It Ain't Rocket Science

Disciplinary matrices (or paradigms) are a particular kind of order that may be discerned in some social structures. These social structures can be called scientific communities. We describe the relevant sense of order by describing the elements of the paradigm--symbolic generalisations, models, values and exemplars.

The values of science can be described at two levels, which apply to the internal cohesion of the community working under the paradigm and to its legitimacy in the broader community (society in general) respectively. The first, then, defines the value of good quality (worthwhile or valuable) research by an individual member within the specific community working under the paradigm. This will often involve standards of precision and thoroughness, writing style and, of course, the orthodox identification of "enemy positions", i.e., those "other" disciplines that do not share the relevant values.

The second, meanwhile, defines the value of the paradigm's research to concerns that go beyond the paradigm. This will also involve its share of "othering", though now in terms of broader social movements. More important, however, are ideas about the value of science in general and the value of the paradigm's research to society. Such values, in turn, come in different varieties. Thus, "strategy research" (a branch of management studies) often emphasises its commitment to "the bottom line", i.e., to making a contribution to the profitability of firms. Some economists subscribe to the same line, and others to a broader notion of "economic efficiency" at a national or international level. Still other economists are committed to "social justice", just as many sociologists pursue lines of research devoted to "cultural criticism". There are natural scientists who are devoted to improving the conditions of life on the planet, whether human, animal or vegetable. And there are natural scientists, philosophers and sociologists who are interested in what they call "knowledge for its own sake" or, simply, "truth". Paradigms may form around any combination of such values.

Values are one of the elements that distinguishes paradigms from each other and they are subject to change. They are often very much a part of what connects a paradigm to its broader social context, even as they mark their autonomy from it. Their description is an important part of the delineation of the order constituted by a disciplinary matrix.

In this correlation, the identity or plurality of men doesn't matter. The first Kafka of "Betrachtung" is less a precursor of the Kafka of the gloomy myths and terrifying institutions than is Browning or Lord Dunsany.

J. L. Borges

"Science does not deal in all possible laboratory manipulations," Kuhn tells us (SSR, X, p. 126). "Instead, it selects those relevant to the juxtaposition of a paradigm with the immediate experience that that paradigm has partially determined." As an example, Kuhn offers Galileo's experiments with pendulums. His most controversial contention here, as he himself notes, is that Galileo was able to see a pendulum, where others--the Aristoteleans--simply were not. What they saw was the "constrained fall" of a stone on a string.

This difference can be understood in many ways that we have already looked at. In terms of symbolic generalisations, the Aristolean would describe the phenomenon by reference to "the weight of the stone, the vertical height to which it had been raised, and the time required for it to achieve rest," (p. 123) while Galileo "measured only weight, radius, angular displacement, and time per swing." In terms of models, Aristotle noted a "change of state rather than a process" and took the stone to be "impelled by its nature to reach its final resting point," i.e., the ground, (p. 122) while Galileo saw "the [pendulum's] motion as symmetrical and enduring; and . . . circular," its impetus deriving not from its tendency toward something, but rather from its distance from it," namely, the fixed point (p. 123-25). Finally, in terms of disciplinary values, Artistoteleans were likely to discuss these issues rather than observe actual pendulums. That is, Galileo valued empirical experiments, while Aristoteleans valued logical argument.

Our focus here is on exemplars. Kuhn emphasises that the paradigm that allowed Galileo's "individual genius" to see a pendulum where Aristotelean science could see only a constrained fall was not of his own making but was part of his scholastic heritage. Thus, Buridan's description of vibrating strings (p. 120) and especially Oresme's description of a swinging stone (which, Kuhn notes, "now appears as the first discussion of pendulums") are precursors of the paradigm shift marked by Galileo's studies. The "view of things" that Galileo had, was part of "the scholastic impetus paradigm for motion", a paradigm whose importance is of course very clear to us today.

The Argentinian writer, Jorge Luis Borges once pointed out that works of literature have a tendency to create their own precursors. Thus, with the work of Kafka, certain connections between hitherto unrelated authors begin to emerge. A tradition is formed that seemed to herald the work of Kafka, but from which we could not have predicted in any detail the character of Kafka's work. The same can be said of landmarks in the history of science. A great many developments within the scholastic tradition become apparent as a drive toward the discoveries of Galileo, allowing us to see pendulums where, in the past, Aristoteleans had been able to see only stones swinging on the end of strings.

In keeping with the spirit of Borges, it may be useful to point out that it is not the person of, say, Sir Isaac Newton, but some of his work that has come to be "paradigmatic" (in the sense of "exemplary") of modern science. Newton also dabbled in alchemy, though neither he nor his colleagues would have called it "dabbling" (they took it very seriously). His studies of planetary motion have served as examples for countless studies since then; his studies of how to turn lead into gold are examplary of quite another set of pursuits. Note also that examplars may be found from a time before a paradigm is fully formed, as the scholastic exemplars for Galileo's work shows.

While exemplars generally have an origin, or at least a set of early applications that have defined their content, it is important to keep in mind also that Kuhn means the actual operations that define the experiment or study, not the historical event of its early attempts. Thus, the pendulum along with a specific kind of analysis (one which in fact defines it as a pendulum) is an examplar of mechanics even today. It is the therefore not just the sort of thing you read about in history books, but the sort of thing you can have hands-on experience with.

Kuhn himself emphasises the importance of exemplars and devotes a good deal of space to them in his postscript (pp. 186-204). There is good reason to heed his emphasis here. One of the most useful ways of getting clear about the formative processes behind a field of research, including your own, is to make explicit what counts as "good work". It is one thing to explicate abstract criteria or norms (i.e., values) of good research; it is another to identify examples of work that meets them. It is also much easier to learn from concrete examples of quality research than to imagine a correspondence between ones own work and a set of formal rules. Good researchers should be aware of their precursors: they should be able to point out what the major successes in their field are.

When describing a disciplinary matrix in terms of its exemplars, the following information should be provided wherever possible. First, the name of the scientist who first carried out the exemplary study. Second, the date of the experiment. Third, the place it was first published, and the places the example may be found today (such as in textbooks). Fourth, a description of the experiment that emphasises the parts of the study that have contributed to forming the "immediate experience" of the paradigm. Paradigms will of course contain many exemplars of good research, so part of the task here is to identify those which are particularily influential.

In all cases, keep in mind that exemplar is always an instance of a successful pairing of problems that are recognized by the field and solutions that are valued by it. Identifying an examplar means identifying work that has been valuable to the formation of the researcher's competences and remains a benchmark in a significant way. This is why a field's progress "creates its own precursors", as Borges puts it. Progress may sometimes make previous exemplars less significant, and may indicate new examplars of what can be an older vintage.

"Metaphysics grounds an age," writes Martin Heidegger in his famous essay, "The Age of the World Picture". The metaphysics of the modern age is revealed, he continues, in its "essential phenomena": science, technology, art, culture and religion. Like us, Heidegger focuses his attention on the first of these. And like us, Heidegger is very interested in the materiality and historicity of science. "Within the complex machinery that is necessary to physics in order to carry out the smashing of the atom lies hidden the whole of physics up to now." Science, he tells us, is fundamentally characterised by its "ongoing activity", or Betrieb in German, which has also been translated as "hustle". We might conceive of science as "hustle and bustle", evoking its fragile, pulsating history, as Foucault does. But science does not lose itself in "random investigations" that "simply amass results" precisely because the hustle and bustle of modern research is disciplined by the "complex machinery" of its procedures.

This is why we can usefully read Chapter III of The Structure of Scientific Revolutions alongside Kuhn's comments in the postscript on "models" or "metaphysical paradigms". For in Chapter III, Kuhn is trying to show how science is normalized by the procedures it uses to "gather facts". The "nature of normal science" is its "metaphysics", its "ground". It is on this ground that the various abstract models that illustrate scientific theories stand out as figures, as meaningful diagrams of basic mechanisms at work in particular object spheres. "Again and again," says Kuhn, "complex special apparatus has been designed to [increase the precision of science], and the invention, construction, and deployment of that apparatus have demanded first-rate talent, much time, and considerable financial backing." With that precision, and at that expense, changes have been brought about in the models according to which the phenomena have been understood. Consider here the ways in which increased precision in the measurement of the position of planets brought us from a metaphysics of winged chariots (mythology), to shining balls mounted on spheres of crystal (Aristotle and Ptolemy), to orbits governed by the force of attraction (Newton) to the current orthodoxy of planets moving through curved space (Einstein). Indeed, the wheel has been a standing model in understanding the manifold of experience since antiquity, forming our understanding of "cycles" in all their variety.

The task here is to describe the role of scientific training (discipline) and equipment (apparatus) in avoiding what Kuhn later calls "a bloomin', buzzin' confusion," quoting William James in Chapter X. An orderly approach to experience is expressed in a "world view" (which can be usefully compared to Heidegger's "world picture"). And in Chapter X, Kuhn indeed understands changes of paradigm as reconfigurations of world-views, noting that these are correlated with changes in the "operations and measurements that a scientist undertakes in the laboratory". Such procedures produce "data", which is Latin for, "what is given", but which are more accurately understood as what has been "collected with great difficulty".

When describing the underlying models of scientific inquiry, keep in mind that these are, in a sense, sublimated expressions of "ways of looking at the world" (theories, Bourdieu reminds us, are "programmes of perception"), and that what is seen when we look at the world in this way are, only in this sense (of having been "sublimated"), brute facts. Metaphysical models are (extraordinarily) simple expressions of the complex perceptual dispositions that form the (ordinary) ongoing activity in which science is always already implicated. Models make science look easy, which is altogether part of their charm.

In the closing paragraphs of Chapter II of the Structure of Scientific Revolutions (SSR, II), Kuhn notes the importance of "esoteric" modes of publication, or what he also calls research "communiqués", for the emergence of normal science or research carried out within what he comes to call a "disciplinary matrix". These are very efficient ways of communicating research results to peers, but largely incomprehensible to lay people. The problem for the lay person, of course, arises from the high degree to which the research can (and does) take the meaning of central terms for granted. In the second section of the post-script (SSR, PS, 2), Kuhn identifies this capacity to be precise with the presence of "symbolic generalisations" in the language used by a research community. It is with the use of these generalisations, that the "communiqués" are produced, allowing scientists to pass from having to write lengthy treatises that derive all results from fundamentals, to writing short papers that present the result of specialized investigations to people who already know how to make sense of them, i.e., can determine their significance both in the sense of brute 'meaning' and in the sense of the relative 'importance' of the results. In so far as it is unclear what a result means to the research of one's peers, it may be "anomalous" and be an advance indication of crisis and revolution. Only history will tell, however, so at the time it will simply not register, i.e., future contenders for paradigmatic status are ignored in the present on par with past contenders.

The presence of terms that clearly indicate their subject matter to initiated peers, then, is called the "symbolic generalisation" of research within a "disciplinary matrix". Part of describing such a matrix (also called a paradigm, for short) is identifying highly generalised symbols available to the researchers when communicating with each other, and unavailable (at least as a presumption) when communicating with non-peers. (They may run into someone that happens to know what they are talking about, but they can't count on it outside the paradigm.) The sense that is made of the symbols is conditioned by the paradigm, so this will also enter into our epistemological descriptions. Thus, in describing a body of knowledge (a scientific discipline) as a "paradigm", the task of describing its symbolic generalisations consists in two sub-tasks: (a) to identify the symbols that generalize the field and (b) to describe their use, i.e., to determine their meaning. So, while Kuhn warns us at the start of Chapter III, not to let the word "paradigm" mislead us into the thinking of research in general by analogy with grammar (SSR, III), the description of symbolic generalisation is very much a matter of delineating the grammar of a particular discipline's research communication. Paradigmatic results may not often be replicated, but their grammatical structure is.

One very important aspect of this element of epistemological description is the difference between "definitional" and "legislative" applications. Where the same symbols recur among different groups of scientists, different paradigms will sometimes be evident, in part, because the same expressions are used primarily definitionally in one and legislatively in another. So it is important to know the difference, and to identify it as part of the description of a paradigm.

Sometimes a generalization like "f = ma" will be used to define a term (like "f", "force") and therefore stipulate the sorts of operations it would take to render them, e.g., empirically observable. In order to determine the force of a rocket in flight, for example, we must determine its accelaration (by observation of its motion) and its mass (by, hopefully, having weighed it before lift-off). The product of these values, then, just "is" the force of the rocket at a given point: "mass times accelaration" is (part of) what force means. Thus, the "force" of an "impact" understood in terms of (Newtonian) mechanics is evident in the acceleration that the impact causes the thing impacted to undergo.

But at other points in the history of mechanics (or in other uses of the language of mechanics) the same expression, "f = ma", may be a statement of law, i.e., it might impart the knowledge that force is always equal to the mass of a projectile times its acceleration. This knowledge can be very useful when attempting to accelerate or decelerate things like rockets. Kuhn calls such an application of a generalisation its "legislative" use.

The next four posts will cover what Kuhn calls the four "components" of a disciplinary matrix. These are symbolic generalisation, models, values and exemplars. None of these are alone sufficient to characterize a disciplinary matrix (or "paradigm" for short) but, taken together, describing these components is a way of delineating the order of experience that constitutes the sense that scientists make of what would otherwise be the "bloomin', buzzin' confusion" of their activities. Kuhn does not offer any clear sense of how these components interrelate, and he points out that the importance of each component will vary from paradigm to paradigm. Some research will be organized mainly around values while others will be organized mainly around symbolic generalisations. But if the science is "normal", i.e., if the research is conducted "under a paradigm", it ought to be possible to describe it in terms of these components.

An important question then goes to how one designs one's descriptions to relate components to each other. One way this may be done is to group the components two-by-two. Thus symbolic generalisations and models go to together somewhat like exemplars and values. Symbolic generalizations are the precise expressions of a particular paradigm's metaphysical models; it is here the language reaches a sufficient level of precision to afford "puzzles" for scientists to solve, rather than grand, sweeping gestures to admire. Similarily, exemplars make the underlying values of a paradigm more precise, since these are the instances that the researchers working under the paradigm deem to be "valuable". Here again, instead of expressing vague sentiments that specialists and non-specialists alike can agree with (everything from the value of human life to the value of careful observation), exemplars reveal more exactly what is meant by these sentiments in practice.

While it is not a hard and fast rule, it may be useful to think of symbolic generalisations and exemplars as means by which paradigms organize themselves at the core of the research process, while values and models are the stuff of which their outer boundaries are composed.

This also suggests another way to organize these components when describing a paradigm, this time involving more directly the historical approach Kuhn espouses. Since paradigms are historical contingencies that instantiate periods of "normal science" punctuated by "scientific revolutions" a paradigm, though always "normal" by definition, may be situated somewhere along the line of development from the revolution that established it to the revolution that will finally replace it. This, indeed, is one way Kuhn's work has been appropriated by scientists themselves in calling for "paradigm shifts" within their own fields. While these appropriations are rarely as orthodox as the approach we have been suggesting here, we can imagine how this would look. The idea would be to show that research within the paradigm has ceased to work at the core (i.e., around generalisations and examplars) and has begun to take an interest in such "philosophical" matters as its moral fibre (values) and its metaphysics (models). Settling issues here on the periphery might then lead to predictable and prescribable changes in the symbolic generalisations employed within the paradigm's core practices, correlating with an emphasis on new examples of proper research.

While the incommensurability thesis precludes making sense of such predictions and prescriptions (based on careful descriptions of the components of the disciplinary matrix) within the paradigm itself, the more philosophically inclined among the field's (often young) revolutionary vanguard will, perhaps, achieve a moment of disciplinary reflexivity (the scientific equivalent of "class consciousness"), allowing the revolution to proceed a bit more smoothly. Alternately, this knowledge can be applied by the old guard within a field in order to delay or even avoid a revolution. Finally, let us allow the possibility that Kuhn was wrong about the inherently revolutionary nature of scientific change and that, say, Popper's conception of "permanent revolution" could be conducted within paradigms under something like continuous reform. This reform process, then, could be guided by the awareness of the conditions of scientific work that Kuhn's conception of paradigms provides both scientists and their constituents.

In the postscript to The Structure of Scientific Revolutions, Kuhn makes an important remark that allows his concept of a "disciplinary matrix" to be used to foster reflexivity within a discipline. He points out that the phenonoma he investigates (the sciences) by historical means are nothing other than what "scientists themselves" (i.e., scientists when they are working within their paradigm: when they are being themselves as scientists), would simply call "theories". He blames philosophy for limiting the sense of this word, and "would be glad if the term can ultimately be recaptured" for his purposes (SSR, PS[2]).

These purposes require a recognition that "theorising" amounts to struggling with a "constellation of group commitments", i.e., elements to which the given scientific community is committed in its "normal" practices, and is therefore not a purely abstract activity.

The relevant elements are precisely those that we have been learning how to describe. Since Kuhn is keen to distinguish between "communities" (community structures) and "paradigms" (disciplinary matrices) analytically, however, it is important to keep in mind that a struggle with the community is not necessarily an instance of theorising. We know someone is theorising when they are engaging with very specific elements, and we characterise the specifically "theoretical" struggle by describing engagements with them.

Paradigms are abstractions of scientific practice, and while they are contingent on historical forces, they mark a "here and now" of this practice that we are able to describe independently of the history that formed it. Describing a disciplinary matrix allows us to see more clearly how the things of immediate experience "look" to researchers working in a particular field (theories, said Pierre Bourdieu, are programmes of perception). But they do not yet explain how things came to look that way, i.e., the history of a way of seeing things.

This way of putting it may seem a bit at odds with Kuhn's historical approach (and suggests his nascent sociological orientation) so it should be added that Kuhn would encourage us to learn the history as well. The reason to stress the "abstract" and "ahistorical" nature of paradigms is that it answers the important question, "A history of what?" when looking at the sciences. We are not interested in the complete social and political history of particular communities that call themselves scientific. We are interested in the history of precisely those aspects of practice in these communities that may be considered "knowledge bearing", i.e., those aspects that shape, form or "gestalt" experience in ways that allow us to make sense of it. The specific sense we are able to make of what goes on is contingent on the current paradigm. And it is that contingency we are trying to understand.

The orthodox description of a disciplinary matrix, then, brings us into the "presence" of research, i.e., allows us to understand how objects can emerge in experience in their "immediate reality". This immediacy, or rather this sense of immediacy is always itself a mediated affair, and the components of the disciplinary matrix are crucial characteristics of this medium. Since it is always impossible to appropriate a complete understanding of one's own history while one is involved in it, disciplinary reflexivity depends more on detaching the historically contigent paradigm from its historical contingencies than on connecting it to them. The descriptive task that will now be outlined is an exercise in producing a suitable occasion to reflect upon how one knows what one knows. It does not yet call any of that knowledge into doubt.