OF IMAGINARY NUMBERS

IN the cloudland of higher mathematics, there is a whole area of study called "imaginary numbers." What is an imaginary number? It is a multiple of the square root of minus one. What is the good of knowing that? Imaginary numbers, according to mathematicians, are useful in figuring out such problems as the flow of air or water past a curved surface like an airplane wing.

In ordinary life, imaginary numbers of a somewhat different kind seem to have become even more useful. From solemn public officials and eager corporations, from newspapers, television (and even, some dare say, from newsmagazines) comes a googol of seemingly definitive and unarguable statistics. They tell us, with an exactitude that appears magical, the number of heroin addicts in New York and the population of the world. By simulating reality, they assure us that facts are facts, and that life can be understood, put in order, perhaps even mastered.

If this sounds fanciful, consider a few specimens from one issue of the New York Times last week:

BANGKOK: In 1965, only 17% of the people in northeastern Thailand were within a day's journey of a main road. Today the figure is 87%.

NEW YORK: The St. Patrick's Day parade cost the city $85,559.61, whereas Puerto Rico Day cost only $74,169.44.

ATLANTA: There are 1.4 million illiterates in the U.S.

KABUL: Caravans traveling between Afghanistan and Pakistan "commonly carry up to 1,200 pounds of opium at a time."

In assuredly reporting these statistics, the Times--like all other journalistic enterprises--is carrying on a tradition founded by Archimedes. He set himself the task of computing the number of grains of sand that could be encompassed within the area of the known universe. After a great deal of figuring, accompanied by many diagrams, he produced an answer that satisfied him. (It mattered not that his data on the universe were wrong.)

The tradition flourishes today at many levels. It has been computed, for example, that the offspring of 450 moths can eat the weight of a diesel locomotive in one year. And that the average housewife washes 2.5 million kitchen utensils during her lifetime, the equivalent of a stack of dishes 70 times as high as the Empire State Building. And that 9.2 billion strokes of a cat's back would generate enough electricity to light a 75-watt bulb for exactly one minute.

These statistics may well be true, and so may most of the Times's figures--but obviously some are truer than others. A census of illiterates in an advanced, well-documented country carries considerably more conviction than a report from the remote corners of Thailand. Nobody is really sure exactly how many people there are in Thailand, after all, much less the distance that one of them can travel in a day, so the margin for error is presumably considerably larger than a precise figure like 17% implies. What makes such numbers imaginary is that most of them are basically collections of someone's estimates of the unknowable. We can assert with some confidence that there are, say, four birds on a branch. As the numbers get larger, we still believe in them, but with less reason.

In almost any area of life today, the best--certainly the most honest--answer to a request for figures would be: Nobody knows. But that makes us feel that somebody has failed at his job; there must be a right answer, therefore a right answer is composed. Last week the Federal Government's Center for Disease Control announced that a certain drug company may have infected 5,000 hospital patients with contaminated intravenous solutions, contributing to the deaths of 500 people. When asked how this figure had been determined, a Government spokesman said that one estimate of 2,000 was "unrealistic" and another estimate of 8,000 was "unfair." So the authorities split the difference.

Imaginary numbers sound true--that is their function, after all --and so they may serve the cause of truth. But they can serve the purpose of falsehood just as well. At the highest levels of government, imaginary numbers can delude even the shrewdest of leaders with "quantifications" of reality. For years, the Pentagon demanded imaginary numbers from combat troops in Viet Nam: body counts, kill ratios, and even computations of the numbers of obscure villages that were free from Viet Cong control (to a certain percentage). With the figures produced, the computers could declare with statistical certainty that the war was being won. "Is it a coincidence," asks Arthur M. Ross, former U.S. Commissioner of Labor Statistics, "that the most elaborately measured war in American history is also the least successful?"

It is not that the figures are falsified, but that we create the figures we want to believe. If the numbers game involves fears and prejudices, imaginary numbers reinforce the prejudice, heighten the fear. Since many heroin addicts in New York commit crimes to buy drugs, to cite one example, it has often been stated that the addicts steal $2 billion to $5 billion worth of goods per year. Max Singer, president of the Hudson Institute, decided to inquire how the figure came to be computed. It turned out, as he reported in The Public Interest, that someone had multiplied an estimated 100,000 addicts by an estimated average habit of $30 per day to determine a collective need of $1.1 billion a year. And since a thief generally sells stolen property to a fence for about one-quarter of its value, four times $1.1 billion produces a theoretical total of $4.4 billion. Singer found, however, that the value of all the stolen goods in New York does not amount to nearly that much, and that the drug addicts probably take property worth about one-tenth of the popularly accepted figure. Conversely, then, there may not be 100,000 drug addicts in New York after all (Singer guesses 70,000 at most), but only in our nightmares.

If every statistic were regarded with similar skepticism, it might well be found that many of our most widely accepted figures are also, at least in part, imaginary numbers. The national rate of unemployment, for example, is now stated to be 5.6%, but that figure is based entirely on people who officially reported themselves out of work. Idle students, housewives who cannot find outside jobs, unsuccessful artisans--such people are not counted.

Statistics on crime are equally uncertain, since they mainly reflect police diligence in rounding up minor offenders and reporting all arrests. Then there are those "police estimates" that name a figure for the unknowable number of prostitutes in Los Angeles or the uncountable crowds outside the White House. If present figures are imprecise, beware of all projections that foretell the future, particularly those that talk of the increasing youthfulness of the "average American." Actually, because both birth and death rates have declined, the "average American" is getting older.

Is nothing, then, to be believed? Yes--the evidence of the senses and the observations of the mind, but not too many of the imaginary numbers that try to provide proof. How many is "not too many"? The computer is working on that.

This file is automatically generated by a robot program, so reader's discretion is required.