Measuring Cultural Information

But there may be more significant ways to characterize civilizations than by the energy they use for communications purposes. An important criterion of a civilization is the total amount of information that it stores. This information can be described in terms of bits, the number of yes-no statements concerning itself and the universe that such a civilization knows.

An example of this concept is the popular game of "Twenty Questions," as played on Earth. One player imagines an object or concept and makes an initial classification of it into animal, vegetable, mineral, or none of these three. To identify the object or concept, the other players then have a total of twenty questions, which can only be answered "Yes" or "No." How much information can be discriminated in this manner?

The initial characterization can be thought of as three yes-no questions: Conceptual or objective? Biological or nonbiological? Plant or animal? If we agree that a particular game of "Twenty Questions" is in pursuit of something alive, we have, in effect, answered three questions already by the time the game begins. The first question divided the universe into two (unequal) pieces. The second question divided one of those pieces into two more, and the third divided one of those pieces into yet two more. At this stage we have divided the universe crudely into 2×2×2=2³=8 pieces. When we have finished with our twenty questions, we have "divided the universe into 2²⁰ additional (probably unequal) pieces. Now, 2¹⁰ is 1,024. We can perform such calculations fairly quickly if we approximate 2¹⁰ by 1,000=10³; therefore, 2²⁰ equals (2¹⁰)², which approximately equals (10³)²=10⁶. The total number of effective questions, twenty-three, has divided the universe into about 2²³, or approximately 10⁷ pieces or bits. Thus, it is possible for skillful players to win at "Twenty Questions" only if they live in a civilization that has an information content of about 10⁷ bits.

But, as I discuss below, our civilization is characterized by perhaps 10¹⁴ bits. Therefore, skillful players should win at "Twenty Questions" only about 10⁷ out of 10¹⁴ times, or one in 10⁷, or one in ten million times. That the game is won more often in practice is because there is an additional rule – usually unstated but well understood: Namely, that the object or concept being named should be one in the general cultural heritage of all the players. But this must mean that 10⁷ bits can convey a great deal of information about a civilization, as indeed it can. Philip Morrison has estimated that the total written contribution to our present civilization from classical Greek civilization is only about 10⁹ bits. Thus, a one-way message, containing what, by the standards of modern radio astronomy, is a very small number of bits, can contain a very significant amount of new information and can have a powerful influence on a society in the long run.

The number of bits communicated in our radio broadcasts is quite enormous, conveying a great deal of information about our culture.