Figure 1 / The puzzling discrepancy between perception and the physical measurements of sources. The solid line represents judgments of brightness elicited by sources of increasing light intensity with a dim background (redrawn from Nundy and Purves, 2002). The dashed line is the expected trend of perceived brightness if vision were analytic.
Figure 2 / The fundamental factors that determine the luminance of any stimulus (or component thereof) are illumination, reflectance, and transmittance. Because behavior in response to the stimulus will be successful only if the relative contributions of each of these factors are in some sense known, seeing lightness or brightness according to the physical intensities (luminances) in the stimulus as such would be a poor strategy of vision.
Figure 3 / The inherent ambiguity of any three dimensional object projected onto a plane. As indicated in this diagram, the same retinal projection can be generated by objects of different sizes at different distances from the observer, and in different orientations with respect to the observer.
An Alternative Interpretation
A plausible answer to this puzzle is to simply abandon the long-held assumption that vision involves seeing or estimating physical properties. In this alternative interpretation, vision works by having patterns of light on the retina trigger reflex patterns of neural activity that have been shaped entirely by the past consequences of visually guided behavior over evolutionary and individual life time. Using the only information available on the retina (i.e. frequencies of occurrence of visual stimuli, light intensities), this strategy gives rise to percepts which incorporate experience from trial and error behaviors in the past. Percepts generated on this basis thus correspond only coincidentally with the measured properties of the stimulus or the underlying objects. In the following sections we discuss various perceptual phenomena using the proposed approach. For those who are interested in thinking about this in more formal terms, see the primer that compares the present approach (called empirical ranking theory) with Bayesian decision theory.
Purves D, Wojtach WT, Lotto RB (2011) Understanding vision in wholly empirical terms. Proc Natl Acad Sci (doi:10.1073/pnas.1012178108, March 7).
Howe, CQ, Lotto RB, Purves D (2006) Empirical approaches to understanding visual perception. J Theor Biol 241: 866-875.
Howe, CQ, Purves, Dale (2005) Perceiving Geometry: Geometrical Illusions Explained by Natural Scene Statistics. New York, NY: Springer Publishing.
Purves D, Williams MS, Nundy S, Lotto RB (2004) Perceiving the intensity of light. Psychological Rev. Vol 111: 142-158.
Purves D, Lotto RB (2003) Why We See What We Do: An Empirical Theory of Vision. Sunderland, MA: Sinauer Associates.
Nundy, S, Purves D (2002) A probabilistic explanantion of brightness scaling. Proc Natl Acad Sci 99(22): 14482-14487.
Purves D, Lotto RB, Williams SM, Nundy S, Yang Z (2001) Why we see things the way we do: evidence for a wholly empirical strategy of vision. Phil Trans Roy Soc London B-Bio Sci 356:285-297.
Berkeley G (1709/1975) Philosophical works including works on vision. (Ayers MR ed) London: Everyman/ J.M. Dent.