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The Mathematical Universe
| Article
# : |
16499 |
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Section : |
NATURAL SCIENCE
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| Issue
Date : |
5 / 1989 |
3,703 Words |
| Author
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John D. Barrow
John D. Barrow is Reader in astronomy at the University of
Sussex in the United Kingdom. His current book is The World
Within the World (New York: Oxford University Press, 1988). |
A Yale professor was once asked to settle a dispute between two rival factions in the university: What was more important, teaching languages or teaching mathematics? "Mathematics is a language" was his answer.
In the world of science, mathematics indeed seems to be the language that allows us to talk most effectively and logically about the nature of things. But mathematics differs from other languages like English or Spanish. Indeed, it possesses a built-in logic, and is thus more akin to a computer language. When we write a grammatically correct English sentence like "All dogs have four legs and my table has four legs, so my table is a dog," there is no guarantee the sentence will be logically correct or correspond with events in the world. Conversely, the grammatical incorrectness of a phrase like "to boldly go where no man have gone before" does not render its realization impossible. One can break a rule of English grammar without falling into meaninglessness, but break a rule of mathematics and disaster ensues. If one false mathematical statement is allowed, it can be used to prove the validity of any mathematical statement. When Bertrand Russell once made this claim during a lecture, he was challenged by a skeptical heckler to prove that the questioner was the pope if twice 2 were 5. Russell at once replied: "If twice 2 is 5, then 4 is 5; subtract 3, then 1 equals 2. But you and the pope are 2; therefore, you and the pope are 1!"
So mathematics is a language with a built-in logic. But what is so striking about this language is that it seems to describe how the world works--not just sometimes, not just approximately, but invariably and with unfailing accuracy. All the fundamental sciences--physics, chemistry, and astronomy--are mathematical sciences. No phenomenon has ever been discovered in these subjects for which a mathematical description is not only possible but also beautifully appropriate. Yet one could still fail to be impressed. After the fact, perhaps, we can force any hand into some glove, and maybe we have chosen to pick the mathematical glove because it is the only one available. It is striking, however, that physicists so often find that some esoteric mathematical structure, invented by mathematicians in the dim and distant past only for the sake of its elegance and curiosity value, is precisely what is required to make sense of new observations of the world. In fact, confidence in mathematics has grown to such an extent that one now expects (and finds) interesting mathematical structures to be deployed in nature. Scientists look no further when they have found a mathematical explanation.
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