The Criterion of Simplicity

One of the principles governing the scientific description of the world is this—of different possible explanations of a phenomenon, the simpler one is to be preferred. This rests on the belief that there is an element of intrinsic simplicity in the behavior of nature. Already in the 14th century William of Ockham enunciated a principle of parsimony which has been stated in a variety of forms: "Plurality is not to be assumed without necessity;" "it is vain to do with more what can be done with less." This was not new as a philosophical principle, but it was used by the friar to argue that there was a good deal of unnecessary fat (as we would say today) in the dogmas and organization of the Roman Catholic church, and that the same spiritual goals could be attained with much less needless encumbrances. It is not surprising that Pope John XII rebuked Ockham in one of his bulls and the great philosopher was imprisoned and excommunicated. As with Galileo, he too was later restituted by the Roman Catholic Church.

In any event, Ockham's principle became a matter of much philosophical and theological controversy. But it has always appealed to the scientist's mind. Newton, in his Principia, noted that "more is vain when less will serve." In our own times a number of philosophers of science have analyzed this concept in detail, and tried to provide a logical justification for it.

The criterion of simplicity may be justified on at least two grounds. First, it reflects the efficiency of a scientific theory or explanation because it accomplishes more with less. Secondly, the hypotheses underlying a theory are unconfirmed statements on what is not directly observed or observable. Hence, the simpler and the less the number of such claims, the more acceptable they should be.

There is also a third reason, partly theological, for accepting the principle. It is that God would not make a universe governed by complicated laws. But this notion was challenged by Pierre Duhem who regarded such an attitude as obsolete. "There was a time," he wrote, "when physicists supposed the intelligence of a Creator to be tainted with the same debility, when the simplicity of these laws was imposed as an indisputable dogma in the name of which any experimental law expressing too complicated an algebraic equation was rejected, when simplicity seemed to confer on a law a certainty and scope transcending those of the experimental method which supplied it.... We are no longer dupes of the charm which simple formulas exert on us; we no longer take the charm as evidence of a greater certainty." But the criterion has certainly not been given up since Duhem wrote these lines in 1906.

Perhaps the best known example of the application of this principle in the course of the 20th century is in the Theory of General Relativity of Einstein. It is known that "...after years of research, he (Einstein) arrived at a particular equation which, on the one hand, explained all known facts and, on the other hand, was considerably simpler than any other equation that explained these facts. When he reached this point he said to himself that God would not have passed up this opportunity to make nature this simple..." Einstein himself expressed the view that the grand aim of science was "to cover the greatest possible number of empirical facts by logical deduction from the smallest number of hypotheses or axioms..."

In this context, it is important to distinguish between a simplistic and a simple explanation. Thus, many unsophisticated, and often naïve explanations of physical phenomena may seem to be simple, but are actually simplistic. Thus, for example, the idea that eclipses are caused by demons which swallow up the sun and the moon for a while is a simplistic explanation, as also the idea that the earth is supported by the giant Atlas or a magical elephant. Such explanations are convincing only to the most simple-minded.

In the scientific context, by simplicity one does not mean something that is easily understandable to anyone and everyone, much less something that is trivial. Rather, one refers by this term to the harmony and logic of the relationships, to the elegance and balance of the conceptual structures that are used in analyzing the world. This is why Einstein's general theory of relativity, which is based on much sophisticated mathematics, is extolled for its simplicity, but only by those who understand it.

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