Clever Mathematician’s Story Adds Up

John Allen Paulos makes a rare and valued companion. He is a mathematician who writes well. In “Once Upon a Number,” he takes as his guide “that most astute philosopher,” David Hume, who wrote, “I cannot but consider myself as a kind of resident or ambassador from the dominions of learning to those of conversation, and shall think it my constant duty to promote a good correspondence betwixt these two states, which have so great a dependence on each other.”

Paulos’ goal is nothing less than lofty. He hopes to reconcile the personal aspect of human life, which refers to the stories we tell and live by, and the impersonal, which is essentially mathematical, statistical and scientific. Literature and science, he says, share an uneasy complementarity, a complementarity Paulos explores in this collection of linked essays.

Each view of the world, Paulos argues, has limitations. The claims of physical science can be seen as an attempt to diminish the personal. These efforts sometimes come a cropper: Statistically, he writes, “the average resident of Dade County, Florida, is born Hispanic and dies Jewish.”

On the other hand, he says, those who want to enhance the realm of the personal may diminish, as some religions do, the impersonal: In religion, he writes, “physical processes . . . and unlikely events are transmuted into personal actions, omniscient actions and dark portents.”

Paulos thinks that maintaining a place for the individual “protected from the overweening claims of religion, society and even science, is an increasingly important unsolved problem.” Its solution, he continues, will require “accepting the indispensability of both stories and statistics and of their nexus, the individual who uses and is shaped by both.”

Abstract though it sounds, Paulos’ writing is playful. Speaking of language, he says that “semi-private languages are part of the common ground of any two significantly related people and appear in any extended story.” He demonstrates how this semi-private code arises with the example of two brothers and their cat, Oscar. When one brother, on vacation, is told that Oscar is dead, he scolds the other for being blunt. You could have said Oscar was trapped on the roof and broke the news gently, he complains. Then, when the man inquires about their mother, the reply shows that his brother has learned his lesson. “She’s on the roof,” he tells him.

Paulos is much taken with the ideas of complexity and disorder. “The brain’s complexity--its factual knowledge, associations, reasoning ability,” he writes, “is necessarily limited. . . . A rough number--three billion bits has been proposed--can be attached to it, but here the existence of the number is more important than its value.”

That number determines what we learn, Paulos suggests, and there are some things we may never understand because we just don’t have enough bits, like the hunt for a theory to explain the universe. “Although they differ ineradicably, both traditional and religious and scientific approaches to a hoped-for theory of everything share the perhaps naive assumptions that such a theory can be found and that its complexity will be sufficiently limited to be understood by us.”

“Why assume that?” Paulos cogently asks. Can human beings apply a number to everything? readers may wonder. Both delightful and wise, this little book cries out to be kept close at hand, to be looked into from time to time, to be treasured as an old friend.