Three-Dimensional and Four-Dimensional Aspects of Human Penetration and Summary of Nature

  • Kazuo Kondo
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 39)


Continuous variables or coordinates are treated generally to work as expoint coordinates to envision higher order space pictures with which three- and four-dimensional lower bounds are remarkably dictated by the Kawaguchi-Hombu Theorem and its extension. Human concepts of nature from the most microscopic to more macroscopic phases have to be given in terms of three- and four-dimensional languages so as to provide the basis of the relativity principle, etc. Physical, psychological and even biological phenomena are characterized by conflicts and reconciliations between (3) and (4).

In particular, the distance axioms are put in terms of three stimuli. It leads to a quantity that has the character of an information-theoretical entropy and stands as the basis for the tristimulus principle covering psychology from trichromaticity to the three-formant structure of vowels leading to the vowel triangles, which can be amplified to a phonetical tetrahedron.


Galois Field High Order Element Mass Quantum Musical Tone Quark Confinement 
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  1. [1]
    A. Kawaguchi, Journal of the Faculty of Science, Hokkaido Imperial University, 9 (1940), 1–152; 10(1941), 77-156.MathSciNetGoogle Scholar
  2. [2]
    M. Kawaguchi, RAAG Memoirs, Vol.III (1962), 718–734; Vol.IV(1968), 577-591.Google Scholar
  3. [3]
    T. Tsunoda, The Japanese Brain — Uniqueness and Universality (translated by Yoshinori Oiwa), Taishu-kan, Tokyo, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • Kazuo Kondo
    • 1
  1. 1.C.P.N.P.Yotsukaido City, Chiba-ken, 284Japan

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