PARADOX OF DISPLACEMENT IN GEOMETRICAL ILLUSION AND THE PROBLEM OF DIMENSIONS

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  • 錯視における偏位の矛盾とディメンジョンの問題
  • サクシ ニ オケル ヘンイ ノ ムジュン ト ディメンジョン ノ モンダイ
  • A CONTRIBUTION TO THE STUDY OF SPACE PERCEPTION

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Abstract

The late Professor Morinaga found in 1954 that spatial displacement of direction differed from that of distance even when the measurement was made in the same figure. This finding was named as “paradox of displacement” in geometrical illusion. The present study was designed to prove the existence of the paradox of displacement in more detailed experimentation. Two types of displacements of direction and distance were measured in each of variant forms of Zöllner's, Hering's and Müller-Lyer's figures. In the figures of Zöllner and Hering types the number of dots filling each of parallels was varied from two or three to several (and including solid lines).<br>1. Paradox of displacement was seen in both Zöllner and Hering types when the number of dots filling the parallels was adequate. This appeared more markedly in a variant form of the Müller-Lyer figure.<br>2. Displacement of both direction and distance increased gradually with the increase of number of dots filling the parallels. The rate of increase of displacement was, however, more prominent for direction than for distance.<br>These results indicate that the displacement seen in geometrical illusion differs from the objective displacement and is related to the shift in respective dimension, distinguished from each other, of spatial perception. They also show an interaction between two dimensions, direction and distance, in some figural structure. Thus the problem of dimensions seems to be important for the construction of the so-called field-theory.

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