For the main conclusions of this final chapter, it is necessary for us to consider at this point a concept, a principle, that was scientific in its origin but which is now recognized to have a much wider significance. This is the concept of complementarity.
The principle of complementarity was first enunciated by Niels Bohr in 1928. The development of the ideas and the debate that clarified the issues were participated in by many of the great scientific figures of that fantastically active and exciting period. In particular, both of the two most important scientific leaders of those days, Bohr and Einstein, were intimately and intensely involved.
In the years just preceding 1928 some upsetting notions had come to the surface. All of them, of course, were consequences of the earlier revolutionary idea of Max Planck that energy is not continuously divisible, but that it always occurs in discrete packets of a precisely specified minimum size.
One set of these ideas was concerned with the fact that quantum theory could be formulated in two different (but as it eventually turned out, analytically equivalent) ways, one of which involved talking about discrete particles (which, since Planck, seemed rather to be the way the theory ought to go), and the other of which (due to Schrödinger but going back to ideas advanced by the French physicist Louis Victor de Broglie a few years earlier) was expressed in terms of continuous waves. The status and interrelationship of these two approaches was a critical issue when it became evident—experimentally evident—that such a basic entity as a photon of light had to be treated under some circumstances as if it were in fact wavelike, but under other circumstances as though it were particle-like. The same embarrassing duality was soon found to apply to electrons. Previously always thought of as “particles,’”’ electrons now also had to be admitted to be wavelike under some circumstances.
At about this same time (February 1927) the brilliant young German physicist Werner Heisenberg developed— and showed the necessity of—the idea that it was impossible experimentally to obtain precise information on both the position and the velocity of a particle. There was a joint uncertainty in the two sets of measurements: as the experimenter made his determination of one of the two quantities (either position or velocity) more and more precise, the error in any simultaneous determination of the other became bigger and bigger. This arose because of the fact, neglected for so long, that an observation necessarily affected the thing observed. This effect is ordinarily of no importance, being negligibly small, when the thing under observation is of substantial size and mass, but it is critically important when observing elementary particles.
To measure position more and more precisely, the experimenter might reflect from the particle in question a more and more energetic pulse of radiant energy; but as this pulse is made more and more intense, it has a greater and greater disturbing effect on the velocity of the particle. To put it roughly, if you bounce off enough energy to tell you precisely where the particle was, the rebound imparts so ~ much unknown velocity to the particle that you don’t know much about how it is moving, and hence about where it now is. This joint uncertainty was not only characteristic of the pair of quantities’ position and velocity, but applied equally to various other pairs of quantities which entered into physical theory.*
Bohr found these ideas so stimulating that he pursued them with what Heisenberg described as “almost terrifying relentlessness.”” Bohr, moreover, considered the wave-particle dualism to be so central a phenomenon that he was convinced that it must be taken as a starting point for any interpretation of the theoretical and experimental exploration of physics.
Previous natural philosophy had been based on the assumption (which Bohr himself remarked was “inherent in ordinary conventions of language’’) that one can successfully distinguish between the behavior of objects and the means used to observe that behavior. But in dealing with atomic and other very fine-scaled processes one has to face and take account of the fact that the measuring and observing procedures have a determining influence on the thing being observed, so that “property observed” and “means of observation” are inescapably related.
At the descriptive level at which the experimenter tells what he has done and seeks to persuade his colleagues to * In quantum theory, such pairs are called ‘canonically conjugate”; another example, in addition to the pair position and velocity, is the pair energy and time agreement, he is forced to use the classical terms of largescale physics and the ordinary linguistic machinery our Western culture has developed. On the other hand, it is necessary to recognize that experiments concerning phenomena which are not included within the range of classical physics cannot be interpreted as giving information about inherent and independent properties of the objects under study, but can only give information which relates to the inseparable combination “object plus procedure of observation.”
These considerations led Bohr to conclude that the information obtained about an object by using one set of experimental conditions of observation should not be expected to be the same as, or necessarily consistent with, the information obtained when using a different set of observational procedures. If the second set of observational conditions excludes the first set, then the information obtained by using one set must be viewed as complementary to the information obtained by using the other observational procedure. However contradictory the two sets of information may appear to be, they must be accepted as equally valid.
It is not only futile, it is essentially meaningless to try to decide whether electrons are particles or are wavelike. Under one set of observational circumstances, electrons must be considered to be particles, and under other observational circumstances, they must be considered to be wavelike. By accepting the two contradictory descriptions and using each under appropriate circumstances, one has a richer and more satisfying concept than is furnished by either description taken alone.
Commenting on the principle, Bohr stated that “.
. any given application of classical concepts precludes the simultaneous use of other classical concepts, which in a different connection are equally necessary for the elucidation of the phenomena.” As this quotation shows, Bohr himself clearly recognized the linguistic aspects of the situation. “From his early youth,” one of his friends and colleagues has written, Bohr had been preoccupied by this problem of the ambiguity of language.”* In his essay “Quantum Theory and Its Implications,’”’ Heisenberg describes an expedition on Bohr’s sailing boat, carried out by a group of scientists at Copenhagen. “Bohr was full of the new interpretation of quantum theory, and as the boat took us full sail southward in the sunshine, there was plenty of time to tell of this scientific event, and to reflect philosophically on the nature of atomic theory. Bohr began by talking of the difficulties of language
. [my italics].” Heisenberg also remarks, ““This concept of complementarity fitted well the fundamental philosophical attitude which he [Bohr] had always had, and in which the limitations of our means of expressing ourselves entered as a central philosophical problem.” ?
In view of what we have noted earlier concerning Whorf’s analysis of the relationship between grammar, culture, and science, and because of what I myself want to say later, it is important to emphasize just what circumstance is responsible for the emergence of Bohr’s Principle of Complementarity.
It is meaningless to assert that nature “really has’ contradictory aspects (“an electron is both a particle and a wave’’). The dilemma arises because we necessarily formulate the results of fine-scaled experiments in the traditional language suited to large-scale, or let us rather say man-sized, experience. When experiments concern man-sized objects and events (as in rolling a sphere down an inclined plane to study the dynamics of ordinary things), the traditionally phrased descriptions of varied experiments are all consistent, one with another. When the experiment dips down into the “little world” of atomic and nuclear affairs, but our language of description and agreement remains at the traditional level of man-sized concepts, then the contradictions arise. It is as though one anthropologist observes a Hopi prayer dance carried out under one set of circumstances, and a second anthropologist observes a Hopi prayer dance carried out under another set of circumstances. Each of the two anthropologists writes his interpretation, in English, of what he has observed and heard. The descriptions are inconsistent, and no wonder.
If we could some day develop a set of concepts, and the necessary linguistic tools, to approach the “‘little world” from below, rather than descending on it from above, then scientists might create a subculture, with its appropriate linguistic apparatus, within which would be completely lacking the hybrid contradictions with which complementarity deals.
It seems to me that this reasoning can be extended to another realm of physics. Just as the nuclear physicist uses man-sized concepts and traditional language in his efforts to describe events in the tiny world of scale less than 10-* cubic centimeters, so the astrophysicist uses the same mansized concepts and language in his attempt to describe cosmic phenomena whose scale is of the order of 107° cubic centimeters. He comes to two different ideas about, for example, the “origin of the universe.” Did it arise as a ‘‘big bang,”’ or did it evolve in a systematic procedure which may be part of a rhythmic process of expanding and reced ing? Or could it be that these two views are complementary, each valid when the questions are asked in the appropriate way, and both necessary for a complete description? For our man-sized language may well be as inadequate at the cosmic scale as at the subatomic scale.
The concept of complementarity has often been extended far beyond the circumstances that led to its enunciation. Bohr himself called attention to problems in psychology and in biology that present complementary aspects. He considered that a complementary relationship often obtained between “‘thoughts” and “feelings,” since if we analyze our emotions, we scarcely possess them any more; and that “instinct”? and “reason” may well also form a complementary pair. He pointed out that a biological experiment aimed at illuminating the concept “life” can very well be an experiment that destroys the life of the organism under study. A complete description of a personal relationship may well involve complementary statements, some of which, made within one context, are phrased entirely in terms of love, and others, within a different context, being phrased in terms of hate.
It may be helpful for the reader to look at a very simple and specific example, which further illustrates the concept of complementarity.
In the case of the simple functional relationship mathematically expressed by the equation y = x’, if you substitute the integer +4 for x, then you get a single value, namely +16, for y. But a different situation arises if we consider the relationship y = \/x. For if we set x = +4, there now are two answers, since the square root of +4 is either +2 or —2, Either number, when multiplied by itself, gives +4.
If a person is interested in positive numbers and asks What is the square root of +4?” the answer is of course
+2. If another person is interested in negative numbers, and asks the same question, the answer is —2. If a third person takes a more embracing view, the answer is that both +2 and —2 are square roots of +4. The third person has a richer and more rewarding total reply, even though the two parts of it are inconsistent.
Several of the comments I have made about the nature of the scientific enterprise may well be judged to be deflating if indeed not derogatory, for I have said that science deals only with very limited aspects of our total experience; that science is never perfect, never final, never fully confirmed; that science does not really “explain,” and indeed never even attempts to answer the query “How?”; that the fundamental assumptions on which theoretical science is based are subject to the limitations imposed by the flaws which exist in the foundations of deductive logic; that modern Western science is by no means a unique invention; that, indeed, the science at any time and place is essentially determined by the interlocked metaphysics and linguistic apparatus of the culture in question, and hence depends upon the kind of questions the culture considers it important to ask, the kind of techniques of exploration that are available, the kind of evidence that is judged convincing, and the kinds of answers that are acceptable and rewarding; and that at its very foundations, science has learned that it must accommodate ambiguity, duality, and contradiction.
These points, however they may be judged by those who (quite mistakenly, I think) consider science to be the ultimate and all-powerful source of unchanging knowledge, should be of real comfort to those who (equally mistakenly) have been led to fear science as a relentless mechanical monster. They should be enthusiastically welcomed by those who believe, as I most firmly do, that the scientific enterprise is basically an artistic endeavor, that it has all the freedom of any other imaginative and creative activity, this activity being characterized by very special traditions of disinterested and unprejudiced open-mindedness together with a built-in protection against serious or prolonged error. Science is one of the most mature of the arts, combining a maximum of both freedom and discipline.
These points, moreover, make it clear that science should have no quarrel with the humane arts or with contemplative fields of thought, nor they with science. They are all, each using its characteristic methods, seeking to perceive order and unity in diversity. They are all based on faith, they are all creations of imaginative minds; they are all alive, growing, changing; they all are limited by what our linguistic apparatus and our cultural concepts permit. They all represent high effort on the part of man to savor and appreciate his surroundings, and thus to enrich his life.
The essential unity of the scientific enterprise and the artistic enterprise has been widely recognized by the great scientists. The physicist J. Robert Oppenheimer (1904–1967) described this interrelationship most perceptively when he wrote: “The artist and scientist both live always at the edge of mystery, surrounded by it. Both struggle to make partial order in total chaos. They can, in their work and in their lives, help themselves, help one another, and help all men.” * It is interesting, I think, to note that this bridge has also been evident to great artists. Dylan Thomas must have recognized all this when he said (as other poets before him had also said), “Beauty is the sense of unity in diversity.” * I get a very special kick out of being told that the poet W. H. Auden, at sixty, subscribed to but one ‘magazine—and that Scientific American!
In a letter he wrote Seventy years ago, the Russian dramatist Anton Chekhov said: “I would like people not to see a conflict where there is none. There has always been knowledge in the world. Anatomy and belles-lettres are of equally noble descent; they both have the same purposes and the same enemy—the devil—and there is absolutely no reason for them to fight each other. There is no struggle for survival here. If a man understands the system of blood circulation, he is rich; if in addition he studies the history of religion and learns by heart the poem, ‘I recall the miraculous moment,’ he will be richer and not poorer; consequently, we are dealing only with positives. That is why geniuses have never fought, and in Goethe the scientist got along beautifully with the poet.” 5 I cannot close my remarks about science without making clear my conviction that the limiting characteristics of the scientific enterprise which I have emphasized paradoxically increase, rather than diminish, its stature. Granting what science sets out to do, granting what it conceptually can do, I think it must be agreed that it is one of the most successful, if indeed not the most successful, activity in which man has ever been engaged. The degree of control over nonliving matter it affords is fantastically well matched to our culture’s appetites and demands. There is every reasonable prospect that it will be able to furnish a similar degree of control over many of the aspects of living matter. The picture which this medium paints of the world about us is one of both intricate detail and sweeping splendor. It is a picture of almost incredible beauty.
It will well serve as a transition to what I want to write about religion if I say something at this point about science and value.
There are many
(including myself in younger days) who have affirmed that science has nothing to do with value. “Facts,” they have said, “are wholly neutral. The scientist discovers facts, and the process of doing so is a totally amoral activity. If someone utilizes these facts in an ugly or immoral way, the fault lies wholly with him.”
The testimony of the scientists who established the possibility of making an atomic bomb rather completely demolishes that argument. And everything we have recognized here about the nature of facts, and indeed about the interaction between culture and science, makes it impossible to establish a clean-cut separation between what scientists do (which is what science is), what they think is worth doing, and the criteria which determine worthwhileness. Just as it is impossible to isolate “facts” from their cultural origins, so it is impossible to quarantine facts from their cultural use.
More specifically, there are recognizable value judgments which are part and parcel of the scientific enterprise. The scientist’s ideas about interest and importance clearly help to determine what “facts” are brought to the surface and made available for application. The scientist does not stumble and grope his way through nature as would a drunken man in a dark attic, bumping by accident into boxes that he opens and examines. The scientist is motivated and guided by a powerful ethic.
He is deeply convinced, for example, that it is his honorable duty to know all that it is possible to know about the world and its living inhabitants. He understands, with a clarity that is scarcely to be found anywhere else among men’s activities, that honesty actually and practically is the best policy. He understands the nature and importance of persuasion and agreement better than does any politician.
Scientists today are broadly recognizing the interrelationships between what they do and the problems and needs of the society of which they are a part. The pages of Science, of Nature, of the Bulletin of the Atomic Scientists, of Daedalus, and of many other journals are full of discussions which clearly recognize that science does not operate in a sort of moral germ-free enclosure, but rather that it exists in the world of affairs, of hopes, and of responsibilities, so that the day-by-day decisions of science inescapably involve all sorts of value judgments.
The scientist takes deep satisfaction in being a part of a dedicated world-wide community. His craft teaches him that he must accept a certain kind of evidence, and he does so with humility and with lack of prejudice, even when the evidence is contrary to his expectations and—human as he is —his desires. He is a highly disciplined individual. The distillation of many varied and complicated experiences, and their compact and powerful expression in a theory of broad generality, gives him a great esthetic pleasure. In his scientific work he is strongly influenced by a sense of beauty. He knows just what he means by a good theory or a good experiment, and he has a right to use the word “good.”
What I have said about science makes it easier for me to express my ideas about religion. These must, moreover, be my ideas. There is sufficient agreement about science so that one can express generally accepted views; but religion is so personal an affair that no one—or at least certainly not I—can speak for others.
Throughout, I will be sustained and liberated by the concept of complementarity. Asking a question from one point of view, I will have one answer. Asking it from another and quite different point of view, I may very well suggest a second answer which is inconsistent with the former, but which can be viewed as complementary to it, the two taken together giving a richer and truer picture than either separately.
First and foremost, I take a liberal position in religion, believing it to be a growing and improving body of thought and precept. I think that religious ideas have matured from primitive notions to the principles of Christ, just a little as science has advanced from the chipping of stone implements to the experimenting of present-day physicists. I sense, however, an important contrast at this point between science and religion. Science is very unlikely to change its outward manifestations (the laws governing gross matter, for example), but it will almost surely have to alter its inner ideas. Religion, on the other hand, will wish to change some of its superficial aspects (forms of worship, specific dogmas defining moral behavior in modern situations), but it is very unlikely to have to make any substantial change in its basic and central ideas. In science, to put it differently, certitude lies near the surface, with uncertainty and confusion near the core; with religion, there often is confusion near the surface, but certitude at the core. In Western religion we will never, I believe, have to alter the central principles which Jesus enunciated, although we certainly must continuously reinterpret them to make them applicable to changing problems.
I cannot conscientiously repeat the Apostles’ Creed, for it contains sentences which begin with the affirmation, “I believe
.”; and in fact I do not so believe. I am not in the least concerned with various other formal dogmas, such as the Immaculate Conception, and the Resurrection. If these should turn out to be folk myths, perhaps introduced so that Christianity could compete on even terms with the claims of other religions, this would not disturb me in the least. I do not worry about the divinity of Christ, primarily I suppose because I simply do not have any understanding of what the words mean. The only Trinity that I understand is the trinity of God, my brother, and me. For two reasons I have no interest in the question: Is there a life after death? First, there is no evidence whatsoever which can be brought to bear on this question, so it seems to me a waste of time to consider it. Second, I am too much preoccupied with the challenges of this life.
None of the traditional religious dogmas seems to me of importance. What is important to me in the Christian religion is the wisdom and beauty of part of the Old Testament and—on a scale of superlative importance—the teachings of Christ.
I have no interest in the supposed instances of direct revelation. Whatever I believe about God, I cannot think that He bothers to chisel messages on tablets of stone or uses a sort of celestial loudspeaker. Certainly I cannot think of Him as an old gentleman with whiskers who occupies the top level of a three-story universe consisting of hell, earth, and heaven.
As to the Bible, I consider much of it to be a marvelous human record of divine wisdom. There is some of it that I think God would be pleased to have eliminated. But since it is so clearly a human record, with a vague and complex history for its component parts and for their centuries-long wanderings through a number of languages, I am not in the least surprised or disturbed at the wide range of quality, nor at the textual inconsistencies. The infiltration of folklore, myth, and poetry adds to the interest and charm, without in the least affecting the validity. For those earnest souls who seem to think that God dictated the Bible in English, complete with punctuation, to the committee of churchmen selected by King James in 1611, I have sympathy but not much comprehension.
I do not think that unique access to God is gained through the linguistic apparatus or the concepts of the West. Although I do not have the scholarship to appreciate them, I have every intuitive basis for thinking that the great religious writings of other cultures, and their views concerning their God, have equal validity. They may not seem to me as pure, or as nobly and simply conceived, but that could be my fault, not theirs. I only say that the principles of Jesus are supreme for me.
I think science and religion share certain linguistic difficulties. Just as the man-sized language of science is (at least so I think) entirely unsuitable at both subnuclear and cosmic levels, the necessarily man-sized language of religion is also very often unsuitable. We simply have no words in which to capture God. Some of the poetry of the Bible comes as close to doing so as it is possible to do.
I have, however, made so many disclaimers that I ought to state what positive views I hold which, taken together, constitute my personal religious belief. And at this point I explicitly invoke the principle of complementarity.
When I ask about the nature of God and do this within an impersonalized and somewhat intellectualized framework, I find it satisfying to say that God represents the moral purpose of the universe, and that He is the author of the grand design, ultimately responsible for its intricate beauty and for our evolving capacity to recognize the lovely unity that pervades all the apparent diversity.
On the other hand, when I am in trouble, when I am frightened about the safety of those I love, when I am wrestling with very personal problems, when I hear the cry of a child in the night, or when I am moved by a well-remembered hymn, then my view of God is paradoxically different. Then He is the ever dependable friend, the loving, comforting, and protecting Father.
I cannot do better than Tolstoy’s affirmation, ‘I believe in God, who for me is Spirit, Love, the Principle of all things. I believe that He is in me, and I in Him.” ®
If the two concepts—the impersonal abstract one and the emotional and very personal one—seem inconsistent or contradictory, then I repeat that they arise under mutually exclusive circumstances and can strictly be viewed as complementary.
Religion, in my view, has no possible reason to resent or deny the magnificent success with which science deals with the problems that lie within its domain. On the other hand, religion is the main guide for a vaster—and to many, a far more significant—range of problems with which science cannot deal—the nonanalytical, nonmeasurable, nonrepetitive part of life, within which intuition, feeling, and emotion play predominant roles, and within which the individual person asks, ““Who am I?”
. “What are my basic purposes?”
. “What ought I do?”
. “What is my duty?”
. “What is the meaning of life?”’
We have seen that the explanations of science, when traced down, disappear in either fog or assumption. The explanations of religion, on the other hand, are founded on faith and conviction. Of the two, the second basis seems to me the more satisfying.
Confirmation in science (even if shaky at its core, as Karl Popper has pointed out)
has the attraction of being widespread. But it is by no means universal; the agreement is widespread only in the sense that the vote is preponderantly favorable within a small elite. Outside that elite, the individuals have no real grounds for agreement, and in fact couldn’t care less. If you tot up all the persons who believe in electrons, accept evolution, understand DNA, and care about quasars, the number is negligible as compared with the number of individuals who believe in God. _
Some scientists would undoubtedly counter by saying that the preceding paragraph is near-nonsense for the reason that the elite who really know about and believe in science do so on the grounds of real evidence (their emphasis), that everyone else believes in science indirectly but significantly because they see applied science and technology work, while (still in their view)
there just isn’t any “real evidence” of the necessity for or the value of religious convictions.
My answer to that is twofold. First, I side with the imagined critics in conceding—in proclaiming—that I too believe in science as a magnificently successful guide in producing, step after step, answers to the questions which science raises. However, I differ completely because I believe that science cannot raise a large proportion of the really significant questions, and believe that it will never be able to. And second, I assert that there is a vast body of evidence in the record of human experience that man needs convictions of a sort which science cannot furnish, and that religion can and does fill that need. The evidence in my Own personal experience is fully as definite and convincing as the results of a laboratory experiment. When I must make a decision as to what I ought to do, my moral conscience furnishes me with instructions that are more explicit than the instructions an electron receives from the probability function y of quantum theory. Or as another case, when I go to church, I feel happier and better than when I do not. It is as simple as that. Let us briefly take stock of the position in which we find ourselves, now that our century is more than two-thirds past.
On the one hand, man is confronted by a multitudinous diversity. Science has, with superb success, described a formidable array of detailed relationships, operating within a structure which reaches out to the farthest star and which probes to the interior of the nucleus and the gene. Art, music, poetry, religion—these all have their special insights, their realms of concern, their differing formulations. The practical world of affairs is fantastically complicated, confused, and puzzling. Life is so wildly multiple and so wildly various that it cannot be compressed into any one neat formulation. Life cannot be backed into a tight corner; no mind can challenge life to a single duel.
The artist, in his great wisdom, has never attempted to do this. He has characteristically looked at small fragments of experience, but looked in such a way that he can see some aspect of the whole mirrored in the part.
Thinking, which is a chief tool used by science, deals competently with certain aspects of experience; but feeling, which often takes over where thinking leaves off, and which is a chief instrument for fashioning the rhythms, the patterns, and the illuminating symbolism of the arts, deals with quite other aspects of experience.
The philosopher has sometimes tried to construct unifying theories for the whole, but I am unaware of any attempt that has gained wide acceptance. One stubborn fact has always blocked such efforts. ‘“Everyday experience confronts us with an inescapable duality: on the one hand, the tough resistant world of things, the complexities of which science is now untangling and reducing to the form of natural law; on the other hand ourselves, the thinkers, feelers, choosers, who do the measuring and ordering, and who seem to belong to a different realm of reality.
. As Descartes pointed out long ago, we may systematically doubt everything, but the one undubitable fact is that something is doing the doubting.” ”
If it is true that we are steadily under the influence of centrifugal tendencies, which lead to more diversity and complexity, it is equally true that centripetal forces are at work, which keep pointing inward to central unities. This is evident in both the physical and the biological sciences. In the former, and despite the almost intolerable variety of the experimental evidence concerning the so-called elementary particles, we appear to be close to a theory which may simplify and unify all this complexity. As to the physical elements, we already have the main outlines of a theory that shows how they could all have evolved from a primitive simple beginning. In the realm of living matter, the unifying sweep of the Darwinian theory of evolution has been crowned by our knowledge of the DNA double helix, the beautiful molecular structure which both summarizes the past and provides for the future by storing genetic history and by possessing the capacity to replicate. Furthermore, this structure has been found to be the common central property of all forms of life, from the simplest single-celled creature to man. It is difficult to imagine any one fact of more impressive, and more unifying, significance.
In religion, historically so tortured by disagreeing factions, we now have ecumenical movements which make slow but promising progress. Even in the world-wide political scene, granting the staggering array of splintering disagreements, we do hold to the concept of an embracing organization. On a smaller, but still on a great scale, our own country is dedicated to the idea that unity can exist within diversity.
It is clear that in all aspects of our lives we have to deal with diversity and must continuously seek, within that variety, unifying features and principles. In my own youth I tolerated diversity primarily by not allowing the conflicting ideas to come to engagement. It was essentially true that I thought about religion on Sunday, about science in the working hours of weekdays, and about the humane arts in spare time.
I now firmly believe that that kind of compartmentalization is unsatisfactory. The paradoxes, the inconsistencies, the multiple contradictions have to be honestly faced; some of them have to be resolved, and some of them have to be accepted. In the relationship between religion and science, I have for myself resolved essentially all of the conflicts by coming to believe in reasonable claims for each. Within science I have to accept certain deep inconsistencies (a wave and a particle) as I also do in religion (the emotional, personal God and the abstract, intellectual God).
These acceptances are formally justified in terms of the principle of complementarity; but they are made more agreeable by my realization that the dualities arise in large part from language and culture-bound limitations from which I cannot conceivably free myself and for which I need feel no responsibility.
I want to conclude by describing a sort of geometrical way of thinking about the relationships between the different realms of our experience and our concern. The geometrical metaphor arises from a useful trick that was introduced into complex variable theory by the great German mathematician Georg Friedrich Bernhard Riemann (18261866).
Several pages back we observed that the square root of a positive real number is a two-valued function, there always being two answers. This is an almost trivially simple case of what are called multiple-valued functions, and in the more sophisticated realm of what the mathematician calls “complex numbers” there can be really complicated situations when one deals with multiple-valued functions. To help in these situations Riemann introduced the idea of a multilayered surface, roughly like sheets of paper stacked on top of each other. The various layers of the multisheeted Riemann surface were cut along certain lines, and then two layers A and B could be interconnected by joining the right side of a cut on A to the left side of a cut on B, and similarly the left side of the cut on A to the right side of the cut on B. Using these crossover joins, a moving point on A could slide onto layer B, or vice versa.
I want you to think of a roughly similar geometrical situation, in which there is a considerable number of sheets in the layered stack, each of the sheets being as large as you please and so negligibly thin that if you concentrate attention on one, you can think of it as being right next to another one which interests you, no matter which this other one is. Each is next to all. That is a sort of Alice in Wonderland concept, but don’t let it worry you.
Now each of our sheets is also cut along lines, as in the mathematical case, and not only are they criss-cross joined along these lines, permitting passage from the one sheet to the other, but a little stretching occurs along each cut so that they overlap on the criss-cross join, there being a band bordering the cut which is recognized to be a common part of both of the joined sheets.
I do hope this doesn’t sound too complicated and fantastic! For in terms of these various sheets, each joined to every other one along a band which they share, I can describe my picture of the way our minds must deal with the multiplicity of the realms of our experience.
One of these sheets might be labeled “Science.” On it there would be regions devoted to all the scientific specialties. These would all have “interior” portions (where topologists speak only to topologists, for example) and common portions (where physicists speak to astronomers, organic chemists to immunologists, and so on). There would be many cuts distributed around on this science sheet, where varying and intermingled viewpoints are criss-cross connected with the viewpoints of nonscientific activities. Thus mathematics shares a boundary strip along a cut which joins to music. The science sheet is cross-connected with a rather broad common band to the sheets devoted to the creative arts and to philosophy, and with a somewhat more narrow common band to the sheet devoted to religion.
All other fields have their sheets, similarly available for cross-connection. I suppose there is a cut and a common band shared between the natural sciences (what we have herein always meant by the word ‘“‘science’’) and what are called the “social sciences”; but at the moment I would envisage that cut as not very extensive, and the band of shared area as being rather narrow and wrinkled.
A person’s concerns can, at one moment, be located on one of the interior portions of a single sheet. This, for example, is the location occupied by the developmental embryologist when he is concentrating on an experiment in his laboratory. When he interprets this experiment, and when he thinks about its implications, he might wander broadly around over the science sheet. When he thinks about the developing embryo within his pregnant wife, he crosses over onto any one of numerous other sheets.
One cannot simultaneously occupy an interior position on two sheets—if he wishes to straddle two sets of concern, he moves to the shared band. He temporarily can, by staying inside his own sheet, compartmentalize his thinking—this often is the way he makes progress within his own field. But he should constantly remember that he also can, and sometimes must, occupy a position in which he is concerned with interconnections.
The whole stack of sheets, each with its own interior tapestry of intricate pattern, accommodates itself to the representation of a vast amount of complexity. The paradoxical fact that each sheet is next to every other sheet, that each sheet is, or can be, connected to any other sheet— that is an expression of the unity that pervades all the diversity. But the sheets are not glued tight together into one solid mass. As Oppenheimer said, “Occasionally between the sciences, and more rarely between a science and other parts of our experience and knowledge, there is a correspondence, or analogy, a partial mapping of two sets of ideas and words
. Everything can be related to anything; everything cannot be related to everything’ (my italics).°
From a single interior position on one sheet, one can frame a question that receives, in this context, one answer. The same question, if framed within the context of another interior position on another sheet, may well receive a quite different—a contradictory—answer. Indeed, from two interior positions on the same sheet he may well receive two inconsistent but complementary answers.
The thinking of an individual is thus both compartmentalized and not compartmentalized. He shifts from a compartmentalized position on one sheet to a compartmentalized position on another sheet. He can carry out the process of shifting almost instantaneously—just stopping thinking about music and starting to think about supper— or he can pause as long as he likes in the common band shared by two sheets, spending a lifetime thinking about the relationships between science and religion.
I earnestly hope that no reader believes that I take this little geometrical fable too seriously. I do not. It does seem to me, however, to furnish a rather vivid way of thinking about the complexity and interrelatedness of our concerns. Our hunches, intuitions, ideas, beliefs, and convictions are partly isolated and partly connected in an interlaced pattern that has portions blessed by consistency and other portions invigorated by contradiction.
The picture here presented does not have the specious tidiness of attempts at unitary viewpoints, but these ideas are supported by the realization that science recognizes that in its most fundamental theories, complementarity must be accepted. There is the comfort of knowing that logic has no power to prove the incorrectness of this viewpoint. It has the validity, the vigor, and the integrity of corresponding to the way life really is. I believe that the ultimate unifying virtues are order, beauty, faith, and love. The emphasis of science decreases as one passes from the first to the last of these four words. The emphasis of religion, on the other hand, increases from first to fourth, culminating on the final one. The arts and the humanities primarily emphasize the central two. But the underlying unity being what it is, all are concerned with all.
As I write these closing lines I am for a time in residence at the Salk Institute of Biological Studies. There is here a most congenial atmosphere, for this organization of the most fundamental biological is engaged in some problems but is determined that these studies be carried out within the context of a wide concern for the utilization of this knowledge for the good of man. Most of the laboratory work here is at the molecular biological level, and I have just been rereading James D. Watson’s marvelous account of the discovery of the structure of DNA.
This discovery of the detailed architecture of the doubly helical molecule that is at the very focus of life is the kind of science that is as artistically beautiful as it is intellectually satisfying. There is presumably a considerable number of scientists (they are chiefly the young ones) who believe that all biological questions, ultimately including those about the behavior of man, will be answered in terms of physics and chemistry. These people are called reductionists. Among the reductionists are the extremists, of whom the British molecular biologist Francis Crick is the leader, who presumably believe® that the three-letter words coded on the DNA molecule* are capable of forming chemical sentences which provide the answers for any conceivable question that can be asked about how a living organism arises, develops, and functions.
Applauding the grand sweep of that idea, I dissent. I do not think molecular biology is going to be able to answer all of man’s questions about himself. Francis Crick, of course, would hoot at this last sentence. He would doubtless point out that molecular biology will be able to answer all the well-posed and sensible questions, and that the other questions ought to be disregarded as trivial or meaningless. On his side would be a small group of very bright but some- *The DNA molecule provides an alphabet of four letters (the four bases which form the stairsteps of the DNA helix). They store the information which can instruct the machinery of the cell what proteins to manufacture. The proteins are formed of long “sentences” made out of twenty “words”
(the twenty amino acids).
If you are lucky enough to have a young teen-ager in your house, he or she can explain to you that with four letters you can make sixteen two-letter words (which isn’t enough to designate the amino acids, since there are twenty of them); whereas with these same four letters you can spell sixty-four three-letter words. This is more than enough, the surplus being used for synonyms, punctuation, and perhaps some non-sense syllables. Hence the genetic code is written out with the sixty-four three-letter words that can be made from four letters. what acidulous young scientists. In the dissenting company are to be found the poets, the saints and the dreamers, the philosophers and the innocents, together with uncounted millions of humble, earnest, simple folk. Indeed, among this latter company, where I choose to be, are also many of the older thoughtful scientists. I could offer quoted testimony from many of them, but I will restrict myself to one example.
Vannevar Bush has been for many years one of the recognized leaders among the scientists of our country. He is a distinguished engineer, the energetic leader of the United States scientific effort in World War II. No one who has ever seen him bite into his pipe and crisply outline a course of practical action would ever think of calling him soft. In the chapter entitled “Threat and Bulwark” in his totally realistic book Modern Arms and Free Men Bush said, “Science has been misread. Science does not exclude faith. And faith alone can meet the threat that now hangs over us.” !° His most recent book, moreover, bears the title Science Is Not Enough.”
In this book the reader has found some very informal comments about myself and my activities, along with other portions which are as serious as I am capable of being. This shuffling up is not due to lazy organization along with an unwillingness to rewrite once again. It is deliberate. I am convinced that this is the way life is. Triviality and significance, gaiety and seriousness—these are complementary one to the other. I have always lived that sort of life, and for as much longer as is granted to me, I always will. I will be seventy-five before this book is printed. At a number of times during its writing I was not at all confident that I would be around until it was finished. “I cannot tell,” the French writer Maurice Goudeket wrote, “how I shall behave when aches and decrepitude come, or that illness which will thrust me, roughly or not so roughly, out of this world I only beg that I may, without weakening, remain true to the oaths that I have inwardly sworn, honor the life dwelling within me to its very last; and even if only a spark remains to me, treat it still as a holy flame."