Quantification of behavior.

Abstract

In what languages can scientific results best be expressed? Since the days of Isaac Newton in the 17th century, scientists, to avoid “the artifice of words,” have chosen the language of mathematics. Quoting Galileo, Fitzgerald and James (1) talk about being able to understand nature only when one has learned mathematics. In his essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Eugene Wigner (2) celebrates the beauty of mathematics for its own sake, and discusses how “mathematical concepts turn up in entirely unexpected connections” as they are used to express regularities discovered in scientific results. He also points out, however, that a mathematician is limited to the exploration of a logical world permitted by his axiomatic system. As we shall see, behavioral scientists historically also have been limited to experimental systems constrained by the requirement for studies simple enough to use reliable methodology and to yield clean, replicable results. In the distant past, it might have been said that the complexity of behavior, the difficulty of behavioral methods, and the shakiness of behavioral results would defy quantification. However, decades of intense work with a variety of organisms, including humans, have created islands of knowledge upon which behavioral scientific methods are reliable and results are replicable. Results are precise—they are grouped tightly around measures of central tendency or are correlated tightly to defined mathematical curves—and they are accurate, meaning that, when a true value is known, they achieve that true value. In some fields within the behavioral and social sciences, the use of mathematical methods would be quite irrelevant. Important advances and significant understanding are reached, nonetheless. We are not addressing those subjects. The purpose of this Sackler Colloquium was narrower: to examine some areas of experimentation in which mathematics is used routinely. The achievements of this field of … [↵][1]1To whom correspondence should be addressed. E-mail: pfaff{at}rockefeller.edu. [1]: #xref-corresp-1-1