For the great Arab mathematician and astronomer Omar Khayyam, science was a rebellion against the intellectual constraints of Islam, a rebellion which he expressed more directly in his incomparable verses:
And that inverted Bowl they call the Sky,
Whereunder crawling cooped we live and die,
Lift not your hands to It for help,
—for It
As impotently rolls as you or I.
For the first generations of Japanese scientists in the nineteenth century, science was a rebellion against their traditional culture of feudalism. For the great Indian physicists of this century, Raman, Bose, and Saha, science was a double rebellion, first against English domination and second against the fatalistic ethic of Hinduism. And in the West, too, great scientists from Galileo to Einstein have been rebels. Here is how Einstein himself described the situation:
When I was in the seventh grade at the Luitpold Gymnasium in Munich, I was summoned by my home-room teacher who expressed the wish that I leave the school. To my remark that I had done nothing amiss, he replied only, “Your mere presence spoils the respect of the class for me.”
Einstein was glad to be helpful to the teacher. He followed the teacher’s advice and dropped out of school at the age of fifteen.
From these and many other examples we see that science is not governed by the rules of Western philosophy or Western methodology. Science is an alliance of free spirits in all cultures rebelling against the local tyranny that each culture imposes on its children. Insofar as I am a scientist, my vision of the universe is not reductionist or antireductionist. I have no use for Western isms of any kind. I feel myself a traveler on the “Immense Journey” of the paleontologist Loren Eiseley, a journey that is far longer than the history of nations and philosophies, longer even than the history of our species.
A few years ago an exhibition of Paleolithic cave art came to the Museum of Natural History in New York. It was a wonderful opportunity to see in one place the carvings in stone and bone that are normally kept in a dozen separate museums in France. Most of the carvings were done in France about 14,000 years ago, during a short flowering of artistic creation at the very end of the last ice age. The beauty and delicacy of the carving is extraordinary. The people who carved these objects cannot have been ordinary hunters amusing themselves in front of the cave fire. They must have been trained artists sustained by a high culture.
And the greatest surprise, when you see these objects for the first time, is the fact that their culture is not Western. They have no resemblance at all to the primitive art that arose 10,000 years later in Mesopotamia and Egypt and Crete. If I had not known that the old cave art was found in France, I would have guessed that it came from Japan. The style looks today more Japanese than European. That exhibition showed us vividly that over periods of 10,000 years the distinctions between Western and Eastern and African cultures lose all meaning. Over a time span of 100,000 years we are all Africans. And over a time span of 300 million years we are all amphibians, waddling uncertainly out of dried-up ponds onto the alien and hostile land.
And with this long view of the past goes Robinson Jeffers’s even longer view of the future. In the long view, not only European civilization but the human species itself is transitory. Here is the vision of Robinson Jeffers, expressed in different parts of his long poem “The Double Axe.”
“Come, little ones.
You are worth no more than the foxes and yellow
wolfkins, yet I will give you wisdom.
O future children:
Trouble is coming; the world as of the present time
Sails on its rocks; but you will be born and live
Afterwards. Also a day will come when the earth
Will scratch herself and smile and rub off humanity:
But you will be born before that.”
“Time will come, no doubt,
When the sun too shall die; the planets will freeze, and the air on them; frozen gases, white flakes of air
Will be the dust: which no wind ever will stir: this very dust in dim starlight glistening
Is dead wind, the white corpse of wind.
Also the galaxy will die; the glitter of the Milky Way, our universe, all the stars that have names are dead.
Vast is the night. How you have grown, dear night, walking your empty halls, how tall!”1
Robinson Jeffers was no scientist, but he expressed better than any other poet the scientist’s vision. Ironic, detached, contemptuous like Einstein of national pride and cultural taboos, he stood in awe of nature alone. He stood alone in uncompromising opposition to the follies of the Second World War. His poems during those years of patriotic frenzy were unpublishable. “The Double Axe” was finally published in 1948, after a long dispute between Jeffers and his editors. I discovered Jeffers thirty years later, when the sadness and the passion of the war had become a distant memory. Fortunately, his works are now in print and you can read them for yourselves.
Science as subversion has a long history. There is a long list of scientists who sat in jail and of other scientists who helped get them out and incidentally saved their lives. In our century we have seen the physicist Lev Landau sitting in jail in the Soviet Union and Pyotr Kapitsa risking his own life by appealing to Stalin to let Landau out. We have seen the mathematician André Weil sitting in jail in Finland during the Winter War of 1939–1940 and Lars Ahlfors saving his life. The finest moment in the history of the Institute for Advanced Study, where I work, came in 1957, when we appointed the mathematician Chandler Davis a member of the institute, with financial support provided by the American government through the National Science Foundation. Davis was then a convicted felon because he refused to rat on his friends when questioned by the House Un-American Activities Committee. He had been convicted of contempt of Congress for not answering questions and had appealed his conviction to the Supreme Court.
While his case was under appeal, he came to Princeton and continued doing mathematics. That is a good example of science as subversion. After his institute fellowship was over, he lost his appeal and sat for six months in jail. Davis is now a distinguished professor at the University of Toronto and is actively engaged in helping people in jail to get out. Another example of science as subversion is Andrei Sakharov. Davis and Sakharov belong to an old tradition in science that goes all the way back to the rebels Benjamin Franklin and Joseph Priestley in the eighteenth century, to Galileo and Giordano Bruno in the seventeenth and sixteenth. If science ceases to be a rebellion against authority, then it does not deserve the talents of our brightest children. I was lucky to be introduced to science at school as a subversive activity of the younger boys. We organized a Science Society as an act of rebellion against compulsory Latin and compulsory football. We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice.
The vision of science as rebellion was articulated in Cambridge with great clarity on February 4, 1923, in a lecture by the biologist J.B. S. Haldane to the Society of Heretics. The lecture was published as a little book with the title Daedalus. Here is Haldane’s vision of the role of scientist. I have taken the liberty to abbreviate Haldane slightly and to omit the phrases that he quoted in Latin and Greek, since unfortunately I can no longer assume that the heretics of Cambridge are fluent in those languages.
The conservative has but little to fear from the man whose reason is the servant of his passions, but let him beware of him in whom reason has become the greatest and most terrible of the passions. These are the wreckers of outworn empires and civilizations, doubters, disintegrators, deicides. In the past they have been men like Voltaire, Bentham, Thales, Marx, but I think that Darwin furnishes an example of the same relentlessness of reason in the field of science. I suspect that as it becomes clear that at present reason not only has a freer play in science than elsewhere, but can produce as great effects on the world through science as through pol
itics, philosophy or literature, there will be more Darwins.
We must regard science, then, from three points of view. First, it is the free activity of man’s divine faculties of reason and imagination. Secondly, it is the answer of the few to the demands of the many for wealth, comfort and victory, gifts which it will grant only in exchange for peace, security and stagnation. Finally it is man’s gradual conquest, first of space and time, then of matter as such, then of his own body and those of other living beings, and finally the subjugation of the dark and evil elements in his own soul.2
I have already made it clear that I have a low opinion of reductionism, which seems to me to be at best irrelevant and at worst misleading as a description of what science is about. Let me begin with pure mathematics. Here the failure of reductionism has been demonstrated by rigorous proof. This will be a familiar story to many of you. The great mathematician David Hilbert, after thirty years of high creative achievement on the frontiers of mathematics, walked into a blind alley of reductionism. In his later years he espoused a program of formalization, which aimed to reduce the whole of mathematics to a collection of formal statements using a finite alphabet of symbols and a finite set of axioms and rules of inference. This was reductionism in the most literal sense, reducing mathematics to a set of marks written on paper, and deliberately ignoring the context of ideas and applications that give meaning to the marks. Hilbert then proposed to solve the problems of mathematics by finding a general process that could decide, given any formal statement composed of mathematical symbols, whether that statement was true or false. He called the problem of finding this decision process the Entscheidungsproblem. He dreamed of solving the Entscheidungsproblem and thereby solving as corollaries all the famous unsolved problems of mathematics. This was to be the crowning achievement of his life, the achievement that would outshine all the achievements of earlier mathematicians who solved problems only one at a time.
The essence of Hilbert’s program was to find a decision process that would operate on symbols in a purely mechanical fashion, without requiring any understanding of their meaning. Since mathematics was reduced to a collection of marks on paper, the decision process should concern itself only with the marks and not with the fallible human intuitions out of which the marks were reduced. In spite of the prolonged efforts of Hilbert and his disciples, the Entscheidungsproblem was never solved. Success was achieved only in highly restricted domains of mathematics, excluding all the deeper and more interesting concepts. Hilbert never gave up hope, but as the years went by his program became an exercise in formal logic having little connection with real mathematics. Finally, when Hilbert was seventy years old, Kurt Gödel proved by a brilliant analysis that the Entscheidungsproblem as Hilbert formulated it cannot be solved.
Gödel proved that in any formulation of mathematics, including the rules of ordinary arithmetic, a formal process for separating statements into true and false cannot exist. He proved the stronger result which is now known as Gödel’s theorem, that in any formalization of mathematics including the rules of ordinary arithmetic there are meaningful arithmetical statements that cannot be proved true or false. Gödel’s theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.
It is a curious paradox that several of the greatest and most creative spirits in science, after achieving important discoveries by following their unfettered imaginations, were in their later years obsessed with reductionist philosophy and as a result became sterile. Hilbert was a prime example of this paradox. Einstein was another. Like Hilbert, Einstein did his great work up to the age of forty without any reductionist bias. His crowning achievement, the general relativistic theory of gravitation, grew out of a deep physical understanding of natural processes. Only at the very end of his ten-year struggle to understand gravitation did he reduce the outcome of his understanding to a finite set of field equations. But like Hilbert, as he grew older he concentrated his attention more and more on the formal properties of his equations, and he lost interest in the wider universe of ideas out of which the equations arose.
His last twenty years were spent in a fruitless search for a set of equations that would unify the whole of physics, without paying attention to the rapidly proliferating experimental discoveries that any unified theory would finally have to explain. I do not need to say more about this tragic and well-known story of Einstein’s lonely attempt to reduce physics to a finite set of marks on paper. His attempt failed as dismally as Hilbert’s attempt to do the same thing with mathematics. I shall instead discuss another aspect of Einstein’s later life, an aspect that has received less attention than his quest for the unified field equations: his extraordinary hostility to the idea of black holes.
Black holes were invented by J. Robert Oppenheimer and Hartland Snyder in 1939. Starting from Einstein’s theory of general relativity, Oppenheimer and Snyder found solutions of Einstein’s equations that described what happens to a massive star when it has exhausted its supplies of nuclear energy. The star collapses gravitationally and disappears from the visible universe, leaving behind only an intense gravitational field to mark its presence. The star remains in a state of permanent free fall, collapsing endlessly inward into the gravitational pit without ever reaching the bottom. This solution of Einstein’s equations was profoundly novel. It has had enormous impact on the later development of astrophysics.
We now know that black holes ranging in mass from a few suns to a few billion suns actually exist and play a dominant role in the economy of the universe. In my opinion, the black hole is incomparably the most exciting and the most important consequence of general relativity. Black holes are the places in the universe where general relativity is decisive. But Einstein never acknowledged his brainchild. Einstein was not merely skeptical, he was actively hostile to the idea of black holes. He thought that the black hole solution was a blemish to be removed from his theory by a better mathematical formulation, not a consequence to be tested by observation. He never expressed the slightest enthusiasm for black holes, either as a concept or as a physical possibility. Oddly enough, Oppenheimer too in later life was uninterested in black holes, although in retrospect we can say that they were his most important contribution to science. The older Einstein and the older Oppenheimer were blind to the mathematical beauty of black holes, and indifferent to the question whether black holes actually exist.
How did this blindness and this indifference come about? I never discussed this question directly with Einstein, but I discussed it several times with Oppenheimer and I believe that Oppenheimer’s answer applies equally to Einstein. Oppenheimer in his later years believed that the only problem worthy of the attention of a serious theoretical physicist was the discovery of the fundamental equations of physics. Einstein certainly felt the same way. To discover the right equations was all that mattered. Once you had discovered the right equations, then the study of particular solutions of the equations would be a routine exercise for second-rate physicists or graduate students. In Oppenheimer’s view, it would be a waste of his precious time, or of mine, to concern ourselves with the details of particular solutions. This was how the philosophy of reductionism led Oppenheimer and Einstein astray. Since the only purpose of physics was to reduce the world of physical phenomena to a finite set of fundamental equations, the study of particular solutions such as black holes was an undesirable distraction from the general goal. Like Hilbert, they were not content to solve particular problems one at a time. They were entranced by the dream of solving all the basic problems at once. And as a result, they failed in their later years to solve any problems at all.
In the history of science it happens not infrequently that a reductionist approach lea
ds to a spectacular success. Frequently the understanding of a complicated system as a whole is impossible without an understanding of its component parts. And sometimes the understanding of a whole field of science is suddenly advanced by the discovery of a single basic equation. Thus it happened that the Schrödinger equation in 1926 and the Dirac equation in 1927 brought a miraculous order into the previously mysterious processes of atomic physics. The equations of Erwin Schrödinger and Paul Dirac were triumphs of reductionism. Bewildering complexities of chemistry and physics were reduced to two lines of algebraic symbols. These triumphs were in Oppenheimer’s mind when he belittled his own discovery of black holes. Compared with the abstract beauty and simplicity of the Dirac equation, the black hole solution seemed to him ugly, complicated, and lacking in fundamental significance.
But it happens at least equally often in the history of science that the understanding of the component parts of a composite system is impossible without an understanding of the behavior of the system as a whole. And it often happens that the understanding of the mathematical nature of an equation is impossible without a detailed understanding of its solutions. The black hole is a case in point. One could say without exaggeration that Einstein’s equations of general relativity were understood only at a very superficial level before the discovery of the black hole. During the fifty years since the black hole was invented, a deep mathematical understanding of the geometrical structure of space-time has slowly emerged, with the black hole solution playing a fundamental role in the structure. The progress of science requires the growth of understanding in both directions, downward from the whole to the parts and upward from the parts to the whole. A reductionist philosophy, arbitrarily proclaiming that the growth of understanding must go only in one direction, makes no scientific sense. Indeed, dogmatic philosophical beliefs of any kind have no place in science.
The Scientist as Rebel Page 2
