Descartes’ Dioptrique of 1637, drawn from his manuscript on L’Homme, promoted a novel account of distance perception. He offered two newly described means for “seeing” (la vision), “perceiving” (faire apercevoir), or “being acquainted with” (connoistre) distance. These are the accom- modation of the eye for various distances so as to keep the retinal image in focus; and the triangle of convergence formed by the inter-ocular distance and the convergence of the lines of sight on a single fixation point at various distances. The first became available in optical theory only with the Kep- lerian anatomy of lens and retinal screen and was first tied to distance perception by Descartes; the second was available before, but, to my knowledge, not theorized until Kepler first drew attention to it. The triangle of convergence has received greater attention, especially in the Anglophone literature, in connection with Descartes’ mention of a “natural geometry.” This attention may stem from the Irish philosopher George Berkeley, in his widely read Essay Toward a New Theory of Vision, having interpreted Descartes’ natural geometry as a kind of mental calculation. This interpretive line has been popular among commentators. This talk first considers the interpretation of mental calcula- tion, in two forms: one in which the mind does the calculations and one in which brain processes calculate. These brain processes control eye-movements and the resulting system may be compared to a proportional compass, a kind of seventeenth-century slide rule. It then adds a third interpretation, also favoring the contribution of the brain, in which the brain mechanisms do not actually calculate or represent distance, but rather act so as to produce states that covary with distance. These states then, by an “institution of nature” (establishing a kind of psychophysiological law), produce the idea or perception of distance in the mind.

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