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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 52, Iss. 5 — May. 1, 1962
  • pp: 565–568

Geometry of a Visual Illusion

MAURICE M. TAYLOR  »View Author Affiliations

JOSA, Vol. 52, Issue 5, pp. 565-568 (1962)

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A new visual illusion is predicted from the assumption that the perceived distance along any path depends on the discriminability for position along the path. A disk is placed between two dots, so that the straight path between the dots is nearly tangent to the disk. It is predicted that, for the perceived straight path between the dots to be tangent to the disk, the disk must overlap the physically straight path between the dots by an amount proportional to its radius. Furthermore, certain patternings of the disk are predicted to reduce the amount of illusion. All predictions are confirmed in detail. The results are compared with those obtained in an experiment on the filled-space illusion.

MAURICE M. TAYLOR, "Geometry of a Visual Illusion," J. Opt. Soc. Am. 52, 565-568 (1962)

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  1. Anonymous, "Popular Scientific Recreations, a storehouse of instruction and amusement: in which the Marvels of Natural Philosphy, Chemistry, Geology, Astronomy, etc., are explained and illustrated, mainly by means of pleasing experiments and attractive pastimes." Translated and enlarged from Gaston Tissandier, Les Recreations Scientifiques, New and Enlarged Edition [Ward, Lock, Bowden and co., London, 1882 (?)], p. 113. The statement does not appear in the original.
  2. W. R. Garner, J. Exptl. Psychol. 43, 232–238 (1952); J. Acoust. Soc. Am. 30, 1005–1012 (1958); M. M. Taylor, Can. J. Psychol. (to be published).
  3. S. S. Stevens and E. H. Galanter, J. Exptl. Psychol. 54, 377–411 (1957); S. S. Stevens, Am. J. Psychol. 71, 633–646 (1958).
  4. W. P. Tanner, J. Acoust. Soc. Am. 30, 922–928 (1958); see also D. M. Green, J. Acoust. Soc. Am. 32, 1189–1202 (1960).
  5. W. R. Garner, reference 2 (1952).
  6. M. M. Taylor, Perceptual and Motor Skills 12, 203–30 (1961).
  7. This expansion may be obtained from the basic equation by using M instead of M2, so that the term (∂D/∂M2)(dM2/dA) is replaced by (∂D/∂M)(dM/dA)=kA/L(∂D/∂M). ∂D/∂M is always evaluated for M = L, so that it is a constant, and this constant will probably not be far from unity, compared with the range of uncertainty in the value of k. For purposes of calculation in this section, it is assumed that ∂D/∂M = 1.
  8. H. G. Spiegel, Psychol. Forsch. 21, 327–83 (1937). A summary in English of his main result is given by Taylor, reference 6.

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