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.