Science: Googol

Mathematician Edward Kasner, 59, of Columbia University, is one of the mythical baker’s dozen of savants who were supposed to be the only men in the world able to understand the Einstein theory of relativity. At Harvard’s Tercentenary celebration in 1936, he showed how to bisect a “horn angle” (an angle formed by two curves tangent to each other), a problem which had stumped mathematicians for 2,000-odd years. His fun: talking to children.

Dr. Kasner was lecturing on the theory of big numbers to the members of a kindergarten. When he asked how many raindrops fell on New York City on a rainy day, the scientist got the children to agree that the number was approximately equal to the number of sand grains at Coney Island. One followed by 20 zeros was a satisfactory expression. Dr. Kasner then proposed a greater number, one of his own, which he called a “googol”: 1 followed by 100 zeros. He also proposed a much greater number still, a “googol plex”: 1 followed by a googol of zeros.

Mathematician Kasner wasn’t fooling.

He has been thinking about googols for some years. It is too large a number ever to be used for physical enumeration, since Sir Arthur Stanley Eddington estimates the number of electrons in the entire universe to be 1 followed by 79 zeros. The googolplex is so large a number that it could not be written on a piece of paper stretching across the visible universe (some 1,000,000,000 light-years).

Nevertheless, the improbability of some events possible in theoretical physics is so great that a number somewhere be tween a googol and a googolplex would be required to express it. However, Dr. Kasner points out that no number is anywhere near infinity so long as it can actually or theoretically be written out.

Since the googolplex could be written out if more writing space were available in the universe, it is nowhere near infinity.

Dr. Kasner last week said he had received letters from several notable persons of eclectic interest, commending him for his choice of the name “googol” for his number. Both “googol” and “googolplex” were suggested to him by his nephew, at that time aged 9.