NEW USES OF THE ABSTRACT—BOEHM 313 
lands heads up the first five times, you might conclude that it is almost 
certainly biased in favor of heads. But if you get three heads and 
two tails, you would certainly ask to experiment further, 
Industry faces this kind of problem regularly. A manufacturer 
with a new product tests it before deciding whether to put it on the 
market. The more he tests, the surer he will be that his decision 
will be right. But tests cost money, and they take time. Now modern 
statistics can help him balance risk against gain and decide how long 
to continue testing. It can also help him design and carry out experi- 
ments. New methods involving a great deal of multidimensional 
geometry can point out how products and industrial processes can be 
improved. A statistician can often apply these methods to tune up 
a full-scale industrial plant without interrupting production. (For 
an example, see the diagrams, figs. 1 and 2.) 
Classical statistics has been extended in another way. One of the 
latest developments is “nonparametric inference,” a way of drawing 
conclusions about things that can be sorted according to size, lon- 
gevity, dollar value, or any other graduated quality. What matters 
is the size of the statistical sample and the ranking of any particular 
object in that sample. It is not actually necessary to measure any of 
the objects, so long as they can be compared. It is possible to say, for 
instance, that if the sample consists of 473 objects, it is 99 percent 
certain that only 1 percent of all objects of this sort will be larger 
than the largest object in the sample. It makes no difference what 
the objects are—people, automobiles, ears of corn, or numbers drawn 
out of a hat. And the statement is still true if instead of largeness 
you consider smallness, intelligence, cruising speed, or any other 
relevant quality. 
In practical application, nonparametric inference is being used to 
test batches of light bulbs. By burning a sample of 63 bulbs, for ex- 
ample, the manufacturer can conclude that 90 percent of all the bulbs 
in the batch will almost certainly (99 chances out of 100) have a longer 
life than the second bulb to burn out during the test. 
One of the most fascinating recent developments in applied mathe- 
matics is game theory, another offshoot of probability theory (see “A 
Theory of Strategy,” Fortune, June 1949). From a mathematical 
viewpoint, game theory is not particularly abstruse; many mathe- 
maticians, indeed, consider it shallow. But it is exciting because it 
has given mathematicians an analytic approach to human behavior. 
Game theory is basically a mathematical description of competition 
among people or such groups of people as armies, corporations, or 
bridge partnerships. In theory, the players know all the possible 
outcomes of the competition and have a firm idea of what each out- 
come is worth to them. They are aware of all their possible strate- 
gies and those of their opponents. And invariably they behave 
