THE NATURE OF SCIENCE

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The history of modern science began with the Renaissance. It developed slowly at first, then faster and ever faster, until it now threatens to dominate our civilization. The general acceptance of the validity of science is a very recent phenomenon. As late as 1880, Huxley complained that "no reply to a troublesome argument tells so well as calling its author a 'mere scientific specialist."' Fifty years later, Belloc complained that "a thing having been said to be established scientifically, there is no questioning of it." Today the attitude of the public is even more "advanced" (to use a dubious adjective). There are many who assume that the powers of science are unlimited, and some who refuse to believe a scientist who says that such and such a thing in his field is impossible.

             All of these attitudes reflect a widespread misunderstanding of the nature of science and, consequently, of its limitations as well as its capacities. Scientists are well aware of this confusion as, indeed, are all men with a good liberal education. But these men seldom discuss the matter in public, and when they do, they rarely reach any considerable audience. 

In the past, this reticence was understandable and perhaps even commendable. Scientists in general are not very articulate; they work in comparative seclusion and they do not cultivate the art of persuasion. But now a new era has emerged, and reticence is no longer a virtue. 

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Knowledge has been accumulating at an ever increasing rate, and knowledge, once it is available, can be used for evil as well as for good. It was inevitable that a day would come when the expanding body of knowledge would sweep across the danger level. That day, as you know, has come – and passed. Knowledge is already available by means of which men could wreck the civilization of the world –and the growth of knowledge continues faster than ever before. 

It is imperative, in our day, that the applications of knowledge be controlled, and controlled not in one nation alone but throughout the world. This problem is the central problem of our time. A wise solution, enforced, will be the greatest landmark in the history of the human race. If no solution is found, there may be no more history. 

The discussion of this paramount problem and its solution should be carried on with a clear understanding of the nature of science and of its applications. Statesmen and citizens alike should use the same language and understand what it is they are saying. Otherwise, the beneficial applications of knowledge may be suppressed along with the dangerous applications, that is, the baby may be thrown out with the bath; or, what is even more important, science may be confused with the applications, and to use another well-worn metaphor, the goose may be killed which lays the golden eggs. 

It is for this reason that the scientists are beginning to talk more freely than hitherto. They speak rather haltingly, to be sure, and somewhat diffidently, but they are driven by a sense of urgency. The subject must be clarified, and those who actually practice the discipline should be able to speak with some authority. What they have to

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say is not entirely new. A few men, including an occasional scientist, have explained the subject fairly well. But others have written nonsense, and the people, if they can, are left painfully to distinguish the good from the bad. 

So the scientists are beginning to talk. They will not all say the same things, they will not necessarily agree on details, but if a sufficient number raise their voices, the essential features of the discipline will emerge rather clearly. This clarification of the problem which overshadows our civilization is the first duty of the scientists. The solution of the problem, and its enforcement, are the responsibility of all men–including the scientists, but only in their position as human beings, not as specialists. 

For myself, I speak as a student of Astronomy, the type specimen of pure science. It is the oldest of, the special disciplines, and it is called the mother of them all. The first notions of law and order in the universe were found in the heavens. When the same ideas were dragged down from the skies to the earth, Physics was born, and then, one by one, the other disciplines followed. But all of the brood were reared in the midst of human society, and all were exposed to the contamination of human desires. The old mother still remained remote and serene, the purest of them all. It is true that certain practical applications of astronomy were devised – time keeping, navigation, and geography – but these specialties have long since been reduced to routine techniques, and removed from the body of the discipline. 

It was not until recently, with the development of spectrum analysis, that this isolation was invaded. Today we look on stars and nebulae as so many celestial laboratories in which atoms can be studied under conditions of 

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temperature and density that far transcend the utmost limits of terrestrial equipment. In the same spirit, the exploration of space may be described as the study of matter and radiation on the grand scale, as distinguished from small-scale studies on the earth. Physics and Astronomy are merging. The first born has come of age, and, indeed, has become head of the family. 

There is a unity in science, connecting all its various fields. Men attempt to understand the universe, and they will follow clues which excite their curiosity wherever the clues may lead. 

But admitting these interrelations, astronomy may still be regarded as the purest of the special disciplines, the farthest removed from practical problems of daily life, and within this field we can most readily identify the essential features of science in general. 

These features are not mentioned in the dictionaries. There you will find a wide range of definitions of science, and they emphasize the confusion in the language of general discourse. No adequate definition of the word has ever been formulated. The remark of the astronomer is perhaps as good as any of the attempts: "equipped with his five senses, man explores the universe around him and calls the adventure science." It is science in this sense that I propose to discuss – the acquisition of objective knowledge concerning the structure and behavior of the physical universe. 

Let me begin with an attempt to emphasize the distinction between science and values, a distinction which is evident in a comparison, for instance, of the laws of motion and the canons of art. The realm of science is the public domain of positive knowledge. The world of 

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values is the private domain of personal convictions. These two realms, together, form the universe in which we spend our lives; they do not overlap. 

Positive, objective knowledge is public property. It can be transmitted directly from one person to another, it can be pooled, and it can be passed on from one generation to the next. Consequently, knowledge accumulates through the ages, each generation adding its contribution. 

Values are quite different. By values, I mean the standards by which we judge the significance of life. The meaning of good and evil, of joy and sorrow, of beauty, justice, success - all these are purely private convictions, and they constitute our store of wisdom. They are peculiar to the individual, and no methods exist by which universal agreement can be obtained. Therefore, wisdom cannot be readily transmitted from person to person, and there is no great accumulation through the ages. Each man starts from scratch and acquires his own wisdom from his own experience. About all that can be done in the way of communication is to expose others to vicarious experience in the hope of a favorable response. 

The distinction between knowledge and wisdom is fully recognized in our time but it was not always so. Men wanted to explore the universe in all its aspects. The attempts began long ago. There was much fumbling; there were many false leads and occasional breath-taking achievements. Eventually it was realized that only one aspect –the world of positive knowledge – could be explored with confidence and, moreover, that success in the venture was measured in terms of disinterested curiosity. Special methods for handling the particular kind

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of subject matter were developed under the leadership of Galileo and Newton, and modern science was launched upon its extraordinary career. 

The requirement of disinterested curiosity was never formulated consciously. Yet it seems to have been the dominant motive in the work of all the "rear men of science. It has inspired the statement that the essential characteristic of science is the simple idea of attempting “to ascertain objective truth without regard to personal desires.” 

Men of science, like all other men, spend most of their lives in the larger world of values. There they play their roles as citizens and as human beings. But occasionally they slip out of the circle into another world that knows nothing of values. There they attempt to explore the universe as it is – not as it should be, but as it is. They may not always achieve complete detachment, yet that is their conscious aim. Driven by sheer curiosity, they seek to understand the world - not to control it, not to reform it, merely to understand it. This approach has been extraordinarily successful within a limited field - the field of science. There seems to be no competing attitude in the exploration of new fields of positive knowledge. 

The subject matter of science has been described as “judgments on which it is possible to obtain universal agreement.” These judgments do not concern individual events, which can be witnessed only by a few persons at most. They are the invariable association of events or properties which are known as the laws of science. Agreement is obtained by observation and experiment – a court of appeal to which men of all races and creeds must submit if they wish to survive. 

If anyone refuses to agree with a judgment, we ask him to go and test it for himself. If he still refuses to concur, we ignore his words and watch his actions. There is a story of Simon Newcomb which illustrates the point. A crank rushed into his office one day (Newcomb was Superintendent of the Nautical Almanac at the time) and announced belligerently that he did not believe in the law of gravity. Newcomb did not argue the matter; he merely invited the fellow to jump out of the window, and then watched to see what would happen. 

The laws of science are derived from, as well as tested by, observation and experiment, and especially from measurement. The measures can never be exact in the absolute sense, and this margin of error must be taken into account all interpretations of the data. The difficulty is met and overcome by the use of “probable errors,” a conception that is peculiar to science. At every stage of an investigation, the uncertainty of each measure and each combination of measures is carefully estimated, and expressed numerically. For instance, a particular measurement is repeated many times and the average of all the results is adopted as the most probable value. Then, from an analysis of the differences in the individual measures, it is possible to say that the error in the adopted mean value has an even chance of being less than, or greater than, a certain quantity. This quantity is called the “probable error.” 

The conception, as I said, is peculiar to science. It has no place in the world of values. Bertrand Russell has discussed the distinction in his best epigrammatic style. After remarking that subjective certainty is inversely proportional to objective certainty, that we are most certain of those judgments we cannot demonstrate, he reminds us that when a scientist has determined a quantity with

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unusual accuracy, he is the first to admit that he is likely to be wrong – sand he knows about how wrong he is likely to be. And Russell then asks the question, “Who ever heard a theologian preface his creed, or a politician conclude his speech with an estimate of the probable error of his opinion?”  These remarks emphasize the fact that science deals with probable knowledge and that the methods of science are adjusted to their proper subject matter; also, they call attention to the fact that a scientist never attempts to speak with personal authority in his field, but merely demonstrates conclusions, which anyone (in principle) may verify if he cares to take the trouble.

The laws which are the subject matter of science take many forms, ranging from simple definitions – such as the invariable association of properties which identify, for example, the element of iron - to very complicated associations of events such as the law of falling bodies.  However, they are all quite general statements, and they apply to numerous actual or possible cases.  The term “invariable” represents an assumption. If an association is observed to hold in many cases of a particular kind, it is assumed that the same association will be found in the next case that will be observed in the future. In carefully controlled experiments the number of test cases may be reduced to a minimum, and occasionally to a single critical trial. The results are confidently stated as laws, merely because they fit into the general pattern of knowledge within the particular field which is based upon innumerable data. Nevertheless, they represent probabilities only. The sun has risen each day in the past. It will probably rise tomorrow, as everyone agrees. 

The nature of the subject matter defines the realm of 

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science. The necessity for general agreement restricts the explorations to the field of positive knowledge, and this knowledge concerns not ultimate reality, but phenomena only. 

The methods of science may be described as the discovery of laws, the explanation of laws by theories, and the testing of theories by new observations. A good analogy is that of the jigsaw puzzle, for which the laws are the individual pieces, the theories local patterns suggested by a few pieces, and the tests the completion of these patterns with pieces previously unconsidered. Following this analogy, just as local theories are built up from pieces, so general theories are built up from local theories. The scientist likes to fancy, although he cannot demonstrate, that sufficient pieces may be assembled to indicate eventually the entire pattern of the puzzle, and thus to reveal the structure and behavior of the physical universe as it appears to man. At any rate, he has found methods which, when restricted to their proper fields, have been constantly advancing in the desired direction, He is bound to continue the explorations unless or until he runs into a blank wall of self-contradictions. 

The laws of science are almost innumerable, but they fall into relatively few general types. The discovery of a new type is a notable event in the progress of science, but once the type is established, lesser men can add individual examples at a rate measured largely by patience and industry. 

The laws derived from observation and experiment are discoveries in the true sense of that word, and a new type generally opens to investigation a previously unexplored field of knowledge. Nevertheless, the laws are the subject matter of science; they are not the finished

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composition. It is theory that integrates the laws, and the making of successful theories is a creative activity whose operation is difficult to understand. 

Science is pragmatic. Theories are judged by a single criterion – do they work? Their origin does not matter. They may be inferred, or invented, or dreamed. Until they are tested they are merely working hypotheses; in other words, they are plausible interpretations of data already available. Ingenious men can and do invent many theories to account for a given set of data. 

Historians play this game endlessly. Froude remarked eighty years ago that “facts of history are like the letters of the alphabet - you may make them spell what you like.” But scientists do not enjoy the same freedom. Each theory, while accounting for the laws already known, predicts new, hitherto unobserved laws. Therefore, the theories of scientists, unlike those of the historian, can be tested by observation and experiment in new fields. And the tests are made. The validity of theories is measured, not by their origins but by the verification of predictions. This procedure is the very essence of the scientific method, and serves to control the powerful but dangerous instrument of inductive reasoning. When theories cannot be tested, their appeal is largely aesthetic. 

In these circumstances, the making of theories is a measure of men. A few seem to have a flair for inventing the right kind of theories - the kind that survive the tests, at least for a time. But the majority of men, however ingenious, are handicapped by the inevitable tests. 

This feature of theory-making is especially prevalent among theories on the higher levels – among the great generalizations which correlate previously isolated theories and furnish the pattern for very large tracts of 

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knowledge. Universal gravitation waited for a Newton; relativity, for an Einstein. 

But even the best of theories are accepted as temporary working hypotheses. The laws of science are relatively permanent, but the theories, which attempt to explain the laws, come and go. They serve their days of usefulness and then they fade away. We know only a little part of the universe, and our knowledge is constantly expanding. We predict what to expect in the new regions, from the information we already possess. When the actual data are found and reported, the theories are always reviewed in the light of the new information. Inconsistencies are pounced upon eagerly because they often point the way to new and broader conceptions. Current theories are discarded, or they are revised or merged into a wider generalization, and the event is welcomed as another step toward the ultimate goal. Such events occur frequently on the low levels of theory when, for instance, the first explorations are rapidly pushed out into newly opened fields. But on the top levels they are rare, as, for instance when Newtonian gravitation was absorbed into the deeper, more inclusive theory of relativity. 

The openings of new fields are exciting periods, and then the methods of science are rather clearly seen. It is like a campaign. Accumulating knowledge piles up at barrier beyond which lies unknown darkness, the land that challenges the explorer, where, he likes to imagine, almost anything is more than likely to happen. A day comes when a weak spot is found in the barrier often by chance.  Immediately, a breakthrough is engineered, hammered out by every means available. Once the break is made, explorations sweep forward like a flood spreading out until it is stopped by more distant 

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barriers. This first sweep is a reconnaissance of the field, guided by the general knowledge already at hand. Next comes the consolidation of the new country – the careful surveys, the accumulation of new laws, the review of old theories, and, perhaps, the formulation of new theories. Finally, when order is established, the territory is integrated into the main body of knowledge, and theory is reviewed on the high levels. 

In principle, the development of a new branch of science begins with observations and simple experiments. The results are reported in terms of measured quantities together with the estimated uncertainties of the measures. These data furnish a growing body of laws which represent the actual subject material. When a sufficient number of laws is assembled, the creation of theories beams. Various laws are grouped together as special cases of a general principle or theory. The work starts tentatively, guided perhaps by analogies in other fields and by a working hypothesis called the uniformity of nature. Most of the theories fail to meet the tests of predictions, but with the accumulating experience of trial and error, men begin to get the feel of the data. A confident, sure touch is developed, and the game becomes exciting. Theorizing on the higher levels follows much the same pattern, until finally the new branch is merged into the general body of science. 

These procedures are based on inductive reasoning. From a few scattered cases, we infer a general principle that should apply to all similar cases. The validity of induction has never been demonstrated. It remains as an unsolved problem of logic. Consequently, the theories of science, as well as the measurements, must be accepted on the basis of probabilities. When a theory collapses, an 

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attempt is made to replace it with a more probable theory, and, in this way, science proceeds as a series of successive approximations. 

When a sufficient body of high-level theories has been assembled, an entirely new chapter is opened. An attempt is made to derive from the theories a limited set of general principles whose implications cover the entire branch just as Euclid's axioms were once supposed to contain implicitly the whole of plane geometry. If such an attempt were ever successful, and the chosen set of principles did close and bound the field, that branch of science would be perfected and written off the programs of the explorers. For then the reasoning would be purely deductive, and the ramifications of the field could be confidently predicted without recourse to further observations. Science could then be taught as elementary geometry is taught. 

This pleasant speculation suggests the intimate relation between science and mathematics. They are not at all the same thing. Mathematics is not science, although it furnishes the scientist with some extremely powerful tools for the analysis of data and the handling of theories especially on the higher levels. But mathematics is akin to pure logic. It concerns relations between postulates. Russell, in another happy epigram, has said that the mathematician never knows whether what he is talking about is true, and wouldn't be interested if he did. Haldane once remarked that mathematics deals with “possible worlds,” that is, with logically consistent systems, and is not interested in any attribute except logical consistency. Following this lead, it might be said that mathematics furnishes us with a vast array of “possible universes,” and that science attempts to identify, among them, the actual universe that 

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we inhabit.  The acquisition of new knowledge is constantly reducing the list of possible universes which must contain our own. It is the task of theoretical, or mathematical, physics to keep us informed as to the minimum number, and to indicate critical tests by which the list may be still further reduced. 

A conspicuous example of this procedure is found in cosmology, a study which concerns the gross, large-scale features of the physical universe. The combined efforts of mathematical physicists and observers have reduced the array of possible universes to such a limited range that it is now possible to predict with confidence that the type of the actual universe will be identified within the foreseeable future, perhaps within the next decade. 

The mathematical physicists are constantly studying the general principles of nature, derived by induction, as though they were postulates which close and bound the fields of science. In the end, the set of postulates must be complete and must be logically consistent. The occasional recognition of inconsistencies has led to reinterpretations of large areas of knowledge, and even to such a major revolution in scientific thought as the theory of relativity. 

A set of postulates derived from observations will probably be incomplete; it is unlikely that we know as yet all of the fundamental principles of nature. Theoreticians attempt to measure these gaps in the sets of postulates by the degree to which the field closed and bounded by the postulates fails to coincide with the observable universe. It is possible that new fundamental principles may be found in this way, but their validity must always be checked by observation. 

This discussion of the nature of science began with the 

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simple observer, exploring the world about him, and has now wandered into the fringe of theory and mathematical abstractions. If it followed a natural course, it would linger for a while in that field, and then conclude with a dissertation on the philosophy of science. I do not propose to follow this course, but I shall tell you a fable concerning the philosophical aspects of scientific research, before passing on to a summary of the ground that has been covered.

The fable is Eddington's tale of the fisherman – Eddington calls him an ichthyologist – and it will take its place as a classic in the literature of science. An ichthyologist set out to study fish in the ocean. He spent his time dipping a net with two-inch meshes into the water and studying the fish he caught. He made two discoveries, namely all fish have gills and all fish are more than two inches long. These results represent empirical and a priori knowledge respectively. He could not predict the gills but he should have predicted the minimum length. In research, the fisherman's net is represented by the scientist's equipment - his tools, his sensory organs, and his brain which operates in certain patterns. A complete knowledge of this equipment, says Eddington, permits us to predict a large portion of the current body of knowledge - the a priori portion - without making a single experiment or observation. The remainder of the body of knowledge – the empirical portion – must be found by the explorers. 

Eddington then proceeds to discuss the two kinds of knowledge, and satisfies himself that all of the important and significant knowledge is a priori, that even the fundamental constants of nature, from the gravitational constant to the rate of expansion of the universe, can be 

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derived within the study.  The empirical knowledge, however curious and interesting, concerns mere trivial details in the scheme of things. 

The problem illustrated by the tale of the fisherman is the central problem in the philosophy of science and the current discussions are highly controversial. Eddington's interpretation represents a minority point of view, but it is presented with such brilliance and persuasive power that it commands respect, if not concurrence. 

The explorers are not deeply impressed by the controversy. They are pragmatists, and interpretations are useful only as long as they work, as long as they predict new phenomena and the predictions are verified. They know that in the past most of the really new fields have been opened by the explorers, using the methods of Galileo and Newton rather than the method of Plato. And they will continue their explorations on the assumption that, in the future as well as the past, new fields will be opened which cannot be predicted from the armchair. 

From the foregoing descriptions and comments, it is seen that science is necessarily restricted to one aspect of the universe - the objective world of phenomena. It deals with probable knowledge only, its methods are empirical, its philosophy is pragmatic. The scientist explores the world of phenomena by successive approximations. He works in an atmosphere of probabilities; he knows that his data are never precise, and that his theories must always be rested. It is quite natural that he tends to develop healthy skepticism, suspended judgment, and disciplined imagination. 

The world of pure values, that world which science cannot enter, has no concern whatsoever with probable knowledge. There finality – eternal, ultimate truth – is ear-

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nestly sought. And sometimes, through the strangely compelling experience of mystical insight, a man knows beyond the shadow of a doubt, that he has been in touch with a reality that lies behind mere phenomena. He himself is completely convinced, but he cannot communicate the certainty. It is a private revelation. He may be right, but unless we share his ecstasy we cannot know.