Fear of Physics by Lawrence M. Krauss Read Free Book Online

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TWO
    THE ART OF NUMBERS
    Physics is to mathematics what sex is to masturbation.
    —Richard Feynman
    Language, a human invention, is a mirror for the soul. It is through language that a good novel, play, or poem teaches us about our own humanity. Mathematics, on the other hand, is the language of nature and so provides a mirror for the physical world. It is precise, clean, diverse, and rock-solid. While these very qualities make it ideal for describing the workings of nature, they are the same qualities that appear to make it ill suited to the foibles of the human drama. So arises the central dilemma of the “two cultures.”
    Like it or not, numbers are a central part of physics. Everything we do, including the way we think about the physical world, is affected by the way we think about numbers. Thankfully, the way we think about them is completely dependent upon how these quantities arise in the physical world. Thus, physicists think about
numbers very differently than do mathematicians. Physicists use numbers to extend their physical intuition, not to bypass it. Mathematicians deal with idealized structures, and they really don’t care where, or whether, they might actually arise in nature. For them a pure number has its own reality. To a physicist, a pure number usually has no independent meaning at all.
    Numbers in physics carry a lot of baggage because of their association with the measurement of physical quantities. And baggage, as anyone who travels knows, has a good side as well as a bad side. It may be difficult to pick up and tiresome to carry, but it secures our valuables and makes life a lot easier when we get to our destination. It may confine, but it also liberates. So, too, numbers and the mathematical relations among them confine us by fixing how we picture the world. But the baggage that numbers carry in physics is also an essential part of simplifying this picture. It liberates us by illuminating exactly what we can ignore and what we cannot.
    Such a notion, of course, is in direct contradiction with the prevailing view that numbers and mathematical relations only complicate things and should be avoided at all costs, even in popular science books. Stephen Hawking even suggested, in A Brief History of Time, that each equation in a popular book cuts its sales by half. Given the choice of a quantitative explanation or a verbal one, most people would probably choose the latter. I think much of the cause for the common aversion to mathematics is sociological. Mathematical illiteracy is worn as a badge of honor—someone who can’t balance his or her checkbook, for example, seems more human for this fault. But the deeper root, I think, is that people are somehow taught early on not to think about what numbers represent in the same way they think about what words represent. I was flabbergasted several years ago when teaching a
physics course for nonscientists at Yale—a school known for literacy, if not numeracy—to discover that 35 percent of the students, many of them graduating seniors in history or American studies, did not know the population of the United States to within a factor of 10! Many thought the population was between 1 and 10 million—less than the population of New York City, located not even 100 miles away.
    At first, I took this to be a sign of grave inadequacies in the social studies curriculum in our educational system. After all, the proximity of New York notwithstanding, this country would be a drastically different place if its population numbered only 1 million. I later came to realize that for most of these students, concepts such as 1 million or 100 million had no objective meaning. They had never learned to associate something containing a million things, like a mid-sized American city, with the number 1 million. Many people, for example, could not tell me the approximate distance across the United States in miles. Even this is