Chartres cathedral, Charlemagne window, detail.

or image with respect to thing generating it and virtue with respect to gen- eration and corruption.”51_{Sometimes they are also called “impressions,” be-}

cause they resemble impressions made in wax by a signet ring or seal.52_The

creation of species is the first effect of the light-radiating agent, making the recipient similar to itself “because the recipient is always potentially what the agent is in actuality.”53_{There is an uninterrupted continuity between the}

first agent—the source of light (lux)—and the last recipient in the universe, and therefore every diversity can be traced back to an original identity.54

In the thirteenth-century synthesis, the philosophy of light (optics) became the key discipline of natural philosophy and science. As the most ex- emplary form of corporeal movement, light was considered to be a special case of the multiplication found also in other phenomena. “We call every multiplication ‘radiant,’ ” Roger Bacon writes, “and we say that ‘rays’ are pro- duced whether they are light or colour or something else. There is another reason for these names, namely that the multiplication of light is more ap- parent to us than the multiplication of other things and therefore we trans- fer the terminology of the multiplication of light to the others.”55 _The

universal role of species, their power to differentiate and unite phenomena with greater precision, represents a radically new articulation of the inher- ited, symbolically structured world.

FROM MEDIEVAL OPTICS TO ARTIFICIAL PERSPECTIVE

The emphasis on the more explicit role of light in understanding and rep- resenting reality did not in itself introduce a new content. It only helped to make more explicit the existing knowledge, particularly in the sphere of cosmology. The traditional cosmologies, based primarily on Neoplatonic thinking, were at the end of the twelfth century already highly idealized and spiritualized representations in which even material symbols became trans- parent and nearly dissolved in the subtleties of a poetic language, domi- nated by abstract metaphors and allegories.56 _{The rehabilitation of the}

natural world together with the more tangible and precise form of repre- sentation restored the most important part of traditional symbolism—the visible body of symbols.57

The multiplication of species reveals in the visible world whole chains of similarities and identities that link things together and give them

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a relatively precise place in the overall order of things. Using different lan- guage, we can describe the multiplication as a process of symbolization in which a common communicative space is created.58_{For Grosseteste and his}

contemporaries the equivalent of communicative space was cosmology, seen not as a system but as a framework that could serve as a paradigm of an incomplete project.59

The philosophy of light reached its most complete synthesis in the work of Roger Bacon.60_{His interpretation of light, expressed consistently}

in the language of geometrical optics, established a tradition that played a decisive role in the formation of Renaissance perspective.61_{How the nature}

of his influence should be interpreted is a question still debated and not well understood. The main source of misunderstanding is, as we have already seen, the geometrical language of optics, which creates an illusion of au- tonomy and separation from other disciplines, particularly metaphysics and theology.62

However, we already know that the separation of optics from other disciplines is historically impossible, and that optics is not a geometry or “physics of causation” of the visible world but a language of natural relations structured by geometry.63_{The role of geometry in the “language of optics” is}

clearly illustrated in a passage of Grosseteste that must be quoted in full:

The usefulness of considering lines, angles and figures is very great, since it is impossible to understand natural philosophy without them. They are useful in relation to the universe as a whole and its individual parts. They are useful also in connection with related properties, such as rectilinear motion. Indeed, they are useful in relation to activity and receptivity, whether of matter or sense; and if the latter, whether of the sense of vision, where activity and receptivity are apparent, or of the other senses, in the operation of which something must be added to those things that produce vision. Since we have spoken elsewhere of those things that pertain to the whole universe and its individual parts and of those things that relate to rectilinear and circular motion we must now consider universal action insofar as it partakes of the nature of sublunary things.64

The things that can be brought in as intermediaries are lines, angles, and figures. It is with their help that the earlier philosophy of light can be made more explicit. It is interesting to see how closely the geometry of light imitates the articulations already accomplished by the language of natural philosophy. The meaning of the operations can be followed step by step only through the dialectics of the philosophical language and geometry, and the result can perhaps best be described as a philosophy more opticorather than as pure optics.65

In the treatises of the perspectivists, the geometrical rays of light are discussed as physical. The ray itself is seen as having a thickness and velocity, and as responding to the resistance of a medium and having a generative power.66_{From the large body of optical knowledge of the per-}

spectivists I shall focus on only a small part, directly relevant to the under- standing of Renaissance perspective.67 _{The perspectivists interpret the}

radiation of light as taking place primarily on three kinds of lines: direct, refracted, and reflected. The generation of species proceeds along a straight line, “provided the medium in which it is multiplied is uniform as air and water or some other substance and no obstacle is encountered.” However, when a species falls obliquely on a medium or body of different density it changes its angle in proportion to the density of the medium (see figure 3.4). “This is properly speaking the refraction of a species. . . . The refracted ray falls between the direct paths and the perpendicular, drawn from the point of refraction.” If the second medium is more dense, the ray falls closer to the perpendicular; if less dense, it turns away from the perpendicular. In cases in which the second medium is impenetrable, a species returns by its own power and “multiplies itself in the original medium, forming an angle; and it is properly called a reflected species.”68_{This interpretation of light in}

terms of lines and angles is a preparation for understanding the propaga- tion of light in terms of figures.

The figure that primarily determines the radiation of species is a sphere, “since an agent produces its species everywhere and in all direc- tions and along all diameters. . . . Thus it is necessary that the agent be a centre from which lines proceed in every direction. But such lines are radii of a sphere, and their terminus must be a spherical surface.” However, in terms of power the most important figure is a pyramid—“not any pyrami- dal figure you please, but that having its base on the face of the luminous

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body and its vertex on the illuminated part of the non-luminous body; for only in this figure are perfect illumination and the action of nature pre- served” (figure 3.7). What makes the pyramidal figure unique? Bacon’s trea- tise has a short answer: “if a ray should come from one part of the agent to one part of the recipient, there would be only one ray and that would not be sufficiently active and therefore nature chooses the pyramid.”69_{Bacon’s def-}

inition is taken almost word for word from Grosseteste’s longer but much clearer formulation.70

The pyramids with their base on the surface of the agent have their apexes projected into individual points of the medium or recipient body. As a result, an infinite number of radiant pyramids is propagated in any one di- rection. But how can a clearly structured world come into existence from an infinite number of radiations? A deeper understanding of the nature of light and species provides the answer. In such an understanding, which geome- try only partly represents, a clear distinction should be established between the essential species represented by perpendicular lines, which are close to the axes of the pyramids, and accidental species represented by oblique lines close to their sides. An even more important distinction should be