How Math Explains the World

HarperCollins Publishers || ISBN 978-0-06-164601-0 || Author: James D. Stein || English || PDF || 288 Pages || 3.23 MB

Not Just a Rock
We advance, both as individuals and as a species, by solving problems. As a rule of thumb, the reward for solving problems increases with the difficulty of the problem. Part of the appeal of solving a difficult problem is the intellectual challenge, but a reward that often accompanies the solutions to such problems is the potential to accomplish amazing feats. After Archimedes discovered the principle of the lever, he remarked that if he were given a lever and a place to stand, he could move Earth.1 The sense of omnipotence displayed in this statement can also be found in the sense of omniscience of a similar observation made by the eighteenth-century French mathematician and physicist Pierre-Simon de Laplace. Laplace made major contributions to celestial mechanics, and stated that if he knew the position and velocity of everything at a given moment, he would be able to predict where everything would be at all times in the future. “Given for one instant an intelligence which could comprehend all the forces
by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”2 Of course, these statements were rhetorical, but they were made to emphasize the far-reaching potential of the solution to the problem. A casual onlooker, seeing Archimedes use a lever to reposition a heavy rock, might have said, “OK, that’s useful, but it’s just a rock.” Archimedes could have replied, “It’s not just this rock—it’s any object whatsoever, and I can tell you what length lever I need to move that object and how much effort I will have to exert in order to move the object to a desired position.” Sometimes we are so impressed with the more dazzling achievements of science and engineering that our inability to solve seemingly easy (or easier) problems appears puzzling. During the 1960s, one could occasionally hear the following comment: If they can put a man on the moon, how come they can’t cure the common cold? We are a little more scientifically sophisticated now, and most people are willing to cut science some slack on problems like this, recognizing that curing the common cold is a more difficult problem than it initially seems. The general feeling, though, is that we just haven’t found a cure for the common cold—yet. It’s obviously a difficult problem, but considering the potential payoff, it’s no surprise that medical researchers are busily trying, and most of us would probably expect them to find a cure sooner or later. Sadly, for those suffering from runny noses and sore throats, there is a very real possibility that a cure for the common cold may never be found, not because we aren’t clever enough to find it, but because it may not exist. One of the remarkable discoveries of the twentieth century is a common thread that runs through mathematics, the natural sciences, and the social sciences—there are things that we cannot know or do, and problems that are incapable of solution. We know, and have known for some time, that humans are neither omnipotent nor omniscient, but we have only recently discovered that omnipotence and omniscience may simply not exist. When we think of the scientific developments of the twentieth century, we think of the giant strides that were made in practically every discipline, from astronomy through zoology. The structure of DNA. The theory of relativity. Plate tectonics. Genetic engineering. The expanding universe. All of these breakthroughs have contributed immeasurably to our knowledge of the physical universe, and some have already had a significant impact on our daily lives. This is the great appeal of science—it.

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