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The Experimental Study of Binocular Vision by Ibn Al-Haytham and Its Legacy in the West*

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The Experimental Study of Binocular Vision by Ibn Al-Haytham and Its Legacy in the West* 127 Hist Ophthal Intern 2018, Vol.2: 127-151 The Experimental Study of Binocular Vision by Ibn al-Haytham and Its Legacy in the West* Dominique Raynaud** Abstract Early modern physiological optics introduced the concept of correspondence through the study of the con- ditions for the fusion of binocular images. The formulation of this concept has traditionally been ascribed to Christiaan Huygens (1667) and to an experiment often attributed to Christoph Scheiner (1619). How- ever, Scheiner’s experiment had already been conceptualized, first by Ptolemy (90–168 AD), then by Ibn al-Haytham (d. after 1040). The extent of the latter’s knowledge of the mechanisms of binocular vision is analyzed. It is explained why Ibn al-Haytham, who addressed this problem as an experimentalist, suc- ceeded in discovering the theoretical horopter (the locus of points in space that yields single vision) and yet failed to recognize that the horizontal line of the horopter could be described as a circular plane around the viewer’s head, credit for which goes to Vieth (1818) and Müller (1826). Through his experiments, Ibn al-Haytham established the notion of corresponding points, explored the cases of homonymous (direct) and heteronymous (crossed) diplopias, and prepared the ground for the discovery of Panum’s fusional area. Finally, the influence of al-Haytham’s pioneering treatise Kitāb al-manāẓir (Book of Optics) on West- ern science is examined, by studying the translations and commentaries that were available in the Latin world. Introduction Galen attempted to rectify this lacuna by A key chapter in the physiology of optics con- deriving a definition of the disparity between siders the conditions for the fusion of the the quasi-images produced by the two eyes quasi- or displaced images generated by the from one of Euclid’s propositions (Optica, two eyes. Interestingly, the ancient Greeks prop. 30). Unfortunately, Galen’s exposition did not explore the questions raised by binoc- on binocular vision is extremely brief 21 and ular vision in any depth. Euclid only devotes its primary aim is to provide an anatomical three propositions to this problem (Optica, description of the ocular paths. prop. 26–28) 33,80 and limits his analysis to Ptolemy’s treatment of binocular vision is what is seen of a sphere in binocular vision. far more comprehensive (Optica, II, 27–46, If the diameter of the sphere is less than, III, 25–62), 39A,10 providing the framework for equal to, or greater than the inter-pupillary Ibn al-Haytham’s research on the same sub- distance, then the two eyes will perceive a ject. A comparison of the texts by the two sa- spherical cap that is greater than, equal to, or vants confirms that many of the results less than the hemisphere, respectively. obtained by Ibn al-Haytham were based on Nowhere does Euclid address the question as the thorough study and critical analysis of his to how disparate visual stimuli are inte- predecessor’s work. Nevertheless, it would grated. appear to be more useful to take the work of Ibn al-Haytham rather than Ptolemy as our departure point to study the development of **Author´s address: the binocular theory of vision. This choice Dominique Raynaud can be justified on two grounds. Université Grenoble Alpes Firstly, while Ptolemy may have furnished UFR SHS, CS 40700 the original matrix for Ibn al-Haytham’s the- F-38058 Grenoble Cedex 9 ory, his ideas are presented in Optica in any- France thing but a systematic manner, with the eMail: [email protected] *The text is adapted from D. Raynaud, Studies on Binocular Vision, Springer, 2016: 71–114. DOI 10.1007/978-3-319-42721-8_5. Permission granted by Springer.com 128 propositions regarding binocular vision strad- ceives visible [things] if the visual ray falls dling Books II and III. What is more, certain upon them. The visible will be seen as unique results appear to be quite tentative, a fact if only one ray falls upon it; if two visual rays that earned him the criticism of Ibn al- fall on it, it will be seen as double … If it hap- Haytham: “[Ptolemy] said that when the eye pens that the two cones emerging from the two eyes separate from each other, such that a ra- gazes at the middle object assumed in the diant cone from each of the two eyes falls on middle of the ruler at the point intersection the same visible [thing], then the same thing of the two diameters, then the two lines or di- will be seen as double. 60A ameters representing the visual axes will be seen as a single line that coincides with the He then constructs a classification of the common axis… But it is an error attested causes – both natural and artificial – which both by reasoning and experience.” 30 In the could result in the separation of the visual final analysis therefore, Ptolemy can con- cones and cause diplopia; among these are tribute little to our understanding of the his- strabismus and the image of two objects lo- tory of binocular vision, because at each turn cated at different distances: we find ourselves having to explain elements that require modification or amendment. It may happen that one single thing will be Secondly, unlike his work Almagest, which seen as double … when a man fixes his pupil circulated widely and was universally read on a close thing and on another thing in the di- between the Duecento and the Cinquecento, rection of that [thing] which he has fixed on Ptolemy’s treatise on optics never achieved but which is further than it from the eye; it is the stature of an authoritative text in Eu- then that he will see one single thing as two. In effect, when he looks at the closer [thing] rope. In contrast, it appears to have been bet- and fixes on it, one of the two rays [from the ter known in the Arab world; we find it cited two eyes] will bend in relation to the other, and two times in Greek and five times in Arabic the two rays will fall on the more distant visi- compared to just twice in Latin treatises from ble [object] in this manner; as a consequence the Middle Ages. Historians have suggested he will see two things. 60B that the eclipse of Ptolemy’s Optics can be ex- plained by the appearance of Ibn al- The term “artificial cause” used by Qusṭā Haytham’s De aspectibus, which was read by Ibn Lūqā, and the fact that he classifies the Latin perspectivists and would orient among these causes both pathological condi- their work. As Smith wrote: “With the con- tions (such as strabismus) and accidental cir- tinued dissemination of Ibn al-Haytham’s cumstances (e.g., pressure exerted on the treatise and the proliferation of Perspectivist eyeball) could give rise to confusion. How- works during the late thirteenth and early ever, he clearly states that diplopia may occur fourteenth centuries, Ptolemy’s Optics was under normal as well as abnormal conditions. bound to lose its status as a legitimate source The disparity arising from the observation of in optics.” 76 In fact, another reason not to objects situated at different distances does take Ptolemy as our reference point is be- not necessarily imply that there is a problem cause Latin authors retained that the expla- with the visual apparatus; it is normal phys- nation of binocular vision was not to be found iological diplopia and one cannot apply the in Ptolemy’s Optics but in Ibn al-Haytham’s theory of neutralization here to explain the De aspectibus. integration of two sets of visual sensations. It is therefore to the Arab world that we Ibn al-Haytham (d. after 1040) was the must turn in our search for the key to a cor- second Arab savant to turn his attention to rect reading of the further development of binocular vision. He is unanimously recog- the theory of binocular vision. As we begin to nized for his work in three fields: mathemat- re-trace this history, one of the first texts that ics (Commentary on Euclid’s Premises; On deserves mention is the Book of the Causes of the Completion of Conics; Exhaustive Treatise the Diversity of Perspectives in Mirrors by the on the Figures of Lunes; On the Regular Hep- Melkite physician and scientist Qusṭā Ibn tagon; On the Measurement of the Paraboloid; Lūqā (820–912), who settled in Baghdad and and On the Measurement of the Sphere, a translated many ancient Greek texts into short tract on what came to be known in Arabic. Qusṭā Ibn Lūqā draws the distinction number theory as Wilson’s theorem, al- between pathological diplopia and physiolog- though al-Haytham was the first to state it), ical diplopia and poses the question: astronomy (On the Determination of the Meridian from One Solar Altitude; On the By what cause is one single thing seen twice or Visibility of Stars; Doubts on Ptolemy; The more? And in how many ways is this possible? Resolution of Doubts on the First Book of the We have said earlier that the sense of sight per- Almagest; The Resolution of Doubts on the 129 Winding Movement), and optics (On Optics; al-manāẓir (III, 2). Chapter 2 is divided into The Discourse on Light; On Spheric Burning six sections. In paragraphs 2.1–2.24 the au- Mirrors; On Parabolic Burning Mirrors; On thor defines various terms and concepts and the Burning Sphere; On the Light of the the qualitative approach that he would adopt Moon; On the Halo and the Rainbow; On the in analyzing the problem of binocular vision.
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