Reversible Perspective Footnotes

1 -See Charles Eastlake's introduction to the English translation of Johann Wolfgang von Goethe's Zur Farbenlehre where he juxtposes Newton and Goethe. Newton's optics is an "old castle," which through centuries, has been pathched-up and at last has become "uninhabitable," abandoned." But with the spirit of Goethe's work, after the "Bastille" has been "demolished", a new terrain, "a free space" will open up. Goethe, Theory of Colours, trans. C. Eastlake, Cambridge Mass., MIT Press, 1970 (originally published 1840).

2 -See Jonathan Crary, Techniques of the Observer: On Vision and Modernity in teh Nineteenth Century, Cambridge Mass., MIT Press, 1990, chapters 2, 3. See also Richard Rorty, (Philosophy and the Mirror of Nature, Princeton, Princeton University Press, 1979.) on the model of the camera obscura and the Enlightenment epistemology of vision.

3 -René Descartes, The Philosophical Writings of Descartes, 2 vols. trans. John Cottingham, Robert Stoothoff, & Dugald Murdoch, Cambridge, 1985, vol. 1, p. 166.

4 -Goethe, pp. 16-17.

5 -"On the Optical Illusion of the Conversion of Cameos into Intaglios, with an Account of other Analogous Phenomena," Edinburgh Journal of Science, 4, 1826, 99-108. Reprinted in N. Wade, Brewster and Wheatstone on Vision, London, Academic Press, 1983, 56-64, hereafter cited as Brewster and Wheatstone. For another history of reversile perspective see J. E. Wallace Wallin, Optical Illusions of Reversible Perspective. Princeton, 1905. Wallin subsribes to the psychophysics, i. e., nativist theory that illusions have their origin in the physical structure of the eye.

6 -"Observations on some remarkable Optical Phaenomena seen in Switzerland; and on an Optical Phaenomenon which occurs on viewing a Figure of a Crystal or Geometrial Solid," The London and Edinburgh Philosophical Magazine and Journal of Science, November 1832.

7 -"On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina," Transactions of the Royal Society of Edinburgh, 15, 1844, 349-368; reprinted in Brewster and Wheatstone, see p. 96.

8 -Ibid., 98.

9 -Brewster's claim that a geometric projection of a pyramid onto a plane would appear, at all points, equally clear to the eye, as opposed to the appearance of an actual pyramid is confusing. Perhaps he meant that because the eye surveys the representation so rapidly, the optical adjustment from, say, the apex to one of the sides would take less time than if the eye were actually moving from the tip of a real pyramid to the edge of one of its sides.

10 -"On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina" ( Brewster and Wheatstone, 99).

11 -Ibid., 100

12 -A Treatise on Optics, Revised Edition, London, 1853.

13 -Optics in the Edinburgh Encyclopedia, vol. XV, 1830, 615. (See also Brewster and Wheatstone 27.)

14 -A treatise on Optics, p. 427. Brewster argued that in a stereoscopic representation an object is seen by the two eyes successively but so rapidly so as to form the impression of a solid.

15 - See Crary, Techniques of the Observer, chapter 4.

16 - "On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina" ( Brewster and Wheatstone, 114).

17 -"Contributions to the physiology of vision -- Part the first. On some remarkabel, and hitherto unobserved, phenomena of binocular vision," Philosophical Transactions of the Royal Society, 128, 1838, chapter four (Brewster and Wheatstone, p. 80).

18 -Ibid., 78-79.

19 -Ibid., 77

20 -Ibid., 77

21 -Ibid., 77

22 -Monge's work in descriptive geometry was also cited by Wheatstone as confirmation of the theory of binocular vision: the use of two planes to locate an object in space conformed to the use of two eyes to map the location of the object. See "Contributions to the physiology of vision -- Part the first. On some remarkabel, and hitherto unobserved, phenomena of binocualr vision," Philosophical Transactions of the Royal Society, 128, 1838, (Brewster and Wheatstone, pp. 78-79).

23 -"On the Optical Illusion of the Conversion of Cameos into Intaglios, with an Account of other Analogous Phenomena," (Brewster and Wheatstone, pp. 64-65)

24 -Ibid., 67.

25 -"On the Optical Illusion of the Conversion of Cameos into Intaglios, with an Account of other Analogous Phenomena," (Brewster and Wheatstone, pp. 64-65)

26 -"Contributions to the physiology of vision -- Part the first. On some remarkabel, and hitherto unobserved, phenomena of binocualr vision," (Brewster and Wheatstone, 81).

27 -Popular Lectures On Scientific Subjects, trans E. Atkinson, London, 1912

28 -Hermann von Helmholtz, Treatise on Physiological Optics, 3 vol., trans. and ed. P. C. Southall, New York, Dover, 1962, vol. III, p. 359. Helmholtz got the idea from Wheatstone who had remarked that he used line drawings without shade or color so he could be sure these factors did not aid the perception of three-dimensions. See his "Contributions to the physiology of vision -- Part the first. On some remarkabel, and hitherto unobserved, phenomena of binocular vision," (Brewster and Wheatstone, p. 72)

29 - Helmholtz was engaged in a debate with both Johannes Müeller and Ewald Hering. Interestingly, Hering, like Brewster, referred to retinal impressions as visual objects, even though they did not necessarily correspond to actual objects in real space, though he considered the eyes as a single organ which he called the double eye. See Ewald Hering, Spatial Sense and Movements of the Eye, trans. C. A. Radde, Baltimore, 1942, pp. 1-5. Although this essay is not specifically about the nativist empiricist debates over spatial perception, they are yet important for an understanding of what models of subjectivity were in dispute in nineteenth century theories of perception. See David Hatfield's The Natural and the Normative, Theories of Spatial Perception from Kant to Helmholtz, Cambridge Mass., MIT Press, 1990.

30 -Popular Lectures, p. 62

31 -Ibid., 242.

32 -Treatise, III, 21.

33 -Treatise, III, 19.

34 -Treatise, III, 28.

35 -Helmholtz, "Recent Progress in the Theory of Vision," in Richard P. Warren and Roslyn M. Warren, ed. Helmholtz on Perception, New York, John Wiley and Sons, 1968, 82. See also W. H. Stromberg, "Wittgenstein and the Nativism-Empirism Controversy," Philosophy and Phenomenology Research, 1-2, 1980, pp. 127-141.

36 -Treatise, III, 18. Helmholtz's definition of color is an illustration of the absence of such a correspondence. "The notion of three fundamental colours as having any objective significance has no meaning . . . For as long as it is simply a question of physical relations, and the human eye is left out of the game, the properties of the compound light are dependent only on the relative amounts of light of all the separate wavelenghs it contains. When we speak of reducing colours to three fundamental colours, this must be understood in a subjective sense and as being an attempt to trace the coulor sensation to three fundamental sensations." Treatise , III, p. 163.

37 -Popular Lectures, p. 268.

38 -According to Ernst Mach, the distinction between sensation and judgment was based on introspection. Optical illusions, however, provided an interesting challenge for the philosophy of psychology. "The expression 'sense-illusion' proves that we are not yet fully conscious, or at least have not yet deemed it necessary to incorporate the fact into our ordinary language, that the senses represent things neither wrongly nor correctly. All that can be truly said of the sense-organs is, that, under different circumstances they produce different sensations and perceptions. As these 'circumstances' now are extremely various in character, being partly external (inherent in the objects), and partly internal (inherent in the sensory organs), and partly interior (having their activity in the central organs), it can sometimes appear, when we only notice the external circumstances, as if the organ acted differently under the same conditions. And it is customary to call the unusual effects, deceptions or illusions." The Analysis of Sensations, London, 1897.

39 -Popular Lectures, p. 276.

40 -Ibid, 272.

41 -For another account of sensation-as-sign see Wilhelm Wundt's Outlines of Psychology, 1902. Wundt suggested that sensations were signs supplementing knowledge already formed through experience. Vision was a "higher order" sign system which could be supplemented by a lower order sign system such as touch. The combination of the two systems could in turn facilitate the formation of visual spatial ideas. (117) Wundt's system, however, was even more abstract as concerns the relation between sensations and signs and was less derivative of a picture theory or linguistic model than Helmholtz's.

42 -Jonathan Crary discusses this rupture in Techniques of the Observer. See especially p. 120 ff.. For an example of a physiological-psychological account of autonomous subjectivity see Wundt's Outlines of Psychology, 1902, where he asserts that perception is not direct knowledge of the thing itself but rather the subject's experience. See also Hermann von Helmholtz, Popular Lectures, pp. 203-204.

43 -Helmholtz, Popular Lectures, p. 274.

44 -Ibid.

45 -Ibid., p. 275.

46 -This conceptual confusion was also rooted in a conflict between two tendencies in the sciences. One was to reduce physiology to physics and chemistry, to provide a physical, causal explanation for perception. The other was an unavoidable psychological supplement which was need to account for the meanings of sensations (as well as the existence of optical illusions) but which also broached metaphysical speculation. James Sully goes so far as to suggest that the problem of illusion naturally brings forth the need for a philosophical analysis of the phenomena of perception. Science, he wrote, "cannot prove but must assume the coincidence between permanent common intuitions [perception] and objective reality . . . and this leads to the question of reality." See James Sully, Illusions: A Psychological Study, New York 1881, 96.

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