Application of Mathematical Group Concept to Human Perceptual Systems, Visual and Auditory

概要

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I. The system of color vision forms a group, having color mixing as an additive operation, neutral white as the identity element, and complementary colors as the inverse elements. II. The system of musical intervals forms a group in the same sense, as does the system of residue classes of natural numbers with respect to an additive operation by congruence modulo 12. III. The system of spoken vowels is supposed to form a double group. The actual demonstration is only made with respect to its subsystem, the AEO subgroup of vowels with neutral vowel e as the identity element; and by assuming a corresponding neutral element in the whole vowel system, the group structure of the latter is theoretically clarified. In this paper the author is intentionally refraining himself from any philosophical argumentation. But, in other papers [especially in 9 and 10], he is trying to draw some epistemological consequences from the above developed theory of perception.
科学基礎論学会の論文
1957-03-31