Knowledge Beyond Numbers


I was recently sent a well-argued report written by sensible people which insisted that a larger place must be found in our schools and colleges for instruction in mathematics and “quantitative thinking.” Scarcely had I finished reading it when a full professor came by to tell me that cliometrics (which applies statistical analysis and the theoretical explanations of social science to investigations of the past) was sweeping the country and threatening to destabilize all future tenure decisions in history departments. What worried him was that this “cognitive mode”—too much fooling around with numbers—would reduce the nature of the past and diminish its meaning. He was as disturbed as Bulfinch would have been if someone had used James Watt’s calculation of the work done when thirty-three thousand pounds are raised one foot in a minute to explain what kind of horse Pegasus was.

There is an issue here that I think readers of this magazine should spend some time thinking about. It can be stated as follows: In a time when the world is trying to organize itself by what is sometimes unfortunately called numeracy —mathematical modeling, statistical probabilities, and so forth—what is the possible contribution of the other means to interpret experience, and indeed, are there really other useful means?

What is involved may be more easily understood if it is put more concretely. I will try to do so with extracts from three conversations I have had in the course of the last thirty years. The first was with a psychologist, and our subject was narration, which is not only the backbone but much of the sinew in the body of knowledge I work with. When I said that the narrative was a form of thought, our canvass of the subject ended because he found the idea irresistibly funny and me too silly to talk to.

The second was with an experimental physicist. He and I and others under his direction were engaged in an effort to improve instruction in our schools from kindergarten through twelfth grade and across the board. One day, going down in an elevator, he asked me what I thought I was doing when 1 taught history. In order to avoid a discussion on the character of a usable past, I said, “I’d like to teach them to think like historians.” “What do you mean?” he said as he was going out the opening elevator door. “There’s only one way to think.”

Once I said to a psychologist friend that I consider narrative a form of thought. He found the idea irresistibly funny and me too silly to talk to.

And the third was with an economist. We were talking about the flight of graduate students from history into the social sciences. “Well,” he said, “it’s easy enough to explain. Bright people go into the easy fields,” by which I took him to mean those fields where the situation can be defined in the satisfying exactitude of an equation.

These were bruising experiences; they forced me to think of what I had to say that would enlarge the kinds of questions put to those who could get right answers. They also, for a time, made me think of the possibility of demonstrating my eligibility for a higher intellectual category by the simple device of switching to an easier field. In the end I decided to stay where I was, with those of us who had been left behind to grope our way through the murkier regions of human experience. In those regions I think the method of sensitized grope is most likely to turn up certain kinds of findings that are indispensable for the better ordering of human affairs.

In preface to further thoughts on this matter, I would like to make two things clear. I believe with my friend the experimental physicist—and a good many others—that if you’re talking about what Hercule Poirot called the “little grey cells,” there is only one way to think. The process of logical deduction from the available evidence is an ordered path of chemical and electrical reactions. The harder the data, the larger the number of knowns, the easier the process.

Also, I believe in the cognitive mode of quantitative thinking or numeracy or however else they put it in modern translation. As a spasmodic investigator of nineteenth-century English literature in my student days, I found my understanding of this way of going at things considerably delayed. My introduction to the power of numbers and mathematical calculations in the organizing of certain kinds of experience was in fact postponed until I was ordered to the staff of the commander, Eastern Sea Frontier, in World War II. His subject at the time was antisubmarine warfare. My instructors were a geophysicist from Princeton and a statistician from a Wall Street investment firm.

They sat all day and many nights before a huge chart of the Atlantic Ocean bounded on one side by the eastern shore of the United States and on the other by the west coast of Europe. On the waters thus framed, the positions of every ship at sea were indicated by small, movable pieces: the merchantmen on their lawful occasions, the U-boats maneuvering to attack these targets, and the men-of-war available to prevent the submarines from fulfilling their destructive purpose.

The information that flowed in to these two men came from many sources. It dealt with cruising speeds, course directions, fuel capacities, submergence depths, land configurations, gun and torpedo ranges, radar readings, present times and positions. Hard data.

From such evidence the two officers then devised programs to modify the disposition of the ships at sea: an evasive change of course for a convoy; reinforcement for a protective screen; the accumulating concentration of fleet elements during a two- or three-day period to fulfill the mission to search and destroy.

It was all as neat and precise and absorbing as a game of chess. I had never seen or conceived of so varied and extensive a human exercise so elegantly ordered and so firmly controlled. We had come a long way from those old bluff days when sea dogs going into action could do no more than damn the torpedoes lying out there in unknown positions and order full speed ahead. When you had the hard facts in enough quantity, you could by taking thought dispel even the fog of war.

This, as I say, was my introduction to the power that lies in numbers and mathematical calculations. Since then I, like about everyone else, have been made aware of the way these agencies can be applied in many other areas to our advantage. For one thing, by these means we have acquired a fairly complete understanding of the organization of nature. And from there we have gone on, by the same means, to develop from the natural resources a technological structure that is almost as complete as the great globe itself. With clear and distinct ideas derived from known quantities by the exercise of the only way to think, we have done wonders, creating out of such things as telephones, jet engines, plastics, and computers an integrated system to live in. If we are now approaching the Pythagorean proposition that all things are numbers, we obviously must, in the interest of the efficient management of our affairs, instruct as many of the young as possible in the informed manipulation and proper use of numbers—quantitative thinking. Only a troglodyte could oppose such a recommendation, especially in view of the fact that while what we have done is truly wonderful, it still isn’t working very well.

I will not belabor a point that anyone who looks at the seven o’clock news can verify for himself. But a historian is uneasy if he leaves a conclusion with no documentation at all. So I will cite a statement in the catalog of one of our leading institutes of technology to the effect that the things it teaches as so far applied have produced a “degradation of our world—both physical and social.” To reverse this process will certainly require more generally distributed quantitative skills, but as the catalog suggests, it will also require the exercise of other kinds of perceptions and a more comprehensive understanding.

To make this point a little clearer, I will draw further on the Pythagoreans. When they said all things are numbers, they really meant it; they had, for instance, a mathematical expression for the kingdom of heaven. To them we owe a great deal, for they laid the foundations for mathematics as demonstrative deductive argument, and they contributed significantly to the development of geometry. For themselves they contrived a numerical system to explain and order conditions in which they established an attractive harmony among all the quantities and ratios. All went well until a man discovered the existence of “incommensurable magnitudes.” Then, to save their system, I have been told and do in part believe, they put the man to death.

With no more than the poetic license expected from the softer side, I would suggest that, within the technological system we have constructed, the most incommensurable magnitude is produced by the human condition—something we have not in recent times taken sufficiently into account. The design of the structure from the time of Watt’s condenser has been determined, on the whole, by the properties of the materials, the calculation of the physical forces, and the continued search for increased operating efficiencies. The requirements of the human being have not been given adequate expression in the existing scheme, and the degradation of the physical and social world will continue until this influence—which resists exact calculation—is made the determining principle in the organization of our technological capacities. This is especially true now that man the incommensurable has, in one of those ironies that occur on my side, made himself at last through his machinery the measure of all things.

This is all very well to declare, but how—either in the classroom or the world at large—does one make the uncertain quantity of human being as clear and convincing as the claims of things that can be measured. This is a hard question. The obvious answer is that there is a good deal more work to do in the way of finding out what man is like in his full dimension—what he must have, what he can’t bear, what he tends to become in pursuing the short-run aims, what he might hope to be in the longer term; what, in brief, he is, warts, biological system, thinking reed, destructive tendency, generous spirit, and all.

The thought here is that some part of the work in this hard field involves the discovery of as much as possible about what man has been like in the past. That brings us back to the beginning and what it may mean to think like a historian. Up to a point he thinks, of course, like any experimental physicist and a good many others in the “only one way to think.” Give him facts—the value of the cotton crop in 1839, the rate of population growth in the decade of the eighties —and he can use the little gray cells to subject the data to reasonable analysis and search for appropriate arrangement.

But beyond a point there are some restrictions laid upon these exercises of pure reason. He cannot, as in the study of physical nature, look for a series of events that progress in obedience to the rules of logic. He cannot verify his findings in the test of recurring episodes. He cannot base a prediction on the observation and description of a known and repeating process. He must seek for illumination through the construction of a particular occasion. And though he may collect a good deal of stable information on which to base his reconstruction, he can never be sure enough of the interaction of his bits of evidence to have confidence that he has fulfilled Leopold von Ranke’s great injunction to tell it like it really was.

So how does the historian proceed in the face of such difficulties to build his first approximations? It is a temptation to reply with clarifying circumlocution. In certain fields there are just not enough numbers to permit incontrovertible programming. But since the findings in these fields were taken by our ancestors as indispensable for the proper conduct of their affairs, they accepted the insight of the Muses when computation faltered. Thus historians—like poets and painters—do what Muses do. Since this may seem like the evasive persiflage expected of my calling, a word of further explanation is provided.

If hard evidence was lacking on some crucial subject, our ancestors sought the insights of the Muses. Thus historians— like poets and painters—do what Muses do.

A distinguished philosopher of the old school (before there were many mathematical models) once said to me that he read history all the time but never read the accurate historians. On crossexamination it developed that he meant those who scrupulously presented the facts they had and let it go at that. He wanted the company of those who were prepared to give energy to the account by using the informed imagination and common sense to organize the structure of an event and interpret its meaning.

The result might not have the magisterial ring of a mathematical formula. But when you are working with unstable forces, what Charles Beard once called the interaction of “fate, contingency, and character” (i.e., “history”), it’s the best way to advance the understanding. And this best should serve well enough. The power that lies in the reconstructed past is that it can take into account the amazing aggregate of a given experience—the large forces, the general tendencies, the singular variations, and the qualifying infinite details that are the stuff of the human condition. And as I have said, I believe the safe and satisfying organization of the future depends upon the outside possibility that the design and use of the available machinery can be made to conform to the nature of that stuff, which may get lost amid the numbers, models, statistical probabilities, and abstract propositions of too much quantitative thinking.

There are many ways in which the illuminations of history can be made to serve in this imperative endeavor. I will mention only two. One has to do with new subject matter. Up to about now, in the writing of the history of Western civilization it has often been possible to get by with passing references to the steam engine, the spinning jenny, and the McCormick reaper. This was in accord with the realities; for almost all of recorded time the energy to make things came from men, animals, wind, and falling water. It was also in accord with certain attitudes formed in those earlier days and continued in the genteel tradition. Machines that did work had small place in the transactions of education, culture, and refinement.

But now that the genteel tradition has lost most of its bite and the texture of life has become a patchwork of machines and technical systems, the subject of technology has become a central interest for the society and so, it follows, for the historian. The record of the last two centuries is filled with evidence of our changing relationship to the machinery we have built and with continuing demonstrations not only of remarkable achievements but of disturbing examples that we have never got it all quite right. From the study of the earliest effort to find the appropriate match-up between the man or woman and the power loom to our latest efforts to find a better controlling context for all our instrumentation than the simple sanctions of Progress or the simplistic sanction of “growth,” there is much to be learned to our advantage as we search for better forms of organization.

My second observation has to do with some of the oldest subject matter of history, the smallest unit in the composition of any particular occasion, the single person. As Aristotle said, this person is a political animal and thus finds much of his point and fulfillment as a member of society; but he is not to be taken as some ant or bee programmed for a specific contribution to the life of a hill or a hive. He is an independent variable whose interaction with his environment can make a difference in what his evolving community will become.

By the careful examination of how the single person has acted in a variety of particular situations we can still learn much about the human condition that must serve as the organizing principle for our technological schemes. My further thought, obviously, is that history is one of the most rewarding means for the examination of the problematical subject matter. It is true, of course, that for those of us who think like historians, some very important evidence is not available. Along with the rest, we do not know much about how men and women will behave when we face the fact that we have the whole world in our hands, when we are the commanding presence confronted with the necessity to command not only external forces but also ourselves. But what there is to know about this presence during its long watch as an aggressive subordinate within nature will still bear directly on all future developments.

For confirmation of what I have been saying, I turn to a historian whom my philosopher friend would have read with pleasure and who was also a master of social organization. Theodore Roosevelt put the matter as well as anyone could, and of course, as with any truth he discovered, he put it frequently and in different ways from that bully pulpit. But the gist remained the same. “Back of the laws, back of the Administration, back of the system—lies the man.” If, as he said, it is sometimes necessary for legal or social reasons to think of people as a class or category, our future safety turns on our recognition that the foundation of society is the individual and the stuff that is in him. “Whether we all go up or all go down depends on whether he does or does not wax in growth and grace.” Our task today is to find those conditions in which the individual does not wane.