Is God a Mathematician? Read Free

particular number: 4.669…To his amazement, when he examined other equations, the same curious number appeared again. Feigenbaum soon concluded that his discovery represented something universal, which somehow marked the transition from order to chaos, even though he had no explanation for it. Not surprisingly, physicists were very skeptical at first. After all, why should the same number characterize the behavior of what appeared to be rather different systems? After six months of professional refereeing, Feigenbaum’s first paper on the topic was rejected. Not much later, however, experiments showed that when liquid helium is heated from below it behaves precisely as predicted by Feigenbaum’s universal solution. And this was not the only system found to act this way. Feigenbaum’s astonishing number showed up in the transition from the orderly flow of a fluid to turbulence, and even in the behavior of water dripping from a tap.
    The list of such “anticipations” by mathematicians of the needs of various disciplines of later generations just goes on and on. One of the most fascinating examples of the mysterious and unexpected interplay between mathematics and the real (physical) world is provided by the story of knot theory —the mathematical study of knots. A mathematical knot resembles an ordinary knot in a string, with the string’s ends spliced together. That is, a mathematical knot is a closed curve with no loose ends. Oddly, the main impetus for the development of mathematical knot theory came from an incorrect model for the atom that was developed in the nineteenth century. Once that model was abandoned—only two decades after its conception—knot theory continued to evolve as a relatively obscure branch of pure mathematics. Amazingly, this abstract endeavor suddenly found extensive modern applications in topics ranging from the molecular structure of DNA to string theory—the attempt to unify the subatomic world with gravity. I shall return to this remarkable tale in chapter 8, because its circular history is perhaps the best demonstration of how branches of mathematics can emerge from attempts to explain physical reality, then how they wander into the abstract realm of mathematics, only to eventually return unexpectedly to their ancestral origins.
    Discovered or Invented?
    Even the brief description I have presented so far already provides overwhelming evidence of a universe that is either governed by mathematics or, at the very least, susceptible to analysis through mathematics. As this book will show, much, and perhaps all, of the human enterprise also seems to emerge from an underlying mathematical facility, even where least expected. Examine, for instance, an example from the world of finance—the Black-Scholes option pricing formula (1973). The Black-Scholes model won its originators (Myron Scholes and Robert Carhart Merton; Fischer Black passed away before the prize was awarded) the Nobel Memorial Prize in economics. The key equation in the model enables the understanding of stock option pricing (options are financial instruments that allow bidders to buy or sell stocks at a future point in time, at agreed-upon prices). Here, however, comes a surprising fact. At the heart of this model lies a phenomenon that had been studied by physicists for decades—Brownian motion, the state of agitated motion exhibited by tiny particles such as pollen suspended in water or smoke particles in the air. Then, as if that were not enough, the same equation also applies to the motionof hundreds of thousands of stars in star clusters. Isn’t this, in the language of Alice in Wonderland, “curiouser and curiouser”? After all, whatever the cosmos may be doing, business and finance are definitely worlds created by the human mind.
    Or, take a common problem encountered by electronic board manufacturers and designers of computers. They use laser drills to make tens of thousands of holes in their boards. In order to