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The Fastest Way to Simplify Things:
Contrary to popular opinion, mathematics is about simplifying life, not complicating it. A child learns a bag of candies can be shared fairly by counting them out: That is numeracy. She abstracts that notion to dividing a candy bar into equal pieces: arithmetic. Then, she learns to calculate how much cocoa and sugar she will need to make enough chocolate for fifteen friends: algebra. And so it goes in mathematics, from the easiest to the hardest. The fastest way to simplify things is to spot the symmetries, or invariances -- the fundamental properties that do not change from one object under study to another.
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The key is spotting the regularity inside the irregular, the pattern in the formless.
When a man goes to clear jungle he has relatively few types of tools: To cut, perhaps a machete; to knock down, a bulldozer; to burn, fire. Science is like that. When we explore the vast realm of natural and human behavior, we find our most useful tools of measurement and calculation are based on surprisingly few basic ideas. When a man has a hammer, all he sees around him are nails to hit. So it should be no great surprise that, wtih our small number of effective mathematical tools, we can find anologies between a wind tunnel and a Reuters screen.
The same quadratic equation with which the ancients drew right angles to build their temples can be used today by a banker to calculate the yield to maturify of a new, two year bond. The same techniques of calculus developed by Newton and Leibniz two centuries ago to study the orbits of Mars and Mercury can be used today by a civil engineer to calculate the maximum stress on a new bridge, or the volume of water to pass beneath it.
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2024 2. kitabı
