In my view, these three types of problems—the determination of significant fact, the matching of facts with theory, and the articulation of theory—seem to occupy almost the whole literature of both experimental and theoretical normal science. Yet they do not occupy the scientific literature entirely. It also contains nonordinary, extraordinary problems, and it may be said that what makes scientific activity as a whole so valuable is precisely the solving of such extraordinary problems. But extraordinary problems are not to be had simply for the asking. They arise only on special occasions prepared by the progress of normal science. Therefore, even when the problems are handled by the most outstanding scientists, the overwhelming majority of them ordinarily fall into one of the three categories summarized above. Research under a paradigm cannot be conducted in any other way, and to abandon that paradigm is to cease practicing the science that it defines. We shall soon see that such abandonment of paradigms does in fact occur. They become the very pivots that lead scientific revolutions. But before beginning the examination of such revolutions, it is necessary to survey the overall view of the normal-scientific research activity that prepares the way to them.
“Notes”
1) Bernard Barber, “Resistance by Scientists to Scientific Discovery,” Science, CXXXIV(1961), 596__602.
2) The only long-standing point of verification that is still widely recognized is the precession of Mercury’s perihelion. The red shift in the spectra of light from distant stars can be derived from considerations more fundamental than general relativity, and it seems that the same argument may be possible for the bending of light around the sun, though this is at present somewhat controversial. In any case, measurements of the latter phenomenon remain ambiguous. One further point for investigation seems to have been established quite recently: the gravitational shift of Mössbauer radiation. Other fields, now so active but long dormant, will no doubt continue to appear one after another. For a concise recent account of this problem, see L. I. Schiff, “A Report on the NASA Conference on Experimental Tests of Theories of Relativity,” Physics Today, XIV(1961), 42__48.
3) For the two parallax telescopes, see Abraham Wolf, A History of Science, Technology, and Philosophy in the Eighteenth Century (2d ed.; London, 1952), pp. 103__5. For the Atwood machine, see N. R. Hanson, Patterns of Discovery (Cambridge, 1958), pp. 100__102, 207__8. For the other two special apparatuses, see M. L. Foucault, “Methode generale pour mesure la vitesse de la lumiere dans l`air et les milieux transparants. Vitesses relatives de la lumiere dans l`air et dnas l`eau...,” Comptes rendus...de l`Academie des sciences, XXX(1850), 551__60; C. L. Cowan, Jr., et al., “Detection of the Free Neutrino: A Confirmation,” Science, CXXIV(1956), 103__4.
4) J. H. P[oynting] surveys twenty-four measurements of the gravitational constant made between 1741 and 1901 in “Gravitation Constant and Mean Density of the Earth,” Encyclopaedia Britannica (11th ed.; Cambridge, 1910__11), XII, 385__89.
5) For the complete transplantation of the concepts of hydrostatics into pneumatic chemistry, see “The Physical Treatises of Pascal” (trans. I. H. B. Spiers and A. G. H. The original introduction to Torricelli’s parallel theory (“We live submerged at the bottom of a great ocean composed of the element air”) appears on p. 164. This view was advanced rapidly by two major studies.
6) Duane Roller and Duane H. D. Roller, The Development of the Concept of Electric Charge: Electricity from the Greeks to Coulomb (“Havard Case Histories in Experimental Science,” Case 8; Cambridge, Mass., 1954), pp. 66__80.
7) See, for example, T. S. Kuhn, “The Function of Measurement in Modern Phuysical Science,” Isis, LII(1961), 161-93.
8) T. S. Kuhn, “The Caloric Theory of Adiabatic Compression,” Isis, XLIX(1958), 132__40.
9) C. Truesdell, “A Program toward Rediscovering the Rational Mechanics of the Age of Reason,” Archive for History of the Exact Sciences, I(1960), 3__36; “Reactions of Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton`s Principia,” Texas Quarterly, X(1967), 281__97. T. L. Hankins, “The Reception of Newton`s Second Law of Motion in the Eighteenth Century,” Archives internationales d`histoire des Sciences, XX(196), 42__65.
10) Wolf, op. cit., pp. 75__81, 96__101; William Whewell, History of the Inductive Sciences (rev. ed.; London, 1847), II, 213__71.
11) Rene Dugas, Histoire de al mecanique (Neuchatel, 1950), Books IV-V.
IV. Normal Science as Puzzle-Solving
Normal Science as Puzzle-solving
Perhaps the most striking feature of the regular research problems we have just examined is that such research rarely aims at producing major novelties, whether conceptual or phenomenal. In the measurement of wavelengths, for example, everything except the most profound details of the result is known in advance, and the typical range of expectation is only slightly widened. Coulomb’s measurements were probably not required to conform to the inverse square law. Those who studied the phenomenon of heating by compression usually expected to obtain one among several possible results.
Nevertheless, even in such cases, the range of results that are expected and therefore assimilable is always narrow compared with the range that imagination permits. And a project whose result does not fit into that narrow range usually becomes a failure of research, a failure that reflects not upon nature but upon the scientist.
In the eighteenth century, for example, experiments that measured electrical attraction with devices such as a pan balance received hardly any attention. Since such experiments produced no consistent results, or not even simple results, they could not be used to articulate the paradigm from which they had been derived. They therefore remained mere facts, unrelated and incapable of being related to the continuing development of electrical research. Only in retrospect, with a later paradigm in hand, can we see what properties of electrical phenomena those experiments revealed. Of course, Coulomb and his contemporaries also possessed this later paradigm, or a paradigm that, when applied to the problem of attraction, yielded the same predictions. This is why Coulomb was able to devise an apparatus that produced results assimilable through paradigm articulation. And it is also why no one was surprised by the results, and why several of Coulomb’s contemporaries were able to predict them in advance. Even a project whose purpose is to articulate a paradigm does not aim at unexpected novelty.
But if the goal of normal science is not substantive major innovation—if failure to come near the predicted result is normally regarded as failure as a scientist—why, after all, are such problems undertaken? Part of the answer has already been suggested above. For the scientist, at least, the results obtained in regular research are significant because they add to the scope and precision with which the paradigm can be applied. Yet that answer does not explain the enthusiasm and devotion that scientists display toward the problems of normal research. No one devotes years solely because of the importance of the information to be obtained, for example, to building an improved spectrometer or to obtaining a better solution to the problem of a vibrating string. The data obtained by calculating ephemerides or by making measurements with existing instruments are often just as significant, but scientists regard such activities as trivial, because they consist largely in the repetition of procedures that have long been performed. This reaction of rejection provides a clue to the fascination of regular research problems. Because the result can be predicted, often in considerable detail, the thing that remains unknown may itself be of little interest; yet the method of achieving that result remains in question. To bring a regular research problem to its conclusion is to arrive at a predicted result in a new way, and this requires the solution of all sorts of complex instrumental, conceptual, and mathematical puzzles. The person who accomplishes this proves himself a master puzzle-solver, and the challenge of the puzzle becomes an important element in what drives the scientist to carry on sustained research.
The terms “puzzle” and “puzzle-solver” emphasize several of the themes that have gradually become clear in the preceding paragraphs. A puzzle, in the full standard sense applied here, refers to that special category of problems which can serve as a test of ingenuity or skill in solution. Dictionary examples are “jigsaw puzzle” and “crossword puzzle,” and these are characterized by features they share with the problems of normal science that we must distinguish here. One of these has just been mentioned. It is not a criterion of excellence in puzzles. On the contrary, truly urgent problems, such as curing cancer or devising a plan to make peace permanent, are often not puzzles at all. In general, the reason is that such problems may not have any solution. Imagine taking pieces at random from two different jigsaw-puzzle boxes and trying to assemble a picture. Since such a problem would leave even the most skillful person with no recourse—though perhaps not—it cannot serve as a test of skill in solution. In the usual sense, it is not a puzzle at all. Intrinsic value is never a criterion for a puzzle, but the certainty that a solution exists is certainly a limiting criterion.
But we have already seen above that one of the things a scientific community acquires by relying on a paradigm is a criterion for selecting problems that may be assumed to have solutions while the paradigm is taken for granted.
For the most part, these problems become the only ones that the scientific community will acknowledge as scientific or encourage its members to engage in. Other problems, including many that had previously been standard, come to be rejected as mere speculation, as matters of concern to another field, or as too troublesome to be anything but a waste of time. In this respect, a paradigm may even isolate the scientific community from problems that cannot be reduced to the form of socially important puzzles. This is because such problems cannot be stated by means of the conceptual and instrumental resources that the paradigm provides.
Such problems can become a source of confusion, a lesson clearly illustrated by certain features of seventeenth-century Baconianism and by some of the modern social sciences.
One reason normal science seems to progress so rapidly is that its practitioners concentrate on problems for which only their own lack of ingenuity blocks the way to a solution.
However, if the problems of normal science are puzzles in this sense, there is no need to ask why scientists attack such problems with passion and devotion. There are all sorts of reasons why a person may become interested in science. Among them are the desire for usefulness, the wonder of exploring new territory, the hope of finding order, and the impulse to test already established knowledge.
These motives, and others as well, also help determine the particular problems that person will later have to deal with. Of course, the results may sometimes prove disappointing, but such motives are primarily sufficient reasons to arouse a scientist’s interest and then to lead him onward.1) Taken as a whole, scientific activity is often judged useful; it opens new territory, reveals order, and tests beliefs long accepted. Nevertheless, the individual engaged in a regular research problem is doing none of these types of activity. Once he has entered science, the scientist’s motive takes on a quite different form. What then challenges him is the conviction that, if he is sufficiently talented, he will succeed in solving a puzzle that no one before him has solved, or has solved properly. The greatest scientific minds have usually devoted themselves as specialists to unsolved puzzles of this sort. In almost every case, in whatever specialized field, there is nothing else to be done, a fact that makes it seem highly fascinating to the orthodox, trained researcher.
Let us now shift the discussion and turn to a more difficult and more revealing aspect of the analogy between puzzles and the problems of normal science. If something is to be classified as a puzzle, a problem must possess characteristics beyond the certainty that it has a solution. There must also be rules that delimit both the nature of acceptable solutions and the steps by which they are to be obtained.
For example, completing a jigsaw puzzle is not simply a matter of “making a picture.” A child, or an artist of the day, could make a picture by scattering selected pieces in abstract forms on some gloomy background. The picture so produced might be more pleasing than the one originally made by fitting the pieces together, and, needless to say, more original.
Nevertheless, that picture would not be a solution. To obtain a solution, all the pieces must be used; the unpictured sides must face downward; and all must fit together exactly, leaving no empty holes. These are among the rules governing the solution of a jigsaw puzzle. Similar restrictive conditions are readily found for deriving acceptable solutions to problems such as crossword puzzles, riddles, and chess.
If the term “rule” is used rather broadly—in some cases as equivalent to “established viewpoint” or “preconception”—then the problems accessible within a given research tradition reveal something very similar to the puzzle-character of this kind. A person devising an instrument for measuring the wavelength of light must not be satisfied merely because some apparatus assigns particular values to particular spectral lines. He is not simply an explorer or measurer. Rather, what he must do is prove, by analyzing his apparatus according to the established concepts of optical theory, that the numbers his instrument gives are indeed equal to the wavelengths in the theory. If an unresolved gap in the theory or an unanalyzed element in his apparatus prevents him from completing that proof, his colleagues in the field are likely to conclude that he has measured nothing at all. For example, the maxima of electron scattering had little meaning when they were first observed and recorded, and were only later diagnosed as indicators of electron wavelengths. Before such results could become measures of anything, they first had to be connected with the theory that had predicted that matter in motion could behave like waves. Even after that connection had been indicated, the apparatus had to be rearranged so that the experimental results could be linked with the theory in an unambiguous quantitative correlation.2) Until these conditions were satisfied, no problem had been solved.
Acceptable solutions are bound by similar restrictions in theoretical problems. Throughout the eighteenth century, scientists who tried to derive the observed motion of the moon from Newton’s laws of motion and gravitation repeatedly failed. As a result, some scholars proposed replacing the inverse square law with another law that deviated from it at short distances. But to do so meant changing the paradigm, defining a new puzzle, and not solving the old one. At last, scientists held to the existing rules as they were, and in 1750 one of them discovered a way in which they could be successfully applied.3) Only through a change in the rules of the game could an alternative have been prepared.
Research in the tradition of normal science reveals many other rules besides these, and those rules provide much information about the commitments scientists have derived from their paradigms. What can we call the principal categories to which these rules belong?4) The most obvious, and perhaps the most binding, will be exemplified by the types of generalization we have just noted. These generalizations are explicit statements concerning scientific laws and scientific concepts and theories. So long as such statements continue to be respected, they help set puzzles and delimit acceptable answers. Newton’s laws, for example, performed such a function throughout the eighteenth and nineteenth centuries. During this period, quantity of matter was a fundamental category of entity for physicists, and the forces acting between pieces of matter were a principal subject of research.5) In chemistry, the law of definite proportions and the law of multiple proportions exerted exactly the same power over many years—organizing the problem of atomic weights, setting limits on acceptable results of chemical analysis, and telling chemists what atoms and molecules, compounds and mixtures were.6) Maxwell’s equations and the laws of statistical thermodynamics possess just such power and function today. Yet rules of this sort are neither the only form revealed by historical examination nor the most interesting variety. At a level lower than that of laws and theories, or on a more concrete plane, there are various positions, for instance, regarding the more desirable forms of instrumentation and the proper manner in which accepted instruments are to be applied. The change in attitude toward the role of fire in chemical analysis played a decisive part in the development of seventeenth-century chemistry.7) In the nineteenth century, Helmholtz encountered fierce opposition from physiologists to the idea that methods of physical experimentation could illuminate their field of physiology.8) And the curious history of chemical chromatography in this century also shows the tenacity of instrumental dependence, for instrumental methods provide scientists with rules of the game as much as laws and theories do.9) If we analyze the discovery of X-rays, we will find the validity of this kind of commitment.
Less bound by region and period, and yet characteristic of science in its changing nature, are the higher-level
It is a quasi-metaphysical position. For example, after about 1630, and especially after the appearance of Descartes’s scientific writings, which exerted a powerful influence on the physics community, most physicists came to believe that the universe was composed of microscopic particles and that all natural phenomena could be explained by the shape, size, motion, and interaction of those particles. This cluster of commitments proved to be both metaphysical and methodological. In its metaphysical aspect, it told scientists what sorts of entities the universe did, and did not, contain. In the universe there was only shaped matter in motion. In its methodological aspect, it told scientists what ultimate laws and fundamental explanations should be like. Laws should specify the motion and interaction of particles, and explanations should reduce any given natural phenomenon to the action of particles under those laws. More importantly, the corpuscular conception of the universe dictated to scientists what many of their research problems should be. For example, chemists who, like Boyle, embraced the new corpuscular philosophy paid special attention to reactions that could be regarded as alchemical transmutations. More than anything else, such changes were thought to reveal the processes of rearrangement among particles that must underlie all chemical change.10) In mechanics, optics, and the study of heat as well, corpuscularism can be seen to have had a similar influence.
Finally, at a still higher level, there exist commitments of a kind without which one could not even be called a scientist. For instance, a scientist must be concerned to understand the world and to extend the precision and range with which that world has been ordered. Such involvement, in turn, leads the scientist, either alone or in cooperation with colleagues, to elucidate experimentally certain aspects of nature in detail. And if, in the course of such exploration, gaps of irregularity become plainly apparent, they confront the scientist with the challenge of refining his observational techniques anew or of clarifying his theory further. Undoubtedly many similar rules still remain, and these are things that have captivated scientists in every age.
The existence of this strong network of commitments—conceptual, theoretical, instrumental, and methodological—is the principal source of the metaphor that relates normal science to puzzle-solving. Because it provides practitioners in a mature specialty with rules that tell them what both the world and their science are like, the researcher can confidently concentrate on the difficult problems defined by those rules and by existing knowledge. The next step, then, is the problem of how the individual scientist is to bring the remaining puzzles to a solution. In this respect and in others, the discussion of puzzles and rules reveals the nature of actual activity in normal science. Nevertheless, on the other hand, such an account may be quite misleading. It is certainly true that the practitioners of a scientific specialty all possess, at any given time, rules to which they can adhere; yet those rules by themselves may not determine everything shared in the activity of the specialists in that field. Normal science is an activity of a highly determinate character, but it need not be determined entirely by rules. This is precisely why, at the beginning of this essay, I introduced shared paradigms as the source of the coherence of normal-scientific traditions rather than as shared rules, assumptions, and views. I suggest that rules derive from paradigms, but that paradigms can guide research even in situations where rules do not exist.
“Notes”
1) The frustration arising from the conflict between the individual’s role in scientific development and the overall pattern is often quite serious. On this subject, see Lawrence S. Kubie, “Some Unsolved Problems of the Scientific Career,” American Scientist, XLI (1953), 596–613; XLII (1954), 104–12.
2) For a brief account of the progress of these experiments, see C. J. Davisson’s lecture in Les Prix Nobel en 1937 (Stockholm, 1938), p. 4.
3) W. Whewell, History of the Inductive Sciences (rev. ed.; London, 1847), II, 101–5, 20–22.
4) I owe this question to W. O. Hagstrom, whose work on the sociology of science at times overlaps with my own.
5) For this aspect of Newtonian theory, see I. B. Cohen, Franklin and Newton; An Inquiry into Speculative Newtonian Experimental Science and Franklin’s Work in Electricity as an Example Thereof (Philadelphia, 1956), chap. vii, esp. pp. 255–57, 275–77.
6) This example is discussed at length in the latter part of Section X.