11) The history of electrical science offers striking examples just like those found in the lives of Priestley, Kelvin, and others.
According to Franklin’s report, Nollet, the most influential of the electrical scientists on the Continent in the mid-eighteenth century, “was left alone in his school, except for Mr. B__his pupil and direct disciple__. [Max Farrand(ed.), Benjamin Franklin`s Memoirs(Berkeley, Calif., 1949), pp.384__86]” Yet the more interesting fact is that entire schools endured their gradual isolation from professional science quite well. Consider, for example, the case of astrology, once a part of astronomy. Or consider the tenacious persistence, in the late eighteenth and early nineteenth centuries, of the formerly respected tradition of “(mystical)” chemistry. Discussions of this tradition may be found in Charles C. Gillispie’s “The Encyclopedie and the Jacobian Philosophy of Science ;A Study in Ideas and Consequences,” Critical Problems in the History of Science, ed. Marshall Clagett(Madison, Wis., 1959), pp.255__89; “The Formation of Lamarck`s Evolutionary Theory,” Archives internationales d`histoire des sciences, XXXVII(1956), 323__28.
12) The advances of the post-Franklin era include the following: the sensitivity of electroscopes was enormously improved, techniques for measuring electric charge became reliable and widely disseminated for the first time, the concept of electrical capacity was born, the relationship between capacity and the newly clarified concept of voltage was elucidated, and electrostatic force was quantified. All of this is treated in the following works: Roller and Roller, op.cit., pp.66__81; W.C. Walker, “The Detection and Estimation of Electric Charges in the Eighteenth Century,” Annals of Science, I (1936), 66__100; Edmund Hoppe, Geschichte der Elektrizität (Leipzig, 1884), Part I, chap.iii-iv.
III. The Nature of Normal Science
The Nature of Normal Science
What, then, is the nature of the more specialized and profound research permitted by a group’s acceptance of a single paradigm? If the paradigm represents research once fully accomplished, what problems does it leave for the unified group to solve? Such questions will seem still more urgent if we now take note of one respect in which the terms used so far may be misleading. In its established usage, a paradigm is an accepted model or pattern, and that aspect of its meaning has led me, for lack of a better word, to appropriate “paradigm” here. But it will soon become clear that the sense of “model” and “pattern” that permits this appropriation is not the usual one in defining a paradigm. In grammar, for example, “amo, amas, amat” is a paradigm because it displays the pattern used in forming the conjugations of many other Latin verbs, as when “laudo, laudas, laudat” is obtained. In this standard application, the paradigm functions by permitting the replication of examples, any one of which could in principle replace the paradigm. In science, on the other hand, a paradigm is rarely an object of replication. Rather, like a judgment determined by common law, it is an object to be further articulated and specified under new or more stringent conditions.
To see how that can be so, we must first recognize how greatly limited a paradigm can be, both in scope and in precision, at the time of its first appearance. A paradigm gains its status because it is more successful than its competitors in solving several problems that the group of specialists has come to feel are urgent. But being more successful does not mean being completely successful with a single problem, or notably successful with a great many.
The success of a paradigm__Aristotle’s interpretation of motion, Ptolemy’s calculation of planetary positions, Lavoisier’s use of the balance, or Maxwell’s mathematization of the electromagnetic field__is at the outset largely only a promise of success discoverable in examples that are still incomplete. Normal science is accomplished through the actualization of that promise, achieved by extending knowledge of the facts the paradigm presents as especially suggestive, by increasing the degree of agreement between those facts and the paradigm’s predictions, and by further articulating the paradigm itself.
In fact, those who are not practitioners of a mature science scarcely realize how much work of this sort of tidying-up a paradigm leaves to be done, nor how fascinating such activity can be in the doing. And these points need to be understood. Mopping-up work is what most scientists engage in throughout their lives. It is precisely this that constitutes what I here call normal science. Examined closely, whether historically or in a contemporary research laboratory, such activity appears to be an attempt to force nature into the preformed and relatively fixed box supplied by the paradigm. No part of the aim of normal science is to call forth new kinds of phenomena. Indeed, phenomena that will not fit into the box are often not seen at all. Scientists do not aim at the invention of new theories, either, and they are generally unwilling to accept those invented by other scientists.1) Rather, normal-scientific research is directed toward the articulation of those phenomena and theories that the paradigm already supplies.
Perhaps these are defects. The areas investigated by normal science are, of course, small. The activity discussed here is confined to an extremely restricted range. But these restrictions, derived from confidence in a paradigm, prove indispensable to the development of science. By concentrating attention on a small range of relatively profound problems, the paradigm compels scientists to explore some part of nature in a detail and depth that would otherwise have been unimaginable. And normal science has an internal mechanism that ensures the relaxation of the limits restricting research whenever the paradigm that induced those limits ceases to function effectively. At that point, scientists begin to behave differently, and the nature of their research problems changes. But so long as the paradigm fits well, the profession will solve problems its members could not even have imagined and would never have been able to tackle. And at least part of that achievement always proves to be permanent.
In order to make clearer what normal, or paradigm__based, research means, I shall now try to classify and describe the problems that in principle constitute normal science. For convenience, I shall postpone theoretical activity and begin with fact__gathering: that is, with the experiments and observations described in the specialized journals through which scientists inform their colleagues of the continuing results of their research. What aspects of nature do scientists ordinarily report on? What determines their choice? And since most scientific observation consumes much time, equipment, and expense, what motivates scientists to pursue that choice through to its conclusion?
I think there are only three normal foci in factual scientific inquiry, and these are not always or permanently distinct. The first is the class of facts that the paradigm has shown to be particularly revealing of the nature of things. By applying those facts to the solution of problems, the paradigm makes them worth determining both more accurately and in a wider variety of circumstances. In every age, significant factual measurements of this sort have been made in many fields. Examples include, in astronomy, the positions and magnitudes of stars, the periods of eclipsing binaries and the periods of planets; in physics, the specific gravities and compressibilities of substances, wavelengths and spectral intensities, electrical conductivity and contact potential; and in chemistry, composition and combining weights, the boiling points and acidity of solutions, structural formulas and optical activity. Attempts to determine such facts more accurately and more extensively are known to occupy a considerable part of the literature dealing with the experimental and observational sciences. Complex special apparatuses have been devised one after another for such purposes, and the invention, construction, and use of such apparatus have required talent of the highest order, a great deal of time, and considerable financial support. Synchrotrons and radio telescopes are only the most recent examples in the long list of instruments researchers will acquire when a paradigm convinces them that the facts they seek are important. From Tycho Brahe to E. O. Lawrence, these scientists gained great reputations not because they made some astonishing new discovery, but because they found methods of very great precision, reliability, and range of application needed to redetermine facts of a kind already known.
In fact, the second class of factual determination is a usual one, though on a smaller scale than the first, and is directed toward facts that are often of no great interest in themselves but can be directly compared with predictions from paradigm theory. As will soon be explained, when we turn from the experimental problems of normal science to the theoretical ones, there are not many areas in which a scientific theory can be directly compared with nature, especially when that theory is given in a distinctly mathematical form. There are only three such areas accessible to Einstein’s general theory of relativity.2) Moreover, even in fields where application is possible, it often requires theoretical and methodological approximations that seriously limit the expected agreement. What is needed is either to improve the agreement between theory and experiment, or, in any case, to find new areas in which such agreement can be demonstrated. The task of improving the agreement between theory and experiment, or at any rate of discovering new areas in which such agreement can be demonstrated, constantly challenges the skill and imagination of the experimenter and the observer. The special telescopes for demonstrating Copernicus’s prediction of annual parallax; the Atwood machine, first devised nearly a century after the Principia and the first to demonstrate Newton’s second law beyond dispute; Foucault’s apparatus, which showed that the speed of light is greater in air than in water; and the enormous scintillation counter designed to demonstrate the existence of the neutrino—these special devices, and many others like them, show the immense effort and ingenuity required to bring nature and theory into ever closer agreement.3) Such attempts to demonstrate agreement constitute a second form of regular experimental research, one that depends more clearly on the paradigm than the first. The existence of the paradigm sets the problem to be solved. Often the paradigm theory is directly implicated in the design of the apparatus capable of solving the problem. Without the Principia, for example, measurements using the Atwood machine would have had no meaning at all.
I take the third class of experiment and observation to encompass all the fact-gathering activity of normal science. It consists of empirical work carried out in order to articulate the paradigm theory, resolving some of its remaining ambiguities and permitting clues to the solution of problems that had previously been merely matters of interest. This third class proves to be the most important of the three, and explaining it requires further subdivision. In the more mathematical sciences, some experiments aimed at articulation proceed toward the determination of physical constants. Newton’s work taught, for example, that the force acting between two unit masses separated by a unit distance is the same for every kind of matter at every place in the universe. But his own problems could be solved without determining the magnitude of this attraction, the universal gravitational constant. And for a century after the appearance of the Principia, no one devised an apparatus capable of determining that constant. Cavendish’s famous measurement in the 1970s was not a definitive solution either. Because of its central position in physical theory, improving the value of the gravitational constant has ever since remained a goal persistently attacked by many outstanding experimenters.4) Other examples of sustained research of this sort would include measurements of the astronomical unit, Avogadro’s number, Joule’s coefficient, the electronic charge, and so on. Some of these refined attempts could not even have been conceived, and nothing could have been carried out, without a paradigm theory that defined the problem and guaranteed the existence of an invariant answer.
But attempts to articulate a paradigm are not confined to determining universal constants. Such efforts are also necessary, for example, in obtaining quantitative laws. Boyle’s law, which expresses the relation between the pressure and volume of a gas; Coulomb’s law for electrical attraction; and Joule’s relation, which connects the heat produced with electrical resistance and current, all belong to this category. It may perhaps not seem obvious that a paradigm is a prerequisite for the discovery of laws such as these. Often such laws are said to have been discovered by examining measurements undertaken for the sake of experiment itself, independent of theory. But history does not support so excessively Baconian a procedure. Boyle’s experiments could not be conceived until air had come to be recognized as an elastic fluid to which all the refined concepts of hydrostatics could be applied; if Boyle’s experiments had been imagined before then, their interpretation would have been mistaken, or else they could not have been explained at all.5) Coulomb’s success was due to his having constructed a special apparatus for measuring the force between point charges. The earlier designs that measured electrical force by using ordinary pan balances and the like ultimately depended on the assumption that the attraction between particles of electric fluid—the only force that could safely be taken as a simple function of distance—was the force by which each particle acted on the others at a distance.6) Joule’s experiments may also explain how quantitative laws emerge through paradigm articulation. Indeed, the relation between qualitative paradigms and quantitative laws is so general and so close that, since Galileo, such laws could often be guessed with the aid of the paradigm years before the apparatus required for experimental measurement had been devised.7)
Finally, there exists a third type of experiment whose aim is to articulate a paradigm.
Compared with the others, experiments of this sort are closer to exploratory work, and they become especially prominent in periods and in sciences that deal more with qualitative aspects of nature’s regularities than with quantitative ones. Often a paradigm developed for one group of phenomena becomes ambiguous in its application to other closely related phenomena. Then experiment becomes necessary in order to choose among alternative ways of applying that paradigm to a new area of interest. For example, the paradigmatic applications of caloric theory applied to heating and cooling by mixtures and by changes of state. But heat could also be released or absorbed in various other ways—by chemical combination, for instance, by friction, or by the compression or absorption of gases—and caloric theory might be made to account for each of these other phenomena. Or it might be that the specific heat of a gas changes as pressure changes. Various other explanations were also offered. Many experiments were performed in order to investigate these diverse possibilities and to distinguish among them.8) Once the phenomenon of heat generated by compression had been established, all subsequent experiments in that field became paradigm-dependent in this way. Given the phenomenon, how else could the experiment to reveal it have been chosen?
Let us now turn to the theoretical problems of normal science, which belong to classes almost exactly like those of experiment and observation. Part of regular theoretical research, though only a small part, consists simply in using an existing theory to predict factual information that has intrinsic value. The production of astronomical ephemerides, the calculation of lens indices, and the construction of radio-wave propagation curves belong to this kind of problem. Scientists, however, generally regard them as activities of little creativity, properly belonging to engineers or technicians.
At any period, such things do not appear often in the major scientific literature. Yet those journals contain a great many theoretical discussions of problems that, to the non-scientist, would appear almost identical. These papers are exercises in the skillful manipulation of an accepted theory, not because the predictions that result from them are intrinsically of great value, but because they can be dealt with directly by experiment. The purpose of such work is either to present a new application of the paradigm, or to increase the accuracy of an application already made.
The need for research of this type arises from the immense difficulties often encountered in developing points of contact between a theory and nature. These difficulties can be briefly illustrated by looking at the history of dynamics after Newton. By the early eighteenth century, the scientists who had found a paradigm in the Principia took the generality of its conclusions for granted, and they had ample reason to do so. Among the achievements known in the history of science, none had simultaneously increased both the range and the precision of scientific research so greatly. With respect to the heavens, Newton had mathematically derived Kepler’s laws of planetary motion and had explained some of the observations in which the moon failed to satisfy Kepler’s laws. With respect to the earth, Newton had mathematically derived several fragmentary observations concerning the pendulum and the tides.
By introducing additional, though arbitrary, assumptions, he was also able to derive Boyle’s law and an important relation for the speed of sound in air. Given the state of science at the time, the success of such demonstrations was extremely impressive. Yet despite belief in the generality of Newton’s laws, their applications were not numerous, and Newton developed few others. Moreover, compared with what a graduate student in physics today can accomplish with those same laws, Newton’s few applications were not even developed with precision. In the end, the Principia had been designed chiefly for application to problems of celestial mechanics. It was by no means clear how it should be applied to terrestrial problems, especially to motion under constraint. In any case, terrestrial problems had already been attacked with considerable success by a very different technique, one originally developed by Galileo and Huyghens and extended on the Continent during the eighteenth century by the Bernoullis, d’Alembert, and many others.
Perhaps their techniques and those of the “Principia” might have turned out to be special cases of a more general formulation, but for some time no one properly found the way.9) Let us now confine our attention for a moment to the problem of accuracy. We have already dealt with its empirical aspect. In order to obtain the special data required by concrete applications of the Newtonian paradigm, unusual apparatuses—devices such as the Cavendish apparatus, Atwood’s machine, or improved telescopes—were needed. On the side of theory as well, similar difficulties accompanied the achievement of agreement. In applying his laws to the pendulum, Newton had, for example, to treat the bob as a mass point (having mass but no size) in order to assign a specific value to the length of the pendulum. Most of his theorems, apart from a few hypothetical and preliminary exceptions, also ignored the effects of air resistance. These were sound physical approximations. Nevertheless, as approximations, they limited the agreement to be expected between Newton’s predictions and actual experiments. In applying Newton’s theory to the heavens, this difficulty appears all the more conspicuously. Simple quantitative telescopic observations show that the planets do not exactly satisfy Kepler’s laws, and Newton’s theory indicates that they should not. In order to derive those laws, Newton had to ignore all actions due to attraction except those between each planet and the sun. Since the planets also attract one another, however, at best only approximate agreement could be expected between the theory as applied and the results of telescopic observation.10)
Even such agreement, of course, was quite satisfying to those who achieved it.
Except for a few terrestrial problems, no theory could do nearly so well. Even such agreement, of course, was quite satisfying to those who achieved it. Except for a few terrestrial problems, no theory could do nearly so well. None of those who doubted the validity of Newton’s work did so because the agreement between experiment and observation had limits. Nevertheless, these limits in agreement left Newton’s successors many attractive theoretical problems. Theoretical ingenuity was required, for example, in order to deal with the motion of two or more bodies attracting one another simultaneously, and in order to consider stability in perturbed orbits. Throughout the eighteenth and early nineteenth centuries, problems of this sort captivated Europe’s finest mathematicians. Euler, Lagrange, Laplace, and Gauss all produced their most brilliant achievements on problems intended to improve the agreement between the Newtonian paradigm and observations of the celestial world. Most of these figures were at the same time engaged in developing the mathematics required for applications that neither Newton nor any contemporary Continental school of mechanics had even attempted. For example, they brought into being an enormous literature and several powerful mathematical techniques concerning hydrodynamics and the problem of the vibrating string. These problems of application explain what the most brilliant and most painstaking scientific research of the eighteenth century was. Other examples are found when one examines post-paradigm periods, such as thermodynamics, or the development of other fields whose fundamental laws belonged to a fully quantitative science. At least in the more mathematical sciences, almost all theoretical research becomes work of this type.
That does not mean, however, that all of it is of that type. Even in the mathematical sciences, the articulation of a paradigm is bound to be accompanied by theoretical problems. Such problems are especially numerous in periods when scientific development is chiefly qualitative in character. In both the more quantitative and the more qualitative sciences, some problems aim at the articulation of a paradigm simply through reformulation. The “Principia,” for example, was not easy to apply in every case, partly because of the unavoidable immaturity of a first venture, and partly because much of its meaning was only implicit in application. In any case, in many applications to the terrestrial world, apparently unrelated Continental techniques seemed far more powerful. Thus, from Euler and Lagrange in the eighteenth century to Hamilton, Jacobi, and Hertz in the nineteenth, Europe’s most eminent mathematical physicists continually strove to recast mechanical theory into forms that were equivalent yet more satisfactory logically and aesthetically. In other words, they wished to express the explicit and implicit lessons of the “Principia” and of Continental mechanics in a logically more orderly form, and such a revision would at once display greater unity and better agreement in its application to newly explored problems of mechanics.11) Work of this kind, reformulating a paradigm, has gone on constantly in every field of science, but most of it has brought about changes of paradigm far more distinct than the reformulations of the “Principia” mentioned above. Such changes arise from the results of empirical research described earlier as aiming at the articulation of paradigms. Yet it was arbitrary to classify that kind of research as empirical. More than any other type of normal science, the problem of paradigm refinement is at once theoretical and experimental. The examples given above will serve the same purpose here. Before Coulomb could construct his apparatus and make measurements with it, he had to invoke electrical theory to decide how that apparatus should be built. The conclusion resulting from his measurements was a refinement of that theory. Or again, those who devised experiments capable of distinguishing among the various theories of the heat generated by compression were generally the very people who had put forward the several interpretations being compared. They were dealing with both fact and theory, and the outcome of their work was not simply new information but a more precise paradigm, obtained by eliminating the ambiguities contained in the original form with which they had begun their research. In many sciences, regular research activity takes on largely this character.