10.1—
A Story about the Maturation of Sciences

I should like to begin by pointing to two features that seem to be common to the sciences that have traditionally been regarded as "mature" and "hard." The first characteristic of such sciences is that they have achieved a certain degree of rigor in their explanations. In particular, they have discovered mathematical expressions that capture, with greater or lesser degrees of exactitude, the relationships among the objects form-

ing the domain of a given science insofar as they take part in the phenomena that that science seeks to explain. The second characteristic of such sciences is that they involve what are sometimes called "structural explanations" or "microexplanations"—or, more generally, connections between domains of discourse. These explanations relate phenomena that occur at one level of description L1 to the objects, relationships, and processes at a more basic level of description L2 that are ultimately responsible for phenomena at L1 . Microexplanation can occur wholly within the bounds of a single science, and it can also occur across the boundaries of sciences, as in the case of the explanation of the combinatorial properties of the elements (chemistry) by reference to the behaviors of charged particles (physics). The issue of whether features such as these are necessary for scientific maturity is an important locus of contention in philosophy of science. Notably, there have been heated disputes about the status of biology in this regard. I wish to sidestep such issues here: I embrace Newton-Smith's (1981) idea that scientific theories can enjoy a plurality of "good-making" qualities. Mathematization and connectivity are two such qualities, and happen to be ones that have been emphasized in the "modern" view of science. My claim here is not that they are essential to a discipline's scientific status, nor that they are the only virtues relevant to scientific maturation, but merely that computational psychology may fruitfully be seen as an attempt to endow psychology with these virtues; and that if it succeeded in doing so, this would be a significant achievement.

A third feature that is often closely connected to the maturation of a science is the occurrence of a conceptual revolution that involves seeing the phenomena a science sets itself to describing and explaining in a fundamentally new way. The use of metaphor often plays a crucial role in such conceptual revolutions, though as often as not the metaphor is abandoned once rigorous mathematical description of the domain in its own right has been achieved. I am inclined to regard conceptual revolution and the use of guiding metaphor more as a feature of crucial stages in the process of maturation rather than a feature of mature sciences as such.^[1] (After all, conceptual change and the use of metaphor are just as much a part of attempts at science that never get off the ground as they are of successful science.) Thus the conclusion of previous chapters that computing machines provide only metaphorical inspiration for computational psychology is in keeping with the role of metaphor in other sciences as well.

A few examples of mathematization and microexplanation may be of

use in setting the stage for a discussion of psychology and computer science.

10.1.1—
Copernicus, Galileo, Newton

The emergence of the "new science" of the sixteenth and seventeenth centuries is sometimes referred to under the heading of the "Copernican revolution" in physics. And it is true that Copernicus played a crucial role in starting a conceptual revolution in astronomy that paved the way for the development of what was to become Newtonian mechanics. It is important to see, however, that Copernican astronomy in its own right is only the first step towards a mature physics.^[2] Copernicus's own concerns were still largely those of an astronomer . He was concerned with finding a description of planetary motion. His own model of that motion, however, was highly influenced by his Ptolemaic predecessors: a system of circular orbits and epicycles around a point close to the sun.^[3] (The sun was not at the center of Copernicus's system; it, like the planets, orbited another point in space. It is also worth noting that Copernicus's model contained more epicycles than Ptolemy's. The virtue of this model lay neither in its elegance nor in its predictive accuracy [see Kuhn 1957: 169-171].) Kepler, by contrast, was engaged in a project of finding a kind of mathematical description of planetary motion that would at once be elegant and exact. One important breakthrough—the one we probably imprinted upon when we learned about the progress of modern physics—was Kepler's discovery of the fact that planetary orbits are elliptical and that orbital speed can be determined on the basis of the area of the ellipse subtended by a portion of the orbit.^[4] But when we learned this, we probably overlooked what was really important about this discovery. The fact that orbits take the form of an ellipse rather than some other conic form is really irrelevant to the progress of physics. What is crucially important is that the motions of the planets can be described exactly by mathematical expressions, regardless of which ones, and that they can all be described by the same kinds of expressions.^[5] Physics would have done just as well if planetary orbits had been of a different, yet precisely describable shape. Celestial mechanics would have gotten nowhere so long as the only descriptions of planetary motion were in terms of a motley batch of epicycles having no discernible overarching pattern.

The further progress of modern physics was facilitated by the emergence of two other mathematical innovations: the development of algebraic geometry allowed for the possibility of performing algebraic cal-

culations upon the motions of the planets through time, and the calculus provided for the possibility of making calculations about acceleration. The culmination of these advances was Newtonian mechanics, which summarized the interactions of gravitational bodies in a set of extremely elegant mathematical equations that came to be known as "Newton's laws." Newtonian mechanics unified the fields of astronomy, celestial mechanics, and sublunary physics under one set of mathematical descriptions, and stood as the standard for scientific theories until displaced by relativity theory (which was, itself, dependent upon the development of differential geometry for its descriptions of space and time).

It is worth emphasizing that Newton's achievement lies in his having left us a rigorous and general description of the effects of gravitational bodies upon one another. His ambivalent attempts to address the why of gravity (his much-discussed flirtation with "forces") add nothing to the picture, and his failure to solve the "why" of gravity detracts not in the least from the power and the utility of Newtonian mechanics.^[6] One might well suspect that gravity amounts to something more than the empirical regularities of how bodies move in relation to one another, and it is appealing to seek some insight into this "something more," but such insight is not needed in order to make Newtonian mechanics "good science."

In brief, Newtonian mechanics provides for the mathematical maturity of a large portion of physics without providing any microexplanation for gravitational attraction in terms of some subgravitational level of explanation. Gravitation is treated as fundamental . And the lack of such an explanatory connection is not generally viewed as a fatal objection to Newtonian mechanics as good science, even though it is in some ways dissatisfying. Moreover, it displaced a Cartesian physics which did offer a microexplanation of gravitation in terms of mechanical interactions of particles.^[7]

10.1.2—
Chemistry

A second example can be supplied by chemistry, which experienced distinctly separate stages of progress towards mathematical and connective maturity. There was a time when chemistry was largely independent of physics. In fact, chemistry attained a remarkable degree of mathematical maturity with very little help from physics, and it is possible to learn large portions of chemistry with little or no knowledge of physics. (Indeed, I believe it is still the practice in teaching chemistry in the schools

first to present a chemistry that involves little or no physics before moving on to those parts where physics becomes crucial.) For there was substantial progress in understanding basic laws governing combinations of the elements before there was any underlying physical theory about what sorts of microstructure might account for these laws. The periodic table (Mendeleev around 1869), the notion of valence (Frankland in 1852), and a remarkable set of laws governing combinations of elements (as early as Lavoisier's work published in 1787) were developed long before these notions were further grounded in a theory of subatomic particles in the twentieth century. With the development of the periodic table, the notion of valence, and laws of combination, chemistry achieved a significant degree of mathematical maturity. In this respect, the age of Lavoisier made a significant step beyond the procedures and wisdom of previous chemists and alchemists, however great their technical skill, because there was, for the first time, a rigorous and systematic description of how the elements reacted in combination.

The major progresses in theoretical chemistry since the time of Mendeleev have been in the connections, the border marches, between chemistry and other disciplines such as physics and biology. In order to understand reactions between large molecules, for example, it was necessary to understand something of their physical structure. The propensities of molecules to combine in certain ways (some of which seemed anomalous) called for an explanation in terms of underlying structure, an explanation supplied by such notions as electron orbitals, ionic and covalent bonding, and the postulation of charged and uncharged subatomic particles. In the process, chemistry became increasingly connected to physics. At the same time, it became evident that many biological phenomena could be accounted for by chemical explanations: the bonding between hemoglobin and oxygen accounts for the transport of oxygen through the circulatory system to cells throughout the body (and hemoglobin's preference for bonding with carbon monoxide explains the ease of carbon monoxide suffocation); important parts of processes such as the Krebs cycle are chemical in nature; and of course the basic element underlying genetics, the DNA molecule, is typified by a particular molecular structure. With the advent of discoveries such as these, chemistry—which already had a high degree of mathematical maturity—acquired a large amount of what we might call connective maturity as well. It is worth noting, however, that most of these connections were not made until the latter half of the twentieth century, more than a century after

chemistry had gained significant mathematical maturity. Some things take time.

It seems safe to say that sciences tend to become both more powerful and more firmly established as they become more intimately connected with one another. Chemistry raises questions that physics has to answer, and provides answers to questions raised by biology. Astronomy provides a lab for physics to study things that cannot be reproduced here and now, and physics provides a lab for testing hypotheses about things that are too far away to investigate firsthand.