The Half-Life of Facts Read Free Page A

a day. But give it one more week. Now we’re getting more than $80 a day. Within a month our allowance is more than $100 million a day!
    Exponential growth gets its name from the use of an exponent: anexponent signifies how many times to multiply another number, the base, by itself. Many times a special constant is used for the base; in the case of exponential growth it is often
e
. Also known as Napier’s constant, it is about 2.72. It’s one of those numbers, like π, that crops up in the weirdest situations, from bacteria doubling to infinitely long sums of numbers. The exponent part of the equation includes what is known as its rate of growth. The larger this value, the faster the quantity grows, and the faster it doubles.
    .   .   .
    THE exponential growth curve was well-known to Price, so when he began to measure the heights of his stacks of journals, he knew immediately what was going on. But maybe he just happened to have gotten the only stack of journals that obeyed this curious pattern. So he began collecting lots of data, a research style that he followed throughout his life.
    He measured the number of journal articles in the physics literature in general, as well as for more specialized fields, such as the subfield that deals with linear algebra. And they all seemed to have elements of the exponential curve. Price began to recognize that this could be a new way to think about how science grows and develops. Price published his findings, under the title “Quantitative Measures of the Development of Science,” in a small French journal in 1951, after presenting this work at a conference the previous year in Amsterdam.
    No one was interested.
    But Price wasn’t deterred. He returned to Cambridge and continued to pursue his research in this new field, the quantitative study of science, or
scientometrics
, as it soon became known. This science of science was still quite young, but Price set himself to collecting vast quantities of data to help him understand how science changes.
    By the 1960s, he was the foremost authority in this field. He gathered data from all aspects of science and marshaled evidencethat enabled him to look at scientific growth as something far from haphazard; this knowledge was subject to regular laws.
    Expanding on his initial research on scientific journals, he gathered data for a wide variety of areas that displayed this growth, from chemistry to astronomy. Price calculated the doubling times—how long it takes for something to double, a proportional increase that implies exponential growth—for these components of science and technology, which then can be used as a rough metric for seeing how different types of facts change over time. Here is a selection of these doubling times from his 1963 book
Little Science, Big Science
:
    Domain
Doubling Time (in years)
Number of entries in a dictionary of national biography
100
Number of universities
50
Number of important discoveries; number of chemical elements known; accuracy of instruments
20
Number of scientific journals; number of chemical compounds known; memberships of scientific institutes
15
Number of asteroids known; number of engineers in the United States
10
    The growth of facts was finally beginning to be subjected to the rigors of mathematics.
    .   .   .
    PARALLEL to Price’s work in the hard sciences, a similar line of research was proceeding in the social sciences. In 1947, a psychologist named Harvey Lehman published a curious little paper in the journal
Social Forces
. Combing through a wide variety of dictionaries, encyclopedias, and chronologies, Lehman set out to countthe number of major contributions made in a wide variety of areas of study over the years. He looked at everything from genetics and math to the arts, whether new scientific findings, new theorems, or even new operas produced. What he found in all of these were exponential increases in output over time. But this wasn’t only over the previous few