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Vladimir A. Lefebvre, “From the Representation of Rationality to the
Representation of Free Will.”
Evening Lecture at the 24th Annual Meeting of European Mathematical Psychology Group,
Institute for Mathematical Behavioral Sciences, University of California, Irvine,
Technical Report Series
, No. 93-34.
The paper is discussing a problem of why some economical models can effectively predict
human choice.
Vladimir A. Lefebvre, “A Rational Equation for Attractive Proportions.”
Journal of Mathematical Psychology, 1992, Vol. 36, No. 1, pp. 100-128.
A hypothetical law governing the generation of aesthetically attractive
proportions in music and geometry is introduced in this paper.
Vladimir A. Lefebvre, “The Golden Section: Myth or Reality?”
Unpublished manuscript, 1992..
The problem of whether the golden section ratio possesses special
attractiveness has been discussed for many centuries. A new attempt to
explain this phenomenon has recently been made with the help of the model
of the subject with multi-layered reflexivity. This model suggests a set of
conditions under which we may hope to observe this phenomenon
experimentally. A retrospective analysis of experiments meeting the
conditions suggested by this model found the presence of a value close to
0.62. The relation of this value to the golden section can be further clarified
by new experiments testing the predictions of the model of the subject with
multilayered reflexivity.
Vladimir A. Lefebvre, "Social Man" vs. "Conscientious Man."
Behavioral and Brain Science, 1989, Vol. 4. pp. 714-716.
The author offers explanation for experimental data by Caporael et al. with
the help of a formal model of bipolar choice.
Vladimir A. Lefebvre, "McClain Circle and Plato's Harp."
Journal of Social and Biological Structures, 1989, Vol. 12, No. 2. pp. 73-81.
McClain depicted Plato’s city of Magnesia as a circle and found that its
structure was based on mathematical ratios which coincide with Just Intonation
set of musical intervals (including nonstandard intervals 4/7 and 7/8). Later
McClain noted that the same set of intervals was deduced formally by the
author of this paper from his model of human reflexion. In this paper the
author put forth the hypothesis that Plato might have known of some formal
correlations analogous to those in this model.