IBN AL-HAYTHAM, ABU ‘ALI ALHASAN IBN AL-HASAN

called al-Baṣri (of Baṣra, Iraq), al-Baṣri (of Egypt),

also known as Alhazen , the Latinized form of first name, al-Hasan

(b. 965; d. Cairo, c. 1040) optics, astronomy, mathematics. For the original article on Ibn al-Haytham see DSB, vol. 6.

There are still many questions relating to Ibn al-Haytham’s biography, such as his origin, his education, the apparently high and demanding administrative position he reluctantly filled in the small Bûyid principality known as al-Basra-and-al-Ahwâz, the whens and wheres of the travels he found distracting, the reason and date of his immigration to Egypt, and the exact date of his death. Scholars have been rewarded, however, by the survival of a large number of his writings, some of which are quite long, in elementary and higher mathematics, physics, several aspects of astronomy and cosmology, all of which promise to receive scholarly attention for a long time.

Perspectives on Natural Philosophy In his brief, tantalizing “Autobiography” (rescued by Ibn Abî Usaybi a in the thirteenth century), Ibn al-Haytham clearly states that early in his intellectual development he embraced Aristotelian empiricism which, as shown in his later mature Optics, he combined with the mathematism he also inherited from Euclid, Ptolemy, and Apollonius. The Optics in fact displays a deliberate synthesis (he called it tarkîb) which accepts the Aristotelian ontology of substances and qualities (ma’ânî), like light and color, to which Ibn al-Haytham added the non-Aristotelian concept of point-forms (not his own term) that behave as the origin of light- and color-radiation from shining “points” (Sabra, 1980), and that naturally extend rectilinearly in all directions. Thus was established the foundation of his physical-mathematical, and experimental, theory of light and vision.

Ibn al-Haytham was not an atomist. But he subscribed to a natural-philosophical doctrine according to which the element earth is divisible down to a point where the earth turns to water, further to air, then to fire, and finally to ether, which alone is not divisible (Ibn al-Haytham III.60, On light, 2–19). He had this doctrine in mind when he argued, in Optics, that normally light shines from a luminous point in a transparent matter, say water or air, along every single straight line passing through that point, but when a minimal thickness of the matter is reached, the light vanishes. Ibn al-Haytham called the light extending along the thinnest possible width of matter “the least light” (aqallu l-qalîl min al-daw’)—a concept for which Isaac Newton found a role in his Opticks, namely as a suitable definition of “ray.”

Ibn al-Haytham’s position as physicist or natural philosopher is conveyed repeatedly in the Optics, that light does not behave in the way it does “for the sake of the eye/sight” (li-ajl al-basar), but, rather, the seeing eye just registers what it simply happens to receive from the passing light. His intention, as was later well-known, was to bury the “visual-ray theory” accepted by Euclid, Ptolemy, Galen, and al-Kindî. And yet, as shown elsewhere by this author, he continued to think in terms of a “single-ray theory” of vision, which he maintained up to Chapter 6 of Book Seven, where he came upon a simple, crucial experiment simply proving for the first time that “all that sight perceives, it perceives by refraction” of rays emanating from a single shining point in the shape of a cone. In the

experiment described in that location, the light proceeding from the shining point along the perpendicular to the surface of the eye cannot enter that surface or the parallel convex surface of the crystalline humor—the perpendicular ray being obstructed by a needle held close to the eye that appears as a shadow over the point seen only by the refracted rays (as in the diagram representing Ibn al-Haytham’s clear and original argument) (Sabra, 2003, 99–102).

It was also as a physicist that Ibn al-Haytham searched, in Books Four and Seven, for explanations of optical reflection and refraction which he borrowed from the Mu’ tazilite mutakallimûn, the dynamical concepts of i'timâd/(endeavour or effort) and tawlîd/(engendering), a substitute for Aristotelian causation. But he was not a practitioner of theological kalâm, as is clear from the titles of early essays of his that have not survived (Sabra, 1998, 10–11).

Other Primary Sources The majority of the extant works making up List III are concerned with astronomy and mathematics. As of 2007 they demand still more attention than they have so far attracted. Some or perhaps many of the short treatises on these subjects may be routine, but Ibn al-Haytham appears to have looked deeper into the astronomical system proposed by the astronomer he referred to as “the excellent Ptolemy/al-fâdil Batlamyûs,” while also judging the Almagest a book containing “more errors than can be enumerated.” In 1962 Schlomo Pines drew attention to Ibn al-Haytham’s work,

III.64: Aporias Against Ptolemy/al-Shukûk’alâ Batlamyûs, which displayed some of “the more serious” of Ptolemy’s errors and contradictions, including the well-known equant hypothesis. But an edition of the Arabic text was only published in 1971 (reprinted in 1996).

In mathematics, Ibn al-Haytham’s interests obviously leaned more toward geometry and number theory than algebra and practical arithmetic. So, here again, he was, logically and philosophically, more involved with concepts of “the knowns” (III.54: al-ma’lûmât) than with “approximations,” and with “analysis and synthesis” (III.53: alta lîl wa l-tarkîb) than with calculation—see examples, below.

It has been argued that “Muhammad ibn al-Hasan” and “al-Hasan ibn al-Hasan” were two individuals, the first being “a philosopher” and non-practicing physician and author of works constituting Lists I and II, which have been preserved, together with List III, by Ibn Abî Usaybi’a; the other, a mathematician and author of works mostly contained in List III (Rashed 1993). This was an unfortunate proposition, ignoring facts discussed elsewhere (Sabra, 1998), and the old well-known Muslim custom of often naming a newborn male after the name of the prophet, “Muhammad,” until a less common name was also adopted (a custom which has sometimes led bibliographers to drop the first name in their alphabetical ordering). Clearly, the author of the Optics presented himself as both a physicist or natural philosopher as well as a mathematician, a fact not uncommon in Arabic science.

SUPPLEMENTARY BIBLIOGRAPHY

Titles preceded by their numbers in IAU’s version of List III, containing 92 titles (see above).

WORKS BY IBN AL-HAYTHAM

III.1. M(aqâla). fî Hay’at al-’âlam: On the Configuration of the World, edited and translated by Y. Tzvi Langermann. New York: Garland Publishing, 1990.

III.3. K(itâb). Al-Manâzir – sab’Maqâlât: The Optics—Seven Books: Bks I-II-III, On Direct Vision, the Arabic text, and Arabic-Latin glossaries, edited by A.I. Sabra. Kuwait: National Council for Culture, Arts and Letters (NCCAL), 1983 (repr. 2006). The Optics of Ibn al-Haytham, Bks I–III, translated, with Introduction and Commentary, by A. I. Sabra, 2 vols. London: The Warburg Institute, 1989.

Alhacen’s Theory of Visual Perception, Bks I–II–III, edited and translated by A. Mark Smith of the Medieval Latin version, 2 vols. Philadelphia: American Philosophical Society, 2001.

The Arabic Text of Bks IV–V, On Reflection, and Images Seen by Reflection, 2 vols., edited by A. I. Sabra, Kuwait: National Council for Culture, Arts and Letters, 2002. Alhacen on the Principles of Reflection, Bks IV–V, edition and translation of the Latin text by A. Mark Smith, 2 vols. Philadelphia: American Philosphical Society, 2006.

III.4. M. fî Kayfiyyat al-arsâd: On the Method of [astronomical] Observations, edited by A. I. Sabra, Journal for the History of Arabic Sciences 2 (1978): 3–37, 155.

III.7. M. fî Samt al-qibla bi’l- isâb: “Ibn al-Haytham’s Universal Solution for Finding the Direction of the Qibla by Calculation,” edited and translated by A mad S. Dallâl, Arabic Science and Philosophy 5 (1995): 145–93.

III.10. M. fî Hisâb al- mu’âmalât: “Der Mu’âmalât des Ibn alHaitams,” [On Business Arithmetic], edited and German translation by Ulrich Rebstock, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften (ZGAIW) 10 (1995–1996): 61–121.

III.12. M. fî Ru’yat al-kawâkib: On Seeing the Stars, edited and translated by A. I. Sabra and Anton Heinen, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 7 (1991–1992): 31–72. See below, III.38.

Rashed, Roshdi. Les mathématiques infinitésimales du IXe au XIe siècles, vol. II, On Ibn al-Haytham. London: Al-Furqân Islamic Heritage Foundation, 1993. This book includes a biographical study (see below) and editions and French translation of the following mathematical works:

III.16. M. fî Mishat al-kura: T(raité). sur la mesure de la sphère, pp. 294–323.

III.17. M. fî Mishat al-mujassam al-mukâfi’: T. sur la mesure du paraboloïd: pp. 208–293.

III.20. M. mukhtasarah fî l-Ashkâl al-hilâliyya: Q(awl). fî lHilâliyyât: T. sur les lunes, pp. 70–81.

III.21. M. mustaqsâh fî l-ashkâl al-hilâliyya: T. sur les figures des lunules, pp. 102–175.

III.26. M. fî anna l-kura awsa’al-ashkâl al-mujassamah allatî i âtâtuhâ mutasâwiyah, wa anna l-dâ’ira awsa’al-ashkâl almusatta a allatî i âtâtuhâ mutasâwiyah: T. sur la sphère qui est la plus grande des figures solides ayant des périmètre égaux, et sur le cercle qui est la plus grandes des figures planes ayant des périmètres égaux, pp. 384–459.

III.30. M./Q(awl). fî Tarbî’al-dâ’ira: T. sur la quadrature du cercle, pp. 82–101. See also: Tamara Albertini, “La Quadrature du cercle d’Ibn al-Haytham: Solution philosophique ou mathématique?,” Journal for the History of Arabic Sciences, 9 (1991): 5–21.

III.38. M. fî Hall shukûk al-maqâla l-’ûlâ min Kitâb al-Majistî yushakkiku f hâ ba’du ahl al-’ilm: partially edited and translated by A.I. Sabra as “On Seeing the Stars, II. Ibn al-Haytham’s ‘Answers’ to the ‘Doubts’ Raised by [Abû l-Qâsim] Ibn Ma’dân,” Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 10 (1995–1996): 1–59. Contains detailed explanation by Ibn al-Haytham of the so-called moon-illusion problem, composed after the Optics, to which it refers.

III.40. Q. fî Qismat al-miqdârayn al-mukhtalifayn al-madhkûrayn fî l—maqâla al-’âshira min Kitâb Uqlîdis: T. sur la division de deux grandeurs différente mentionnées dans la première proposition du dixième livre de l’ouvrage d’Euclide, pp. 324–329.

III.49. M fî l-Athar alladhî fî l-qamar: Treatise on the Mark [seen on the face] of the moon. Edited by A. I. Sabra, Journal for the History of Arabic Sciences I (1977): 5–19.

III.53. M. fî l-Ta lîl wa l-Tarkîb: “L’ analyse et la synthèse,” edited and translated by Roshdi Rashed, Mélanges de l’Institut Dominicain d’Etudes Orientales du Caire 20 (1991): 31–231.

III.54. M. fî 'l-Ma’lûmât: “Les connus,” edited and translated by Roshdi Rashed, Mélanges de l’Institut Dominicain d’Études Orientales du Caire, 21 (1993): 87–275.

III.61, or III.63. M. fî Harakat al-iltifâf: “On the Motion of iltifâf,” or “M. fî Hall shukûk arakat [ajrâm] al-iltifâf,” edited by A. I. Sabra. Journal for the History of Arabic Sciences 3 (1979): 183–212. Arabic text and English summary.

III.74. M. fî Amal al-musabba’fî l-dâ’ira: “La construction de l’heptagone régulier par Ibn al-Haytham,” edited and translated by Roshdi Rashed, Journal for the History of Arabic Sciences 3 (1979): 309–387.

III.77. M. fî Amal al-kura l-mu riqa: “T. sur la sphère ardente.” In Géométrie et dioptrique au Xe siècle, edited and translated by Roshdi Rashed, 111–132. Paris: Les Belles Letters, 1993.

Ibn al-Haytham’s Completion of the Conics. Edited by Jan P. Hogendijk. New York: Springer Verlag, 1985. Based on a single surviving manuscript.

M. fî Thamarat al- ikma: “On the Fruit of Wisdom,” In Dhakî Naguib Ma mûd, Kitâb Tadhkârî, the Arabic text edited and introduced by M. Abd-al-Hâdî Abû Rîda. Kuwait: Kuwait University, 1987.

OTHER SOURCES

Eastwood, Bruce S. “Alhazen, Leonardo, and Late-Medieval Speculation on the Inversion of Images in the Eye.” Annals of Science 43 (1986): 413–446.

El-Bizri, Nader. “A Philosophical Perspective on Alhazen’s Optics.” Arabic Sciences and Philosophy 15 (2005): 183–218.

Fennane, Khalid Bouzoubaâ. “Réflexions sur le principe de continuité à partir du Commentaire d’Ibn al-Haytham sur la Proposition I.7 des Eléments d’Euclide.” Arabic Sciences and Philosophy 13 (2003): 101–136.

Hogendijk, Jan P. “al-Mu ’ taman’s Simplified Lemmas for Solving ‘Alhazen’s Problem’.” In From Baghdad to Barcelona. Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet, edited by Josep Casulleras and Julio Samsó, vol. I. Barcelona: Instituto Millas Vallicrosa de Historia de la Ciencia Arabe, 1996.

Lindberg, David C. Theories of Vision from al-Kindi to Kepler. Chicago: University of Chicago Press, 1976. Chapter 4 is especially worth noting.

Omar, Saleh B. Ibn al-Haytham’s Optics: A Study of the Origins of Experimental Science. Minneapolis, MN: Bibliotheca Islamica, 1977.

Raynaud, Dominique. “Ibn al-Haytham sur la vision binoculaire: Un précurseur de l’optique physiologique.” Arabic Sciences and Philosophy 13 (2003) : 79–99.

Sabra, Abdelhamid I. “An Eleventh-Century Refutation [by Ibn al-Haytham] of Ptolemy’s Planetary Theory.” In Science and History: Studies in Honor of Edward Rosen (Studia Copernicana XVI), 117-31. Wroclaw, Poland: The Polish Academy of Sciences Press, 1978.

———. “Sensation and Inference in Alhazen’s Theory of Visual Perception.” In Studies in Perception. Interrelations in History of Philosophy and Science, edited by Peter Machamer and Robert G. Turnbull. Columbus: Ohio State University Press, 1978.

———. “‘Form’ in Ibn al-Haytham’s Theory of Vision.” Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 5 (1980): 115–140.

———. “Psychology versus Mathematics: Ptolemy and Alhazen on the ‘Moon Illusion.’” In Mathematics and Its Application to Science and Natural Philosophy in the Middle Ages: Essays in Honor of Marshall Clagett, edited by Edward Grant and John E. Murdoch. Cambridge, U.K.: Cambridge University Press, 1987.

———. “The Physical and the Mathematical in Alhazen’s Theory of Vision.” In Optics, Astronomy and Logic. Aldershot, U.K.: Variorum, 1994.

———. “One Ibn al-Haytham or two? An Exercise in Reading the Bio-Bibliographical Sources.” Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 12 (1998): 1–50.

———. “Conclusion.” Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 15 (2002–2003): 95–108.

———. “Ibn al-Haytham’s Revolutionry Project in Optics: The Achievement and the Obstacle.” In The Enterprise of Science in Islam, New Perspectives, edited by Jan P. Hogendijk and Abdelhamid Sabra. Cambridge, MA: MIT Press, 2003.

———. “The ‘Commentary,’ That Saved the Text. The Hazardous Journey of Ibn al-Haytham’s Arabic Optics.” Early Science and Medicine 12 (2007): 117–133.

———. “Alhazen’s Optics in Europe: Notes on What It Said and What it Did Not Say.” Preprint: Workshop on “Inside the Camera Obscura.” Berlin: The Max Planck Institute for the History of Science, forthcoming.

Sesiano, Jacques. “Un mémoire d’Ibn al-Haytham sur un problème arithmétique solide.” Centaurus 20 (1976): 189–195.

Simon, Gérard. “L’Optique d’Ibn al-Haytham et la tradition ptoléméenne.” Arabic Sciences and Philosophy 2 (1992): 203–235.

Smith, A. Mark. “Alhazen’s Debt to Ptolemy’s Optics.” In Nature, Experiment, and the Sciences, edited by Trevor H. Levere and William R. Shea. Dordrecht, Netherlands: Kluwer, 1990.

———. “Ptolemy, Alhazen, and Kepler and the Problem of Optical Images.” Arabic Sciences and Philosophy 8 (1998): 9–44.

———. “The Latin Source of the Fourteenth-Century Italian Translation of Alhacen’s De aspectibus (Vat. Lat. 4595).” Arabic Sciences and Philosophy 11 (2001): 27–43.

———. “The Alhacenian Account of Spatial Perception and Its Epistemological Implications.” Arabic Sciences and Philosophy 15 (2005): 219–240.

Abdelhamid I. Sabra