Time Essay: Getting Dizzy by the Numbers

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Nowadays the commonest statistics about the world and the nation—from the megatonnages of the SALT debate to the dollars of the defense budget—tend to defeat the ordinary imagination. The world population is supposedly 4.2 billion. The nation's 3.N.P. is running at about $2.39 trillion. Washington debates whether defense spending will increase to as much as $122 billion (see cover story for an idea of the realities underlying the number). In truth, far smaller figures can overtax ordinary people, many of whom, after all, have trouble fathoming the weather service's temperature-humidity index.

Scientific news is loaded with even more forbidding challenges. Voyager I, it seems, found a hot spot in the vicinity of Jupiter that is 300 million to 400 million degrees centigrade. Later, Voyager II, going almost 45,000 m.p.h., came as close as 404,000 miles to Jupiter's cloud tops on its way to Uranus—some 1.6 billion miles out there. Science now has an electron microscope that can magnify 20 million times and so can photograph a particle with a diameter of about 4 billionths of an inch. Computers can do 80 million calculations a second (and ostensibly 6.9 trillion a day). Other recent news: a suspicion that the proton, a basic natural building block, may be unstable. It may indeed be decaying at such a rate that it would peter out in a million billion billion billion years. The effect of that notion is finally not mathematical but purely poetic.

It is not clear at just what magnitude (or diminutude) a number passes beyond the capacity of an ordinary person to grasp —that is, to picture the quantity. Yet obviously a great effort is required even to cope with what is symbolized by a billion. The proof lies in those familiar tormented illustrations that writers cook up in the hope of suggesting the amount of a billion: the 125-mile-high stack of dollar bills that would add up to about a billion, the airplane propeller turning around the clock at 2,400 r.p.m. that would fall short of spinning a billion times in a year, the fact that a billion minutes ago (A.D. 77) the Christian era had scarcely got under way. Still, such efforts to evoke the actuality of a billion are far likelier to give the curious a picture of an extremely tall stack of currency than of the quantity of a billion units. In truth, most mega-numbers (and micro-numbers) that fly by these days paralyze the mind almost as much as a googol.

Indeed, the googol might be a good symbol for a time when the world is under the sway of technology, when it has no choice, as Jacques Ellul says in The Technological Society, but to "don mathematical vestments." The googol is the figure 1 followed by 100 zeros (see above). It was made famous, or infamous, in the 1930s by Mathematician Edward Kasner. He also offered the googolplex, which is 1 followed by a googol of zeros — so many zeros, said Kasner, that no matter how tiny they could not all be written on a piece of paper as wide as the visible universe.