The unknown Fechner

Summary Despite Fechner's universal fame as the founder of psychophysics, his work is not very well known among contemporary psycholgists. To correct this situation, the present issue of Psychological Research contains some excerpts from previously untranslated works of Fechner. By way of introduction to the translations, some popular misconceptions about Fechner's outer psychophysics are corrected, and a brief introduction to his inner psychophysics is given.     

Fechner as a statistician

The work of Gustav Theodor Fechner (1801–1887) related to probability and statistics and, in particular, to the treatment of observations is described. From a mathematical point of view his arguments were often insufficient, but his work proved to be highly fruitful, and the relevant comments of such scholars as Pearson and von Mises are presented. As the originator of psychophysics, Fechner opened up a new field for quantification. Subsequent workers rejected some of his findings, while at the same time acknowledging their debt to him.     

An n-dimensional Weber Law and the Corresponding Fechner Law

Weber's law of 1834, DeltaS/S=c for the just noticeable difference (jnd), can be written as S+DeltaS=kS, k=1+c. It follows that the stimulus decrement required to elicit one jnd of sensation is S-DeltaS*=k(-1)S. If generalized for two stimulus dimensions and two corresponding response dimensions, Weber's law would have to state such equations for all directions of change in the plane. A two-dimensional Weber law with exactly these properties is realized by [S(x)+DeltaS(x)(straight theta), S(y)+DeltaS(y)(straight theta)]=[k(sin(straight theta))S(x), k(cos(straight theta))S(y)] which determines the stimulus coordinates for all stimuli just noticeably different from the stimulus (S(x), S(y)) in all directions 0R(2)) is [x, y]mapsto[log(k)(x), log(k)(y)]. The solution is generalized to arbitrarily many dimensions by substituting the sin and cos in the generalized Weber law by the standard coordinates of a unit vector. Copyright 2000 Academic Press.     

Fechner, information, and shape perception

How do retinal images lead to perceived environmental objects? Vision involves a series of spatial and material transformations—from environmental objects to retinal images, to neurophysiological patterns, and finally to perceptual experience and action. A rationale for understanding functional relations among these physically different systems occurred to Gustav Fechner: Differences in sensation correspond to differences in physical stimulation. The concept of information is similar: Relationships in one system may correspond to, and thus represent, those in another. Criteria for identifying and evaluating information include (a)?resolution, or the precision of correspondence; (b)?uncertainty about which input (output) produced a given output (input); and (c)?invariance, or the preservation of correspondence under transformations of input and output. We apply this framework to psychophysical evidence to identify visual information for perceiving surfaces. The elementary spatial structure shared by objects and images is the second-order differential structure of local surface shape. Experiments have shown that human vision is directly sensitive to this higher-order spatial information from interimage disparities (stereopsis and motion parallax), boundary contours, texture, shading, and combined variables. Psychophysical evidence contradicts other common ideas about retinal information for spatial vision and object perception.     

Stevens vs Fechner: A plea for dismissal of the case

Fechner's Law is based on the assumption that jnd's can be concatenated in order to get a measure of sensation. Stevens contended this assumption; he argued that measurement of sensation by measuring jnd's is ‘indirect’. His ‘direct’ methods, however, appear to be much less direct than originally assumed. Especially Stevens' (implicit) assumption that subjects use numbers on an absolute scale appears to be unwarranted. Ratio scaling is therefore nothing more than cross-modality matching between the number scale and another modality. This view has two consequences. Firstly, it is quite natural to find power functions by cross-modality matching, even when Fechner's Law holds for both modalities. Secondly, if Stevens' power law is true, there will be an overestimation of all exponents by a factor 2.5. All typical power functions will be concave downward after correction for this effect. The discussion boils down to a discrimination between two quite similar curve families: log functions and power functions with an exponent below 0.6. The practical significance of this discussion is doubted.     

Gustav Theodor Fechner: life and work in the mirror of his diary

The diaries of Gustav Fechner reveal much about his motivations to develop the field of psychophysics, as well as some of the steps toward its formulation. Together with his publications on various subjects, the diaries show how psychophysics fits into Fechner's broader scientific program, illuminate his worldview, and reveal his hopes for acceptance of his work by his colleagues.     

Understanding wheel dynamics

In five experiments, assessments were made of people's understandings about the dynamics of wheels. It was found that undergraduates make highly erroneous dynamical judgments about the motions of this commonplace event, both in explicit problem-solving contexts and when viewing ongoing events. These problems were also presented to bicycle racers and high-school physics teachers; both groups were found to exhibit misunderstandings similar to those of naive undergraduates. Findings were related to our account of dynamical event complexity. The essence of this account is that people encounter difficulties when evaluating the dynamics of any mechanical system that has more than one dynamically relevant object parameter. A rotating wheel is multidimensional in this respect: in addition to the motion of its center of mass, its mass distribution is also of dynamical relevance. People do not spontaneously form the essential multidimensional quantities required to adequately evaluate wheel dynamics.     

To honor Fechner and obey Stevens: relationships between psychophysical and neural nonlinearities

G. T. Fechner (1860/1966) famously described two kinds of psychophysics: Outer psychophysics captures the black box relationship between sensory inputs and perceptual magnitudes, whereas inner psychophysics contains the neural transformations that Fechner's outer psychophysics elided. The relationship between the two has never been clear. Moreover, psychophysical power laws are found in almost every sensory system, yet the vast majority of neurons show sigmoid nonlinearities. Here, we selectively review the literatures on psychophysical and physiological nonlinearities and show how they can be placed within a framework for understanding the relationship between inner and outer psychophysics: a neural organization with a logical structure commensurate to outer psychophysical theory. In theoretical treatments of Stevens's law, the power law is a consequence of combining a Weber's law scaling of inputs with a Weber's law-like scaling of sensation magnitudes, yielding an exponent that is the ratio of the Weber constants. A neural derivation using physiological sigmoid nonlinearities should be commensurate to this internal logic. There is a class of models in which two nonlinear neural mechanisms (e.g., a sensory channel and the cortical numerosity mechanism tapped by magnitude estimation) are coupled through feedback, yielding power law behavior as an emergent property of the system, with an exponent that is a ratio of neural coupling strengths. Rather than a discrepancy between psychophysics and physiology, these models suggest complementarity between inner and outer psychophysics, because the Weber constants required for outer psychophysics modeling can be derived from the sigmoid nonlinearities of inner psychophysics.     

Psychotechnology and insanity at the wheel.

The article discusses psychological testing of automobile drivers performed by the Psychopathic Clinic affiliated with the Traffic Court of the Detroit Recorder's Court. Between 1936 and 1965 more than 15,000 drivers who had either run afoul of the traffic codes or been involved in a traffic collision. A statistical analysis of these cases reveals that the psychologists and psychiatrists working at the clinic were reinforcing existing ethnic, racial, and gender stereotypes in their pursuit of traffic safety. Patients who were deemed unfit drivers were recommended to the judges for sanctions ranging from license revokations to forced committment.     

A running wheel tachometer

A photocell-actuated tachometer for running wheels is described. The number of counts generated per revolution of the wheel is a function of the number of trip wires inserted in the hub of the wheel axle. The circuit is presented in configurations that actuate relay contact closures and as a direct driver of TTL logic.     

Perceiving the centroid of configurations on a rolling wheel

Undergraduates observed configurations of point-lights undergoing wheel-generated motions and judged how wheel-like the movement of each stimulus appeared on a 7-point scale. Viewer judgments were predicted by a metric defining the variable parameters for the motion path of each configuration’s geometric center—the centroid. The effects on judgments of eye movement and the stimulus characteristics of rotation, translation, and configuration were explored in six experiments. First, a strain operation on the dynamic stimuli did not affect the ability of the metric to predict perceptual judgments. Second, the predictive strength of the metric did not interact with the type of eye movements used in viewing the stimuli, though judged wheel-likeness was greater under pursuit vision than under static fixation. Third, variations in the extent of translation yielded little, if any, effect on observers’ judgments, nor did translation in a circular path. Finally, for stimuli having two lights extremely close together in the configuration, the metric’s predictive value was slightly lessened but only at the limits of visual acuity. Thus, within a wide range of presentation conditions, and for a wide variety of configurations, a metric that defined the variable parameters for the motion path of the centroid was an accurate predictor of observers’ judgments of goodness of perceived rotary motion.     

Natural paths to invention: Reinventing the wheel

Four studies explored candidate pathways underlying the invention of the “wheeled cart.” In Study 1, heuristics were abstracted from subjects’ judgements of different precursor paths to the wheeled cart. In Studies 2 and 3, these heuristics were tested for generality across different precursor paths. In Study 4, subjects ranked the order of incorporating parts into the wheeled cart. While the studies cannot “prove” that the wheeled cart developed in one of the candidate ways, they show that interesting and important heuristics of invention can be uncovered from subject’s judgements. Examining candidate paths to important inventions is a method worthy of exploration. Together, the four studies indicate that important historical inventions might be examined experimentally. Doing so yields potentially important invention heuristics.