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  • Seeing in Perspective

    This is Chapter 22 of The Future Does Not Compute: Transcending the Machines in Our Midst, by Stephen L. Talbott. Copyright 1995 O'Reilly & Associates. All rights reserved. You may freely redistribute this chapter in its entirety for noncommercial purposes. For information about the author's online newsletter, NETFUTURE: Technology and Human Responsibility, see http://www.netfuture.org/.

    It's impressive, the wizardry we place in the hands of the 3-D graphics programmer. He is barely out of college -- or perhaps not even that -- and we entrust to him a mechanism for turning the world inside out. And the mechanism itself is pure simplicity: a 4x4 mathematical matrix. Armed with this little matrix, he can take any scene, real or imagined, apply a coordinate system to it, and then recompose the scene point by point until we see it from an entirely different perspective. That is, he can project the scene any way he wishes -- which includes projecting it realistically onto a two-dimensional surface. Moreover, he can do all this with absolute fidelity to the original.

    Well, almost. Absolute fidelity, it turns out, is as challenging a standard to meet in this context as it is in some others. To see just how challenging, we need to look back toward the age of faith, to when the projective laws -- usually called the laws of linear perspective -- were just being discovered.

    Renaissance virtual reality

    When, in early fifteenth-century Florence, Filippo Brunelleschi contrived the first painting in "true perspective," he raised a sensation. Partly, of course, this was due to his showmanship. He insisted that his friends stand exactly where he himself had stood while painting the panel, and directed them to look upon the original scene he had painted. Then he held the painting up with its backside directly in front of the viewer's face. A tiny eyehole was drilled through the middle of the panel. Gazing through the eyehole, a viewer simply witnessed the original scene. But if a mirror was held up in front of the painting, he now beheld the painting instead -- and it was so accurately drawn in perspective that it was indistinguishable from the original.

    Brunelleschi's cunning extended even further, however, for instead of painting a sky in the upper part of the work, he put burnished silver there. Now, with the aid of the mirror, the astonished viewer saw wind-blown clouds drifting across the top of the painting. Here, in this calculated confusion of real world and artifice, the technological quest for virtual reality was launched.

    So, too, was the controversy. The new, perspectival art struck viewers with the force of a powerful and deceitful illusion, as had even Giotto's earlier, purely empirical experimentations with perspective. "There is nothing," Boccaccio said, "which Giotto could not have portrayed in such a manner as to deceive the sense of sight." Much later the Dutch artist Samuel van Hoogstraeten, acknowledging that his task was to "fool the sense of sight," went on to urge that the painter must thoroughly understand "the me