curacy is now the standard of excellence in all sciences that are capable of pragmatically embracing it.
The value placed on quantitative accuracy extends beyond the judging of hypotheses; it can affect one’s choice of scientific field. Highly quantitative sciences are not intrinsically superior to nonquantitative sciences; individual tastes are not comparable.
Simplicity is a value that is implicit to the scientist’s objective of identifying patterns, rules, and functional similarity among unique individual events. Yet all hypotheses seek order amid apparent complexity, so how does one apply the criterion of simplicity? William of Occam, a 14th-century English philosopher, developed ‘Occam's Razor’ as a method of cutting to the truth of a matter: “The simplest answer is the one most likely to be correct.” Also known as the maxim of parsimony, Occam’s Razor is an imperfect rule of thumb, but often it does select correctly among hypotheses that attempt to account for the same observations. The ‘simplest answer’ is not necessarily the one most easily comprehended. Often it is the one with the fewest assumptions, rationalizations, and particularly special cases, or it is the most elegant idea.
Sherlock Holmes countered the emphasis on simplicity by saying, “When all other contingencies fail, whatever remains, however improbable, must be the truth” [Doyle, 1917]. Yet when scientists resort to hypothesizing the improbable, they usually discover the actual truth later, among options that had been overlooked.
I still remember a sign that I saw on a restroom paper-towel dispenser twenty years ago: “Why use two when one will do?” The advice is in accord with Occam’s Razor: two or more hypotheses, each of which explains part of the observations, are less likely to be correct that one umbrella hypothesis that accounts for all of the data. Similarly, if an explanation becomes more and more complex as it is modified to account for incompatible observations, it becomes more suspect according to Occam’s Razor.
Complexity can result, however, from the interactions among two or more simple phenomena. For example, simple fractal geometric rules of repetition, when applied at different scales, can result in apparently complex patterns such as branching river systems and branching trees. Molecular biologists have long puzzled over how simple amino acids made the evolutionary leap to complex DNA; now these researchers are exploring the possibility that a few simple rules may be responsible [Gleick, 1992c].
The value on simplicity leads most scientists to be distrustful of coincidences. We recognize that they occur, but we suspect that most mask simple relationships.
Not everyone values simplicity similarly. Georg Ohm, a mathematics professor in Cologne, proposed in 1827 that electrical current in a wire is simply proportional to the potential difference between the wire ends. His colleagues considered this idea to be simplistic, and he was forced to resign his position. Eventually, his hypothesis was accepted and he resumed his academic career -- this time as professor of experimental physics. Today Ohm’s Law, which says that potential difference equals the product of current and resistance (in ohms), is the most useful equation in electricity.
Consistency, an aspect of simplicity, is valued in all sciences. The hypothesis should be consistent with relevant concepts that have already been accepted, or else it will face the formidable hurdle of either overthrowing the established wisdom or uneasily coexisting with incompatible hypotheses. Such coexistence is rare; one example is the physics concept of complementarity,
