With these words Socrates, in Paul Valéry's Eupalinos, defines the two poles between which the mind of the artist always seems to oscillate: on one side, reality as represented by nature in all its aspects, and on the other, the dream of absolute perfection. This is the fundamental problem of the eternal conflict between the laws of nature and the canon of aesthetic proportions, which presents itself in different, though often related, guises. Here I will try to identify, using simple and schematic ideas worthy of deeper discussion, the problematic knots of a phenomenon that the champions of ideal proportions have always had to face and often had to hide, even from themselves, when confronted with the evidence of facts.

In the history of architectural theory, one of the most striking conflicts is between the canons of numerical proportion and those of the natural laws of visual perception. Deriving his ideas from Greek sources, Vitruvius describes a proportional canon based on the image of the ideal male body in the unrealistic representation of a frontal view. What Vitruvius is regarding is an immobile man, without volume or inner vitality; he is a simple ideogram characterized merely by the potential of his measurements to form geometric and proportional relationships. Yet such a model, once translated into architecture, has to face the visual evaluation of an actual viewer, whose position— whatever it may be—can never coincide with that conventional vanishing point at infinite distance from which Vitruvius regards the man and from which the appearance of the building must be designed. Thus, a relationship (either static or dynamic) is inevitably established between the subject and the object of vision—a relationship that generates a conflict with the immutability of a predetermined canon of proportion.

Vitruvius, fully aware of the problem, suggests a series of corrections to the very canon that he himself had proposed, with the intention of re-establishing the visual appearance of the ideal initial proportions (Fig. 1).