Thurstone's discriminal process model is geometrized and discussed from the information‐system theoretical point of view. That is, a probability density function (p.d.f.) based on the discriminal processes is defined in the state space (this is the concept of grasping simultaneously the physical stimulus and its response. A parameter space spanned by parameters of the p.d.f. is defined, and fundamental metrics are introduced into the space based on Fisher's information; thus, the space is considered to be a Riemannian space. In the space, the psychophysical functions are derived as certain geometrical invariants. As the results, when the “discriminal dispersion,” i.e., the distribution of the response (the response function) to the input stimulus is to be Gaussian, the power law and the logarithmic law are obtained as psychophysical laws with respect to the mean values of the distributions. From this, relations between difference thresholds, the discriminal process and the psychophysical function are clarified. At the same time, the formalization of the problems and conclusions in [2] are justified from the information‐system theoretical point of view. Further the functional forms of the response functions are also investigated, and it is shown that almost the same conclusions can be obtained even if the Gaussian assumption is repalced by the exponential, the two‐sided exponential, or the logarithmic Gaussian distributions.
Numerizing and describing various sensations are important in the discussion of human information processings as well as in the construction of an information processing system, simulating human recognition and behavior. This paper considers the psychophysical function when the stimulus is multidimensional and the corresponding sensation is one‐dimensional. We define a state space spun by several physical continua and a psychological continuum, which is regarded as an n‐dimensional Riemannian space. the psychophysical function is defined as a certain geometrical invariant in this space. A metric is introduced into this state space based on the threshold of discrimination, and functions are derived which are permissible in this case as psychophysical functions. As an application of this formulation a problem is considered to establish a correspondence between the luminance and the brightness of the colored light. It is shown that when Weber's law and Ekman's law apply to the threshold of discrimination, Stiles' law and Abney's law can be derived as the permissible psychophysical functions.
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