Why Does a Public that Hates Numbers Put Up with So Many Numbers?

January 22, 1999

Book Review
Philip J. Davis

The Measure of Reality: Quantification and Western Society 1250-1600. By Alfred W. Crosby, Cambridge University Press, Cambridge, 1997, 245 + xii pages, $24.95.

Trust in Numbers: The Pursuit of Objectivity in Science and Public Life. By Theodore M. Porter, Princeton University Press, Princeton, 1995, 310 + xiv pages (about 70 of which contain notes and bibliography), $37.50.

Quantitize, quantitize
Let no chance evade your eyes.
--With a nod to Tom Lehrer

We live with international ratings of schools and curricula. We have numericized the quality of living. We have scanned the corruption indices of countries. The characteristics of a marriage can be mathe-matized, as can the quality of a page of prose. The temperature of a feverish man, the average yearly number of suicides in Liechtenstein, the strength of an earthquake, the percentage of the daily potassium requirement in a morning dish of bananas and cream all form part of appropriate databases.

I suspect that if someone has not already proposed one, there will soon be a numerical criterion for what is sex and what isn't. In the light of recent events, one immediately perceives the advantages to such a standardization.

Quantification goes on and on and on. Is nothing at all immune from it? Our civilization is obsessed with its processes, and its magic power holds sway over many areas of life. Yet an appendix full of numbers will bring on yawns from readers and a demand that the author get down to the meat of the situation (a euphemism for something more exciting). The manner in which quantification is established, its credibility, the connections it is able to make, its merits, its downsides, its history, its social psychology all form the bases of the two books under review.

Crosby, a professor of American studies, history, and geography at the University of Texas, Austin, tells the story of Western quantifications, from the 13th century, around the time Roger Bacon was measuring the angle between a rainbow and the sun's rays, to the revolution in applied mathematics in the 16th century. Porter, a professor of the history of the natural and social sciences at UCLA, and the occasional director of the UCLA Center for the Cultural Studies of Science, Technology, and Medicine, brings us up to date. But these books are by no means continuations of one another. Each has a distinct textual quality, and each has a primary message it wants to deliver. These messages differ considerably. If one goes back as far as the ninth century, the brilliant East regarded Western Europe contemptuously, as merely a source of "eunuchs, slave-girls and boys, brocade, beaver skins, glue, sables, and swords, and not much more" (Crosby, page 3).

Beginning in the 13th century, this low condition was followed by absolutely stunning progress in science, technology, armaments, navigation, cartography, business practice, bureaucracy, music, and painting. Crosby implies that the superiority of the West can be ascribed to its penchant for "pantometry," i.e., the measurement of everything. A century ago, the famous German sociologist Max Weber saw the superiority of Northern Europe as due to the prevailing Protestant ethic. Are they saying the same thing in different words?

Crosby's book, despite its many useful bibliographical references, is a relatively easy read. It provides a historical narrative of how our perceptions of time and space were altered by quantification, and how quantification was interlinked with developments in bookkeeping, painting, and music. His chapter describing the mathematization of music, and the way in which the introduction of polyphonic singing forced an accurate approach to tempi and led to the development of musical notation, was an eye opener for me.

Quantification, writes Crosby, was what led the Western world away from the "venerable model," which stressed qualities, to the "new model," now prevailing, which stresses quantities. Modern culture has a rationalistic character that is "precise, punctual, calculable, standard, bureaucratic, rigid, invariant, finely coordinated, and routine" (Crosby, page 230, quoting sociologist E. Zerubavel).

With the exception perhaps of his chapter on music, a good deal of what Crosby writes will be familiar territory to those who know something of the history of late mediaeval mathematics. For those who do not, I can recommend his book highly. Porter digs deeper---psychologically, sociologically---and he focuses on the industrial and postindustrial periods. He suggests that quantification, particularly in the social areas, can be seen as a response to a decline of faith and trust in personal judgments or the judgments of small knowledgeable elites. This decline, in turn, is tied to increasing democratization. Porter's book might also have been subtitled "quantification and group psychology."

Porter's book is not an easy read. Though quite free of the professional lingo of the historian or sociologist, its paragraphs are densely packed with statements that seem to shout out to the reader: "Have you ever thought about such and such? No? Then why don't you?" At these points I would lay the book down and think through what was being said. For example:

"The drive for objectivity in (business) accounting did not follow naturally from a logic of finance. Neither was it the result of unchecked power on the part of professional experts. It was a consequence of self-aggrandizing self-effacement, the methodological equivalent of gray suits, adopted by men who would otherwise have had even less chance of acting autonomously" (Porter, page 98).

Despite such heavy passages and a slower reading pace, its ideas are rewarding, and I feel that Trust in Numbers deserves much more review space than I am able to give it here.

The scope of the book goes far beyond the sole question of why quantification now rules the waves in science, and increasingly in life. Porter gives numerous historical case studies in detail, from the influence of the Ecole Polytechnique in 19th-century Paris to today's concern with cost-effectiveness. Moreover, such topics as "how objective can laboratory experiments be when reproducibility is quite hard to achieve," or "how quantification serves the demand for the depoliticization of administrative decisions" or "why French industrialists believe that training in higher mathematics is useless" spin off from the author's word processor like sparks from a grindstone.

The ambiguities and contradictions of technocracy and of quantification are laid out: For example, quantification derives from the spirit of democracy; it feeds into technocracy, which is authoritarian:

"[Technocratic] reasoning finds interference from vested interests, ideologies, and party politics intolerable. . . . Technocrats . . . tend to suspect parliamentary democracy and prefer 'the rule of the fittest' and a managed polity" (Porter, page 146, quoting historian Richard Kuisel).

The most common explanation, according to Porter, for the high regard for numbers, for their power and prestige in the social and economic spheres, is their success in physics. Though this success---this magic if you will---is essentially inexplicable, despite the many explanations that have been given, the humanistic technicians latch onto the outlines of the magic and believe that its effectiveness will carry over.

Granting the successes in physics and other "hard sciences," Porter is not satisfied with this explanation for the social areas. He views numbers as "strategies of communication" intimately related to communities of people. These communities and the mathematics they invoke are part of a social technology, a technology of distance, wherein the uniformity of mathematics, its highly structured rule-bound nature, its inner neutrality, is easily manipulated and easily shipped.

"Quantification," he writes, "is preeminent among the means by which science has been constructed as a global network rather than merely a collection of local research communities."

Later in the book, Porter remarks---perhaps with tongue in cheek, and thinking (as I am) of the Eurocrats sitting in Brussels who promulgated mathematical criteria for what is and what is not a cucumber---that the world language of the future will be not English but numbers.

The key concept underlying both of the books under review is the intimate relation of quantification to objectivity. Now, what is objectivity? According to Porter, it is

"one of the classic ideals of science. It refers to a cluster of attributes: first among them is truth to nature, but there is also impersonality, fairness, universality, and in general an immunity to all kinds of local distorting factors like nationality, language, personal interest, and prejudice" (page 217).

"The ideal of objectivity is a political as well as a scientific one. Objectivity means the rule of law, not of men. It implies the subordination of personal interests and prejudices to public standards" (page 74).

And, I would add, it means the subordination of the ethical component. Quoting the famous biostatistician Karl Pearson, "one of the great worshippers of quantification," Porter points out that quantification arises from the necessity of "taming human subjectivity" (pages 20, 32).

The pluses of quantification and of the resulting "objectivity" are clear to all of us. The virtues of standardization have been preached to a fare-thee-well, to the point that a patient admitted to a hospital is treated largely as a chemico-mathematical structure, an element of a certain category (diabetic, cardiac, . . .), equipped with a time-varying vector of parameters and a bundle of graphs. And on the whole have we not profited from this abstraction?

As perceived by Porter, there is more to the downside than the alienation of the individual. Quantification legitimizes administrative actions. It provides a way of hiding behind the numbers and stats and becomes a refuge from personal responsibility. (I can't help you. I only know what the computer tells me.) "Subjectivity," on the other hand, "creates responsibility" (Porter, page 196).

The pervasiveness of quantification, then, is in part a response to our civilization of growing personal distrust, and of suspicion of personal judgments that could lead to favoritism, nepotism, malpractice, and prejudices. "The drive to supplant personal judgement by quantitative rules," Porter writes, "reflects weakness and vulnerability" (page xi). Elsewhere, though, he describes numbers as "among the gentlest and yet most pervasive forms of power in democracies" (page 48).

Is absolute objectivity ever achieved? Rarely; and if it were achieved, it would be a dangerous thing. However, everyone seems to agree that quantification and its encasing mathematics, with its de-contextualized, value-free symbols and processes, enable us to come as close to objectivity as is humanly possible.

What of the future? Discussion of this question is largely avoided by both authors, but I append here a few views of my own. As regards the hard sciences, I think that the famous aphorism of Lord Kelvin is alive and well:

"When you can measure . . . and express it in numbers you know something about it" (see, for example, Crosby, page 225, for Kelvin's statement).

Numbers, construed in the generalized sense of the whole mathematical corpus, surely now rule the roost in theoretical physics. Despite the recent maunderings of physicists on what might be termed theophysics, despite metaphysical arguments as to whether it is we or Nature who writes The Grand Books of the Universe (Galileo's words), quantification has not yet exhausted its potential.

As regards the social sciences and their applications, I think that quantification is just getting off the ground. It will be a very long while before we cease mathematizing cucumbers and writing prescriptions for society in an arcane language that would baffle even physicians. We may be furious with watchdog acts, such as the 1997 Government Performance and Results Act, which mandates periodic performance measurements for all grants awarded by federal agencies in the U.S. We may wonder about the cost-effectiveness of an act whose origins can be found in the idolatry of cost-effectiveness. Or we may be gratified by our ability to hide behind rules that invoke quantification.

The driving forces behind additional mathematizations are more substantial than these. They are the attitudes, the education, the personnel, the mathematics itself, the hardware, the expectations that are all in place.

"The need for relevant data is not just the peculiar craving of academic social scientists," Robert Solow, Nobelist in economics, wrote recently in The New York Review of Books (November 5, 1998). "It is the lifeblood of rational social policy and its evaluation." We have too large an investment in the process to abandon it suddenly.

Reason, faith, and their interplay are topics that have been on the minds of philosophers and popes for centuries. Quantification surely represents reason; personal judgment is faith. Or do I have it backward?

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island.

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