Science in the Looking Glass: What Do Scientists Really Know?, E. Brian Davies , Oxford U. Press, New York, 2003. $29.95 (295 pp.). ISBN 0-19-852543-5
Science in the Looking Glass: What Do Scientists Really Know?, by E. Brian Davies, is a book about science and mathematics, written by a mathematician and intended for the general public. Much of it ought to be understandable for nonscientists. It can perhaps be best characterized as an extended essay that counsels caution against assigning “truth” to scientific models and by implication warns against philosophical overinterpretation of science.
Beginning with examinations of the human visual system, various theories of the mind and consciousness, and the social aspects of language, the author stresses the extra-scientific influences—especially of language—on our scientific view of the world. (I remember a seminar debate, however, in which physics Nobel laureate Percy Bridgman emphatically declared that he did much of his thinking without the use of words!) In two chapters on mathematics, Davies makes clear that, in contrast to many prominent mathematicians, he is not a Platonist: He does not believe mathematical theorems exist in an eternal Platonic universe of pure ideas, ready to be discovered by diligent research. Mathematics, instead, is a human construction. Davies also considers that controversies about the foundations of mathematics, intellectually challenging though they may be, are quite irrelevant to the actual practice of his craft.
Turning next to astronomy and classical physics, the book discusses determinism and its limitations, set not only by the existence of chaotic motions but also by some other, much less familiar breakdowns of the Newtonian equations for particles. In one fascinating example, Davies presents a “noncollision singularity,” a five-body system that speeds to infinity in a finite time. The supersession of Newtonian mechanics by the theory of relativity leads the author to make some good points about the difference between the “truth” of a theory and its use as a mathematical model.
After presenting various aspects of probability theory, the book takes up quantum mechanics, rounding up all the usual suspects to show its weirdness. Twice, however, the author commits a basic error: Never mentioning degeneracy or spontaneous symmetry breaking in a confusing discussion, Davies claims that because the quantum mechanical Hamiltonian is invariant under reflection, its eigen-states must also be invariant. Thus the theory would rule out molecules with chirality, which are nevertheless found in nature. He fails to make clear that the puzzle is not the existence of certain molecules that are left-handed or right-handed but the observed prevalence of one isomer over the other.
After a very good discussion of biological evolution and the contemporary assaults on all the variants of Darwinism, the author takes up a subject about which he obviously has intense feelings: He strongly attacks reductionism. However, the implication of his presentation is that reductionists insist that each of the fields in the usual hierarchy—as he puts it, theory of everything ← physics ← chemistry ← molecular biology ← cell biology ← brain physiology ← consciousness ← social structures—requires all the elements of the fields below it for explanations. I know of no reductionist—and I am one—who takes such a position. Davies argues, for example, that because the Navier–Stokes equation governs the behavior of diverse fluids with quite different molecular structures, it is irrelevant that the equation can be derived from the underlying particle dynamics and therefore wrong to think of the motion of a fluid as having been reduced to the movements of its constituents. In his view, it is also perfectly acceptable for the explanation of a phenomenon in one field (say, physics) to use elements from another above it in the hierarchy (say, consciousness). I disagree: My objection to the anthropic principle as an explanation of anything (rather than merely as a peripheral observation) is based exactly on my rejection of explanations of this kind. In my view, the existence of intelligent creatures on Earth no more explains the size of certain constants in the universe than it does the extinction of the dinosaurs. (In fairness, Davies does reject most of the uses of the anthropic principle.)
These criticisms notwithstanding, Science in the Looking Glass is worth reading in your leisure time. It is stimulating even when you disagree with the author.
