Knowledge Beyond Numbers


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.