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Reductionism Redux

It used to be traditional for college courses on the history of philosophy to begin around 600 BC with Thales of Miletus. According to later writers, Thales taught that everything is made of water. Learning about Thales, undergraduates had the healthy experience of starting their study of philosophy with a doctrine that they knew to be false.

Though wrong, Thales and his pre-Socratic successors were not just being silly. They had somehow come upon the idea that it might be possible to explain a great many complicated things on the basis of some simple and universal principle—everything is made of water, or everything is made of atoms, or everything is made of atoms, or everything is in flux, or nothing ever changes, or whatever. Not much progress could be made with such purely qualitative ideas. Over two thousand years later Isaac Newton at last proposed mathematical laws of motion and gravitation, with which he could explain the motions of the planets, tides, and falling apples. Then in the Opticks, he predicted that light and chemistry would someday be understood “by the same kind of reasoning as for mechanical principles,” applied to “the smallest particles of nature.”

By the end of the nineteenth century physicists and chemists had succeeded in explaining much of what was known about chemistry and heat, on the basis of certain assumed properties of some ninety types of atoms—hydrogen atoms carbon atoms, iron atoms, and so on. In the 1920s physicists began to be able to explain the properties of atoms and other things like radioactivity and light, using a new universal theory known as quantum mechanics. The fundamental entities to which this theory was applied were no longer the atoms themselves but particles even more elementary than atoms—electrons, protons, and a few others—together with fields of force that surround them, like the familiar fields that surround magnets or electric charges.

By the mid-1970s it had become clear that the properties of these particles and all other known particles could be understood as mathematical consequences of a fairly simple quantum theory, known as the “standard model.” The fundamental equations of the standard model do not deal with particles and fields, but with fields of force alone; particles are just bundles of field energy. From Newton’s time to our own we have seen a steady expansion of the range of phenomena that we know how to explain, and a steady improvement in the simplicity and universality of the theories used in these explanations.

Science in this style is properly called reductionist. In a recent article in these pages1 Freeman Dyson described reductionism in physics as the effort “to reduce the world of physical phenomena to a finite set of fundamental equations.” I might quibble over whether it is equations or principles that are being sought, but it seems to me that in this description Dyson has caught the essence of reductionism pretty well. He also cited the work of Schroedinger and Dirac on quantum mechanics in 1925 and 1927 as “triumphs of reductionism. Bewildering complexities of chemistry and physics were reduced to two lines of algebraic symbols.”

You might have thought that these illustrious precedents would inspire a general feeling of enthusiasm about the reductionist style of scientific research. Far from it. Many science kibitzers and some scientists today speak of reductionism with a sneer, like post-modernists talking about modernism or historians about Whig historiography. In 1992 John Cornwell, the director of a project at Jesus College, Cambridge, on the sociology of science, convened a group of well-known scientists and philosophers to meet there to discuss reductionism. It was at this symposium that Dyson gave the talk on which his eloquent New York Review article was based. The collected papers of this symposium, Nature’s Imagination,2 contains articles with titles such as “Must mathematical physics be reductionist?” (Roger Penrose), “Reductive megalomania” (Mary Midgley), and “Memory and the individual soul: against silly reductionism” (Gerald Edelman). A review of this book by the mathematician John Casti, in Nature, calls these the “good guys in the white hats” as opposed to the un-reconstructed reductionists at the meeting like the chemist Peter Atkins and the astronomer John Barrow.

Casti is a fellow of the Santa Fe Institute, a haven for non-reductionist science. Dyson himself remarks that he has a “low opinion” of reductionism. (Coming from Dyson, this really hurts. He played a major role in the development of quantum field theory, which has been the basis of the reduction of all of elementary particle physics to the standard model.) What has gone wrong? How has one of the great themes in intellectual history become so disreputable?

One of the problems is a confusion about what reductionism is. We ought first of all to distinguish between what (to borrow the language of criminal law) I like to call grand and petty reductionism. Grand reductionism is what I have been talking about so far—the view that all of nature is the way it is (with certain qualifications about initial conditions and historical accidents) because of simple universal laws, to which all other scientific laws may in some sense be reduced. Petty reductionism is the much less interesting doctrine that things behave the way they do because of the properties of their constituents: for instance, a diamond is hard because the carbon atoms of which it is composed can fit together neatly. Grand and petty reductionism3 are often confused because much of the reductive progress in science has been in answering questions about what things are made of, but the one is very different from the other.

Petty reductionism is not worth a fierce defense. Sometimes things can be explained by studying their constituents—sometimes not. When Einstein explained Newton’s theories of motion and gravitation, he was not committing petty reductionism. His explanation was not based on some theory about the constituents of anything, but rather on a new physical principle, the general principle of relativity, which is embodied in his theory of curved spacetime. In fact, petty reductionism in physics has probably run its course. Just as it doesn’t make sense to talk about the hardness or temperature or intelligence of individual “elementary” particles, it is also not possible to give a precise meaning to statements about particles being composed of other particles. We do speak loosely of a proton as being composed of three quarks, but if you look very closely at a quark you will find it surrounded with a cloud of quarks and antiquarks and other particles, occasionally bound into protons; so at least for a brief moment we could say that the quark is made of protons. It is grand reductionism rather than petty reductionism that continues to be worth arguing about.

Then there is another distinction, one that almost no one mentions, between reductionism as a program for scientific research and reductionism as a view of nature. For instance, the reductionist view emphasizes that the weather behaves the way it does because of the general principles of aero-dynamics, radiation flow, and so on (as well as historical accidents like the size and orbit of the earth), but in order to predict the weather tomorrow it may be more useful to think about cold fronts or thunderstorms. Reductionism may or may not be a good guide for a program of weather forecasting, but it provides the necessary insight that there are no autonomous laws of weather that are logically independent of the principles of physics. Whether or not it helps the meteorologist to keep it in mind, cold fronts are the way they are because of the properties of air and water vapor and so on, which in turn are the way they are because of the principles of chemistry and physics. We don’t know the final laws of nature, but we know that they are not expressed in terms of cold fronts or thunderstorms.

One can illustrate the reductionist world view by imagining all the principles of science as being dots on a huge chart, with arrows flowing into each principle from all the other principles by which it is explained. The lesson of history is that these arrows do not form separate disconnected clumps, representing sciences that are logically independent, and they do not wander aimlessly. Rather, they are all connected, and if followed backward they all seem to branch outward from a common source, an ultimate law of nature that Dyson calls “a finite set of fundamental equations.” We say that one concept is at a higher level or a deeper level than another if it is governed by principles that are further from or closer to this common source. Thus the reductionist regards the general theories governing air and water and radiation as being at a deeper level than theories about cold fronts or thunderstorms, not in the sense that they are more useful, but only in the sense that the latter can in principle be understood as mathematical consequences of the former. The reductionist program of physics is the search for the common source of all explanations.

As far as I can tell, Dyson’s objections are entirely directed at reductionism as a research program rather than as a world view. He regrets that Einstein and (in later life) Oppenheimer were not interested in something as exciting as black holes, and blames this on their belief that “the only problem worthy of the attention of a serious theoretical physicist was the discovery of the fundamental equations of physics.” This is pretty mild criticism. Dyson does not question the value of the discovery of fundamental equations (how could he?) but only tells us that there are other things in physics to think about, like black holes. This is like a prohibitionist who is against gin because, good as it is, it distracts people from orange juice. And I am not sure that Dyson is even entirely right about Einstein and Oppenheimer as examples of the dangers of the appeal of reductionism.

I recall as a Princeton graduate student going to seminars at the Institute for Advanced Study, where Dyson was a professor and Oppenheimer the director. I always sat in back and kept quiet, while Oppenheimer always sat in front and carried on a detailed technical dialogue with the speaker, whatever the topic might be. He certainly seemed interested in everything that was going on in physics, not just at the reductive forefront. In fact, even in the 1920s and 1930s, when he was doing his best research, Oppenheimer’s work had much less to do with finding fundamental equations than with calculating the consequences of existing theories. By the time I met him, Oppenheimer’s own research had pretty well ended, and I can believe that he explained this even to himself in the way that is cited by Dyson; but I suspect that the truth is that he had just become too famous and too busy to have time for research.

  1. 1

    Freeman Dyson, “The Scientist as Rebel,” The New York Review, May 25, 1995, pp. 31–33.

  2. 2

    This book contains interesting articles on the foundations of mathematics and on other subjects, which I will not discuss here because I want to concentrate on reductionism in the natural sciences.

  3. 3

    Grand and petty reductionism correspond more or less to what the evolutionary biologist Ernst Mayr has called “theory reductionism” and “explanatory reductionism” in his article “The Limits of Reductionism,” Nature 331 (1987), p. 475.

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