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.
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