The pi mechanisms of W S Stiles: an historical review

The origins, development, and status of the pi mechanism theory are reviewed. The paper is divided into four sections. In the first section Stiles's general ideas about 'color mechanisms' are examined, and it is concluded that foremost amongst these is a mathematical theory that specifies certain formal rules or laws that should govern a certain class of observations. In the case of pi mechanisms, the class of observations is that of two-color thresholds, and the defining laws are the two well-known displacement laws. Five other laws that two-color increment-threshold observations should obey, if the latter are governed by ideal pi mechanisms, are abstracted from Stiles's writings. In the second section literature pertinent to the testing of the seven Stilesian laws is reviewed, and it is asked whether or not the seven pi mechanisms of Stiles do in fact obey the laws. In the third section the relation of the pi mechanism concept to physiological concepts is examined, and its relation to the 'cone fundamental' is discussed; the evidence pertinent to the question: "Are any of the pi mechanisms of the single-fundamental type?" is then reviewed. The last section is devoted to the evolution of Stiles's ideas in the period after 1959 when Stiles's own investigations and those of others propelled him to reject the initial (1953) pi mechanism theory as an adequate characterization of the data of the two-color threshold.