Scientists like to say that nature is simple. What they mean is that it has been found possible to describe parts of nature—the parts we understand—in a simple way. Without the underlying faith in simplicity and the rewards of success, scientists would lack the stamina to overcome the obstacles to understanding that line the route to the discovery of simplicity. As every student of science is well aware, the simplicity of nature is not synonymous with ease of comprehension. The theory of general relativity, viewed as a formal structure, is exceedingly simple. But to understand it and to use it requires a heroic effort of the mind, for the concepts employed, and the ways of thinking required, are largely foreign to our everyday experience. Simplicity to the scientist means economy and compactness—of assumptions, of fundamental concepts, of mathematical equations. The fewer the basic elements of a theory and the greater the range of phenomena described by the theory, the simpler do we declare nature to be.
Throughout human history, the faith in simplicity has been a primary motivating force in science. In essence it is the faith in the possibility of science at all, that nature, or parts of nature, follow an orderly and predictable pattern governed by fixed laws. It is more than just a faith that nature follows laws that can be expressed mathematically; it adds a conviction that these laws are sufficiently simple that scientists dare hope to find and comprehend them. So powerful was the faith in simplicity among some Greek philosophers that simplicity itself came to be regarded as a sufficient test of the truth of a theory. Aristotle accepted circular motion as the rule in the heavens not because careful measurements showed the stars and planets to move in circles, but because the circle is the simplest (or most “harmonious,” or most “perfect”) of plane figures. In describing motion on Earth, he advanced a theory of utmost economy. It required but four elements—earth, water, air, and fire (which today we can interpret as solid, liquid, gas, and energy)—and but two kinds of natural motion, vertically up and vertically down. Surely the simplicity of Aristotelian physics must have contributed to its durability.
The birth of modern science in the sixteenth and seventeenth centuries brought with it no change in the ancient faith in the simplicity of nature. Rather a new element was added: the reliance on accurate observations (usually in carefully controlled experiments) to test the acceptability of a theory. The pyramiding successes of science in the past few centuries have richly rewarded the scientist’s faith in simplicity coupled with insistence on experimental confirmation.
Because the simplicity of basic science is so little appreciated, it is proper to emphasize it, even to extol it. At the same time, we must keep in mind that, at least in part, science is fundamentally simple because we humans have made it so. From science we get simple answers because we ask easy questions. But what exactly is an easy question? Compare these two, the first scientific, the second nonscientific:
1. What is the transition probability for radiation from the n=2 level in the hydrogen atom that gives rise to the Lyman Alpha line?
2. What are the advantages of foreign travel?
The average reader without scientific training will regard the first question as incomprehensible and therefore obviously difficult. But anyone should be willing to venture an answer to the second, which appears easy enough. Upon a little reflection, of course, you should convince yourself that it is after all the first question that is easy, the second that is difficult. Assuming the first question is meaningful (it is) and that science has progressed to the point that an answer exists (it does), then the answer is just a simple number upon which the thousands who can give an answer amicably agree, and which the millions of others as amicably accept. The second question, on the other hand, deals with what is good for humankind, and there are no harder questions that we have posed to ourselves than questions of good and evil.
Too often we think that science began in the seventeenth century after millennia in which superstition and blind faith reigned. The evolution of human thinking about the system of the world clearly shows otherwise. The faith in simplicity, the assumption that mathematics describes nature—these essential attributes of modern science were equally parts of ancient science.
For the development and growth of science, criteria for rejection of an idea may be even more important than criteria for acceptance. Ptolemy rejected and revised Aristotle’s picture of the world in order to get rid of the excessive number of intermediate spheres. The accumulated complexity of the later Ptolemaic picture led Copernicus to reject it in favor of a simpler Sun-centered model. Kepler found the Copernican universe still excessively complex (as well as insufficiently accurate) and rejected it even before he had discovered the true laws of planetary motion. The necessary precondition for his great step forward was dissatisfaction with existing explanations. The groundwork for modern science was laid by scientists who sought simplicity and believed in the mathematical basis of natural phenomena.