got to look so much like a twig; why the Moon seems to follow us as we walk; what prevents us from digging a hole down to the center of the Earth; what the definition is of “down” on a spherical Earth; how it is possible for the body to convert yesterday’s lunch into today’s muscle and sinew; or how far is up—does the universe go on forever, or if it does not, is there any meaning to the question of what lies on the other side? Some of these questions are pretty easy. Others, especially the last, are mysteries to which no one even today knows the answer. They are natural questions to ask. Every culture has posed such questions in one way or another. Almost always the proposed answers are in the nature of “Just So Stories,” attempted explanations divorced from experiment, or even from careful comparative observations.
But the scientific cast of mind examines the world critically as if many alternative worlds might exist, as if other things might be here which are not. Then we are forced to ask why what we see is present and not something else. Why are the Sun and the Moon and the planets spheres? Why not pyramids, or cubes, or dodecahedra? Why not irregular, jumbly shapes? Why so symmetrical, worlds? If you spend any time spinning hypotheses, checking to see whether they make sense, whether they conform to what else we know, thinking of tests you can pose to substantiate or deflate your hypotheses, you will find yourself doing science. And as you come to practice this habit of thought more and more you will get better and better at it. To penetrate into the heart of the thing—even a little thing, a blade of grass, as Walt Whitman said—is to experience a kind of exhilaration that, it may be, only human beings of all the beings on this planet can feel. We are an intelligent species and the use of our intelligence quite properly gives us pleasure. In this respect the brain is like a muscle. When we think well, we feel good. Understanding is a kind of ecstasy.
But to what extent can we really know the universe around us? Sometimes this question is posed by people who hope the answer will be in the negative, who are fearful of a universe in which everything might one day be known. And sometimes we hear pronouncements from scientists who confidently state that everything worth knowing will soon be known—or even is already known—and who paint pictures of a Dionysian or Polynesian age in which the zest for intellectual discovery has withered, to be replaced by a kind of subdued languor, the lotus eaters drinking fermented coconut milk or some other mild hallucinogen. In addition to maligning both the Polynesians, who were intrepid explorers (and whose brief respite in paradise is now sadly ending), as well as the inducements to intellectual discovery provided by some hallucinogens, this contention turns out to be trivially mistaken.
Let us approach a much more modest question: not whether we can know the universe or the Milky Way Galaxy or a star or a world. Can we know, ultimately and in detail, a grain of salt? Consider one microgram of table salt, a speck just barely large enough for someone with keen eyesight to make out without a microscope. In that grain of salt there are about 1016 sodium and chlorine atoms. This is a 1 followed by 16 zeros, 10 million billion atoms. If we wish to know a grain of salt, we must know at least the three-dimensional positions of each of these atoms. (In fact, there is much more to be known—for example, the nature of the forces between the atoms—but we are making only a modest calculation.) Now, is this number more or less than the number of things which the brain can know?
How much can the brain know? There are perhaps 1011 neurons in the brain, the circuit elements and switches that are responsible in their electrical and chemical activity for the functioning of our minds. A typical brain neuron has perhaps a thousand little wires, called dendrites, which connect it with its fellows. If, as seems likely, every bit of information in the brain corresponds to one of these connections, the total number of things knowable by the brain is no more than 1014, one hundred trillion. But this number is only one percent of the number of atoms in our speck of salt.
So in this sense the universe is intractable, astonishingly immune to any human attempt at full knowledge. We cannot on this level understand a grain of salt, much less the universe.
But let us look a little more deeply at our microgram of salt. Salt happens to be a crystal in which, except for defects in the structure of the crystal lattice, the position of every sodium and chlorine atom is predetermined. If we could shrink ourselves into this crystalline world, we would see rank upon rank of atoms in an ordered array, a regularly alternating structure—sodium, chlorine, sodium, chlorine, specifying the sheet of atoms we are standing on and all the sheets above us and below us. An absolutely pure crystal of salt could have the position of every atom specified by something like 10 bits of information.* This would not strain the information-carrying capacity of the brain.
If the universe had natural laws that governed its behavior to the same degree of regularity that determines a crystal of salt, then, of course, the universe would be knowable. Even if there were many such laws, each of considerable complexity, human beings might have the capability to understand them all. Even if such knowledge exceeded the information-carrying capacity of the brain, we might store the additional information outside our bodies—in books, for example, or in computer memories—and still, in some sense, know the universe.
Human beings are, understandably, highly motivated to find regularities, natural laws. The search for rules, the only possible way to understand such a vast and complex universe, is called science. The universe forces those who live in it to understand it. Those creatures who find everyday experience a muddled jumble of events with no predictability, no regularity, are in grave peril. The universe belongs to those who, at least to some degree, have figured it out.
It is an astonishing fact that there are laws of nature, rules that summarize conveniently—not just qualitatively but quantitatively—how the world works. We might imagine a universe in which there are no such laws, in which the 1080 elementary particles that make up a universe like our own behave with utter and uncompromising abandon. To understand such a universe we would need a brain at least as massive as the universe. It seems unlikely that such a universe could have life and intelligence, because beings and brains require some degree of internal stability and order. But even if in a much more random universe there were such beings with an intelligence much greater than our own, there could not be much k
nowledge, passion or joy.
Fortunately for us, we live in a universe that has at least important parts that are knowable. Our common-sense experience and our evolutionary history have prepared us to understand something of the workaday world. When we go into other realms, however, common sense and ordinary intuition turn out to be highly unreliable guides. It is stunning that as we go close to the speed of light our mass increases indefinitely, we shrink toward zero thickness in the direction of motion, and time for us comes as near to stopping as we would like. Many people think that this is silly, and every week or two I get a letter from someone who complains to me about it. But it is a virtually certain consequence not just of experiment but also of Albert Einstein’s brilliant analysis of space and time called the Special Theory of Relativity. It does not matter that these effects seem unreasonable to us. We are not in the habit of traveling close to the speed of light. The testimony of our common sense is suspect at high velocities.
Or consider an isolated molecule composed of two atoms shaped something like a dumbbell—a molecule of salt, it might be. Such a molecule rotates about an axis through the line connecting the two atoms. But in the world of quantum mechanics, the realm of the very small, not all orientations of our dumbbell molecule are possible. It might be that the molecule could be oriented in a horizontal position, say, or in a vertical position, but not at many angles in between. Some rotational positions are forbidden. Forbidden by what? By the laws of nature. The universe is built in such a way as to limit, or quantize, rotation. We do not experience this directly in everyday life; we would find it startling as well as awkward in sitting-up exercises, to find arms outstretched from the sides or pointed up to the skies permitted but many intermediate positions forbidden. We do not live in the world of the small, on the scale of 10−13 centimeters, in the realm where there are twelve zeros between the decimal place and the one. Our common-sense intuitions do not count. What does count is experiment—in this case observations from the far infrared spectra of molecules. They show molecular rotation to be quantized.
The idea that the world places restrictions on what humans might do is frustrating. Why shouldn’t we be able to have intermediate rotational positions? Why can’t we travel faster than the speed of light? But so far as we can tell, this is the way the universe is constructed. Such prohibitions not only press us toward a little humility; they also make the world more knowable. Every restriction corresponds to a law of nature, a regularization of the universe. The more restrictions there are on what matter and energy can do, the more knowledge human beings can attain. Whether in some sense the universe is ultimately knowable depends not only on how many natural laws there are that encompass widely divergent phenomena, but also on whether we have the openness and the intellectual capacity to understand such laws. Our formulations of the regularities of nature are surely dependent on how the brain is built, but also, and to a significant degree, on how the universe is built.
For myself, I like a universe that includes much that is unknown and, at the same time, much that is knowable. A universe in which everything is known would be static and dull, as boring as the heaven of some weakminded theologians. A universe that is unknowable is no fit place for a thinking being. The ideal universe for us is one very much like the universe we inhabit. And I would guess that this is not really much of a coincidence.
* Chlorine is a deadly poison gas employed on European battlefields in World War I. Sodium is a corrosive metal which burns upon contact with water. Together they make a placid and unpoisonous material, table salt. Why each of these substances has the properties it does is a subject called chemistry, which requires more than 10 bits of information to understand.
CHAPTER 3
THAT WORLD
WHICH BECKONS LIKE
A LIBERATION
To punish me for my contempt for authority,
Fate made me an authority myself.
EINSTEIN
ALBERT EINSTEIN was born in Ulm, Germany, in 1879, just a century ago. He is one of the small group of people in any epoch who remake the world through a special gift, a talent for perceiving old things in new ways, for posing deep challenges to conventional wisdom. For many decades he was a saintly and honored figure, the only scientist the average person could readily name. In part because of his scientific accomplishments, at least dimly grasped by the public; in part because of his courageous positions on social issues; and in part because of his benign personality, Einstein was admired and revered throughout the world. For scientifically inclined children of immigrant parents, or those growing up in the Depression, like me, the reverence accorded Einstein demonstrated that there were such people as scientists, that a scientific career might not be totally beyond hope. One major function he involuntarily served was as a scientific role model. Without Einstein, many of the young people who became scientists after 1920 might never have heard of the existence of the scientific enterprise. The logic behind Einstein’s Special Theory of Relativity could have been developed a century earlier, but, although there were some premonitory insights by others, relativity had to wait for Einstein. Yet fundamentally the physics of special relativity is very simple, and many of the essential results can be derived from high school algebra and pondering a boat paddling upstream and downstream. Einstein’s life was rich in genius and irony, a passion for the issues of his time, insights into education, the connection between science and politics, and was a demonstration that individuals can, after all, change the world.
As a child Einstein gave little indication of what was to come. “My parents,” he recalled later, “were worried because I started to talk comparatively late, and they consulted the doctor because of it … I was at that time … certainly not younger than three.” He was an indifferent student in elementary school, where he said the teachers reminded him of drill sergeants. In Einstein’s youth, a bombastic nationalism and intellectual rigidity were the hallmarks of European education. He rebelled against the dull, mechanized methods of teaching. “I preferred to endure all sorts of punishment rather than learn to gabble by rote.” Einstein was always to detest rigid disciplinarians, in education, in science and in politics.
At five he was stirred by the mystery of a compass. And, he later wrote, “at the age of 12 I experienced a second wonder of a totally different nature in a little book dealing with Euclidean plane geometry.… Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which—though by no means evident—could nevertheless be proved with such certainty that any doubt appeared to be out of the question. This lucidity and certainty made an indescribable impression upon me.” Formal schooling provided only a tedious interruption to such contemplations. Einstein wrote of his self-education: “At the age of 12 to 16 I familiarized myself with the elements of mathematics together with the principles of differential and integral calculus. In doing so I had the good fortune of finding books which were not too particular in their logical rigor, but which made up for this by permitting the main thoughts to stand out clearly and synoptically … I also had the good fortune of getting to know the essential results and methods of the entire field of the natural sciences in an excellent popular exposition, which limited itself almost throughout to qualitative aspects … a work which I read with breathless attention.” Modern popularizers of science may take some comfort from these words.
Not one of his teachers seems to have recognized his talents. At the Munich Gymnasium, the city’s leading secondary school, one of the teachers told him, “You’ll never amount to anything, Einstein.” At age fifteen it was strongly suggested that he leave school. The teacher observed, “Your very presence spoils the respect of the class for me.” He accepted this suggestion with gusto and spent many months wandering through northern Italy, a high school dropout in the 1890s. Throughout his life he preferred informal dress and manner. Had he been a teen-ager in the 1960s or 1970s rather than the 1890s, conventional people would almost certai
nly have called him a hippie.
Yet his curiosity about physics and his wonder about the natural universe soon overcame his distaste for formal education, and he found himself applying, with no high school diploma, to the Federal Institute of Technology in Zurich, Switzerland. He failed the entrance examination, enrolled himself in a Swiss high school to satisfy his deficiencies, and was admitted to the Federal Institute the following year. But he was still a mediocre student. He resented the prescribed curriculum, avoided the lecture room and tried to pursue his true interests. He later wrote: “The hitch in this was, of course, the fact that you had to cram all this stuff into your mind for the examination, whether you liked it or not.”
He managed to graduate only because his close friend Marcel Grossmann assiduously attended classes and shared his notes with Einstein. On Grossmann’s death many years later, Einstein wrote: “I remember our student days. He the irreproachable student, I myself disorderly and a dreamer. He, on good terms with the teachers and understanding everything; I a pariah, discontented and little loved … Then the end of our studies—I was suddenly abandoned by everyone, standing at a loss on the threshold of life.” By immersing himself in Grossmann’s notes, he managed to graduate from college. But, he recalled, studying for the final examinations “had such a deterring effect on me that … I found the consideration of any scientific problem distasteful to me for an entire year.… It is little short of a miracle that modern methods of instruction have not already completely strangled the holy curiosity of inquiry, because what this delicate little plant needs most, apart from initial stimulation, is freedom; without that it is surely destroyed … I believe that one could even deprive a healthy beast of prey of its voraciousness, if one could force it with a whip to eat continuously whether it were hungry or not …” His remarks should be sobering to those of us engaged in higher education in science. I wonder how many potential Einsteins have been permanently discouraged through competitive examinations and the forced feeding of curricula.