Reproduced from: sci-hub.tw/10.2307/27826254

SCIENCE AND COMPLEXITY
Author(s): WARREN WEAVER
Source: American Scientist, Vol. 36, No. 4 (OCTOBER 1948), pp. 536-544
Stable URL: http://www.jstor.org/stable/27826254

SCIENCE AND COMPLEXITY

By WARREN WEAVER

Rockefeller Foundation, New York City

Based upon material presented in Chapter I, “The Scientists Speak,” Boni & Gaer, Inc., 1947. All rights reserved.

SCIENCE has led to a multitude of results that affect men’s lives. Some of these results are embodied in mere conveniences of a relatively trivial sort. Many of them, based on science and developed through technology, are essential to the machinery of modern life. Many other results, especially those associated with the biological and medical sciences, are of unquestioned benefit and comfort. Certain aspects of science have profoundly influenced men’s ideas and even their ideals. Still other aspects of science are thoroughly awesome.

How can we get a view of the function that science should have in the developing future of man! How can we appreciate what science really is and, equally important, what science is not? It is, of course, possible to discuss the nature of science in general philosophical terms. For some purposes such a discussion is important and necessary, but for the present a more direct approach is desirable. Let us, as a very realistic poli­tician used to say, let us look at the record. Neglecting the older his­tory of science, we shall go back only three and a half centuries and take a broad view that tries to see the main features, and omits minor de­tails. Let us begin with the physical sciences, rather than the biological, for the place of the life sciences in the descriptive scheme will gradually become evident.

Problems of Simplicity

Speaking roughly, it may be said that the seventeenth, eighteenth, and nineteenth centuries formed the period in which physical science learned variables, which brought us the telephone and the radio, the automobile and the airplane, the phonograph and the moving pictures; the turbine and the Diesel engine, and the modern hydroelectric power plant.

The concurrent progress in biology and medicine was also impressive, but that was of a different character. The significant problems of living organisms are seldom those in which one can rigidly maintain constant all but two variables. Living things are more likely to present situations in which a half-dozen, or even several dozen quantities are all varying simultaneously, and in subtly interconnected ways. Often they present situations in which the essentially important quantities are either non­-quantitative, or have at any rate eluded identification or measurement up to the moment. Thus biological and medical problems often involve the consideration of a most complexly organized whole. It is not surpris­ing that up to 1900 the life sciences were largely concerned with the necessary preliminary stages in the application of the scientific method­ preliminary stages which chiefly involve collection, description, classification, and the observation of concurrent and apparently correlated effects. They had only made the brave beginnings of quantitative the­ories, and hardly even begun detailed explanations of the physical and chemical mechanisms underlying or making up biological events.

To sum up, physical science before 1900 was largely concerned with two-variable problems of simplicity; whereas the life sciences, in which these problems of simplicity are not so often significant, had not yet become highly quantitative or analytical in character.

Problems of Disorganized Complexity

Subsequent to 1900 and actually earlier, if one includes heroic pioneers such as Josiah Willard Gibbs, the physical sciences developed an attack on nature of an essentially and dramatically new kind. Rather than study problems which involved two variables or at most three or four, some imaginative minds went to the other extreme, and said: “Let us develop analytical methods which can deal with two billion variables.” That is to say, the physical scientists, with the mathematicians often in the vanguard, developed powerful techniques of probability theory and of statistical mechanics to deal with what may be called problems of disorganized complexity.

This last phrase calls for explanation. Consider first a simple illustra­tion in order to get the flavor of the idea. The classical dynamics of the nineteenth century was well suited for analyzing and predicting the motion of a single ivory ball as it moves about on a billiard table. In fact, the relationship between positions of the ball and the times at which it reaches these positions forms a typical nineteenth-century problem of simplicity. One can, but with a surprising increase in diffi­culty, analyze the motion of two or even of three balls on a billiard table. There has been, in fact, considerable study of the mechanics of the standard game of billiards. But, as soon as one tries to analyze the motion of ten or fifteen balls on the table at once, as in pool, the problem becomes unmanageable, not because there is any theoretical dif­ficulty, but just because the actual labor of dealing in specific detail with so many variables turns out to be impracticable.

Imagine, however, a large billiard table with millions of balls rolling over its surface, colliding with one another and with the side rails. The great surprise is that the problem now becomes easier, for the meth­ods of statistical mechanics are applicable. To be sure the detailed his­tory of one special ball can not be traced, but certain important ques­tions can be answered with useful precision, such as: On the average how many balls per second hit a given stretch of rail? On the average how far does a ball move before it is hit by some other ball? On the average how many impacts per second does a ball experience?

Earlier it was stated that the new statistical methods were applicable to problems of disorganized complexity. How does the word “disorgan­ized” apply to the large billiard table with the many balls? It applies because the methods of statistical mechanics are valid only when the balls are distributed, in their positions and motions, in a helter-skelter, that is to say a disorganized, way. For example, the statistical methods would not apply if someone were to arrange the balls in a row parallel to one side rail of the table, and then start them all moving in precisely parallel paths perpendicular to the row in which they stand. Then the balls would never collide with each other nor with two of the rails, and one would not have a situation of disorganized complexity.

From this illustration it is clear what is meant by a problem of dis­organized complexity. It is a problem in which the number of variables is very large, and one in which each of the many variables has a be­havior which is individually erratic, or perhaps totally unknown. How­ever, in spite of this helter-skelter, or unknown, behavior of all the individual variables, the system as a whole possesses certain orderly and analyzable average properties.

A wide range of experience comes under the label of disorganized complexity. The method applies with increasing precision when the number of variables increases. It applies with entirely useful precision to the experience of a large telephone exchange, in predicting the average frequency of calls, the probability of overlapping calls of the same number, etc. It makes possible the financial stability of a life in­surance company. Although the company can have no knowledge what­soever concerning the approaching death of any one individual, it has dependable knowledge of the average frequency with which deaths will occur.

This last point is interesting and important. Statistical techniques are not restricted to situations where the scientific theory of the individual events is very well known, as in the billiard example where there is a beautifully precise theory for the impact of one ball on another. This technique can also be applied to situations, like the insurance example, where the individual event is as shrouded in mystery as is the chain of complicated and unpredictable events associated with the accidental death of a healthy man.

The examples of the telephone and insurance companies suggests a whole array of practical applications of statistical techniques based on disorganized complexity. In a sense they are unfortunate examples, for they tend to draw attention away from the more fundamental use which science makes of these new techniques. The motions of the atoms which form all matter, as well as the motions of the stars which form the uni­verse, come under the range of these new techniques. The fundamental laws of heredity are analyzed by them. The laws of thermodynamics, which describe basic and inevitable tendencies of all physical systems, are derived from statistical considerations. The entire structure of mod­ern physics, our present concept of the nature of the physical universe, and of the accessible experimental facts concerning it rest on these sta­tistical concepts. Indeed, the whole question of evidence and the way in which knowledge can be inferred from evidence are now recognized to depend on these same statistical ideas, so that probability notions are essential to any theory of knowledge itself.

Problems of Organized Complexity

This new method of dealing with disorganized complexity, so power­ful an advance over the earlier two-variable methods, leaves a great field untouched. One is tempted to oversimplify, and say that scientific methodology went from one extreme to the other – from two variables to an astronomical number – and left untouched a great middle region. The importance of this middle region, moreover, does not depend pri­marily on the fact that the number of variables involved is moderate­ large compared to two, but small compared to the number of atoms in a pinch of salt. The problems in this middle region, in fact, will often in­volve a considerable number of variables. The really important char­acteristic of the problems of this middle region, which science has as yet little explored or conquered, lies in the fact that these problems, as con­trasted with the disorganized situations with which statistics can cope, show the essential feature of organization. In fact, one can refer to this group of problems as those of organized complexity.

What makes an evening primrose open when it does? Why does salt water fail to satisfy thirst? Why can one particular genetic strain of microorganism synthesize within its minute body certain organic com­pounds that another strain of the same organism cannot manufacture? Why is one chemical substance a poison when another, whose molecules have just the same atoms but assembled into a mirror-image pattern, is completely harmless? Why does the amount of manganese in the diet affect the maternal instinct of an animal? What is the description of aging in biochemical terms? What meaning is to be assigned to the question: Is a virus a living organism? What is a gene, and how does the original genetic constitution of a living organism express itself in the developed characteristics of the adult? Do complex protein molecules “know how” to reduplicate their pattern, and is this an essential clue to the problem of reproduction of living creatures? All these are certainly complex prob­lems, but they are not problems of disorganized complexity, to which statistical methods hold the key. They are all problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole. They are all, in the language here proposed, problems of organized complexity.

On what does the price of wheat depend? This too is a problem of organized complexity. A very substantial number of relevant variables is involved here, and they are all interrelated in a complicated, but nevertheless not in helter-skelter, fashion.

How can currency be wisely and effectively stabilized? To what extent is it safe to depend on the free interplay of such economic forces as supply and demand? To what extent must systems of economic control be employed to prevent the wide swings from prosperity to depression? These are also obviously complex problems, and they too involve analyzing systems which are organic wholes, with their parts in close interrelation.

How can one explain the behavior pattern of an organized group of persons such as a labor union, or a group of manufacturers, or a racial minority? There are clearly many factors involved here, but it is equally obvious that here also something more is needed than the mathematics of averages. With a given total of national resources that can be brought to bear, what tactics and strategy will most promptly win a war, or bet­ter: what sacrifices of present selfish interest will most effectively con­tribute to a stable, decent, and peaceful world?

These problems – and a wide range of similar problems in the bio­logical, medical, psychological, economic, and political sciences – are just too complicated to yield to the old nineteenth-century techniques which were so dramatically successful on two-, three-, or four-variable prob­lems of simplicity. These new problems, moreover, cannot be handled with the statistical techniques so effective in describing average behavior in problems of disorganized complexity.

These new problems, and the future of the world depends on many of them, requires science to make a third great advance, an advance that must be even greater than the nineteenth-century conquest of prob­lems of simplicity or the twentieth-century victory over problems of dis­organized complexity. Science must, over the next 50 years, learn to deal with these problems of organized complexity.

Is there any promise on the horizon that this new advance can really be accomplished? There is much general evidence, and there are two recent instances of especially promising evidence. The general evidence consists in the fact that, in the minds of hundreds of scholars all over the world, important, though necessarily minor, progress is already be­ing made on such problems. As never before, the quantitative experi­mental methods and the mathematical analytical methods of the physi­cal sciences are being applied to the biological, the medical, and even the social sciences. The results are as yet scattered, but they are highly promising. A good illustration from the life sciences can be seen by a comparison of the present situation in cancer research with what it was twenty-five years ago. It is doubtless true that we are only scratching the surface of the cancer problem, but at least there are now some tools to dig with and there have been located some spots beneath which almost surely there is pay-dirt. We know that certain types of cancer can be induced by certain pure chemicals. Something is known of the inherit­ance of susceptibility to certain types of cancer. Million-volt rays are available, and the even more intense radiations made possible by atomic physics. There are radioactive isotopes, both for basic studies and for treatment. Scientists are tackling the almost incredibly complicated story of the biochemistry of the aging organism. A base of knowledge concerning the normal cell is being established that makes it possible to recognize and analyze the pathological cell. However distant the goal, we are now at last on the road to a successful solution of this great problem.

In addition to the general growing evidence that problems of organ­ized complexity can be successfully treated, there are at least two promising bits of special evidence. Out of the wickedness of war have come two new developments that may well be of major importance in helping sci­ence to solve these complex twentieth-century problems.

The first piece of evidence is the wartime development of new types of electronic computing devices. These devices are, in flexibility and capacity, more like a human brain than like the traditional mechanical computing device of the past. They have “memories” in which vast amounts of information can be stored. They can be “told” to carry out computations of very intricate complexity, and can be left unattended while they go forward automatically with their task. The astounding speed with which they proceed is illustrated by the fact that one small part of such a machine, if set to multiplying two ten-digit numbers, can perform such multiplications some 40,000 times faster than a human operator can say “Jack Robinson.” This combination of flexibility, capacity, and speed makes it seem likely that such devices will have a tremendous impact on science. They will make it possible to deal with problems which previously were too complicated, and, more importantly, they will justify and inspire the development of new methods of analysis applicable to these new problems of organized complexity.

The second of the wartime advances is the “mixed-team” approach of operations analysis. These terms require explanation, although they are very familiar to those who were concerned with the application of mathematical methods to military affairs.

As an illustration, consider the over-all problem of convoying troops and supplies across the Atlantic. Take into account the number and effectiveness of the naval vessels available, the character of submarine attacks, and a multitude of other factors, including such an imponderable as the dependability of visual watch when men are tired, sick, or bored. Considering a whole mass of factors, some measurable and some elusive, what procedure would lead to the best over-all plan, that is, best from the combined point of view of speed, safety, cost, and so on? Should the convoys be large or small, fast or slow? Should they zigzag and expose themselves longer to possible attack, or dash in a speedy straight line? How are they to be organized, what defenses are best, and what organ­ization and instruments should be used for watch and attack?

The attempt to answer such broad problems of tactics, or even broader problems of strategy, was the job during the war of certain groups known as the operations analysis groups. Inaugurated with brilliance by the British, the procedure was taken over by this country, and ap­plied with special success in the Navy’s anti-submarine campaign and in the Army Air Forces. These operations analysis groups were, moreover, what may be called mixed teams. Although mathematicians, physicists, and engineers were essential, the best of the groups also contained physiologists, biochemists, psychologists, and a variety of representatives of other fields of the biochemical and social sciences. Among the out­ standing members of English mixed teams, for example, were an endocrinologist and an X-ray crystallographer. Under the pressure of war, these mixed teams pooled their resources and focused all their different insights on the common problems. It was found, in spite of the modern tendencies toward intense scientific specialization, that members of such diverse groups could work together and could form a unit which was much greater than the mere sum of its parts. It was shown that these groups could tackle certain problems of organized complexity, and get useful answers.

It is tempting to forecast that the great advances that science can and must achieve in the next fifty years will be largely contributed to by vol­untary mixed teams, somewhat similar to the operations analysis groups of war days, their activities made effective by the use of large, flexible, and highspeed computing machines. However, it cannot be assumed that this will be the exclusive pattern for future scientific work, for the atmos­phere of complete intellectual freedom is essential to science, There will always, and properly, remain those scientists for whom intellectual freedom is necessarily a private affair. Such men must, and should, work alone. Certain deep and imaginative achievements are probably won only in such a way. Variety is, moreover, a proud characteristic of the American way of doing things. Competition between all sorts of methods is good. So there is no intention here to picture a future in which all scientists are organized into set patterns of activity. Not at all. It is merely suggested that some scientists will seek and develop for them­ selves new kinds of collaborative arrangements; that these groups will have members drawn from essentially all fields of science; and that these new ways of working, effectively instrumented by huge comput­ers, will contribute greatly to the advance which the next half century will surely achieve in handling the complex, but essentially organic, problems of the biological and social sciences.

The Boundaries of Science

Let us return now to our original questions. What is science? What is not science? What may be expected from science?

Science clearly is a way of solving problems – not all problems, but a large class of important and practical ones. The problems with which science can deal are those in which the predominant factors are subject to the basic laws of logic, and are for the most part measurable. Science is a way of organizing reproducible knowledge about such problems; of focusing and disciplining imagination; of weighing evidence; of decid­ing what is relevant and what is not; of impartially testing hypotheses; of ruthlessly discarding data that prove to be inaccurate or inadequate; of finding, interpreting, and facing facts, and of making the facts of nature the servants of man.

The essence of science is not to be found in its outward appearance, in its physical manifestations; it is to be found in its inner spirit. That austere but exciting technique of inquiry known as the scientific method is what is important about science. This scientific method requires of its practitioners high standards of personal honesty, open-mindedness, focused vision, and love of the truth. These are solid virtues, but science has no exclusive lien on them. The poet has these virtues also, and often turns them to higher uses.

Science has made notable progress in its great task of solving logical and quantitative problems. Indeed, the successes have been so numerous and striking, and the failures have been so seldom publicized, that the average man has inevitably come to believe that science is just about the most spectacularly successful enterprise man ever launched. The fact is, of course, that this conclusion is largely justified.

Impressive as the progress has been, science has by no means worked itself out of a job. It is soberly true that science has, to date, succeeded in solving a bewildering number of relatively easy problems, whereas the hard problems, and the ones which perhaps promise most for man’s future, lie ahead.

We must, therefore, stop thinking of science in terms of its spectacular successes in solving problems of simplicity. This means, among other things, that we must stop thinking of science in terms of gadgetry. Above all, science must not be thought of as a modern improved black magic capable of accomplishing anything and everything.

Every informed scientist, I think, is confident that science is capable of tremendous further contributions to human welfare. It can continue to go forward in its triumphant march against physical nature, learning new laws, acquiring new power of forecast and control, making new material things for man to use and enjoy. Science can also make further brilliant contributions to our understanding of animate nature, giving men new health and vigor, longer and more effective lives, and a wiser understanding of human behavior. Indeed, I think most informed scientists go even further and expect that the precise, objective, and analytical techniques of science will find useful application in limited areas of the social and political disciplines.

There are even broader claims which can be made for science and the scientific method. As an essential part of his characteristic procedure, the scientist insists on precise definition of terms and clear characteriza­tion of his problem. It is easier, of course, to define terms accurately in scientific fields than in many other areas. It remains true, however, that science is an almost overwhelming illustration of the effectiveness of a well-defined and accepted language, a common set of ideas, a common tradition. The way in which this universality has succeeded in cutting across barriers of time and space, across political and cultural boundaries, is highly significant. Perhaps better than in any other intellectual enterprise of man, science has solved the problem of communicating ideas, and has demonstrated the world-wide cooperation and community of interest which then inevitably results.

Yes, science is a powerful tool, and it has an impressive record. But the humble and wise scientist does not expect or hope that science can do everything. He remembers that science teaches respect for special competence, and he does not believe that every social, economic, or political emergency would be automatically dissolved if “the scientists” were only put into control. He does not – with a few aberrant excep­tions – expect science to furnish a code of morals, or a basis for esthetics. He does not expect science to furnish the yardstick for measuring, nor the motor for controlling, man’s love of beauty and truth, his sense of value, or his convictions of faith. There are rich and essential parts of human life which are alogical, which are immaterial and non-quantitative in character, and which cannot be seen under the microscope, weighed with the balance, nor caught by the most sensitive microphone.

If science deals with quantitative problems of a purely logical charac­ter, if science has no recognition of or concern for value or purpose, how can modern scientific man achieve a balanced good life, in which logic is the companion of beauty, and efficiency is the partner of virtue?

In one sense the answer is very simple: our morals must catch up with our machinery. To state the necessity, however, is not to achieve it. The great gap, which lies so forebodingly between our power and our capacity to use power wisely, can only be bridged by a vast combina­tion of efforts. Knowledge of individual and group behavior must be improved. Communication must be improved between peoples of differ­ent languages and cultures, as well as between all the varied interests which use the same language, but often with such dangerously differing connotations. A revolutionary advance must be made in our understand­ing of economic and political factors. Willingness to sacrifice selfish short­ term interests, either personal or national, in order to bring about long­ term improvement for all must be developed.

None of these advances can be won unless men understand what sci­ence really is; all progress must be accomplished in a world in which modern science is an inescapable, ever-expanding influence.

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Reproduced from: sci-hub.tw/10.2307/985228

The Imperfections of Science
Author(s): Warren Weaver
Source: Proceedings of the American Philosophical Society, Vol. 104, No. 5 (Oct. 17, 1960), pp. 419-428
Published by: American Philosophical Society
Stable URL: http://www.jstor.org/stable/985228

THE IMPERFECTIONS OF SCIENCE

WARREN WEAVER

Vice-President, Alfred P. Sloan Foundation

(Dinner Address, April 22, 1960)

As my title indicates, I am going to be speaking of imperfections; but I must warn you that I will also be speaking of something which I love. My text is, therefore, almost inevitable:

My mistress’ eyes are nothing like the sun;
Coral is far more red than her lips’ red:
If snow be white, why then her breasts are dun;
If hairs be wires, black wires grow on her head.
I have seen roses damask’d, red and white,
But no such roses see I in her cheeks;
And in some perfumes is there more delight
Than in the breath that from my mistress reeks.
I love to hear her speak, yet well I know
That music hath a far more pleasant sound.
I grant I never saw a goddess go,
My mistress, when she walks, treads on the ground.

And yet, by heaven, I think my love as rare
As any she belied with false compare.

Yes, if I were going to over-load this talk with a sub-title, it would have to be “The Dark Lady of the Laboratories.”

I propose to consider two questions. First, why does science command the respect, prestige, and admiration which it obviously possesses? Second, does science really deserve the reputation which is often, if not usually, given to it by scientists and public alike: and is it not possible to take a more restrained, more candid, and, I believe, more accurate attitude toward science which honestly concedes certain limitations, while still permitting one to declaim “And yet, by heaven, I think my love as rare….”

It may seem surprising, and even trivial, to ask why science has so great a reputation. We are, in the modern world, completely surrounded by science and by the technological achievements which science makes possible. By this powerful partnership we are warmed and cooled, clothed and fed, protected, cured, transported, and enter­tained. Science has made possible color television and jets, dial telephones across the continent and short-wave radio across the oceans, polio serum, hi-fi and stereo, heart-lung and kidney-function machines which substitute temporarily for our own damaged internal parts, electronic com­puters that play chess and compose music, satellites about the earth and rockets to the moon, automatization and micromimaturization, ma­chines that think and which learn from experience (which is more than some people do), nuclear energy, and G. L. 76 in toothpaste. If we have not yet conquered cancer, cardiac disorders, and the degenerative diseases of later life; if we are uncertain about the genetic effects of long con­tinued low doses of radiation; if we miss recover­ing a nose-cone now and then; if we are a little puzzled about psychology and psychiatry and are not yet sure whether the mind is in the head; if we still have cavities in our teeth, aches in our joints, and clocks that won’t run in our auto­ mobiles – well, surely these are minor gaps which will soon be filled in by science.

Indeed, there is a good deal of evidence that if science once chooses to drive a path out into the wilderness of ignorance, then, no matter where that path is headed, there seems to be no inherent limitation to the distance science can penetrate, no limit to the amount of experience that can be explained and brought under control by the methods of science. These continuing successes have been convincing enough in the field of the physical sciences – in astronomy and chemistry and physics, for example. In our modern physical laboratories we transmute the elements, and change mass to energy and vice versa. We experiment with fantastic entities ludicrously called elementary particles – the most evanescent of which exist for less than one one­ hundred-thousandth of a billionth of a second. The high polymer chemist has become a skilled atomic architect, using atoms to build molecules of which nature never thought, synthesizing a whole array of new materials of great beauty and utility, each built to blueprint specifications con­cerning the desired strength, density, color, thermal and electric properties, resistance to wear, or stain, or corrosion, etc. We create an electrical disturbance in the recently discovered radiation belt thousands of miles above the surface of our earth; and, sure. enough, auroral lights appear at another and far distant location on our planet, just at the time theoretically predicted.

Yes, the triumphs of the physical scientists are impressive enough to explain why science has a great reputation. But the triumphs of those parts of science which are concerned with living nature are, in many ways, to be interpreted even more seriously. For it seems, on the whole, reasonable and proper for man to analyze his physical environment. But the mysteries of life-perhaps they are intended to remain mysteries.

Therefore the reputation of science becomes even greater, even more formidable, perhaps even more disturbing, when one success after another seems to indicate that many central and precious vital phenomena will one day be explainable in terms of chemistry and physics, that the very stuff of life will one day be weighed and measured and put on the shelf in neatly labeled bottles.

The age-long history of man’s learning about plants and about the lower animals contributed to the good reputation of science without creating any large counter-feeling of apprehension. But when the first brave anatomists invaded the human body, and the early physiologists began to analyze man’s own parts in mechanical terms, then the philosophers and humanists and theo­logians were convinced that they could hear the distant footsteps of an all-conquering science monster.

The great Darwinian movement, whose cen­tennial we have so recently celebrated here, has seemed to many to constitute the major indication that man, if he is indeed nothing but an improved beast, can by one more easy step be nothing more than a mere machine – and thus surely an object which science can wholly analyze, wholly capture within its special framework.

When experiments show that the normal mothering behavior of an animal – the concern to feed and clean and protect the very young offspring – is destroyed by leaving a metallic trace element out of the diet; when the modern bio­chemist can explore inside the mitochondria within a cell and analyze the enzyme systems there; when the microbiologist can take a virus apart into chemically identifiable and wholly “dead” pieces and then can reconstitute these pieces into an organism which can reproduce it­self – then indeed science begins to earn a reputa­tion which is in many senses great, but which is also in some senses frightening.

Modern advances in genetics, and especially in the fundamental biochemical aspects of genetic phenomena, may well be the greatest and most spectacular, as well as the most formidable, tri­umph of science in its attack on the living world. It is convincing enough – and fearsome enough­ – when the physicist learns to control the energy in the nuclei of atoms. But what will we think of science, and how will we order our lives, when the biologist has learned how to control the gene? This will clearly present the greatest intellectual and moral challenge that man has ever faced.

So science has never really been blocked, it seems, no matter in what direction it seeks to move.

So science has, it seems, been so successful that it has inevitably earned a great and strange reputation. If it has never yet been defeated, presumably it is all-powerful. And since science is, after all, the work of scientists – for one seldom encounters disembodied science – then presumably these scientists are both so clever and so wise that they can do anything. Perhaps we should turn the world over to this superbreed. Perhaps they could, if properly supported, really liberated, and put in charge – perhaps they could solve all problems of human relations, of economic stability, of international peace, and of the good life. Perhaps they should design not only the churches, but the creeds also. Perhaps the best music and the loveliest poetry will, in a short time, come out of a machine.

The sad fact is that some scientists themselves appear to believe precisely this. And this arrogant attitude quite naturally irritates, or even angers. the social scientists, the humanists, the moralists, and the creative artists. The classic protest is surely that of Keats.

Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in Heaven:
We know her woof, her textures; she is given In the dull catalogue of common things.
Philosophy will clip an Angel’s wings.

In more contemporary terms, and at the same time that the electronics engineer is programing his computer to write verse, the modern poet e. e. cummings writes

I’d rather learn from one bird how to sing, than teach ten thousand stars how not to dance.

or, in still more up-to-date idiom,

While you and I have lips and voices which are for kissing and to sing with,
Who cares if some one-eyed son-of-a-bitch invents an instrument to measure Spring with

Our first question is thus answered. Science has its remarkable reputation primarily because of its record of success in dealing with inanimate nature – with the physical universe – and second­arily because of the promising advances it has already made in understanding and controlling vital phenomena. These have brought to science a great prestige and respect. Often this prestige and respect rest upon quite the wrong evidence­ on relatively trivial matters, or on advances which are essentially technological rather than basically scientific in character. And these successes have, while earning admiration from some, aroused resentment and fear and opposition in others. Worst of all, these successes have tended to sepa­rate scientists out as a special breed, and have widened, rather than narrowed, the gap between scientific thought and general learning.

To advance to our second question, does science deserve either the favorable or the un­favorable parts of its reputation? Can science not be given a more true, more realistic, and more constructive interpretation?

I think that the favorable part of the present reputation of science is often significantly mis­understood; and I think that the unfavorable part is largely if not wholly false. And in explaining why, I shall at the same time be giving my personal answer to the other aspect of our second question; namely, is there not a more balanced view of science which puts both its power and its limitations into a more clear and more correct focus?

To deal with these questions we must start with pretty basic considerations. When man­ – scientific man – confronts any object, any natural phenomenon. what does he wish to do? He does not elect to disregard, he dislikes being mystified, he is not willing to fear. On the contrary, he has a deep craving to understand. The difference between the state of not understanding and of understanding is a complex and subtle matter which has several aspects, of differing importance to different persons. It seems best to start by describing what aspects of understanding are of major importance to a scientist. We do not have time to consider the way in which the scientific view on this point has changed, as science has developed; nor do we have time to describe the differing views that are held by scientists even today. I shall state only a view which is held by a good many experts, particularly among the quantum theorists, this being incidentally the view which. with certain modification, I myself find congenial.

For a scientist, a phenomenon is understood provided he possesses a satisfactory theory for this phenomenon. But this statement is not very illuminating until one goes on to say what a satisfactory scientific theory is , how it operates, and in what senses it is useful or interesting or both.

The theory, in refined cases and in the physical sciences, is likely to consist of a body of mathe­matical equations. These equations state the interdependence of a few or several quantities, represented simply by letters in the equations. If you point to one of the letters and ask, “What is this: what physical thing does this represent?” then the answer, at least from the group here being described, is that you have asked an irrelevant and improper question.

For associated with this body of equations is a set of procedural rules. You are told: “Per­form such and such observations, either in a laboratory experiment set up thus and so, or directly upon nature in such and such a way. Take the numbers which result from those ob­servations, and put them into these equations, substituting the numbers for certain specified letters. Then solve the equations. thus obtaining numerical values for certain other letters. Now go back to your experiment (or another similar one), or go back to nature and make certain further observations. This will provide you with a new set of numbers: and if you have a sound theory, these new numbers will coincide (with certain probabilistic error which need not confuse us at the moment) with the numbers which were previously solved out of the equations.”

Now I am fully aware of your disappointment over this statement. It sounds very formal and abstract – and it is. The procedure sounds complicated – and often it is in fact exceedingly complicated. And how can this procedure possibly bring about understanding?

Let us, therefore, drop this line of attack for a moment, and consider a more friendly, more understandable sort of understanding. A person says, “I don’t understand genetics at all. I don’t understand genes and chromosomes.” He is told, “Vv’ell, a chromosome (in every cell of your body, incidentally) is sort of like a string of beads, each bead being a gene. And each gene determines, or helps to determine, one of your characteristics, such as your blue eyes, or your attached earlobes, or, for that matter, your sex.” And the person thinks, “Well, this is something like it; I am beginning to understand.”

Or this same eager person says, ” I don’t understand radio waves.” And he is told, “Well, throw a small stone into a still pond of water. See those circular ripples expand, getting weaker as they go? See the wave length, which is merely the distance from the crest of one ripple to the crest of the adjacent ripple? See how these waves would keep expanding out, if you kept throwing little stones in at the same spot? Well, radio waves are like that, although of course they are three-dimensional spherical ripples.” And again the person thinks. “I am beginning to understand.”

With these extreme examples before us – of a very abstract and formal theory on the one hand, and of a friendly, loose, incomplete, but neverthe­less useful analogy on the other hand, we can now contrast two extreme concepts of under­standing.

One of these, the friendly, man-in-the-street variety, attempts to explain by describing an unfamiliar phenomenon in terms of its similarity to a familiar phenomenon. The fact that this kind of explanation by analogy is comforting, that it satisfies the listener, is, if you stop to think about it, rather surprising. For logically and philosophically this procedure is a complete fraud. The unfamiliar is explained in terms of the familiar. But the familiar, if one examines the situation honestly and in detail, is itself simply not understood. It has been familiar long enough so that curiosity concerning it has dis­ disappeared: but that is all.

Although referred to here as the “man-in-the­-street” type of explanation, it should be pointed out that scientists are often found in this same street. Science very frequently uses this form of explanation, and it has to recommend it not only the fact that it is comforting, but also the fact that it is useful. For if radio waves are “like” water waves or more generally like waves in other familiar media, then to the new and strange phenomena of radio can at once be applied a lot of the previously accumulated knowledge about more familiar waves.

The other, formal, type of procedure is, again, clearly not an explanation, in any normal sense of that word. In fact it baldly states that the scientist has no business to ask, “What is the real nature of physical phenomena”; or to ask, “Are there really precise deterministic laws be­hind the statistical data which I observe”; or to ask. “How can light be both a wave motion and a beam of particles”; or to ask. “What sense does it make for a particle to have electric charge but zero mass?”

These are, to the one who accepts the formal procedure, senseless assortments of words. For the formal procedure makes no pretense whatso­ ever of “explaining.” The formal procedure, in fact, says “It is impossible to explain phenomena, and it is in fact senseless to try. All you can do – and this is a triumph of great dimensions­ is to deal successfully with phenomena.”

The equations, or more generally the theory, are a sort of “black box.” You can feed one set of numbers into this black box, turn the crank. and out comes a second set of numbers. If this second set correlates properly with numbers which can be determined, following given rules, from nature, then you have a successful theory. You must accept the result, be thankful, and ask no further questions.

This idea of not explaining, but of dealing suc­cessfully with phenomena deserves a few further words. What, to the scientist, constitutes a really satisfactory sort of success for a theory?

The answer lies largely in the words generality, elegance, control, and prediction. If one single theory – one black box – is capable of grinding out results that relate to a wide range and a large apparent diversity of experience, then the theory has the obvious practical ad­ vantage of generality. It is a convenient intel­lectual tool that will handle a lot of different jobs. And this generality also has an important aesthetic aspect, for it reveals underlying unity in apparent diversity – a procedure which the creative artist recognizes as very closely related to the concept of beauty. If in addition the theory is stated in compact form, then it possesses the illusive but lovely trait which the scientist calls “elegance.”

Suppose that the black box of our theory has certain dials on one of its faces, and that we set these dials, before inserting input data, to values which are characteristic of the particular experi­ment in question. Then the numbers ground out by our black box will depend not only on the numbers we insert. but also on our dial settings. And then by changing these dial settings one can answer such a question as “How will the result change if I vary one or more of the circumstances of the experiment?” As more specific examples, “How will the electrical resistance of this alloy change if I put more tin in the alloy? … How much further can the aircraft fly if I increase the fuel capacity by 500 gallons? … How much faster will I lose weight if I reduce from 1,400 calories a day to 1.200 calories?” Under useful circumstances such as these, the theory has brought the phenomenon under control. You know just what to do in order to modify the result in the desired way.

Finally, the black box. if it is a really good one, must be able to grind out numbers which will prove to correlate properly with numbers which you will obtain in an experiment or ob­servation not yet made. That is to say, the theory should be able to predict.

We can now state in more compact summary what the modern scientist – or at least one important school of scientists – calls a good theory. It is a small and neat black box which works for a wide range of problems, which has external dials which can be set, and which can be used in advance. In other words, it is a theory which is general and elegant, which puts us in control of the phenomena in question, and which can predict. But notice that I have not said one single word about explaining. The advocates of abstract theories have to agree that the scientist understands a phenomenon when he can control and predict it, and that as a product of his creative imagination he appreciates and admires the theory the more, the more general and elegant it is. Wiithin the formal view here being described, nothing more by way of explanation can in the nature of things be demanded or expected.

It is essential to my general argument to point out at once that many scientists enthusiastically disagree with this position. One of the most competent and moving objections would be made hy the distinguished scholar Michael Polyani, earlier a physical chemist and now a social scien­tist and philosopher. Polyani, to whose general views we will return later, considers that the abstract and formal procedures in science are, in fact, useless and senseless unless, quite in addition and as a subjective and very personal experience, the totality of the formal manipulation “makes sense.” Polyani points out that he himself has traced every successive step involved in the proof of certain theorems, but that nevertheless

They have conveyed nothing to me, for I have not been able to grasp their sequence as a whole…. To look at a mathematical proof by merely verifying each consecutive step – says Poincare – is like watch­ing a game of chess, noting only that each step obeys the rules of chess. The least that is required is a grasp of the logical sequence as a purposeful pro­cedure: what Poincare describes as the “something which constitutes the unity of the demonstration.”

Having characterized a successful scientific theory, we can now use some of the terms of that description to restate the reasons why science has so great a standing.

Indeed, the general and popular reputation of science rests largely on its success at control, and to a lesser degree upon its ability to predict. Un­fortunately, only scientists themselves, and a few others who make a real effort, achieve the knowledge that makes generality important, and elegance lovely.

When we restrict attention to moderate-scale phenomena, involving, say, objects above electron-microscopic size, and if we stay away from such phenomena as the toss of a single coin or the decisions of a single mind, then science can often offer “explanation by analogy,” this being useful, interesting, and curiously comforting. But this kind of explanation is, fundamentally, a complete illusion: and at the other extreme the strict and formal abstract type of a scientific theory contains nothing whatsoever that con­stitutes, in any ordinary sense, explanation.

This is a rather shocking thing to say – that science does not furnish any really ultimate or satisfying explanation. And this imperfection leads at once to the question: does science have other important imperfections?

Without claiming completeness, I want to speak here of a total of five imperfections. You will not be surprised, I think, to have me say that these are not, actually, so much imperfections in science as imperfection in the views that are held by some concerning science. To those who ex­pect science to be perfect, who expect it to be irresistibly all-powerful, who think of it as being infinitely precise and logically impeccable, who see science marching relentlessly forward “explaining” one thing after another in cold and mechanical terms, who even feel that science squeezes the beauty and mystery out of all that it touches – to all such persons it is necessary to say: my friends, you are mistaken. Science is amazingly successful at the surface, so to speak. But at its logical and philosophical and artistic core, it has, at least in my view, a number of limitations which can be viewed as imperfections. These are the blemishes that make science a human and endurable enterprise. These are the faults – if you will call them that – or the limita­tions – if you will permit a fairer term – that should allow science and art and philosophy and theology to become mutually respecting and mutually reinforcing partners.

For example, the fact that science is superbly successful at dealing with phenomena, but that it possesses the inherent defect (which I assume it shares with many other fields of thought) that it cannot furnish ultimate explanation, is, in my own view, really not a defect at all, but rather an example of the honesty and clarity that comes with maturity. And again, this defect has the virtue that it joins science to the rest of life, rather than separating it off in cold perfection. Second, it is an obvious imperfection that scien­tists themselves do not, and apparently cannot, agree about certain of the deepest and most cen­tral aspects of science. I indicated earlier that many scientists are quite unwilling to accept the abstract type of “black-box” theory discussed here. Einstein always disliked the formal pro­cedures of quantum theory, and persisted in thinking (if I interpret correctly) that under­neath the apparently indeterministic vagary of individual atomic events was some substratum of deterministic reality (whatever that means) which science will eventually be able to reveal and understand ( whatever that means).

But the intelligibility of the terms of the dis­agreement is irrelevant. For the point is that scientists – even the greatest ones in the most advanced field of physics, such as Einstein and Bohr and Planck and Dirac – cannot agree as to whether and how science explains anything.

This imperfection of science I find a most at­tractive one; for it reflects the fact that science is not monstrous and monolithic, but is a very human enterprise, exhibiting the same lively and useful diversity which one finds in philosophy, art, music, etc.

Thirdly, you are all aware of the nineteenth­ century fear that science was in the process of imposing purely mechanistic and deterministic interpretations upon all phenomena, including ultiimately the individual decisions of an individual per­son. And you are all aware – for this has been widely publicized – that science has itself now abandoned this view. Science recognizes that the individual events, down at the level of electrons, protons, photons, mesons, etc., are all probabilistic in character, and individually simply not predictable. Since all large-scale events – the falling of a stone, say – are ultimately composed of individual events, the large-scale events are themselves, strictly speaking, probabilistic also. But the large­ scale phenomena are nevertheless dependable. The stone does, after all, fall. And this is simply because this large-scale event is the net result of so incredibly vast a number of small-scale events that the eccentricities always average out. Large­ scale nature is, so to speak, a life insurance company with so many billion, billion, billion, billion … clients that she knows very precisely what fraction will die each week, even though she is completely unable to say whether or not one given individual will die.

So it is an imperfection of science,. if you choose so to name it, that it is essentially sta­tistical in nature. This means, for example, that perfect accuracy is unattainable in any measure­ment, that certainty is impossible in any pre­diction.

But does this make one admire science the less? Can you conceive of wanting to marry a woman who is completely perfect and totally predictable? Does this element of ultimate unpredictability, moreover, not remove an otherwise insuperable barrier between science and the rest of life?

My fourth defect is related to the fact that there are those who say, “I will admit that science is no doubt more strictly logical than any other field of intellectual activity, but logic is a cold and relentless master, and I am not so sure that I want my life dominated by it.”

Logic is indeed an integral and central part of science. But logic, although a vastly useful mental tool, does not now have the reputation which it was once supposed to deserve. I have had previous occasion to write about this point, so I will repeat here very briefly the essential conclusion of what is necessarily a somewhat technical argument.

There are two main types of logic: deductive and inductive. In the former, one starts by making a certain number of pure assumptions­ technically speaking, he adopts the postulates of the system under examination. Then with the addition of a certain accepted vocabulary of signs, certain assumed formation rules for com­bining the signs, and certain assumed transforma­tion rules for deriving new formulas from old ones – with this assumed machinery one then pro­ceeds to – to do what?

Of course, all he can possibly do is to unroll, in all its lovely and unsuspected complexity, the truths – or more properly, the formally correct relationships – which were inherent in what he originally assumed. This procedure is, of course, quite powerless to create truths – it can only re­veal what has been previously and unconsciously assumed.

But apart from this inherent limitation on de­ductive logic, which has of course been long recognized, there have rather recently been dis­covered, by Gödel, wholly unsuspected and startling imperfections in any system of deductive logic. Gödel has obtained two main results, each of which is of the most massive importance. He proved that it is impossible – theoretically impossible, not just unreasonably difficult – to prove the consistency of any set of postulates which is, so to speak, rich enough in content to be interesting. The question, “Is there an inner flaw in this system?” is a question which is simply unanswerable.

He also proved that any such deductive logical system inevitably has a further great limitation. Such a system is essentially incomplete. Within the system it is always possible to ask questions which are undecidable.

If deductive logic has these vital and built-in limitations, how about inductive logic, the branch of reasoning which examines all the observed case recorded in the evidence, and seeks to induce therefrom general laws, this being the way in which the mind of man attempts to reach universals by the study of particulars. To quote from my previous paper on this subject:

Over 200 years ago David Hume bluntly denied the propriety of inductive logic. Ever since, certain skeptics have urged the necessity of practicing induction without pretending that it has any rational foundation; certain deductionists have vainly tried to prove Hume wrong; certain philosophers have optimistically hoped that a mild and friendly attitude towards such words as “rational” and “reasonable” could of itself sanction their application to state­ments referring to future and hence unexamined cases; and certain scientists have felt that it is vaguely sensible to suppose that future phenomena would conform to past regularities.

Deep and troublesome questions are involved here. Consider, just for a moment, the question: When and why does a single piece of past evidence give useful information about a future situation? If one takes a single piece of copper and determines that it con­ducts electricity, then it seems sensible to suppose that other future pieces of copper will also conduct electricity. But if we pick out a man at random and determine that his name is John, this does not at all lend credence to the idea that all other men are named John. The first of these seems to lead to a “lawlike statement,” and the second to an “unlawlike” one; but no one, so far as I know, has ever been able to give workable form to this distinction.

In fact, in spite of many attempts to make induction intellectually tolerable, the matter remains a mess.

For recent researches, primarily by Dr. N. Goodman, have shown that, when strictly examined

… the ability of induction to deal with a future case collapses; and since this is the only useful aspect of induction, we are faced by total collapse. Thus I must report to you that discouraging news has leaked out of the citadel of logic. The external walls appear as formidable as ever; but at the very center of the supposedly solid fortress of logical thinking, all is confusion. As practical tools, no one doubts the continuing value of the armaments. But in terms of ultimate and inner strength, the revelations are astounding indeed. The ultimate basis of both types of logical thinking is infected, at the very core, with imperfection.

Thus, one ends up by recalling Dr. Charles F. Kettering’s characteristic warning “Beware of logic. It is an organized way of going wrong with confidence.”

As the fifth imperfection in science I come to a topic which, because of its depth and subtlety, deserves a far more extensive and far more com­petent summary than I can give. This particular element of imperfection has to do with the sup­posed objectivity of science.

It is widely recognized that any natural event has a number of possible explanations. It has been demonstrated that if a certain body of experience can be usefully interpreted through one particular theory, then there is always, in fact, an infinite number of other theories each of which will equally well accommodate the same body of experience. There may be very important aesthetic reasons for preferring certain of the theories. Often, there is a tendency to accept, of the alternative explanations, the one which seems in some general sense to be “the most credible,” and the “ultimate in criteria of credibility” says a recent writer,¹ “is scientific objectivity.”

Careful thinkers have for long been skeptical about the supposed objectivity of so-called scien­tific facts. In the translator’s preface to one of the master works of Poincare, George Bruce Halsted said a half-century ago

What is called “a knowledge of the facts” is usually merely a subjective realization that the old hypotheses are still sufficiently elastic to serve in some domain; that is, with a sufficiency of conscious or unconscious omissions and doctorings and fudgings more or less willful.

The idea that the so-called objective facts of science may not be so sacrosanct is thus not an exclusively recent suspicion. But this idea has within the last couple of years been given an analysis that is outstanding for the clarity and honesty of its thought, for the many years of meticulous and scholarly care that were involved in the writing, and for the high and deserved reputation of its author. I refer to Michael Polyani’s book Personal Knowledge.

This is a long and hard, but very rewarding book. I cannot possibly do more than make a few bold statements about Polyani’s position, hoping that some of you will find the ideas either interesting enough, or shocking enough, or both, so that you will read the book.

He totally rejects the ideal of scientific detach­ment. He does not believe that knowledge is, or can be, impersonal, universally established, com­pletely detached, objective. He regards knowing as an act of comprehension that involves change in the person carrying out the act of compre­hension. Thus comprehension is essentially an irreversible process, and is non-critical in the sense that there is no permanently fixed frame­ work within which critical testing can occur. On the other hand, he does not consider knowledge to be wholly subjective. He does believe that active and skillful comprehension can establish contact with “a hidden reality,” and it is this strange and almost mystic blend of passionate contribution in the personal act of knowing, to­ gether with a thereby established contact with objective reality, which he designates as personal knowledge. “Even in the exact sciences ‘knowing’ is an art, of which the skill of the knower, guided by his passionate sense of increasing contact with reality. is a logically necessary part.”

The grand sweep of his argument, the thorough­ness and depth of his inquiry, and the dramatic art with which he develops his theme are hinted at by the mere titles of the chapters – Objectivity, Probability, Order, Skills, Articulation, Intel­lectual Passions, Conviviality, The Logic of Af­firmation, the Critique of Doubt, Commitment, the Logic of Achievement, Knowing Life, The Rise of Man. You will not, I think, be surprised that this scientific and social philosopher, ending with a description of the efforts of responsible man to move towards ultimate liberation con­cludes his book with the sentence, ” And that is also, I believe, how a Christian is placed when worshipping God.”

We have spoken thus far of five imperfect as­pects of science. Let us summarize the view necessitated by these five points.

Science has, as a tool for dealing with nature, proved to be superbly successful. With respect to physical nature, and at all moderate scales of space or time – say larger than an atom and smaller than a galaxy, say more persistent than 10^-10 seconds and less than a billion years­ science seems to have unlimited ability. With the extremely small or the extremely large, with inconceivably brief or extended phenomena, science has a difficult time. It is by no means clear that our present concepts or even our existing language is suitable for these ranges. In the realm of animate matter, science has made wonderful but more limited progress. And we can, at the present, see no fixed barriers to further progress.

We must agree that all this adds up to a very great intellectual achievement – very possibly the greatest that man has, as yet, to his credit.

But if one looks deeply within this system, instead of encountering a harder and harder inner core, instead of meeting more and more depend­able precision, more and more rigidity, compulsion, and finality, instead of finally reaching permanence and perfection, what does one find?

He finds unresolved and apparently unresolvable disagreement among scientists concerning the re­lationship of scientific thought to reality – and concerning the nature and meaning of reality itself. He finds that the explanations of science have utility, but that they do in sober fact not explain. He finds the old external appearance of inevi­tability completely vanished, for he discovers a charming capriciousness in all the individual events. He finds that logic, so generally sup­posed to be infallible and unassailable. is in fact shaky and incomplete. He finds that the whole concept of objective truth is a will-o-the-wisp.

Lest you think that these views are peculiar only to your speaker, permit me to quote briefly from The Logic of Scientific Discovery by Karl R. Popper, Professor of Logic and Scientific Method at the University of London, and a scholar of whom the authoritative Manchester Guardian has said that he “has probably introduced a greater number of important ideas into the philosophy of science than any other living philosopher.”

Science is not a system of certain, or well­ established statements; nor is it a system which steadily advances toward a state of finality…. The old scientific ideal of epistēmē – of absolutely certain, demonstrable knowledge – has proved to be an idol. The demand for scientific objectivity makes it in­evitable that every scientific statement must remain tentative for ever. It may indeed be corroborated, but every corroboration is relative to other state­ments which, again, are tentative. Only in our sub­jective experiences of conviction, in our subjective faith, can we be “absolutely certain.”

The empirical basis of objective science has thus nothing ”absolute” about it. Science does not rest upon rock-bottom. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or “given” base; and when we cease our attempts to drive our piles into a deeper layer, it is not because we have reached firm ground. We simply stop when we are satisfied that they are firm enough to carry the structure, at least for the time being.

For those who have been deluded, by external appearances and by partial understanding, into thinking of science as a relentless, all-conquering intellectual force, armed with finality and perfection, the limitations treated here would have to be considered as damaging imperfections. You will have realized, however, from the pride and enthusiasm with which I have exhibited these points, that I do not myself think of them as unpleasant imperfections, but rather as the blemishes which make our mistress all the more endearing.

And this remark leads at once to the final point – the fault which I do in fact consider a serious imperfection. This is not a weakness which is inherent in the nature of science, but one which has been created by the attitude of scientists and non-scientists alike.

I refer to the fact that many scientists – and the public which they have over and falsely impressed – have created a horrid and dangerous gap be­tween science and the rest of life. This is the tragedy of the “Two Cultures,” which have been so brilliantly discussed by C. P. Snow. “I be­lieve,” says this scientist who is also a distin­guished essayist and novelist, “the intellectual life of the whole of western society is increasingly being split into two polar groups.”

The two cultures referred to by Snow are formed, on the one hand, of the scientist and the very few non-scientists who have bothered to understand science and its role in modern life, and on the other hand, of the literary intellectuals, the artists – in a broad sense the humanists. Snow comments that “thirty years ago the cultures had long ceased to speak to each other: but at least they managed a kind of frozen smile across the gulf. Now the politeness is gone, and they just make faces.”

Snow writes with wit and with compelling wisdom about the revolution, in its attitude towards science, which our society must some­ how achieve. This must involve assimilating science “as part and parcel of the whole of our mental experience.” This cannot be brought about unless

politicians, administrators, an entire community … know enough science to have a sense of what scien­tists are talking about … closing the gap between the two cultures is a necessity in the most abstract intellectual sense, as well as in the most practical. When these two senses have grown apart, then no society is going to be able to think with wisdom.

Snow seems to place a rather greater blame for this perilous dichotomy upon the literary intellectuals, whom he considers the more seriously impoverished because of the scorn which motivates their attitude towards science.

They still like to pretend that the traditional culture is the whole of “culture,” as though the natural order didn’t exist … as though the scientific edifice of the physical world was not, in its intellectual depth, complexity, and articulation, the most beautiful and wonderful collective work of the mind of man.

I am myself more inclined to place the greater blame upon the scientists. Although some scientists seem almost childishly eager to leave their laboratories to talk about things which they do not understand, they have been pretty reluctant to leave their laboratories to talk and write intel­ligently about what they do superbly understand. Far too little have they been concerned with gen­eral interpretation of their methods and their results.

But there is blame enough for all elements of society to deserve a substantial portion; and allocation of the blame is not a constructive task. What we must do – scientists and non-scientists alike – is close the gap. We must bring science back into life as a human enterprise, an enterprise that has at its core the uncertainty, the flexibility, the subjectivity, the sweet unreasonableness, the dependence upon creativity and faith which permit it, when properly understood, to take its place as a friendly and understanding companion to all the rest of life.

I began with a sonnet – a classical one. I close with a modern sonnet by Clarence R. Wylie, Jr., who is a poet and a mathematician:

Not truth, nor certainty. These I foreswore
In my novitiate, as young men called
To holy orders must abjure the world.
“If … , then … ,” this only I assert;
And my successes are but pretty chains
Linking twin doubts, for it is vain to ask
If what I postulate be justified,
Or what I prove possess the stamp of fact.

Yet bridges stand, and men no longer crawl
In two dimensions. And such triumphs stem
In no small measure from the power this game,
Played with the thrice-attenuated shades
Of things, has over their originals.
How frail the wand, but how profound the spell!

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Reproduced from: https://www.jstage.jst.go.jp/article/jafpos1956/2/2/2_2_98/_pdf/-char/en

Warren WEAVER,
The Emerging Unity of Science,
Annals of the Japan Association for Philosophy of Science, 1961-1965,
Volume 2, Issue 2, Pages 98-113,
https://doi.org/10.4288/jafpos1956.2.98

THE EMERGING UNITY OF SCIENCE

Warren Weaver

Alfred P. Sloan Foundation, New York

Preliminary Ideas – Science and Complexity

To develop the set of ideas I have in mind I must start by summarizing (and bringing up to date) the viewpoints I presented in two earlier papers.

In Science and Complexity² were advanced the concepts of problems of simplicity, problems of disorganized complexity, and problems of organized complexity.

The physical sciences have, until recently, made a large part of their magnificent progress in understanding and controlling inanimate nature through success in dealing with problems of simplicity. These relate to phenomena which can be significantly dealt with in terms of two, three, or at most four variables; and in order that the phrase “significantly dealt with” apply, these must be phenomena that can dissected out of, and treated as isolated from, the totality of all other physical phenomena. Thus the relationship between tension and length of a steel bar; or between electrical resistance and temperature of a copper wire; or between the rate and temperature of a chemical reaction; or between gravitational attraction, mass, and distance; or between the refractive index and the angles of incidence and reflection; or between the pressure, volume, and temperature of a perfect gas – these are examples of the very many relationships which, although strictly imperfect in almost all instances because of the neglect of minor effects, have largely furnished the basis for the grand success of the physical sciences, and for all the technological achievements based on science.

At the other extreme, as regards numbers of parameters, are problems of disorganized complexity. A good example is furnished by the kinetic theory of gases. With many billions of billions of molecules involved (say 1024), each colliding with and otherwise interacting with all other molecules, it would be unthinkable to attempt a detailed theory which would describe the individual events. But the random nature of the complexity is such that probabilistic methods can be used with confidence. Although in general it is impossible to give any microscopic (of course sub-microscopic) description of the underlying separate events, the important macroscopic variables can be analyzed in their dependence on the microscopic variables. The gas-law, PV =RT, can at one stage of scientific sophistication be dealt with as a 4-variable case of a problem of simplicity. At a later stage, science recognizes that the simplicity is only apparent; and that behind this simple macroscopic behavior are vastly complicated molecular phenomena which, in spite of their multiplicity, can nevertheless be handled because of randomness.

In many other cases the apparent simplicity of the problems of simplicity results either from a conscious decision to limit the accuracy required of the theory, or from an unconscious disregard of the fact that the ” simple ” variables are in reality macroscopic and statistically stable consequences of an underlying random complexity.

Thus problems of simplicity and problems of disorganized complexity are closely interrelated. In both instances the final and applicable theory is essentially a simple one, concerned with a few macroscopic variables. In the case of problems of disorganized complexity the cloud of underlying complexity is recognized and dealt with by statistical techniques. In the case of problems of simplicity, there is usually a similar cloud of underlying complexity but it is depressed, ignored, or unsuspected.

Thus problems of simplicity and problems of disorganized complexity, considered more carefully and deeply, often if not usually merge into a single case; namely that in which there is a useful theory involving two, three, or four variables, which may be macroscopic in nature and thus underlaid by a very large number of random variables. This underlying complexity is explicitly recognized in some cases (thus leading to the label “disorganized complexity”) or totally disregarded in others (thus leading to the label “simplicity”).

These two interconnected limiting cases, of very few or of very many variables, by no means cover the whole range of important phenomena. On the contrary, there is very great interest indeed in the intermediate variety of problems of organized complexity, which involve a number of variables which is greater than four, and which may well be one or even several hundred. These variables are significantly interrelated, so that a useful theory cannot be obtained if one neglects some of the variables. And the individual behavior of the variables is important, so that the substitution of a smaller number of averaged out variables, obtained by statistical techniques, is not useful.

The matter of the “isolatibility” of the phenomena dealt with in problems of simplicity is an essential point. One can take the hairspring out of a watch, and then determine how its dynamical characteristics depend upon temperature, am­plitude of oscillation, fatigue, etc. The facts thus determined, when the hairspring is totally removed from its normal environment, have validity when the hairspring is put back into a watch. But one cannot remove an internal organ – say the liver­ from a living creature and study its operation apart from its total interconnection with its normal environment. One cannot, I should suppose, usefully study in isolation the effect of one single factor among all those which, in the economics of trade, affect price, or demand, or supply. Obviously one cannot study the social behavior of an isolated individual.

No more will be said at this point concerning problems of organized complexity, for a discussion of the present and the emerging situation in the analysis of such problems will be the primary theme of a later section of this paper.

Further Preliminary Ideas – The Limitations of Science

I will also wish to refer to ideas I have previously expressed concerning certain characteristics of science which may be viewed by some as constituting imperfections, but which I myself think of as attractive features, which serve to unite scientific activity with other human activities. These ideas were published in a paper with the title The Imperfections of Science³. To save time, I will list in a very condensed summary the principal ideas of this paper. These are:

1. That science deals successfully with a wide range of natural phenomena, in the sense of providing a theory which relates the relevant variables and parameters, and thus furnishes a basis for modifying or controlling the phenomena; but science does not supply anything which, in any more ultimate sense, constitutes an explanation. Thus Newton’s law describes gravitational action in a most useful way; but does not in the least explain it.
2. That, as regards the philosophical or metaphysical goal of explanation, scientists themselves differ widely and enthusiastically as to whether and how science “explains” anything. Thus science has no agreed and orthodox position on this point.
3. That scientific information is essentially and inescapably statistical in nature, so that perfect accuracy is unobtainable, and certainty (including certainty of prediction) is impossible.
4. That logic, a chief tool of scientific thought, itself has limitations and defects. I refer to the inability of deductive logic to reveal anything not implicit in the assumptions; to the great discoveries by Gödel that any significant system of deductive logic is necessarily incomplete and that questions concerning its inner consistency are essentially unanswerable; and to the fact that there has never been developed, so far as I know, any satisfactory explanation of how inductive logic can deal with a future case.
5. That the supposed objectivity of science is, to say the least, questionable⁴.

If these are indeed true characteristics of modern science, as I believe them to be, then there would seem to be no inherent reasons why scientific activity cannot be brought into a mutually useful symbiotic relation with all other phases of human activity, in particular with all aspects of the creative and humanistic arts.

The Natural History of a Scientific Field

Suppose that for any particular scientific field (atomic spectra, physiological optics, protein structure, quantum dynamics, solid state physics, biochemistry of mitochondria, etc., etc.) one makes a graph which shows the way the complication of the theory (estimated in any sensible way you please) changes with time. If time is the horizontal variable (abscissa) and complication the verticol variable (ordinate), then the usual picture is that of a rather irregular “jiggly” curve, with some minor declines, but with a general rise as time progresses.

Figure 1. The graph of complexity, as a function of time, of any special field of science.

An advance in theory often leads to refined experiments which reveal previously unknown details, or which make more precise certain measured values. These advances in empirical knowledge, in turn, require further refinements in the theory; and these are often achieved by the addition of new theoretical ideas which, although they meet the momentary demands of observation, do complicate the theory, and do in turn lead to still further refinements in observational technique.

So the situation progresses, with an occasional gain which simplifies the theory (producing a small drop in the curve), but with increases in complexity the usual price for greater precision or greater inclusiveness.

It is easy to give any number of illustrations; perhaps the field of atomic spectra is as good as any. Roughly a century ago J. Stoney noticed that, of the four visible lines in the spectrum of hydrogen, three had frequencies that stood in the ratio 20 : 27 : 32. Shortly thereafter it was determined that the occurrence of simple harmonic ratios in spectra was no more frequent than would occur through chance. An improvement in theory was called for; and the game of the rising curve had been started.

Next came the Balmer series, the improvements by Rydberg, by J. Hahn, and particularly by Ritz. About 1913 the Bohr-Rutherford atom model was proposed, and within a half-dozen years the alternation and displacement laws for singlet, doublet, and triplet spectral types were in hand. By 1923 Sommerfeld, Lande, and others had introduced a new and more precise explanation of pressure shifts, and for resonance widening, for the line splitting in magnetic fields known as the Zeeman effect, and for the corresponding electric field effects discovered by Stark. Even more elaborate theories of hyperfine structure followed, as the theory became more and more precise and inclusive – but also more and more detailed and complicated, with multipole interactions, magnetic dipole interactions, etc., etc. The current copies of the Physical Review which are on my desk as I write contain articles on the Stark Broadening of Hydrogenic Ion Lines in a Plasma, and on Hyperfine Structure of Fe⁵⁷ in Yttrium-Iron Garnet from the Mossbauer Effect, etc.

Thus this particular time-complication curve is still jiggling upward, and promises to continue to do so for an indeterminate time, for the data being dealt with seem inherently detailed and complex.

But once in a rare while a great genius appears on the scene, and produces a truly devastating idea, classic in both its simplicity and its power. When such a tremendous intellectual event occurs, one or more of these irregularly rising curves of complexity comes crashing downwards – as at moment T* on the figure – to a level of inspired and inspiring simplicity.

This is not, I would claim, a fanciful description: for one can point to several of these extraordinary moments T*. One occurred when Newton enunciated his universal law of gravity; one occurred when Gregor Mendel counted his peas; one occurred when Charles Darwin published the Origin of Species; one certainly occurred when Einstein enunciated the general theory of relativity.

It is my own conviction that the present situation with respect to the theories of the so-called elementary physical particles is one of intolerable and unstable complexity, poised precariously high up on a peak of the curve, overdue for a plunge down to some acceptable level of reasonableness and simplicity. Where and how this will come, I cannot guess. But come it must. And it will almost surely involve a complete and refreshing collapse of the barriers which still exist between electromagnetic field theories, relativity theories, and quantum theories.

The Natural History of the Whole of Science

Each separate field of science, I think, produces its individual this-complexity curve of a sort just described. But just as, in statistical mechanics, the Boltzman H-theorem relates the erratic and apparently quite undirected and reversible be­havior of small parts of a system to the grand, over-all, irreversibly forward sweep of the system, so for the intellectual history of science there is, I believe, a recognizable and describable forward movement of the whole which statistically absorbs the eccentricity of development of all the component branches.

The Second law of thermodynamics states that closed inanimate systems always spontaneously change from a more orderly and less probable state to a less orderly and more probable one. A great steel bridge would, in time, rust, decay, disinte­grate, and merge with its environment: but a mountain of iron ore will not spontaneously organize itself into the improbable pattern of a great steel bridge.

In the mathematical theory of information, when one is faced by a situation which includes No possible cases or events of equal a priori probability, it requires an amount of information

to reduce the number N₀ of possible cases to a smaller number N. That is, information reduces probability, reduces entropy, and increases negentropy, to use the word and the concept which Professor Leon Brillouin uses so effectively in his excellent book⁵.

Since entropy is proportional to the probability of occurrence of the state, the entropy of a closed inanimate system increases, leading eventually to the ”heat­ death” in which the universe is a totally disorderly pile of ashes at a (very low) uniform temperature. But organic life is the “defender⁶ against the heat death”; and a chief purpose of science is to reduce complexity by revealing order in phenomena which, apart from scientific insight, would appear chaotic. Thus the progress of scientific theories, taken as a whole and as more and more information is brought to bear, should be in the direction of decreasing entropy.

Statistical mechanics learns to live with complexity by submitting to it, by succumbing to it, by allowing the complexity to continue to exist. But the attack on problems of complexity must win by victory, not by defeat.

In other words the over-all history of scientific theories must involve movement away from the easy conquest of problems of simplicity and problems of disorganized complexity, both of which may be viewed as dealing with highly probable behavior, to the much more difficult conquest of problems of organized complexity, the key word organized implying that they deal with situations of very low probability of occurrence.

Is science as a whole in fact moving in this direction? I think it rather easy to show that it is. Why has this inevitable movement been so long delayed – for science up to very recently has been primarily concerned with problems of simpli­city or of disorganized complexity? I think this is also easy to answer.

The Modern Attack on Problems of Organized Complexity

The basic answer to the question last proposed is that problems of organized complexity are very much more difficult than problems of simplicity or of disor­ganized complexity; and substantial progress cannot be made until science possesses analytical and experimental tools of very great power, flexibility, and scope.

There is strong evidence, I believe, that in the past quarter century science has begun to mature to the degree that makes possible effective progress in problems of organized complexity. I will mention a few examples of areas in which progress has occurred, and will speak in a little more detail of one example which is particularly relevant to the total topic of this paper.

The techniques of so-called “operational research” largely developed during World War II, involve classical types of quantitative analysis, probabilistic argu­ments, intuitive judgments, and the combined insights of the mathematical, physical, biological, and medical sciences; and bring all of these to bear as problems of otherwise quite perplexing complexity. Some of the special procedures which have thus been developed, such as linear programming, queueing theory, the design of optimum networks, etc., promise to be of very extensive usefulness. Game theory and the Monte Carlo method deserve mention in this same connection.

Modern advances in the physics of the solid state deserve a place in a list of recent successes with organized complexity. It is not too incorrect to speak of this theory as the quantitative sociology of impurities, imperfections, and disloca­tions in an otherwise ordered lattice.

In this list belongs the beautiful solutions of the exact amino acid sequence of insulin⁷ (with 51 amino acid residues), ribonuclease⁸ (with 124), and still more recently, the tobacco mosaic virus⁹ (with 158); and the magnificent unravelling of the structure of hemoglobin. The progress made in the quantitative analysis of economic input-output systems, involving 50 to 100 or even more variables in an example which illustrates the fact that present day electronic computers, with their capacity, logical flexibility, and incredible speed, are important tools for handling organized complexity. Advances in machine translation, and the related studies of the logical structure of the grammars of all languages, would, for instance, hardly have occurred apart from the stimulation of the computer possi­bilities. And the whole man-machine relationship which is thus evolving, with more and more automation, ever smaller and more rapid and more reliable elements for computing and automatic control, and with the elaboration of machine self­-programming techniques, make clear that we do indeed now have new tools with which to deal with complexity.

The over-all and organized approach to the interrelated problems of the earth, sea, and air, as exemplified in the recent International Geophysical Year program, indicates that modern facilities for travel and communication materially assist in combined attacks on certain of the complex problems of this planet.

I strongly suspect that recent progress in the behavioral sciences, in learning about the processes of learning, and in neurophysiology, deserve a place in any list of promising instances of progress in dealing with organized complexity.

The example, however, which seems to me most convincing and most hopeful is furnished by the present state of advance of our knowledge of certain aspects of the biochemistry within an individual cell. Working with the universal unit out of which all living things are organized, these theories seem to me to be of the highest possible interest and promise.

At the recent Cold Spring Harbor Symposium on “cell regulating mechanisms” there were beautiful reports on our present knowledge of the 1000-2000 enzymes, all contained within a single cell and simultaneously controlling the chemical reac­tions occurring there; on the synthesis of RNA by DNA, the material composing the genes; on the subsequent role of RNA as an intermediate conveying genetic information from the genes to ribosomes in the cytoplasm, thus dictating the structure of the protein enzyme being synthesized; on the feed-back whereby the products of an enzyme activated reaction inhibit the enzyme activity; on the “enzymatic adaption phenomenon” whereby certain regulator genes control the synthesis of the enzymes.

All this shows that we are at last beginning to get some real understanding of the total economp of cellular metabolism. It would be hard to imagine an example more clearly exhibiting organized complexity, nor an example more basic and universal.

The role of the mitochondria in all this chemical traffic within the cell is, at the same time, being beautifully clarified¹⁰. These tiny objects within the cell are known to consist of polymers of several thousand monomeric units. Each of these units contains a complete electron transport system of the sort necessary to couple the aerobic oxidation of some substance (usually pyruvic acid) to the oxidative phosphorylation which results in the biologically usable phosphate bond of ATP (adenosine triphosphate). But, highly revelant to our general argument here, the single units of the mitochondria cannot carry out this coupling. “Coupling requires a group of enzymes and factors other than those of the electron transport chain.” That is, a complex but organized system is necessary to carry out the transduc­tion, so absolutely basic to all living things, of unavailable energy to a biologically usable form.

Concerning the biochemical role of mitochondria the authors of the paper just cited say “We do not know all the answers yet, but we know most of the ques­tions, and we can ask them in great detail.” When this is the case, as the history of science shows, the battle is much more than half won.

The Emerging Unity

There is a primary reason why I have been discussing the trend of science toward the stage at which it can successfully cope with organized complexity. For as science moves into this stage, and doubtless partly just because it is now powerful enough to treat the multiple interconnection between various scientific aspects of phenomena, the boundaries between the various classical disciplines of science are tending to disappear.

Indeed, unless I wholly misjudge the situation, progress has proceeded so far in many branches of learning that a new intellectual unity is beginning to be apparent. I can give evidence only from the field with which I have some familiarity – science; and can only express the hope that what is happening there can happen, or is happening, or will happen, in other areas.

The way in which the improved understanding between previously separated disciplines is being accomplished can perhaps be roughly indicated by a metaphor. Suppose that various groups of men were distributed at different points on the surface of the earth, near enough to each other so that they could shout back and forth messages of encouragement and information and discovery. (When the Royal Society was founded in England in 1660 it included architects, astronomers, political economists, divines, anatomists, physicists, etc. They met weekly, and such were the then circumstances that, after their formal meetings, they could effectively “withdraw for mutual converse.”)

Then suppose that all these thinkers, in whatever fields, start digging down through layers of ignorance, each going deeper and deeper in his penetration of the previously unknown. By the word thinkers I do not imply pure mental activity. These persons will combine research, using whatever tools, with all methods of analysis – always being stimulated by curiosity and imagination, always inspired by the creative urge, always finding beauty in the revelation of new order in old confusion, always sustained by faith in the reasonableness of nature and the discoverability of knowledge.

As these persons dig deeper and deeper, each in his own ditch so to speak, each finds it necessary to develop aids, verbal and mental, which are special to his task. This makes it more and more difficult for the thinker in one ditch to communicate effectively with the thinker in any other ditch – even one near by. And as the ditches become deeper and deeper it becomes progressively harder for one thinker to shout up out of his deep crevice with hope that his queer and special sounds will intelligibly reach other thinkers, each one of them equally deep in his own private crevice.

Each thinker sadly observes ”I am becoming more and more isolated. What seems so important and lovely to me is gradually being considered, by all others, as more and more remote, more and more special.”

But it is possible that, as these individual thinkers dig down deeper and deeper, they come to fissures running out in various directions. And then a tunnel opens up which connects so effectively with some other ditch – or with several – that he begins again to hear the remarks of other thinkers. And it is conceivable that a thinker ultimately finds himself penetrating down into some large subterranean open space – some really mammoth cave – with chambers radiating out in all directions. And at this moment he finds himself again in free communication with all his fellows; finds that, at a deep enough level, they are not isolated, are not working at disconnected topics, but rather are all back together discussing common interests. Each, to be sure, brings the insight of his special experience; but he brings it to bear on a common task.

Three hundred years ago, at the time of the founding of the Royal Society in England, we were all up on the surface, visible and audible to each other.

Then specialities began to develop, and men had to dig deep. For a century or two, the parts of science penetrated into the secrets of nature, and in the process they became more and more specialized, more and more isolated.

But this trend is now reversed. In the great imaginative period of physics during the nineteen twenties and thirties, the penetration down to fundamental levels was so successful and deep that it revealed delicate details of the inner construction of atoms, and furnished theoretical explanations for the forces which bind one atom to others when they join to form molecules, and for the bonds that must be broken when one atom or group of atoms separates from a given molecule, either to join on to another or to exist separately. But if you look up “chemistry” in the dictionary, you are told that this is the branch of science which “treats the constitution of substances and the transformations which they undergo “; and this is precisely what the newer physics makes possible. In other words, about thirty-five years ago, physics and chemistry penetrated deeply enough so that they broke out into a common chamber, and the basic distinction between physics and chemistry disappeared.

Although each branch of the physical sciences does continue to have, chiefly at more applied levels, its own skills and procedures, the fact remains that there has been emerging, over the last half century, a great and closely interrelated body of knowledge which can be called simply “physical science.” And the chemist, the physicist, the geologist, the meteorologist, the astronomer ….are simply members of sub-committees of a great unified group. The various members apply their methods to different sorts of problems, just as, in fact, physicists themselves have always done. The basic distinctions have really disappeared.

This is perhaps not so surprising – for after all matter is matter, and it should not set researchers apart in isolated categories just because one studies a bit of magnetized iron, another some acid in liquid form, another a piece of rock, another an ice crystal in a rain cloud, and still another a star.

This newly discovered (or really newly rediscovered) unity of all physical science is, however, only the less exciting part of the total story. We have been accustomed to use the phrases “dead matter” and “living matter “; and it used to seem proper – indeed it really seemed necessary – to assume that living matter was essentially different from dead matter. Living matter contained some mysterious con­stituent that one called “the spark of life,” or ” elan vital,” or for which one used some other equally vague nomenclature.

We all remember the embarrassment of the older elementary texts on biology when they tried to define life. Any characteristic – mobility, growth, ability to reproduce, etc. – which was tentatively adopted as serving to discriminate the living from the non-living, turned out to be ineffective, since obviously “dead” matter exhibited, at times, all these same characteristics. But this did not really weaken anyone’s conviction that there was a basic distinction, whether or not it had been discovered and described.

The events of, roughly, the past thirty years have, however, forced a quite new attitude toward this matter of the distinction between dead matter and living matter.

Two closely interrelated matters have been of chief importance in bringing about the new view. First, there has been the steadily and impressively mounting evidence that any well-defined phenomenon of living matter can be investigated, analyzed, and explained by using precisely the same concepts and experimental procedures which work in the case of dead matter. The details of intermediary metabolism, the energy cycles within the cell, the subtle and complicated mechanism of immunology, the molecular explanation of diseases such as sickle cell anemia and even of certain mental disorders, and – as a tremendous climax – the exquisite details of biochemical genetics, with molecular and indeed atomic explanations for the processes of inheritance – successes such as these have made it seem more and more probable that explanation of this type – biochemical and in the last analysis molecular, atomic, and subatomic – will uninterruptedly keep on having one success after another in analyzing vital phenomena.

This is of course not to say that everything has already been made clear. But rather than talking about the “mysteries” of biological processes, science now ought really to speak only of questions as yet unanswered.

I want to emphasize, as clearly as I can, one point. I hove not at all said that there may not be something essentially different about a man – some character­istic which is not shared, to any extent or degree, by non-living matter. Personally I am convinced (by faith, not by logic) that there is such a difference. What I have said is that there is no difference as the two are viewed by, or will ever be viewed by, science. Any scientifically meaningful question can eventually be answered by scientific techniques, whether that question is applied to dead or living matter. And the whole framework of technique and mental procedure is the same in the two instances.

At the same time that biology is, so to speak, becoming more physical, the physical sciences, in their studies of fats, starches, glycogens, nucleic acids, and proteins (to go up the scale of chemical complexity) are coming closer and closer to the concept – even potentially the act – of the spontaneous generation of a living organism. That is to say, the physical sciences are becoming more biological. As a great biologist, George Waid, has said “To make an organism demands the right substances in the right proportions and in the right arrangements.” This admit­tedly is a very large order; but this is the statement of a problem rather than the description of a mystery.

A second main contribution to the new view of the relationship between living and non-living matter is found in the dramatic fact that science has produced the prize exhibit!

It has produced a pure, indeed crystalline and stable substance, as inert as any chemical powder that was ever put in a bottle on the shelf, which will sit there in the bottle, deader than a dead duck for as many years or centuries as you care to wait; but this same substance, when put into the proper environment, is alive! It reproduces its kind (according to genetic laws now understood), it “feeds” off its environment, it destroys its enemies – and then it may well lapse back into its “dead” phase, from which, however, it can be brought back to the living phase not nine times, but as many times as you please.

I am, of course, talking about viruses. Each is composed of a core of one chemical substance, surrounded by a sort of overcoat of another chemical substance. Scientists have even taken the overcoats off and put them back on – without altering the fact that this entity is before and after this operation both alive and dead. They have swapped overcoats, and altered certain properties, but still retaining the strange capacity to be alive at times and dead at times.

With all of physical science closing in on one side, with biological science closing in on the other, and with an example of matter both dead and alive sitting straddled across the boundary line, it should be reasonably obvious that the old classical distinctions between the biological and the physical sciences are fast disappearing. It is becoming less and less important to emphasize the labels of the orthodox divisions of the last two or three centuries, and is becoming more and more necessary that we think of a great massive unified body of knowledge which should be called simply science – natural philosophy, to use the fine old phrase, in the sense of the analysis of the whole of nature, living or dead.

The effective joining up of the physical and the biological sciences received a great impetus with the development of the body of knowledge now usually referred to as “molecular biology.” I believe this kind of terminology was first formally used when Dr. William T. Astbury was, in 1945, made a Professor of Biomolecular Structure at the University of Leeds; but now there are several outstanding centers for molecular biology – at University College, London, and at Massachusetts Institute of Technology, for example.

Within recent years the brilliant work of Professor Linus Pauling has given rise to the related term “molecular disease.” Professor Pauling has very recently added, to his work on sickle-cell anemia, a promising new molecular theory of anesthesia¹¹.

Another very convincing illustration of the emerging unity within science has been set forth¹² by my friend and colleague, Dr. Frank L. Horsfall, Jr., President and Director of the Sloan-Kettering Institute for Cancer Research. Dr. Horsfall’s exposition is centered around a beautiful photograph (see Figure II) of a single large crystal. He describes how this crystal would be viewed, described, and analyzed by a crystallographer, a chemist, a physical chemist, an electron micro­scopist, an immunologist, a virologist, and a geneticist. For the crystal, so lovely in its precise symmetry, is in fact composed of Type I poliomyelitis virus, a small number of the individual particles of which (perhaps 30) could induce a severe paralysis in man.

Fig. II. Crystal composed of Type I Poliomyelitis Virus.¹³

What is the study of this crystal? Is it physics, is it chemistry, is it biology, is it medicine? Obviously it is all of these. ”It is no more possible now to make a clear distinction among cytologists, geneticists, immunologists, or virologists than it is among chemists, physical chemists, and physicists…. The accumulation of seemingly unrelated technical details that has plagued and often discouraged the student of the life science is beginning to aggregate in a meaningful way…. Biology, like chemistry, is in a position to discard many of its descriptive shackles. The unifyihg principles that emerged from knowlege of the structure of the atom, which so changed the ideas in the physical sciences, now have their counterparts in new knowledge of the structure of the gene, which is, of course, the elementary basis for the continuity of life.”

From the examples just briefly cited one can identify some of the factors which, over the last half century and at an accelerated pace over the last quarter century, have been cooperating to assist the emergence of the unity that is now discernible. To list only the labels for the problems, the techniques, and the ideas that have been critically useful, and starting with the theories which made possible the union of physics and chemistry we have: classical and quantum theories of atomic structure, cybernetics, information theory, electronic computers, translation theory, protein structure, and (perhaps most critically important of all) biochemical genetics, and the structure and role of DNA.

It must not be assumed that all biologists welcome the merging with all the rest of science of what they view, with professional pride, to be “their field.” My friend, Professor Barry Commoner, a most able plant physiologist, has written an article In Defense of Biology¹⁴ in which he points out that certain of the traditional problems of biology – differentiation and its genetic control, for example­ still resist the successful invasion of chemistry and physics; and he fears that emphasis upon the most modern and most physical techniques (“semiconductor theory, radio isotopes and information theory”) will lead to “circumstances which preclude a close contact with taxonomy, evolution and morphogenesis.”

Professor Commoner is himself so able and successful a virologist and biochemist that perhaps his biological conscience leads him to have romantic moments of subconscious regret for the good old days of natural history; but his basic worry seems to be that important parts of biology remain isolated from the new union. Thus he opposes a partial unity, rather than opposing unity itself. He says that he believes “that the proper correlation of physics and biology requires that the integrity of both sciences be maintained in the collaboration process.” I would reply that in the most perfect and complete human marriages the integrity of both the husband and the wife unquestionably is maintained. And, indeed, Pro­fessor Commoner himself, in the concluding portion of his valuable paper, calls for “a true alliance between real sciences rather than the creation of rootless hybrids.”

What Must We Do?

To summarize the argument up to this point, I have tried to indicate that science is, by virtue of its new capacity to deal with organized complexity, breaking down the old barriers between classical fields and is connecting them all up in a closely knit network of significant interconnection. Moreover, this involves just the sort of problems and of techniques which will enable science to move forward, over a still wider front, in an attack on individual behavioral problems, and ultimately to those interconnected behavioral problems which constitute the subject matter of the social sciences.

At the same time it has become clear that science, although uniquely successful, shares many inner properties with other fields of human activity, including the humanities and the creative arts. As long as anyone really believe that science succeeded because of absolute precision complete objectivity, total agreement, impeccable and all-powerful logic, and a mechanical inevitability – for that time no one could realistically hope that science could be absorbed into all the rest of life. There have been horrid – and ridiculously false – notions around that scientists are exclusively preoccupied with perfect precision, with the reduction of all reality to numbers correct to eleven decimal places, with the suppression of all imaginative elements in our thinking, with a scornful dismissal of the value of intuition, with cold and unassailable logic, with rigorous “proof” and objective “fact”: whereas the poet, the artist, and the theologian are concerned with inspiration and revelation, and imagination, and faith. I believe these views of science and of scientific activity to be fundamentally incorrect.

We now have major reasons for hoping that the unity which is visibly emerging within science can, in fact, enlarge to include other fields and to enrich all the intercontacts.

Is there anything that we should do about this, other than passively observe the development? I think there are two things that require attention. Time will permit these to be mentioned briefly; but if I have at all succeeded up to this point, there should not be need for detailed argument.

First, and for the most basic intellectual and aesthetic reasons, scientists must be more active and more successful in interpreting the essential nature of science to the general public. There are many other persuasive arguments¹⁵ in favor of this interpretation; but I am here concerned only with the necessity of re-integrating the whole of men’s intellectual, artistic, and moral lives. The time has arrived, I believe, when material is at hand to bridge the gap so clearly described by Sir Charles P. Snow in his “Two Cultures.” I do not think mankind can happily or stably exist in a continuing state of intellectual schizophrenia; and I think a remedy for this is now coming to hand.

Second – and I must devote more space to this final point, for it has not been, as far as I know, well recognized – we must substantially reform educational pro­cedures to conform to the possibilities of the new unity; and in particular, we must change the structure of universities.

Universities still preserve many of the features of organization that were discernible in the University of Paris in the twelfth century. There are easily recognizable remnants of the regulations, set down by Gregory IX in 1231, for three “superior” faculties of theology, law, and medicine, and one “inferior” one of arts. There has, of course, been much evolution; but it is my impression that the organization of universities is not today very different from the one which was common a century – or even two centuries – ago. We still have rigidly organized departments in all the classic and orthodox subjects, each with a stoutly defended and tightly controlled budget – often each with a specified number of formally approved tenure positions.

At least partly for that reason it is always troublesome, usually difficult, and often impossible to furnish a favorable setting – one of honor and support – for activities which do not fall into the old classical hierarchies.

To be sure, a very few hybrid subjects have developed to the point that, at least in some institutions, they too have been given departmental status. This has happened in many places with biochemistry, in a few with geophysics, in still fewer with biophysics or meteorology. But generally speaking, universities have failed to recognize, at least in their formal structure, what is happening to know­ledge. They now fail to recognize the new emerging unity.

This takes on really ludicrous aspects at times. A very great university in the United States, attempting the minor and very partial goal of recognizing the essential oneness of botany and zoology, went down to defeat because of argument as to whether a microbiologist was to enter the combination through the portal of botany or zoology.

Suppose that a university wishes to recognize the very significant growing interrelation between economics and mathematics (this priesthood has a name, econometrics, but the aspirants have not as yet been frocked). The head of the mathematics department thinks this is a fine idea (provided of course that the chap is not too much of an economist), but he is jolly well not going to use up any of the precious budget of his department for what is called a joint appointment, but what he thinks of as a disjointed appointment. The chairman of the department of economics – but need I continue?

At times administrations invent new” Institutes,” which both are and are not a part of the university. In many cases, these Institutes have both a remote and an artificial connection with the university itself. And in the selection of even their key personnel they are often quite outside the stream of good academic practice.

I am well aware of the fact that so-called “inter-disciplinary” activities are often scorned as being too weak, or too curious, to find a congenial and appreciated home in either of the component disciplines. But have you ever tried to raise roses in the gravel path between two well-fertilized, well-cultivated, and well­ watered beds?

Can additional and new flexibility not be built into the structure of our modern universities, which will enable them, with no sacrifice of classical virtues, to adjust more effectively to the changing pattern of greatly increasing new interrelationship between all fields of learning and research? Can the many interests arising between two or three or even five older disciplines, rather than neatly inside one, not be furnished a more favorable climate?

I read, in the article in the Encyclopaedia Britannica, that “the early univer­sities rose in response to new wants.” I suggest that again we have new wants, and that some fresh arising is in order.

The new unity which is emerging within science and the presentday under­standing of both the power and the limitations of scientific method combine to furnish a basis for the effective absorption of science into the whole of our culture. The citizens of the world must be given an opportunity to understand the true nature of science; and universities must readjust educational procedure so that the oncoming generations take full advantage of this wonderful new opportunity for a richer life for all.

1. Dr. Charles E. Goshen, Sat. Review, February, 1960.
2. American Scientist, Autumn, 1948
3. Proceedings of the American Philosophical Society, October 17, 1960, and American Scien­tist, March, 1961.
4. See Personal Knowledge, by Michael Polanyi, University of Chicago Press, 1958.
5. Science and Information Theory, by Leon Brillouin, Academic Press, New York, 1956.
6. Can We Increase our Entropy? H. S. Seifert, American Scientist, June, 1961, p. 124a.
7. Sanger, etc., 1955.
8. Stein and Moore, 1960.
9. Shram, Fraenkel-Conrat, Stanley, etc., late 1960.
10. D. E. Green and Y. Hatefy, The Mitochondria and Biochemical Machines, Science, 6 January, 1961.
11. Molecular Theory of General Anesthesia, by L. Pauling, Science, 7 July, 1961, p. 15.
12. On The Unity of the Sciences, Science, 7 April, 1961, p. 1059.
13. Reproduced by permission from the Biochemical-Biophysical Acta, 28 (1958), pp. 241-246. Article by Steere and Schaffer.
14. Science, 2 June, 1961, p. 1745.
15. See Science and People (Science, Dec. 30, 1955); Science and the Citizen (Science, Dec. 13, 1957); Why Science is Important (Chemical Engineering News, Feb. 13, 1961) by W. Weaver.