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On Alberti's "sign": vision and composition in quattrocento painting - Leon Battista Alberti's commentary 'On Painting'
Art Bulletin, The, Dec, 1997 by Jack M. Greenstein
Here among painters points and lines are not what they are among mathematicians, where infinite points fall in a line. From our definition, a point is a sign [signum], because the painter senses [sensiat] it as something median [medium quoddam] between the mathematical point and a quantity which falls under number, such as atoms perhaps are. And when the painter takes from nature, which is imitated, first lines and angles and then lights and colors of surfaces, [he takes] whatever of it falls under number and consists of the divisible parts not in the thing made but in nature. Moreover, who said that there are as many rays of light in a line of one foot as in a line of two feet? In short, because of this, possibly existing things, not infinite ones, are to be posited by reasoning about possible works [sunt . . . possibilia fieri . . . infinita not sunt ex rationibus possibilium operum]. May this small thing be enough to have responded to my detractors.(85)
Alberti's response rehearses the status of painting as intermediate between mathematics and natural philosophy. Intermediate sciences use geometric demonstrations to explain the changing world of sense. In mathematics, the elements of geometry are abstract intelligibles, which by definition cannot be embodied in sense or imagination. However, because objects of perception are finite and material, the intermediate sciences construct their models out of finite units, which are thought to exist, rather than out of purely abstract intelligible units, which cannot exist. Aristotle credits to Democritus the theory that all corporeal things are composed of possibly existing, finite, indivisible units of matter termed atoms.(86) Atoms also figure prominently in an early theory of vision, advanced by Democritus, which was known to Alhazen and Thomas Aquinas and taken up by Henry of Langenstein and others.(87) This theory explains vision as a "reflection" in the eye, brought about by atoms or "material likenesses" imprinting themselves in sense like a seal in wax.(88) (Alberti alludes to this theory when he suggests that "images are figured in the surface of the eye, as in an animate mirror" [I.6].) Because they are material, these atoms inhere as discrete parts of corporeal bodies; yet, because they are too small to be perceived or measured, they are discovered only through reasoning. Conversely, in Metaphysics (1016b25-29), Aristotle argues that mathematical points are indivisible quantities that have position.(89) The points with which painters are concerned, Alberti argues, are halfway between the immaterial, indivisible, positioned points of mathematics and the discrete, indivisible packets of matter called atoms in natural science. Like points in Aquinas's discussion of "separated substances," they are sensed as the smallest possible division between perceived things, even if they cannot be perceived by themselves.
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