Philip W. Anderson analyses a reductionist approach to great intellect

Prominently displayed on the jacket of Peter Atkins' * Galileo's Finger * is extravagant praise from Richard Dawkins suggesting that Atkins is the first natural scientist to deserve the Nobel prize in literature for his ability to expound science to the layperson. It may be unfair to hold this book up to quite such an exacting standard, but the recommendation had the effect of sharpening my mind by forcing me to ask: how would the non-scientific reader cope with these great scientific ideas, as expressed by Atkins? If we compare this book with Stephen Hawking's * The Universe in a Nutshell * , which I also reviewed in * The THES * , Hawking's bestseller gave readers the sense of having been in touch with some pretty deep stuff but did not tell them much about it, whereas Atkins makes a real effort to explain an enormous range of modern science, up to and including the universe.

* Galileo's Finger * is nobody's idea of a nutshell, but it may be as close as a general reader can hope to get to understanding the essentials of modern science. Everything important is here, although in my view the reader needs some basic grounding in science to grasp it all.

Galileo's mummified middle finger is, in fact, gruesomely on display in a silver-and-crystal chalice at a museum in Florence. The conceit of the book is to allow the finger to propose ten "great ideas" in science, each of which then get a chapter explaining the science supporting that idea. The ideas range from evolution ("evolution proceeds by natural selection") to cosmology ("spacetime is curved by matter"), with a final chapter somewhat arbitrarily devoted to discrete mathematics ("if arithmetic is consistent then it is incomplete"). The author's intention is to follow historical order from the complexity of the everyday world - biology and Newtonian physics - through the abstractions of genetics and thermodynamics, through the molecular and atomic world to the deeper abstractions of quantum mechanics, and the role of symmetry in leading us to the standard model of the elementary particles and beyond. However, some aspects of this progression are illogical even though pedagogically satisfactory. For example, DNA comes before atoms and the periodic table, and we reach string theory under symmetry before the explanation of quantum theory. At the end, we jump to the expanding universe and general relativity, with a few pages of cosmological speculations.

All the material is discussed at a level of detail - scientific, historical and personal - that is amazing. The chapter on evolution does the following in 36 pages: it remarks on primitive and theological creation myths, discusses taxonomy (both Linnaean and the up-to-date method of cladistics), and follows this with a detailed discussion of the species concept. Then on to paleontology, where Atkins finds it necessary to introduce the reader to the concept of plate tectonics before properly addressing the facts of evolution and the evidence against creationism. A brief discussion of punctuated equilibrium, and of retrograde evolution follows. Then on page 18 he takes up Darwin, in which a few pages of personalia about the man and his contemporaries precede the statement of the basic principles of natural selection. Catastrophic extinctions and "arms races" are dealt with, and then again we get a rather thorough geology lesson, complete with eras, periods and epochs, and their respective flora and fauna. After that come two major problems remaining for the theory of evolution: sex and the unit of heritability. Finally, Atkins gives a thorough summary of human palaeontology, stopping at last to draw breath after the Cro-Magnons enter the stage. There are no missing steps or fudges on the way, but all this would be a challenge for even a very bright, highly motivated layperson to absorb; it takes a year at most universities.

Let me offer one compliment and raise one query in passing. It is a nice bit of evidence against creationism that one can easily find instances where evolution has made, and then preserved, mistakes in design. (However, the figure meant to illustrate this contains one of the few errors in the book; the blood vessels referred to in the caption are nowhere to be seen.) The query concerns the unit of heritability. Atkins seems in favour of the "selfish gene", which I thought modern concepts of gene networks had cast in considerable doubt, and he follows fashion, if not good sense, in rejecting group selection.

Skipping over chapter two on molecular biology, which Atkins tackles with barely a pause at breakneck pace, one reaches some material with which I am intimately familiar. Chapters three and four are about, respectively, energy - entailing all of classical Newtonian physics - and entropy. They are taken more slowly, reflecting quite properly the fact that the layperson tends to find biology easy, physics hard. Unfortunately, even to a physicist the discussion is not particularly lucid. I disagree on some details, and note that often the discussion refers to material presented in later chapters. The same is true of the following chapter, on atoms and their chemistry, in which pictures of atomic wave functions and the build-up of the periodic table precede by two chapters the explanation of quantum mechanics. Leon Lederman's pedagogy - fundamentals first - could have been useful here.

But chapter six, on symmetry, subtitled "The quantification of beauty" - is a triumph that meets with my almost unmitigated admiration and by itself makes the book worth reading. That quantum theory is basically applied symmetry is a secret that is too often kept even from fairly advanced students. At the very least, quantum field theory is the best formalism for taking advantage of the symmetries of space, time and the particles themselves.

After first giving us a primer on the nature of symmetry groups, Atkins emphasises the three fundamental ideas that make symmetry so important to physics: Emma Noether's theorem that to a symmetry there corresponds a conservation law and vice versa; the gauge principle, that all the interactions of physics result from gauge symmetries; and the fact that permutation symmetry of identical particles leads to Fermi and Bose statistics. And then he gives us a kind of account of strings! The whole chapter is a * tour de force * , especially since Atkins has not yet formally introduced the reader to quantum mechanics.

That comes in chapter seven, where we go through the fascinating, if painful, history of the rise of quantum theory, and finally confront the paradoxical nature of the quantum world when looked at from our "classical" point of view (or vice versa). Oddly enough, Atkins' inversion of the logical and historical order here seems valid pedagogically. It makes sense to worry readers about quantum paradoxes only * after * they have learnt how logically inevitable the theory is.

The final two natural-science chapters are cosmological. Starting from the establishment of the fact that the universe expands, Atkins probes deeper and deeper into the history of the "Hot Big Bang" to bring us right up to date with the latest data showing that the universe is, at least, not decelerating, as it should be under gravity. He goes, briefly, into the latest speculations about strings, alternative universes and the like.

One point in this fascinating tale brought me up sharp, however, and left me wondering about the precision of the historical details with which the book is richly endowed. The search for cosmic background radiation in the 1960s is said to have been "forestalled by two postdoctoral students, Penzias and Wilson, whose job it was to clear pigeon droppings from a large microwave antenna". At Bell Laboratories at that time, where I was working, there were no experimental postdoctoral students, and no one had the authority to "assign" scientists to such a task.

Chapter nine teaches us general relativity, all the way to the knotty problems of quantum gravity. One hopes that the reader who has made it thus far can handle this beautifully compressed and de-mathematised presentation. Finally, shifting gears entirely, Atkins takes on the problem of the logical foundations of mathematics, starting, as mathematicians do, with the premise that everything must begin with the natural numbers, 1, 2, 3..., and defining the continuum in terms of them - essentially arithmetising all of mathematics. My strong view is that this approach has more to do with the peculiar way that mathematicians think than with the mathematics of the real world: of the standard model and general relativity with their continuous symmetries, and all that. In some sense, the discreteness of mathematicians' mathematics has no more to do with natural science than with philosophy. The human mind knows continuous space before it can count. To take seriously the idea that the world is fundamentally discrete, as Atkins does, is a little more than controversial.

So, how is the reader doing? The writing is pungent and often felicitous, if on occasion a bit florid: "...an acorn of an idea that ramifies into a great oak tree of application, a spider of an idea that can spin a great web and draw in a feast of ...elucidation... (O)ther superspiders... would capture other juicy flies of science." Sometimes the "fuller explanations" seemed to me merely to confuse the reader unnecessarily. For example, the insistence that heat and work are not forms of energy but of energy transfer is surely only a counter-productive quibble. And the attempt to do without mathematics until the final chapter creates some major problems - for example, trying to describe gauge theory without introducing complex numbers. (The imaginary unit "i" would also be useful to the discussion of general relativity.) When "i" finally appears, in the mathematics chapter, it is as a footnote only.

As for errors, even Atkins is human. In addition to a tendency to present radical speculations with less caution than they merit, I noticed a few definite mistakes: it was the lack of scatter in Mendel's results that Fisher found odd; and quantum theory really does conserve energy.

Finally, the book could have been less utterly reductionist. It could have travelled up the ladder of complexity as well as down, mentioning such ideas as chaos, broken symmetry and scale invariance. But that would have been a different book.

Should you read it if you are not a scientist? Yes. None of the above criticisms alters the fact that for breadth and authenticity of material * Galileo's Finger * is a true model, not available elsewhere so far as I know.

Philip W. Anderson, Nobel laureate, is emeritus professor of physics, Princeton University, New Jersey, US.

## Galileo's Finger: The Ten Great Ideas of Science

Author - Peter Atkins

ISBN - 0 19 860664 8

Publisher - Oxford University Press

Price - £20.00

Pages - 380

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