Experimental evidence, concerning the functional relationship between distance perception and convergence, was gathered from several regions of binocular visual space, namely: within, above, and below the eye-level plane, and is discussed in terms of an intrinsic geometry of binocular visual space. Using the Hillebrand alley experiment as a base, and assuming Luneburg’s choice of geodesics, it is possible to fit both classical and current data with a variety of functions. Within the limits imposed by confined laboratory conditions, any of these functions would permit qualitative predictions. Quantitative predictions necessitate further empirical evidence on distance perception for small angles of convergence, i.e., for very distant objects.
A review of all the available data leads us to question Luneburg’s choice of the geodesic for the parallel alleys. The suggestion is made to refer the definition of the geodesic to the far point, rather than to the visual axis passing through the two eyes. Among other things, this could have the effect, ceteris paribus, of changing the curvature of visual space from negative to positive—given the aggregate results of the alley experiments as they now stand. Thus, the specification of the parallel alley geodesic must take precedence over the determination of the sign of K. In fact, until the implications of this suggestion are more fully understood, and tested, we cannot determine the sign of the curvature from the alley experiments.
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