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Time Essay: Getting Dizzy by the Numbers

7 minute read
Frank Trippett

“The very hairs of your head,” says Matthew 10:30, “are all numbered.” There is little reason to doubt it. Increasingly, everything tends to get numbered one way or another, everything that can be counted, measured, averaged, estimated or quantified. Intelligence is gauged by a quotient, the humidity by a ratio, the pollen by its count, and the trends of birth, death, marriage and divorce by rates. In this epoch of runaway demographics, society is as often described and analyzed with statistics as with words. Politics seems more and more a game played with percentages turned up by pollsters, and economics a learned babble of ciphers and indexes that few people can translate and apparently nobody can control. Modern civilization, in sum, has begun to resemble an interminable arithmetic class in which, as Carl Sandburg put it, “numbers fly like pigeons in and out of your head.”

Most of this numbering is useful, and a good deal of it is indispensable. In any event, the world could hardly have wound up otherwise. Human beings began counting and “falling under the spell of numbers,” in H.G. Wells’ words, well before they could write. Long ago, the entire species was like some modern aboriginal peoples (the Damara and some Hottentots in Africa, for example) who possess words only for numbers up to three, every larger quantity being simply expressed as “many.” A fascination with the multiplicity of things, together with a quenchless scientific yen, pushed the main body of mankind, however, inevitably into its present plight—a time when so many stunning measurements are bandied about that numbers plunge in and out of the brain more like galaxies than pigeons.

The trouble is that with everything on earth (and off, too) being quantified, micro and macro, the world is becoming woefully littered with numbers that defy useful comprehension. Biology, for example, estimates that the human brain contains some 1 trillion cells. But can any imagination get a practical hold on such a quantity? It is easy to picture the symbolic numerals: 1,000,000,000,000. Still, who can comprehend that many individual units of anything at one time? The number teases, dazzles the mind and even dizzies it, but that does not add up to understanding. Biology ought to find out what happens to the brain when it tries to visualize 1 trillion.

Boggling figures of that sort have been popular as curiosities ever since Archimedes tried to calculate how many grains of sand the universe could contain (1051, he said). Today, however, mind-walloping numbers are no longer oddities; they are the stuffing of ordinary news and public discourse. While even the biggest figures no doubt possess meaning, it is impossible not to suspect that many casually circulated numbers might as well be the music of the spheres.

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.

It could be that the googol’s emergence marked the time when mankind’s fascination with indigestible numbers slipped beyond the pale. In the same decade that the googol appeared, Sir Arthur Eddington opened his absolutely serious book, The Philosophy of Physical Science, with the sentence: “I believe there are 15,747,724,136,275,002,577,605,653,961,181,555,468,044,717,914,527,116,709,366,231,425,076,185,631,031,296 pro tons in the universe and the same number of electrons.”

Plainly, a world that feeds on such impenetrable figures suffers a peculiar compulsion that might be called googolmania The hunger is, whatever else, a marvel to behold, providing the spectacle of a species unable to solve a 13% inflation rate, yet eager to be informed by the Guinness Book of World Records that the world weighs 6,585,600,000,000,000,000,000 tons.

The human craving for numbers tells a good deal about man kind. It is both sign and cause of man’s long trek from the days of one, two, three, many. It can be taken as a symptom of exuberant joy in the quantity and multiplicity of things. Still, the dizzy acceptance of those truly incomprehensible figures might also be construed as a vicarious variation of the old Faustian game: the yearning to know the unknowable.

So far, the game has not cost the species its unquantifiable soul. Enough of that remains to nurture widespread excitement over, let us say, a World Series. A googol may not tell us much about where we stand today, but even Edward Kasner would have appreciated the true human relevance of 4-3 Pirates

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