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THERE ought to be a very good reason for assembling two volumes of essays, mostly book reviews, that have appeared before over a decade or so only as isolated pieces. Raisons d'etre for a few dozen pieces don't necessarily add up to the right one for a 650-page work. Most of the articles in James Newman's new collection make interesting reading; some could stand very well on their own; a few seem to belong neither in Science and Sensibility nor in Scientific American. Taken together, they titillate without really satisfying.
Newman writes that "The collection is a miscellany because I have miscellaneous interests, yet it is not altogether helter-skelter. Perhaps the title, which, I will not deny, gave some difficulty, is reasonably descriptive." It is, and the two volumes are also largely descriptive writing. What will make a reader uneasy are the occasional flirts with analysis and elliptical judgments: these offer unblushingly direct ideas of what Newman's interests mean to him but an oblique and unsatisfactory view of his criteria of judgment on men of science.
He writes mostly of quasi-biographical works on great scientists in every important century. Other reviews are grouped into two sections dealing with subjects in a specific historical setting. One treats of Greek education in antiquity, early Chinese civilization, and other pre-Newtonian subjects. The other slips into a discussion of specifically modern crises and attitudes in science; Pascal and Maxwell give way to Bohm, Schrodinger, and Charles Darwin A long and careful piece on Einstein near the end of the first volume signals the shift from traditional to contemporary concerns. At the close of the second is a melange of little treatises on comets, albatross and so forth, which will be read by anyone who has enjoyed what came before.
The essays show Newman as a knowledgeable writer whose diverse curiosities have taken him beyond an interest in the better-known men of science to figures and folios which the Scientific American reader wouldn't otherwise reach. I'm not sure that his mixture of explicit summary and speculative essay is altogether a good thing. Newman's four-volume compilation of mathematical writings The World of Mathematics is a classic editorial feat; Mathematics and the Imagination (which Newman wrote with the late mathematician Edward Kasner) was, on the other hand, an original work that popularized lucidly some nontrivial aspects of mathematics. Echoes of both the editor and the expositor trail through the pages of this latest compendium: Newman, I think, is trying to have the best of two worlds in his essays.
At times the attempt comes off, but reading the less successful pieces can be trying. The author's most frequent peccadillo in these pages is a bland humanist sentimentality. He may conclude that a mathematician's work was wrong or that metaphysics taints Eddington's cosmology, and yet refuse to pass adverse judgment on the scientific value of his subject's work. I have in mind particularly his approach to Eddington: "His penchant for paradoxes, his gift for seductive images, his untenable philosophical interpretations of physical events, made him a prime target for clear thinkers." Yet, "he was a major benefactor of society. He stimulated the teaching and learning of physical science; he enlarged understanding of its scope and methods; he excited a taste for adventure in scientific thought." All this may be true; the ten or twelve pages of lucid essay which have preceded these pronunciamentos convinced me they are true. But Newman is asking us to opt for the pragmatic perspective of science rather than make our own decision on what he has given us.
This is not a very subtle way of going about things. I suspect that, had he wished, the author could have written his essay to convince me that Eddington's philosophical misapprehensions were minor flaws in a cosmic vision. Instead he presents a nicely balanced study and then asks us to accept just half of it.
I would be much more comfortable about judging Eddington with a better idea of what to go on. One can't say much for Newman's own criteria; they are usually obscure, and distressingly inadequate when he spells them out. Of Eddington he concludes, "He deserved to see farther than other men, and time, I suspect, will prove he did." Newman's enthusiasm for the scientist's social contribution has distorted his evaluation of the validity of his scientific work. Eddington, it seems, will prove to be farsighted mostly because he deserved to be farsighted. "His work is graced by a poet's sympathy, illumined by a poet's sense of truth and unity," Newman writes. The same could be said of Einstein and Schrodinger; Newman has made what is only a necessary condition for greatness into a sufficient one.
Newman has better criteria, he is keeping them to himself. His treatment of Eddington's cosmology is almost willfully negligent:
Another objection to Eddington's principle is that the so-called constants of nature,--for example, the fine-structure constant, 137--when derived in accordance with his ideas, are "absolutely constant," whereas in several cosmological theories they are represented as increasing decreasing, depending in one way or another on the age of the universe at the time when the are measured.
This sort of statement raises a number of questions which the writer ignores If they can't be answered within limits of his review they should at least be acknowledged; the reader who senses them is going to be distictly uncomfortable. Is it important to a cosmology that the natural constants remain constant? If so, why is it? If we can't decide whether it's crucial? why not? The questions are not trivial; the answers aren't obvious. Newman has begged them, then passed judgement on Eddington's contributions without indicating where he stands on the points of difference with other theories.
One can find rather easily, in fact, that Eddington's absolute constant of 137 began as 136. Eddington added a unit when that value became inconsistent with better experimental values of the electron charge and the speed of light. Max Born's Experiment and The-Physics gently dissects Eddington under an aegis that most critics want to share: evaluation of what seems reasonable and what seems unreasonable. I have the feeling that Newman, with his long experience mathematics, could also have something interesting to say about Eddington's attempt to fit the constants of nature to a Procrustean bed of positive integers at a time when so many physicists have been concerned to verify values of these constants out to five decimal places.
NEWMAN'S approach to Eddington is not an extreme example of his distressingly glib judgments in Science Sensibility. The point is typified by a remark in one of the earlier essays: "I agree entirely with Bertrand that intellectually Pythagoras was one of the most important men that ever lived, both when he was wise and when he was unwise.'" We're by now with the notion that and unwisdom generate scientific progress. But it is one thing to say that one scientist's mistakes send another in the right direction, and quite another that unwisdom in a wayward scientist presents no contradiction to his greatness. The English mathematician G. H. Hardy said the first of Ramanujan, the Indian genius: "Ramanujan's false statement was one of the most fruitful he ever made, since it ended by leading us to all our joint work on partitions."
Most of the essays are tantalizingly short, far too short to answer the questions they raise. This is more apparent with three dozen of them gathered together. The thematic element is lacking: Newman has not cared to make his scientific values explicit, or to defend his obvious and probably justified bias for mathematics in the scheme of things. True, Science and Sensibility is offered as the compendium of personal interests; but I still believe that Newman's concerns must be bound together by more than a Scientific American cover.
He has done much better on the few occasions when he treats his subjects at length. His favorite sort of topic is covered by two major articles in the first volume, one on Einstein and the other (by far the longest piece in the set) on the nineteenth-century mathematician William Kingdon Clifford. Scientific American readers will recognize neither of these: the Clifford piece was the introduction to a 1946 edition of Clifford's The Common Sense of The Exact Sciences, and the excellent survey of Einstein's more important work came out as a separate article three years ago.
Newman wrote something of everything in the long section on Clifford: biography, as detailed as I'd want to read; a fascinating treatment of Clifford's work; and glimpses of the twentieth-century relevance of his visions. These are carefully partitioned, hence Newman's touch is convincing here as nowhere else. Clifford emerges as a superb mathematician even in the company of the nineteenth-century geniuses. He was one of the last to work with equal success on several mathematical fronts, Poincare being perhaps the last who managed it. Clifford spun out the consequences of the new non-Euclidean geometries and of Abelian function theory; he also gripped the prickly legacy of Kantian skepticism and took to the lecture stand with clear thinking on different epistemological questions of the day.
One can read out of Newman's descriptions a really extraordinary role for this English genius who lived to be only 35 and had just 15 productive years. He died almost is the year Frege and Boole began the systematic restructuring of mathematical foundations, but his work on the specific foundations of all the known geometries represents some of the most acute thinking in mathematics with regard to the relation between geometry and physics. Lord Russell has recalled that his own early work was done in ignorance of Clifford's, but ventured that Clifford in the 1870's was thinking ahead of the best minds of his day. In Einstein's time the geometry of the real world lost its reliability as a frame of reference and became properly a part of physics itself. One can infer from both Newman and Russell that this inversion, an alien notion to most nineteenth-century thinkers was already half-formed in Clifford's mind.
Another prescient insight was Clifford's careful questioning of exactness of measurement:
"The knowledge of an exact law in the theoretical sense would be equivalent to an infinite observation. I do not say that such knowledge is impossible to mean; but I do say that it would be absolutely different in kind from any knowledge that we possess at present."
This sort of thinking was not appreciated until well into this century when physicists began worrying seriously about the limits of measurement.
Newman takes the space and the care of look thoroughly into Clifford's presuppositions; the result is a thoughtful and interesting sketch. The selection on Einstein is shorter but no less satisfying. Einstein's own questions are dealt with fairly in a coherent outline of his discoveries and some of his own classic illustrations. The editor and the expositor in Newman have somehow blended perfectly here.
HE follows these with a group of intriguing reviews on Pascal, Mill, Wittgenstein, and others of more sensibility than science. The discussion of The Age of Analysis picks up Morton White's rewarding distinction between the "hedgehogs" and "foxes" of twentieth-century philosophy (taken from the Greek poet Archilochus: "The fox knows many things, but the hedgehog knows one big thing.")
The subsequent essays built around causality and determinism in modern physics should be all means be read, if for no other reason than to form some impression of the quicksilver state of physics with regard to these concepts. Wave-particle duality and the Heisenberg uncertainty principle are still hard to get used to, but there has for several decades already been a flux of speculation about their meaning. Ernest Cassirer, David Bohm, and Erwin Schrodinger are writing in a realm where it is
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