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Ptolemy, Alhazen, and Kepler and the Problem of Optical Images

Published online by Cambridge University Press:  24 October 2008

A. Mark Smith
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“Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena (1604), “henceforth the [visible] representations of objects should be considered as paintings [picturae] that are actual[ly projected] on paper or some other screen.” While not intended as a historical generalization (“up to now” having surely been meant within the narrow context of the treatise itself), this claim nonetheless reflects historical reality. Virtually all visual theorists before Kepler did, in fact, conceive of optical images as subjective, not objective constructs – or, to put it in modern terms, as virtual rather than real entities. By current lights, of course, the distinction between virtual and real images is both obvious and common-place: whereas the latter can be physically projected upon a screen, the former cannot.

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Research Article
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Arabic Sciences and Philosophy , Volume 8 , Issue 1 , March 1998 , pp. 9 - 44
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Copyright © Cambridge University Press 1998

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References

1 “Cùm hactenus Imago fuerit Ens rationale, iam figurae rerum verè in papyro existentes, seu alio pariete, picturae dicantur,” Ad Vitellionem Paralipomena, ch. 5, section 3Google Scholar, “definitio,” in Johannes Keplers gesammelte Werke, vol. 2, ed. Hammer, Franz (München, 1939), p. 174.Google Scholar

2 That Kepler thought of the crystalline lens as a mere refracting-device is clear from his likening it to glass balls and water-filled flasks (“Quaecunque ferè hactenus de crystallino dicta sunt, eorum vulgaria passim cernuntur experimenta in pilis crystallinis, inque vitris vrinariis limpida aqua repletis,” Paralipomena 5, 3, p. 162).Google Scholar The subsequent analysis of light-rays passing through such spherical balls or flasks concludes with a demonstration of the point-to-point focusing properties of a refracting sphere (such as the crystalline) whose posterior surface is hyperbolic (Paralipomena 5, 3, props. 19–24, pp. 175–9).Google Scholar Finally, the function of the retina as a screen for the projection of images by the crystalline lens is spelled out by Kepler in Paralipomena 5, 2, p. 151: “Visionem fieri dico, cùm totius hemisphaerii mundani, quod est ante oculum, et amplius paulò, idolum statuitur ad album subrufum retinae cauae superficiei parietem.”Google Scholar

3 Kepler's picturae are objective inasmuch as their constituent colors are physically real. Their objectivity does not, however, extend to their status as representations.Google Scholar Thus, like any other painting, the pictura projected by the crystalline lens upon the retinal screen requires perceptual interpretation – hence Kepler's recourse to visual spirits as perceptual mediators (“Quomodo idolum seu pictura haec spiritibus visoriis, qui resident in retina et in neruo, coniungatur, et vtrum per spiritus intro in cerebri cauernas ad animae seu facultatis visoriae tribunal sistatur, an facultas visoria, ceu quaestor ab Anima datus, è cerebri praetorio foras in ipsum neruum visorium et retinam, ceu ad inferiora subsellia descendens, idolo huic procedat obuiam, hoc inquam Physicis relinquo disputandum,” Paralipomena 5, 2, pp. 151–2).Google Scholar

4 It was primarily in the analysis of the rainbow that water-filled globes were used to simulate the reflective and refractive effects of raindrops upon incident sunlight; see Boyer, Carl B., The Rainbow: From Myth to Mathematics (New York, 1959). In a more general context, the passage of light through refracting spheres was analyzed by medieval theorists to account for image-magnification and distortion. As far as the focusing of light is concerned, most medieval theorists concentrated their analysis on spherical lenses. A noteworthy exception, however, is the tenth-century Arab mathematician, Ibn Sahl, who demonstrated that the correct surface of refraction for focusing light (i.e., the anaclastic) is hyperbolicGoogle Scholar; see Rashed, Roshdi, “A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses,” Isis, 81 (1990): 464–91.CrossRefGoogle Scholar

5 Recently-uncovered diplomatic correspondence between Milan and Florence during the 1460s indicates that Florentine lens-grinders could supply corrective lenses graded for five-year intervals from 30 to 70 as well as for two stages (de meza visa and de longa [visa]) of myopia; see Ilardi, Vincent, “Renaissance Florence: The optical capital of the world,” The Journal of European Economic History, 22 (1993): 507–41.Google Scholar In the third book of his Photismi de lumine, which was completed by 1554 but not published until 1611, Francesco Maurolyco remarks that “some time back, … the makers of glasses exercised such care that they indicated by small marks – one for each year – the age for which the spectacles were suited,” trans. Crew, Henry, The Photismi de Lumine of Maurolycus: A Chapter in Late Medieval Optics (New York, 1940), p. 118.Google Scholar

6 “Lorsque les lentilles furent présentées aux savants, ceux-ci les examinèrent et émirent une sentence … Ils déclarèrent que les lentilles ‘trompaient,’ … et donc qu'elles ne devaient pas être utilisées,” L'optique: Scieiwe de la vision (Paris, 1966), p. 30.Google Scholar According to Ronchi, this sentence aveuglant was codified in “une phrase terrible: Non potest fieri scientia per visum solum”Google Scholar (ibid., p. 31), which discouraged any serious effort to understand visual optics during the high and later Middle Ages.

7 It is perhaps not surprising that, for Ronchi, the final revolt against the sentence aveuglant of scholasticism was spearheaded by the Italian hero, Galileo, who restored faith (“la ‘foi’ de Galilée”) in both vision and lenses through his telescopic researches (see ibid., pp. 59–64).

8 For a definitive refutation of Ronchi's claims about the scholastic mistrust of vision, see Lindberg, David C. and Steneck, Nicholas H., “The sense of vision and the origins of modern science,” in Debus, Allen G. (ed.), Science, Medicine and Society in the Renaissance (New York, 1972), pp. 29–45.Google Scholar For a critical appraisal of Ronchi's overall approach to the history of optics as laid out in his classic Storia della luce, see Lindberg's, David review of the 1970 English version (The Nature of LightGoogle Scholar, trans. Barocas, V.) in Isis, 62 (1971): 522–4.Google Scholar

9 The classic account of the Perspectivist tradition and its evolution is contained in Lindberg's, DavidTheories of Vision from Al-Kindi to Kepler (Chicago, 1976). (1) For a Latin edition of Alhazen's De aspectibus in its entiretyGoogle Scholar, see Risner, Friedrich, Opticae thesaurus (Basel, 1572Google Scholar; repr. New York / London, 1972). For an English translation of the first three books – a translation, however, based on the Arabic original rather than the Latin version upon which the Perspectivists relied – see Sabra, A.I., The Optics of Ibn al-Haytham. Books I–III On Direct Vision, 2 vols. (London, 1989). (2) A critical edition of Roger Bacon's Perspectiva (the fifth part of his Opus majus) can be found inGoogle ScholarLindberg, David C. (ed. and trans.), Roger Bacon and the Origins of Perspectiva in the Middle Ages (Oxford, 1996); this supersedes the Bridges edition of 1900 and the Burke translation of 1928.Google Scholar (3) For a critical edition of Bacon's, Roger De multiplicatione specierum, see Lindberg, David C. (ed. and trans.), Roger Bacon's Philosophy of Nature (Oxford, 1983). (4) For a critical edition of the portion of Witelo's Perspectiva dealing explicitly with visual perception (books 2 and 3)Google Scholar, see Unguru, Sabetai (ed. and trans.), Witelonis Perspectivae liber secundus et liber tertius (Wroclaw / Warsaw/Cracow, 1991).Google Scholar A Latin version of the whole of Witelo's Perspectiva is to be found in Risner's Opticae thesaurus of 1572.Google Scholar (5) A critical edition of Pecham's, John Perspectiva communis can be found in Lindberg, David C. (ed. and trans.), John Pecham and the Science of Optics (Madison, WI, 1970).Google Scholar

10 For Euclid's articulation of this visual model, see the first three definitions of the Optics in Heiberg, I.L., Euclidis Opera Omnia, vol 7 (Leipzig, 1895), p. 2.Google Scholar

11 Euclid has recourse to this explanation in proposition 3 of the Optics (“For every visible object there is a distance at which it is no longer seen”); see ibid., pp. 4–6.

12 The foundations for Euclid's account of spatial perception are laid in definitions 4–6 of the Optics; see ibid., p. 2.

13 Probably composed sometime between 160 and 170 A.D., Ptolemy's Optics survives in a somewhat mangled twelfth-century Latin version that was drawn from a yet-undiscovered Arabic translation of the lost Greek original. All citations from Ptolemy's Optics will be from the recent English translation in Smith, A. Mark, Ptolemy's Theory of Visual Perception, Transactions of the American Philosophical Society 86.2 (Philadelphia, 1996).Google Scholar Since references will be by book and paragraph number, all citations can be easily crosschecked against the critical Latin edition by Lejeune, Albert, L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile: Édition critique et exégétique augmentée d'une traduction française et de compléments (Leiden/ New York/ Kφbenhavn/Köln, 1989).Google Scholar

14 Although Ptolemy does not explicitly cite the pupil's responsibility for the shape and angular extent of the visual cone, he implies it at various reprises in the Optics. For a detailed discussion of the issue, see Lejeune, Albert, Euclide et Ptolémée: Deux stades de l'optique géométrique grecque (Louvain, 1948).Google Scholar

15 As Ptolemy puts it in Optics III, 16: “The rays that pass through the cornea and radiate … from the origin-point, which lies within the ocular sphere at the centerpoint, all form perpendiculars to the surface of the pupil [i.e., the cornea], which assumes the nature of a convex mirror in terms of its shape and smoothness”Google Scholar (Ptolemy's Theory, p. 137).Google Scholar See also Optics IV, 3–5, ibid., pp. 175–6.

16 There is fairly good reason to suppose that Ptolemy located the seat of sentiency and reason in the brain. That the anatomy of the visual system was fairly thoroughly charted by Ptolemy's time is attested by the sophisticated treatment of ocular anatomy and physiology provided by Galen, whose account in books nine and ten of the De usu partium depended heavily on the Alexandrian tradition established by Herophilus and Erasistratus in the third century B.C.; for details, see von Staden, Heinrich (ed. and trans.), Herophilus: The Art of Medicine in Early Alexandria (Cambridge, 1989).Google Scholar Thus, it was well known by Ptolemy's time that the optic nerves branched out from two points at the forefront of the brain and that they crossed at the optic chiasma before proceeding to their respective eyes. The Apex-point mentioned in this passage is the point of origin for what Ptolemy calls the “common axis,” which lies precisely midway between the two visual axes and keeps those axes working concertedly to ensure that the two eyes yield one image (see Optics III, 35 in Ptolemy's Theory, pp. 144–5). Although Ptolemy did not explicitly link that Apex-point to the optic chiasma, both Alhazen and Roger Bacon took the link for grantedGoogle Scholar; see Alhazen, , De aspectibus III, 2, [12]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 232–3Google Scholar; see Bacon, Perspectiva 2, ii, 1Google Scholar, in Bridges, , Opus Majus, II, 93.Google Scholar

17 “Among the things that are common to the senses according to the origin of nervous activity [secundum principium nervosum],” Ptolemy tells us in Optics II, 13, “sight and touch share in all except color, for color is perceived by no sense but sight”Google Scholar (Ptolemy's Theory, pp. 74–5).Google Scholar It is fairly clear that, in Ptolemy's view, this principium is a certain Governing Faculty (virtus regitiva) that corresponds to the Stoic hegemonikon, which is the central clearing-house for all perceptual and rational functions. Thus, for example, in explaining the visual perception of motion, Ptolemy claims in Optics II, 76 that “… motion and rest [are apprehended] not by the visual faculty but by the sense of touch that extends to the Governing Faculty, in the same way that we do not discern the motion of our hands by sight when our eyes are closed but by means of a continuous [sense-link] that reaches to the Governing Faculty”Google Scholar (Ptolemy's Theory, p. 103). The Governing Faculty thus provides the viewer with a necessary sense of self-reference without which spatial perception (i.e., perception of place, disposition, size, motion, and so forth) would be impossible.Google Scholar

18 That Ptolemy, like Aristotle, views color as the only sensible quality appropriate to sight is clear from his extended discussion in Optics II, 5–13Google Scholar (see Ptolemy's Theory, pp. 71–5).Google Scholar It is therefore from a feeling or passion (passio) of “coloring” that visual perception of secondary qualities such as shape and size arises; hence, as Ptolemy describes it in Optics II, 23, “we see any luminosity or color by means of a passion arising in the visual flux, while we see the secondarily visible properties that remain through the accidents that this passion conveys”Google Scholar (Ptolemy's Theory, p. 79). When we “see” an object in all its physical manifestations, then, we are really inferring perceptually from the primally visible data of color and color-contrast.Google Scholar

19 Harking back at least to Democritus, the theory of emphasis (“reflection” or “imprinting”) is based on the idea that visible bodies make a sort of physical/material impression in the air that is eventually stamped upon the cornea (generally referred to as the “pupil”). This corneal impression, in its turn, serves as the means by which visual perception is ultimately carried out; for a basic account see von Fritz, Kurt, “Democritus' theory of vision,” in Underwood, E.A. (ed.), Science, Medicine, and History, vol. 1 (London, 1953), pp. 83–99.Google Scholar Although Ptolemy never explicitly mentions emphasis, there are several strong hints of it in his account of seeing; see, e.g., Optics II, 23; III, 16; and IV, 4–5Google Scholar, in Ptolemy's Theory, pp. 80, 137 and 175–6.Google Scholar

20 For a detailed account, see Ptolemy's Theory, pp. 27–34.Google Scholar

21 See Optics II, 50 in Ptolemy's Theory, p. 91.Google Scholar

22 For the directional privilege of the Ptolemaic ray, see Optics II, 26 in Ptolemy's Theory, p. 82; for Ptolemy's account of the visual angle as a factor in size-determinationGoogle Scholar, see Optics II, 52 in Ptolemy's Theory, p. 92.Google Scholar

23 The viewer's innate sense of ray-length, and thus of distance, complements his sense of directional privilege. Thus, as Ptolemy puts it in Optics II, 26, “whatever is seen with a longer ray appears farther away, as long as the increase in [the ray's] length is sensible”Google Scholar (Ptolemy's Theory, p. 82). The ability to estimate distances allows us to judge relative size among objects that subtend equal, as well as unequal, visual angles. Yet another factor in size determination is slant. Hence, although two objects may lie the same distance from the center of sight and may subtend the same visual angle, if one lies at a slant, it will be judged as largerGoogle Scholar; see Optics II, 52–63, in Ptolemy's Theory, pp. 92–8.Google Scholar

24 For Ptolemy's claim that light and visual flux, as well as color, share the same genus, see Optics II, 23, in Ptolemy's Theory, p. 80.Google Scholar As far as intensity is concerned, Ptolemy claims in Optics II, 21 that “the farther such powers [i.e., visual power] extend from their sources, … the weaker they become – as, e.g., [the power of] projection [in relation to] the thrower, or of heat in relation to the heater, or of illumination in relation to the light-source.Google Scholar Therefore, … it necessarily follows that the visual perception of what lies far from the vertex of the [visual] cone is carried out by a more weakly-acting ray” (Ptolemy's Theory, p. 78). For an explicit critique of Euclid's account of radial intersticesGoogle Scholar, see Optics II, 50–51, in Ptolemy's Theory, pp. 91–2.Google Scholar

25 The relationship between visual acuity and distance from the visual axis is discussed by Ptolemy in Optics II, 20 (Ptolemy's Theory, pp. 77–8). Although he never explicitly mentions scanning as the means to visual certification, Ptolemy implies it in his discussion of binocular vision and the clarity of sight at the point where the two visual axes convergeGoogle Scholar; see, e.g., Optics II, 27, in Ptolemy's Theory, p. 82. Euclid also recognizes the need to scan an object in order to grasp it fullyGoogle Scholar; see Optics, prop. 1.Google Scholar

26 For a detailed discussion of Ptolemy's understanding of the dynamics of visual radiation, see Smith, A. Mark, “Extremal principles in ancient and medieval optics,” Physis, 31 (1994): 113–40, esp. 121–8.Google Scholar

27 How the image of something as large as a mountain can shrink to fit the pupil was a problem for the intromissionists, particularly the atomists, who believed that vision depended on the reception of eidola or simulacra, which were atom-thick skins or impressions actually cast off by the surfaces of visible objects. See Lindberg, Theories of Vision, pp. 2–3.Google Scholar

28 “We say,” asserts Ptolemy in Optics II, 2 and II, 5, “that the visual faculty apprehends corporeity, size, color, shape, place, activity, and rest; [hence, although] colors are primarily visible, [they] are not visible per se without light. Indeed, colors are never seen in darkness, except for [the color of] an object that shines from inherent whiteness or that is exceedingly polished, for each of these is a case of brightness, and brightness is a kind of luminosity”Google Scholar (Ptolemy's Theory, pp. 71–2). Ptolemy is thus in general accord with both Plato and Aristotle that, without light's being present, color is not actually visible.Google Scholar

29 The lion's share of the Optics as it presently exists is devoted to the problem of image-distortion in reflection and refraction. Such distortion involves spatially-determined characteristics such as location, orientation, size, and shape, all of which can be affected in various ways by the shape of the reflecting or refracting surface, as well as by the density-differential at the interface of refraction.

30 See Smith, A. Mark, “Saving the appearances of the appearances: The foundations of classical geometrical optics,” Archive for History of Exact Sciences, 24 (1981): 73–100;CrossRefGoogle Scholar and “Ptolemy's search for a law of refraction: A case-study in the classical methodology of ‘saving the appearances’ and its limitations,” Archive for History of Exact Sciences, 26 (1982): 221–40.Google Scholar For Ptolemy's discussion of visual illusions in general and their rationalization, see Optics II, 83–142 in Ptolemy's Theory, pp. 106–28.Google Scholar

31 This point has been made with considerable force and elegance by Simon, Gérard, Le regard, l'être et l'apparence dans l'Optique de l'antiquité (Paris, 1988).Google Scholar

32 That the Latin version of Ptolemy's Optics influenced at least some scholastic thinkers is clear from Ptolemaic traces in Bacon's Opus Majus and Witelo's Perspectiva; for details see Ptolemy's Theory, pp. 58–60. For a discussion of the connections between Ptolemy's Optics and Alhazen's De aspectibusGoogle Scholar, see Smith, A. Mark, “Alhazen's debt to Ptolemy's Optics,” in Levere, T.H. and Shea, W.R. (eds.), Nature, Experiment, and the Sciences (Dordrecht/Boston/London, 1990), pp. 147–64CrossRefGoogle Scholar; see also Sabra, , Optics of Ibn al-Haytham, II, lviii–lxi.Google Scholar

33 In De aspectibus I, 6 [56]-[58], Alhazen argues against extramissionism on the basis of logical economy. Whether through visual flux or a transparent medium, he contends, something has to be conveyed to the eye for vision to occur. That being the case, then it is superfluous to posit an extramission of flux through which visual impressions can be conveyed back to the eye when a single line of transmission from object to eye through the transparent medium will accomplish that endGoogle Scholar; see Sabra, , Optics of Ibn al-Haytham, I, 80–1. Alhazen finds strong empirical support for intromissionism in the existence of afterimages, which suggests that visual impressions are somehow stamped upon, and thus retained by, the eyeGoogle Scholar; see De aspectibus I, 4 [1]-[7]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 51–2.Google Scholar

34 “It is a property of light,” contends Alhazen in De aspectibus I, 6 [], “that it affects the sight, and … it is in the nature of sight to be affected by light,”Google ScholarSabra, , Optics of Ibn al-Haytham, I, 63. For Perspectivist parallelsGoogle Scholar, see: Witelo, Perspectiva 3, prop. 6; Bacon, Perspectiva 1, x, 2;Google ScholarPecham, Perspectiva communis 1, prop. 1.Google Scholar

35 See De aspectibus 1, 3 [140]-[143]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 50.Google Scholar For Perspectivist parallels, see: Witelo, Perspectiva 2, definition 2 and prop. 4Google Scholar; Bacon, , De multiplicatione specierum 1, 3 and Perspectiva 1, ix, 2 and 1, x, 2Google Scholar; Pecham, , Perspectiva communis 1, prop. 3. By “physical passage” I mean the sort of passage characterized by projectile motion; Alhazen and his Latin followers all agreed that, while light-radiation necessarily occurs in bodies (so it is physical in that sense), it is not of bodies.Google Scholar

36 De aspectibus I, 3 [110]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 43. For Perspectivist parallelsGoogle Scholar, see: Witelo, Perspectiva 2, postulate 6;Google ScholarBacon, , De multiplicatione specierum 2, 8;Google ScholarPecham, , Perspectiva communis 1, prop. 6.Google Scholar

37 “What mathematicians call ‘lines of the ray’ [are] imaginary lines only … that determine the direction in which the eye is affected by the form,” De aspectibus I, 6 [62],Google Scholar in Sabra, , Optics of Ibn al-Haytham, I, 82.Google Scholar For Perspectivist parallels see: Witelo, ,Perspectiva 2, prop. 3;Google ScholarBacon, , De multiplicatione specierum 2, 1.Google Scholar

38 See, e.g., Lindberg, Theories of Vision, pp. 85–86;Google ScholarRashed, Roshdi, “Lumière et vision chez Ibn al-Haytham,” in Taton, René (ed.), Roemer et la vitesse de la lumière (Paris, 1978), pp. 19–44Google Scholar; Smith, “Extremal principles”; and Simon, Gérard, “L'Optique d'Ibn al-Haytham et la tradition Ptoléméenne,’ Arabic Sciences and Philosophy, 2 (1992): 203–35.CrossRefGoogle Scholar

39 See De aspectibus 1, 5 for Alhazen's description of the eye and its composition. For Perspectivist parallels seeGoogle Scholar: Witelo, , Perspectiva 2, prop. 4Google Scholar; Bacon, , Perspectiva 1, ii and iiiGoogle Scholar; Pecham, Perspectiva communis 1, props. 31, 33. and 34.Google Scholar Figure 4, which illustrates the ocular model described by Alhazen, is adapted from Figure C.1.ii of Sabra's, Optics of Ibn al-Haytham, II, 48.Google Scholar

40 As will become clear below, Alhazen's account of how the visual impression passes through the ocular humors – in particular through the interface between the glacial and vitreous humors – necessitates a difference in refractivity between the two humors; in fact, according to the norms of refraction, the vitreous humor must be optically denser than the glacial; see, e.g., De aspectibus 2, 2 [7]-[10]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 116–17. For Perspectivist parallels seeGoogle Scholar: Witelo, Perspectiva 3, prop. 21Google Scholar; Bacon, , Perspectiva 1, vii, 1Google Scholar; Pecham, , Perspectiva communis 1, prop. 40.Google Scholar

41 See De aspectibus 1, 5 [2]-[3]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 55–6.Google Scholar For Perspectivist parallels see: Witelo, Perspectiva 2, prop. 4;Google ScholarBacon, , Perspectiva 1, ii, 1Google Scholar; Pecham, , Perspectiva communis 1, prop. 32.Google Scholar

42 See De aspectibus 1, 5 [14]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 57.Google Scholar For Perspectivist parallels see: Witelo, Perspectiva 2, prop. 4Google Scholar; Bacon, , Perspectiva 2, i, 3;Google ScholarPecham, , Perspectiva communis 1, prop. 33.Google Scholar

43 Alhazen and his Perspectivist followers all agreed that the anterior surface of the lens senses the impingment of visible forms upon it. This sensation (or “passion” – note the parallel with Ptolemy) takes the form of a low-level pain, one that can, however, become intense when the visible impression is too intense; see De aspectibus 1, 6 [67]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 84Google Scholar; Witelo, , Perspectiva 3, prop. 16Google Scholar; Bacon, , Perspectiva 1, iv, 2Google Scholar; Pecham, Perspectiva communis 1, prop. 43. For the claim that the lens selects out the forms that strike it along the orthogonalsGoogle Scholar, see De aspectibus 1, 6 [62]-[66]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 82–4Google Scholar; Witelo, Perspectiva 2, prop. 17Google Scholar; Bacon, , Perspectiva 1, vi, 1 and 2Google Scholar; Pecham, , Perspectiva communis 1, props. 28 and 37.Google Scholar

44 Note that, because the anterior surface of crystalline humor and cornea are assumed by Alhazen and his followers to be concentric, rays that are perpendicular to the crystalline lens are also perpendicular to the cornea, so they pass unrefracted through the albugineous humor.

45 Actually, this account of visual selectivity is somewhat simplified, because Alhazen and his Perspectivist followers believed that the visible impressions received along the perpendiculars were reinforced by certain obliquely-incident impressions from the same source-point on the visible object; see De aspectibus 7, prop. 37Google Scholar, in Risner, Opticae thesaurus, pp. 268–9; for Perspectivist parallelsGoogle Scholar, see: Witelo, Perspectiva 2, prop. 17;Google ScholarBacon, , Perspectiva 1, vi, 2Google Scholar; Pecham, , Perspectiva communis 1, prop. 42. Although it is unclear how Alhazen thought these obliques reinforced the impression acquired along the perpendicular, there is good reason to suppose that what he meant was that the reinforcing impressions are refracted at the corneal surface in such a way as to strike the anterior surface of the crystalline lens at precisely the same spot as the orthogonal impression; cf.Google Scholar, however, Lindberg, Theories, pp. 76–8Google Scholar and Simon, “L'Optique d'Ibn al-Haytham,” pp. 222–4.Google Scholar

46 On the necessity of having the rays refract at the interface between the crystalline and vitreous humors, see De aspectibus 2, 6 [6]-[8]Google Scholar, in Sabra, , Optics of Ibn alHaytham, I, 115–16Google Scholar; Witelo, , Perspectiva 3, props. 20–22Google Scholar; Bacon, , Perspectiva 1, vii, 1Google Scholar; Pecham, , Perspectiva communis 1, props. 35 and 40. Alhazen makes it clear, however, that the process of radial refraction is not simply mechanistic; it is also governed by the animacy of the media.Google Scholar “Thus,” he cautions us in De aspectibus II, 2 [11–13], “the occurrence of the forms in the sentient body is not like their occurrence in transparent bodies, for the lines of the ray are merely an instrument by means of which the crystalline's sensation is achieved. [Because, therefore,] the manner in which the vitreous receives the forms is not like the manner in which the anterior part of the crystalline receives them, nor is the receptive power in the vitreous the same as that in the anterior part, … the forms are … refracted at the vitreous on two accounts: one is the difference in transparency between these two bodies, and the other is the difference in their manner of sensitive reception,”Google ScholarSabra, , Optics of Ibn al-Haytham, II, 117–18. In other words, the channeling of visual forms to the opening of the optic nerve is “physico-physiological” in nature. For Perspectivist parallelsGoogle Scholar, see Witelo, , Perspectiva 3, prop. 22Google Scholar; Bacon, , Perspectiva 1, vii, 1;Google ScholarPecham, , Perspectiva communis 1, prop. 40.Google Scholar

47 As Bacon puts it, “and in this we must admire the power of the soul's excellences, whereby it compels a species to follow the twisting of the nerve, so that it proceeds along a twisting line, rather than a straight line as in inanimate bodies of the world,” Perspectiva 1, vii, 1Google Scholar, Lindberg, Origin, pp. 97–9. For discussions of the perceptual and intellectual completion of visionGoogle Scholar, see Sabra, A.I., “Sensation and inference in Alhazen's theory of visual perception,” in Machamer, P.K. and Turnbull, R.G. (eds.), Studies in Perception (Columbus, Ohio, 1978), pp. 160–85Google Scholar; Smith, A. Mark, “Getting the big picture in perspectivist optics,” Isis, 72 (1981): 568–89CrossRefGoogle Scholar; and Smith, A. Mark, “Picturing the mind: The representation of thought in the Middle Ages and Renaissance,” Philosophical Topics, 20 (1992): 149–70.CrossRefGoogle Scholar

48 For an extended discussion of Ptolemy's and Alhazen's use of dynamic models to explain vision, see Smith, “Extremal principles.”

49 It should be borne in mind, however, that the center of the eye represents the actual viewpoint for Ptolemy, whereas for Alhazen it represents the virtual viewpoint. As such, it serves as the imaginary focus of the cone of visible radiation and, therefore, as the ultimate reference-point for the geometrical analysis of vision.

50 Alhazen makes no bones about his acceptance of the visual cone as an analytic device: “When the eye faces a visible object there is formed between the object and the center of the eye a cone with that centre as vertex and the surface of the object as base. There is thus between every point on the object's surface and the centre of the eye an imaginary straight line perpendicular to the surfaces of the eye's coats” (De aspectibus 1, 6 [63]Google Scholar, in Sabra, , Optics of Ibn al-Haytham, I, 82–3).Google Scholar

51 See Perspectiva 1, vii, 2–4. In a somewhat more guarded way than Bacon, Pecham seems also to support the idea of an emission of visual power from the eye;Google Scholar see Perspectiva communis 1, prop. 46.Google Scholar

52 The Elements of Vision: The Micro-Cosmology of Galenic Visual Theory according to Hunayn Ibn Ishaq, Transactions of the American Philosophical Society 72.5 (Philadelphia, 1982); see esp. pp. 3–7.Google Scholar

53 The Book of the Ten Treatises on the Eye Ascribed to Hunain ibn Is-hâq (A.D. 809–877), ed. and trans. Meyerhof, Max (Cairo, 1928), p. 4.Google Scholar

54 See, e.g., Grassus, Benvenutus, De oculis eorumque egritudinibus et curis (early 12th century?), trans. Wood, Casey A. (Stanford, 1929), p. 27Google Scholar, and de Laguna, Andrés, “Anatomica methodus (1535),” trans. Lind, L.R. in Studies in Pre-Vesalian Anatomy: Biography, Translations, Documents (Philadelphia, 1975), pp. 263–94, p. 289. On the artistic side, Leonardo da Vinci (who was no mean anatomist) clearly thought that the crystalline lens occupied a central position in the eye and, moreover, was essentially spherical in shapeGoogle Scholar; for details see Lindberg, Theories, pp. 154–68, and for a general discussion of ocular anatomy as understood during the later Middle Ages and RenaissanceGoogle Scholar, see ibid., pp. 168–77.

55 “Inter ea, quae ad visum spectant, dignitatis arcem obtinent glacialis siue chrystallinus humor, quem et pupillam appellare meo iudicio possumus: in qua visiua virtus, tamquam in sede consistit” (Photismi, p. 69). The echoes of Hunayn's reasoning are, if course, unmistakable in this passage.Google Scholar

56 The diagram of the eye provided in Vesalius' De fabrica of 1543 has the lens occupying the very center of the ocular globe. This diagram was adopted (and adapted) byGoogle ScholarMaurolyco in Photismi, p. 72. I am persuaded by Gül Russell's argument that the failure of Vesalius and his successors to find the lens in the correct place was due not to observational error but to theoretical expectation. In other words, all of these anatomists “saw” the lens precisely where they were constrained by preconception to see it. To have seen it otherwise, therefore, would have required far more than improved observation; it would have entailed nothing less than a theoretical gestaltswitch.Google Scholar

57 Two anatomists in particular deserve mention in this regard: Platter, Felix, author of De partium corporis humani structura et usu libri III (1583)Google Scholar, and Jessen, Johannes, author of Anatomia Pragensis (1601). Both placed the lens toward the front of the eye, and Platter transferred the point of visual sensitivity from the anterior surface of the crystalline lens to the retina and optic nerve. Kepler based his account of the eye upon these two authors, although he followed Platter more closely than he did Jessen.Google Scholar See Paralipomena 5, 1, pp. 144–51; see also 5, 2, pp. 159–61 for Kepler's diagram of the eye. For a general discussion of Platter's and Jessen's contributions and their relationship to KeplerGoogle Scholar, see Lindberg, Theories, pp. 175–7 and 190–3.Google Scholar

58 Alhazen and his Perspectivist disciples do refer to cataracts and lesions to the optic nerve, but only as evidence for the primal role of the lens in vision. Bacon, however, discusses visual disorders somewhat more broadly, to include such physiological impairments as drunkenness; see Perspectiva 2, i, 3.Google Scholar

59 De oculis, p. 59 in Wood translation.Google Scholar

60 Bacon, Perspectiva 2, i, 3, Lindberg, Origin, p. 171.Google Scholar

61 Bacon, , Perspectiva 2, i, 1, Lindberg, Origin, pp. 165–7. Benvenutus Grassus suggests that the excess moisture of old eyes weakens vision by dispersing the visual power undulyGoogle Scholar; see De oculis, section 3, pp. 29–30 in Wood translation.Google Scholar

62 Bacon, Perspectiva 2, ii, 1, Lindberg, Origin, p. 163. For a similar accountGoogle Scholar, see Benedetti, Alessandro, Anatomice (1497), bk. 3, chap. 27, trans.Google ScholarLind, in Pre-Vesalian Anatomy, pp. 81–137, p. 121.Google Scholar

63 For a useful interpretive account of the development of artistic perspective in the fifteenth century, see Edgerton, Samuel Y., The Renaissance Rediscovery of Linear Perspective (New York, 1975).Google Scholar In his recent The Heritage of Giotto's Geometry: Art and Science on the Eve of the Scientific Revolution (Ithaca, N.Y. / London, 1991), Edgerton suggests that anyone “who wears spectacles must appreciate that the very laws of optometry that sharpen vision as one reads the newspaper are the same as those that were applied to perspective picture making in the Renaissance” (p. 5). In fact, I would suggest the very opposite: namely, that familiarity with the techniques of artistic perspective – which are based on the visual cone rather than on punctiform radiation from external objects – would have hindered rather than promoted appreciation of “the very laws of optometry that sharpen vision.”Google Scholar

64 Of the thirteen extant manuscripts containing Ptolemy's Optics, one dates from the fifteenth century, eight from the sixteenth century, and one from the seventeenth century. Hence, nearly eighty percent of the extant manuscripts were produced during the Renaissance. Further evidence of the Renaissance interest in ancient optics can be found in two abortive attempts to publish Ptolemy's Optics: the first by Georg Müller, known as Regiomontanus (d. 1476), who died before fulfilling his intention, and the second by Georg Hartmann, publisher of Pecham's, JohnPerspectiva communis (1542), who gave up for lack of an adequate manuscript version upon which to draw. For a discussion of the textual history of the OpticsGoogle Scholar, see Smith, Ptolemy's Theory, pp. 7–9 and 58–61.Google Scholar

65 See, e.g., Bacon, Perspectiva 3, ii, 4, in Bridges (Latin), pp. 157–8, and Burke (English) pp. 574–5.Google ScholarKepler, Paralipomena 5, prop. 28, p. 181, admits having at one time thought that presbyopia was corrected by magnification. This bears out Ronchi's point about lenses and visual deception, since the apparent magnification involves a misrepresentation of the object under visual scrutiny.Google Scholar

66 Photismi, p. 76. Maurolyco refers explicitly to Roger Bacon and John Pecham as champions of the theory (which is incorrect by Maurolyco's lights) that only orthogonal rays are selected by the lens (“Absurdum igitur est, quod Bachon, et Petsanus asserunt, radios scilicet visorum in pupillam [i.e., the crystalline lens] perpendiculariter ingredi”). For a general discussion of Maurolyco's theoryGoogle Scholar, see Lindberg, Theories, pp. 180–2.Google Scholar

67 “Cum ergo in conuexo vtrinque diaphano tam incidentes quam prodeuntes radii in ipsis incidentiarum, egressuumque punctis frangantur ad axem medium accedentes … iam et in pupilla, cui huiusmodi figuram natura comparauit, id idem facient visuales radii: quibus talis organi forma, vel ob id commoda fuit, quod vtrinque coadunandi fuerant; extrinsecus quidem, vt per exiguum uveae foramen ingressuris; intrinsecus autem, vt ad opticum neruum speciem rei visae congregaturis” (Photismi, pp. 76–7).Google Scholar

68 “Hic itaque humor [crystallinus] in visione recipit species, receptasque per opticum neruum ad communis sensus iudicium defert” (Photismi, p. 70).Google Scholar

69 Photismi, p. 77. Presumably, if the convergence occurs too soon, the image presented to the optic nerve will be smaller than normal; so its constituent features will be less easily discerned by the perceptual faculty.Google Scholar

70 “Conspiciliorum enim diuersa forma diuersificat radios: hos siquidem, vt dictum est, conuexa coadunant: concaua dilatant … Igitur cum conspicilia naturae defectum corrigant, iam hoc non facient, nisi aut disgregatos coadunando, aut coeuntes nimium radios dilatando” (Photismi, p. 78).Google Scholar

71 In citing physical shape as the root cause of presbyopia and myopia, Maurolyco would seem to be tending (at least by implication) toward an objective model of vision that is governed solely by the laws of physics rather than the “laws” of spirits. Whatever the implications of his analysis, however, Maurolyco failed to realize them in any effective way. The danger of reading too much into the text is illustrated by Crew's remark on page 116 of the English translation of the Photismi that Maurolyco's account “apparently contains the essential features of the modern explanation of short sight.” This judgment is, of course, both anachronistic and inaccurate.

72 Maurolyco's belief in the lens' visual selectivity is evident from his claim that the lens “is enclosed by two convex surfaces, so that by the anterior surface it may receive the species of visible things and by the posterior surface transmit them [in proper order] to the common sense” (trans. Lindberg, Theories, p. 180; for the Latin see Photismi, p. 74).Google Scholar

73 “Radii visuales ad coincidentiam properantes, minime proveniunt ad remotiora dispicienda” (Photismi, p. 77).Google Scholar

74 “Expansiores radii ad longius spectandum feruntur, concursu iam protelato” (Photismi, p. 77).Google Scholar

75 “Item concauis conspiciliis breuem obtutum extendi, atque conuexis longum breuiari; quoniam scilicet illis collecti dilatantur, his vero dilatati colliguntur radii” (Photismi, p. 79).Google Scholar

76 For an overview of Kepler's analysis of the retinal image and its formation, see Lindberg, Theories, pp. 188–202. For Kepler's own accountGoogle Scholar, see Paralipomena 5, 2 and 3 (esp. props. 19–27), pp. 151–9 and 175–81.Google Scholar

77 Kepler's acceptance of image-inversion and reversal on the retina follows from his geometrical analysis of light-radiation through glass globes. Thus, although his conclusions about the formation of visual images were anything but traditional, the methods by which he reached those conclusions were entirely traditional. For Kepler's rationalization of the inverted image, see Paralipomena 5, 4, pp. 183–7.Google Scholar

78 The overall shape of the eye, particularly toward the rear, is therefore dictated by the need to focus all of the radiation that passes through the crystalline lens as clearly as possible so that the resulting pictura will be distinct throughout. For that reason, Kepler supposes that the posterior surface of the crystalline lens is neither plane nor spherical (as supposed by his predecessors) but hyperbolic: “Et hyperbola quidem vel ei cognata figura est in posteriori parte crystallini, vt qui inter hyperbolam deorsum tendunt eiusdem recti coni radii conuergentes ad idem punctum, ii ad idem sed breuius distans punctum colligerentur: quod non in alia figura fieri posse…”Google Scholar (Paralipomena 5, 2, p. 158).Google Scholar

79 For Kepler's account of the lenticular correction of myopia and presbyopia, see Paralipomena 5, 3, prop. 28, pp. 181–3.Google Scholar

80 For a more-or-less parallel assessment of Kepler's theory on much the same grounds, see Simon, Gérard, “Kepler ou les leçons d'un contre-exemple en épistémologie,” La Pensée (1977): 43–61; repr.Google Scholar in Sciences et savoirs aux XVIe et XVIIesiècles (Paris, 1996), pp. 77–101.Google Scholar

81 “Hoc … dici potest: spiritus pati à coloribus et luminibus, passionemque hanc, esse quandam, vt ita dicam, colorationem et illustrationem. Nam resident in visu species fortiorum colorum, post intuitum factum, et miscentur coloribus à novo intuitu impressis fitque confusus ex vtroque color. Haec species separabilis à praesentia rei visae existens, non est in humoribus aut tunicis, vt supra probatum: ergò in spiritibus et per hanc impressionem specierum in spiritus, fit visio. Impressio verò ipsa non est optica, sed physica et admirabilis” (Paralipomena 5, 2, pp. 152–3). Kepler explains the increasing clarity of vision toward the center of the visual field by recourse to the weakening of the visual spirits as they pervade the retina. As a result, the farther from the source at the juncture of the optic nerve and retina the less intensely they suffer the impressions of light and color conveyed to them by the lens: “Denique virtus sensoria, seu spiritus per neruum infusus, illic, vbi retina directis conis obiicitur, est collectior et fortior, et fontis et orbis ratione: ab eo puncto cum ipso retinae sphaerico diffunditur, et à fonte discedit, quare et debilitatur”Google Scholar (Paralipomena 5, 2, p. 156).Google Scholar

82 Although he is at pains to emphasize Kepler's ties with the Perspectivist past, Lindberg makes much the same point in the conclusion to his Theories (see esp., pp. 205–8). See also Simon, “Kepler ou les leçons,” p. 83. For a provocative account of Kepler's ambivalence about optical images and their ontological statusGoogle Scholar, see Malet, Antoni, “Keplerian illusions: Geometrical pictures vs optical images in Kepler's visual theory,” Studies in History and Philosophy of Science, 21 (1990): 1–40. Malet's basic claim is that, superficial appearances to the contrary, Kepler did not think of his picturae as real images in the sense that optical theorists of the second half of the seventeenth century did. The reason, Malet contends, is that Kepler never fully weaned himself from the notion of “image” as an intentional entity. While I find this assessment of Kepler's understanding of optical images plausible, I am unpersuaded by Malet's subsequent argument that Kepler subscribed to a fundamentally Neoplatonist, “immediatist” theory of visual perception, as exemplified in Cusa and Ficino.CrossRefGoogle Scholar