Letters

Leonardo, Vol. 10, pp. 261-264. Pergamon Press 1977. Printed in Great Britain LETTERS Readers’comments are welcomed on texts published in Leonardo. The Editors reserve the right to shorten lettersfor reasons of space. Letters should he written in English or in French. PERCEPTION OF PICTORIAL SPACE IN PERSPECTIVE PICTURES On page 282 of John L. Ward’s article [Leonardo9,282 (1976)], he misquotes Helmholtz when he cites Phvsiological Optics. Vol. I l l [I] as the source for the claim that ‘straight lines viewed in peripheral vision appear convex to the point at which the gaze is directed‘ (italics mine). The pertinent passage from Helmholtz is as follows: ‘. ..But as soon as the point of fixation is shifted to some distance on one side or the other of the row of stars, then immediately and very distinctly the line will appear concave toward this point, the concavity being mpre and more pronounced, the farther the point of fixation is from the row of stars. This shows that. when the eye looks steadily in one direction. a great circle of the celestial sphere will not appear to be without curvature unless it passes through the point of fixation; otherwise, it will appear concave toward that point. A further consequence is that lineson the celestialsphere which, in the peripheral parts of the field,are said to be without curvature, must really be convex toward the point of fixation’ (italics mine). To demonstrate that lines that appear straight in peripheral vision really are convex to the point of fixation, Helmholtz then suggests this experiment: ‘The best way to do is to bend far over and look down on the top of a large table, because under such circumstances it is not likely that any recognizable straight lines, toward which the gaze might be directed, will be in the field of view. Now look steadily at a point on the top of the table, and then try to arrange three bits of paper or some other bright objects along a straight lineat somedistanceaway from the point of fixation. Invariably, as soon as we look at the pieces of paper themselves, we find that they have been placed on an arc that is convex toward the previous point of fixation.’ Helmholtz presents a diagram of a chessboard that when viewed with oneeyeat a distance of lessthan half itsdiameter will appear as a grid of straight vertical and horizontal boundaries between dark and light squares (see diagram). But the projections. he reports. ‘are found to be hyperbolas in this case’. and the diagram indeed isconstructed of intersecting hyperbolas in the periphery, convex to the fixation point, which is at the intersection of ‘horizon’ and ‘zenith-line’, the only actually straight lines. Although I was ignorant of Helmholtz’ discoveries when I published my article [2] and am indebted to Rudolph Arnheim for pointing out to me this essential source, it seems to me now that anyone who wishes to dispute the curvilinear appearance of straight lines in peripheral vision should first study Helmholtz and should carry out the experiments with onek own visual experience that Helmholtz prescribes. This leads me to observe that disputes over visual perception and representation often overlook a principal difference of opinion, that is, the statusof subjectiveintrospection. ‘A’knows and reports his own visual sensations and compares them with what he knows about the tangible, measurable world of optics and objects; ‘B’ dismisses visual sensations as subjective nonsenseand arguesonlywhat heknows about,vision,opticsand objects. The discussion might be briefer and clearer if both investigated and trusted the testimony of their own eyes, as well as conducting objective tests [3]. Pirenne [4], whom Ward finds convincing, is to my mind an example of an expert, a biophysicist and physiologist, who does not permit subjective curvature, which he appears to have observed himself, to temper his conclusions. He calls central t A I perspective ‘the only method which is capable of producing a retinal image having the same shape as the retinal image of the actual objects depicted’. But in his demonstration of central perspective, the peripheral flat plane projections (of spheres, for instance) of his pinhole camera photographs are foreign to the retinal...