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On the Importance of Numbers

One common attribute of a scientist is an unusually acute sense of numbers and their implications. I think it was Bertrand Russell who once observed that mankind would rather commit suicide than learn arithmetic. In other words, the meaning and implications of some numbers are often lost on most people—even when those numbers bring a very important message. George Bernard Shaw stated that one distinguishing characteristic of an educated person is that he or she can be emotionally moved by statistics.

A sense of numbers—why do I dwell on this observation? Perhaps it's because we who come from a background of engineering, mathematics and science tend to convey concepts and findings in terms of numbers; yet many for whom our messages are intended find our communications (full of numbers as they are) unappetizing, boring, unconvincing and a bit standoffish.

Consider this set of numbers: During the interval between Thomas Jefferson's death (1826) and the mid-1990s, the U.S. human population roughly quintupled, and the GDP (gross domestic product) per person increased by a factor of eight. The impact of human activity on the environment (open space, water, air) is roughly proportional to the product of population times GDP per person, or an increase of about 40-fold over that 175-year period. Such unprecedented expansion was managed and even facilitated by advances in the technologies of health, pollution control, etc. But how much longer can we keep up the pace? Is indefinite expansion of population and consumption humankind's supreme goal? What treasures do we leave behind and deny our descendents as we forge ahead with this kind of expansion? Quiet, empty spaces? Wondrous biodiversity? A sense of independence? Without a sense of numbers, these could be doomed to loss before we realize the ultimate absurdity of our exponential world and undertake some mid-course corrections.

Here's another set of numbers. When the latest failure of the artificial test of the new "Star Wars" ballistic-missile interceptor occurred this month, one high-level spokesperson at the Department of Defense seemed to imply that one success out of three attempts wasn't all that bad. True, it's a very challenging thing to intercept ballistic missiles. But a sense of numbers also tells us that any commitment to begin to deploy such a costly defense system would be foolhardy at best, especially since there appear to be "low-tech" ways to overwhelm it, even if the interceptor tests were to succeed. However passionately we may feel about shifting from offensive to defensive strategies, we must be guided by facts—numbers. In Disney's world, "wishing will make it so," but that doesn't work in the world we must live in.

What's the message for Sigma Xi members and other readers of American Scientist? Help more people gain a sense of numbers—how exponentials diverge, why semi-log graphs can be so informative—how to be emotionally moved by statistics!

John H. Gibbons
President, Sigma Xi

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