The Bible describes the early universe as "without form and void" (Genesis 1:2). This is certainly true, according to Marcus Chown, in terms of how much information was in the universe then. Expanding on the ideas of physicist Stephen Hsu, Chown argues that, just after the Big Bang, the universe contained no more than 200 bytes of information. By comparison, the first two sentences of this article contain 190 bytes of information. A universe with so little content would certainly seem "void." But today, the amount of information just within arms' reach—to say nothing of the rest of the universe—seems infinite. Where did all that information come from? Hsu argues that it came from quantum processes, the observation of which caused probabilistic states to collapse, thus injecting information into the universe. In other words, information exists because of randomness.

In his article in this series, Randy Isaac has summarized Hsu and Chown's arguments, providing perspective on what these ideas mean for the inhabitants of a "random reality." We are surrounded by randomness, and one might say we owe our existence—or at least the information that verifies our existence—to randomness. But randomness, Isaac states, is not synonymous with a lack of purpose or design. What is randomness, and how can we understand it in light of a universe that appears orderly?

Mathematics offers a way. To a mathematician, the word "random" describes a process that, rather than being without purpose, is without predictability. We say the flip of a fair coin is random because the outcome of one toss gives no information about the outcome of the next. On the other hand, a toss of a biased coin is predictable, therefore less random, and the outcome of a toss conveys less information. This view of randomness offers at least two insights that could be helpful.

First, we see that there is an inverse relationship between predictability and information content. The more random an event is, the more information its outcome contains; and the outcome of a fully predictable event contains no information. Another way to view this is that information reduces uncertainty, and the information content of a random variable can be measured by the degree to which uncertainty is reduced by its outcome. So the more information we see, the more randomness was at work to produce it—but the less uncertain we are about the universe by having seen it.

Second, while individual outcomes of a random variable are unpredictable, aggregates of outcomes often form well-defined patterns. The length of a specific person's life cannot be known in advance, but the average lifespan of a large group of people with similar characteristics can be predicted with a high degree of accuracy. (Just ask the insurance companies.) In this way, randomness and unpredictability on the small scale often lead to regularity on the large scale.

Viewing randomness through the lens of mathematics helps us realize that randomness is not opposed to purpose and in fact can provide our lives with purpose by way of the information that the outcomes of random events convey.

Robert Talbert is associate professor of mathematics at Grand Valley State University in Allendale, Michigan.

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