Is God a Mathematician?

Is God a Mathematician? by Mario Livio Page B

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Authors: Mario Livio
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great Aristotle, for instance, thought that stones, apples, and other heavy objects fall down because they seek their natural place, which is at the center of Earth. As they approached the ground, Aristotle argued, these bodies increased their speed because they were happy to return home. Air (and fire), on the other hand, moved upward because the air’s natural place was with the heavenly spheres. All objects could be assigned a nature based on their perceived relation to the most basic constituents—earth, fire, air, and water. In Aristotle’s words:
    Some existing things are natural, while others are due to other causes. Those that are natural are…the simple bodies such as earth, fire, air and water…all these things evidently differ from those that are not naturally constituted, since eachof them has within itself a principle of motion and stability in place…A nature is a type of principle and cause of motion and stability within these things to which it primarily belongs…The things that are in accordance with nature include both these and whatever belongs to them in their own right, as traveling upward belongs to fire.
    Aristotle even made an attempt to formulate a quantitative law of motion. He asserted that heavier objects fall faster, with the speed being directly proportional to the weight (that is, an object two times heavier than another was supposed to fall at twice the speed). While everyday experience might have made this law seem reasonable enough—a brick was indeed observed to hit the ground earlier than a feather dropped from the same height—Aristotle never examined his quantitative statement more precisely. Somehow, it either never occurred to him, or he did not consider it necessary, to check whether two bricks tied together indeed fall twice as fast as a single brick. Galileo Galilei (1564–1642), who was much more mathematically and experimentally oriented, and who showed little respect for the happiness of falling bricks and apples, was the first to point out that Aristotle got it completely wrong. Using a clever thought experiment, Galileo was able to demonstrate that Aristotle’s law just didn’t make any sense, because it was logically inconsistent. He argued as follows: Suppose you tie together two objects, one heavier than the other. How fast would the combined object fall compared to each of its two constituents? On one hand, according to Aristotle’s law, you might conclude that it would fall at some intermediate speed, because the lighter object would slow down the heavier one. On the other, given that the combined object is actually heavier than its components, it should fall even faster than the heavier of the two, leading to a clear contradiction. The only reason that a feather falls on Earth more gently than a brick is that the feather experiences greater air resistance—if dropped from the same height in a vacuum, they would hit the ground simultaneously. This fact has been demonstrated in numerous experiments, none more dramatic than the one performed by Apollo 15 astronaut David Randolph Scott. Scott—the seventhperson to walk on the Moon—simultaneously dropped a hammer from one hand and a feather from the other. Since the Moon lacks a substantial atmosphere, the hammer and the feather struck the lunar surface at the same time.
    The amazing fact about Aristotle’s false law of motion is not that it was wrong, but that it was accepted for almost two thousand years. How could a flawed idea enjoy such a remarkable longevity? This was a case of a “perfect storm”—three different forces combining to create an unassailable doctrine. First, there was the simple fact that in the absence of precise measurements, Aristotle’s law seemed to agree with experience-based common sense—sheets of papyrus did hover about, while lumps of lead did not. It took Galileo’s genius to argue that common sense could be misleading. Second, there was the colossal weight of Aristotle’s

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