The Luneburg theory states that the visual space can be represented by one of the Riemannian spaces of constant curvature. This implies that the visual space is Desarguesian. The Desarguesian property may be stated as follows: If two vertices of a triangle are jointed by segments to the opposite sides, these segments intersect. This proposition was tested by having observers move small lights so as to construct apparent segments on a given triangle. Six such experiments were performed using two triangles and five observers. In all cases the minimum physical distance between the two curves determined by the average settings of the lights was between 20 and 220 sec. In two of the six cases this distance was not significantly different from zero. Four determinations of the threshold for discriminating the nonintersection of two segments yielded values in the range of 59 to 92 sec. It was concluded that the visual spaces of a significant proportion of the observers are Desarguesian; those of others may be non-Desarguesian.
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