What Gerard Piel KnowsJuly 3, 2002
Able to expound on the major ideas of 20th-century science with, in the word of our reviewer, "grace and understanding," Gerard Piel nonetheless admits to an ignorance of mathematics.
By Philip J. Davis
The Age of Science: What Scientists Learned in the 20th Century. By Gerard Piel, Basic Books, New York, 2001, 460 pages, $40.00.
Gerard Piel was the man who in 1948 revived Scientific American and then saw it through to its emergence as a preeminent popular magazine of science. He was involved with the running of the magazine until 1988 and over the years has been the recipient of many honors. I had met Piel many years ago (in a nonscientific context), and I used the appearance of his book, which I wanted to review for SIAM News, as the occasion to renew this acquaintance.
I wrote to Piel proposing an interview. I indicated that I would bring neither tape recorder, laptop, nor notebook to our get-together. He immediately invited me to lunch.
On April 10, we spent a leisurely hour and a half over lunch, during which our conversation ranged widely. Piel is a lively character, full of wit, stories, and genial laughter. A public-spirited fellow, he has served on all kind of boards, both scientific and cultural, and has won many awards. Not suprisingly, he has known "everybody."
Piel graduated from Harvard in 1937, with a major in European history. He was a tutee (in the Harvard sense) of historian Michael Karpovich. He was an admirer of Robert K. Merton, one of the first scholars in the "sociology of science" and at that time a young faculty member at Harvard. Shortly after his graduation, Piel took a job as a science reporter with Henry Luce's new LIFE magazine. In those days, the amount of science journalism was slight.
The Age of Science expounds on space, time, quantum theory, cosmology, light and matter, the living cell, geology, the evolution of life in considerable detail. Technology is not covered, nor is medical science. Given his early training in history, it is not surprising that Piel has embedded his narratives in historical settings.
Bibliographical references are provided for each chapter, including many relevant articles published over the years in Scientific American. Considering the large corpus of material and the depth at which it is expounded, what I find incomprehensible and paradoxical is that so much of the world is claimed to be comprehensible. (And not just in this book.)
One difficulty with material targeted to a general readership is this: A sequence of words (for the most part at least vaguely familiar) and sentences is presented, but the reader's understanding of the words in the scientific context can be remote. When, for example, I read (on page 256, well into Piel's chapter on the living cell) that "The 5-carbon sugar plus phosphoric acid groups link up into long chains, shedding molecules of water, just as the amino-acid peptide groups do in proteins," I am floundering in an unfamiliar sea, and the previous material has provided me with very few planks to grasp. Although I can repeat the words, I do not understand them. If this is true for me, I suspect it to be true for people in general; and if it is true for science, it is doubly true for mathematics.
Nonetheless, it was plain to me that The Age of Science is a virtuoso performance, and from it I was able to acquire a familiarity with the vocabulary of the various sciences and to learn something of their methodology.
Though admitting that science creates new problems even as it provides solutions to old ones, Piel exudes optimism about its future. I diverge from his optimism, disagreeing---to name a specific instance---with his approving quotation (page 23) from the inaugural address of molecular biologist Jacques Monod on his election, in 1967, to the Collège de France:
"The sole end, the sovereign good, the supreme value in the ethic of knowledge---let us acknowledge it---is not the happiness of man, much less his comfort and security-it is objective knowledge itself."
Readers of my reviews know that, stimulated by the book under review, I like to take off and expatiate on a few related ideas of my own. In arranging to meet Gerard Piel, I told him frankly that I was looking for him to give me a "hook" around which to wrap my review. So back to our lunch.
From memory, I've reproduced (or partially fabricated) the essence of one part of our conversation:
PJD: You know, there's no math in your book.
GP: Yes, I know.
PJD: Why is that the case?
GP: Because I'm ignorant of math.
PJD: How much math did you have in school?
GP: Up through trigonometry at Phillips Andover.
PJD: Well, that's not total ignorance. You're probably aware that everything you've written about in, say, theoretical physics has a tremendous base of advanced math.
GP: I am aware of that. And I also know that when the public thinks of math, it thinks that it's just arithmetic. I myself know better than that, but still I'd call myself ignorant. You know, the word "innumerate" is used today to describe people such as myself, but I don't like the word.
PJD: I don't like it either. How would you describe yourself, then?
GP: As ignorant. Possibly as "immathematical."
PJD: Have you known any famous mathematicians over the years?
GP: I've known many mathematicians, but I believe they were all mathematicians manqués.
Here we have a person, in some ways an "average" person, in others very far from average, who can expound on the major ideas of 20th-century science with grace and understanding and who, at the same time, admits to ignorance of mathematics. Now doesn't that raise some questions as to how much mathematical knowledge is necessary for the average person to live intelligently and productively in today's world?
Gliding over the difficult and constantly argued questions of how much math the "average" person ought to know and be able to do, and the extent to which more than a minimal amount contributes to a liberal education, let me put forward what I think the average person ought to know "about" mathematics and its function in today's life.
Mathematics includes theories of quantity, space, and pattern. It is also the study of the abstract symbolic, representational structures (both visual and multimedia) and deductive structures that are employed within these theories.
The public should be aware that abstract theoretical studies often (but not always) contribute to the development of our techno-mathematical civilization. Our daily lives have been increasingly mathematized, even though the mathematizations themselves are hidden from view by hardware and software. All the physical sciences, economics, and some of the social sciences have tended toward increased mathematization. The digital computer in all its manifestations has an extremely complex and deep mathematical underlay. The "engine" of today's world is a mathematical engine.
Mathematizations do not come down from heaven: They are created and installed by humans, and they exhibit human frailties. The computer and the various information networks supported by it are not the final judges of what is or what should be or what will be the case. An economic, social, or even physical theory is not more "objective" simply because it is expressed in mathematical symbolisms. Mathematical models, computerized or not, are often claimed to be wiser than us. This can be a dangerous and dehumanizing precept.
The tendency toward the installation of mathematics in all aspects of life is likely to increase. Mathematics consists of shared structures of thought, and such structures, like physical or social structures, can both support us and restrain us. They can affect people and society sometimes positively and sometimes negatively. The public can and should react with both positive and negative feedback to the mathematizations that have been put in place.
I have often found that the "average citizen" does not realize that absolutely new mathematics and applications of old mathematics are constantly being created by the scientific community and implemented by the technological community. Mathematics is no longer merely a liberal art, a science, or a useful craft. Mathematics, when applied, has become a product, and as such it becomes subject to market forces, political and legal actions, and court decisions.
I'm sure that for all his professed ignorance of mathematics, Gerard Piel knows about and appreciates these aspects of mathematics. It is clear to me that if this sort of "math appreciation" were widespread, it would be a great educative step forward. It would extend the meaning of the word "numeracy" and enlarge the horizon of those who assert that their only connection to mathematics is that they've put their checkbooks more or less in order.
Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at email@example.com.