 Ibn alHaytham

▪ Arab astronomer and mathematicianIntroductionLatinized as Alhazen, in full, Abū ʿAlī alḤasan ibn alHaythamborn c. 965, Basra, Iraqdied c. 1040, Cairo, Egyptmathematician and astronomer who made significant contributions to the principles of optics (optics) and the use of scientific experiments.LifeConflicting stories are told about the life of Ibn alHaytham, particularly concerning his scheme to regulate the Nile. In one version, told by the historian Ibn alQifṭī (d. 1248), Ibn alHaytham was invited by alḤākim (Ḥākim, al) (reigned 996–1021; also known as “The Mad Caliph”) to Egypt to demonstrate his claim that he could regulate the Nile. However, after personally reconnoitering near the southern border of Egypt, Ibn alHaytham confessed his inability to engineer such a project. Although still given an official position by the caliph, Ibn alHaytham began to fear for his life, so he feigned madness and was confined to his own home until the end of alḤākim's Caliphate. Ibn alQifṭī also reports that Ibn alHaytham then earned a living in Egypt largely by copying manuscripts; in fact, he claimed to possess a manuscript in Ibn alHaytham's handwriting from 1040.There are three lists of Ibn alHaytham's writings, the first of which comes with his autobiography (1027), that collectively enumerate almost 100 works. It has recently been plausibly argued that there were two Ibn alHaythams: alḤasan ibn alḤasan, the mathematician who wrote on optics, and Muḥammad ibn alḤasan, the astronomerphilosopher who wrote the autobiography and the works in the first and second lists.Major worksIbn alHaytham's most important work is Kitāb almanāẓir (“Optics”). Although it shows some influence from Ptolemy's 2nd century AD Optics, it contains the correct model of vision: the passive reception by the eyes of light rays reflected from objects, not an active emanation of light rays from the eyes. It combines experiment with mathematical reasoning, even if it is generally used for validation rather than discovery. The work contains a complete formulation of the laws of reflection and a detailed investigation of refraction, including experiments involving angles of incidence and deviation. Refraction is correctly explained by light's moving slower in denser mediums. The work also contains “Alhazen's problem”—to determine the point of reflection from a plane or curved surface, given the centre of the eye and the observed point—which is stated and solved by means of conic sections (conic section). Other optical works include Ḍawʾ alqamar (“On the Light of the Moon”), alHāla waqaws quzaḥ (“On the Halo and the Rainbow”), Ṣūrat alkusūf (“On the Shape of the Eclipse”; which includes a discussion of the camera obscura), and alḌawʾ (“A Discourse on Light”).In his Ḥall shukūk fī Kitāb Uqlīdis (“Solution of the Difficulties of Euclid's Elements”) Ibn alHaytham investigated particular cases of Euclid's theorems, offered alternative constructions, and replaced some indirect proofs with direct proofs. He made an extended study of parallel lines in Sharḥ muṣādarāt Kitāb Uqlīdis (“Commentary on the Premises of Euclid's Elements”) and based his treatment of parallels on equidistant lines rather than Euclid's definition of lines that never meet. His Maqāla fī tamām Kitāb alMakhrūṭāt (“Completion of the Conics”) is an attempt to reconstruct the lost eighth book of Apollonius's Conics (c. 200 BC). Among his other mathematical works are treatises on the area of crescentshaped figures and on the volume of a paraboloid of revolution (formed by rotating a parabola about its axis).Ibn alHaytham's most famous astronomical work is Hayʾat alʿālam (“On the Configuration of the World”), in which he presents a nontechnical description of how the abstract mathematical models of Ptolemy's Almagest can be understood according to the natural philosophy of his time. While this early work implicitly accepts Ptolemy's models, a later work, alShukūk ʿalā Baṭlamyūs (“Doubts about Ptolemy”), criticizes the Almagest, along with Ptolemy's Planetary Hypotheses and Optics.InfluenceIbn alHaytham's greatest work, “Optics,” appears to have been neglected in the East until the commentary on it by the mathematician Kamāl alDīn Abuʾl Ḥasan Muḥammad ibn alḤasan alFārisī (d. 1320). A Latin translation of it—sometimes literal and sometimes interpretative—was made by an unknown scholar, probably early in the 13th century. The work had a major influence not only on 13thcentury thinkers such as Roger Bacon (Bacon, Roger) but also on later scientists such as the astronomer Johannes Kepler (Kepler, Johannes) (1571–1630). There were several Latin translations of the “Configuration of the World,” a book which influenced Georg Peuerbach (Peuerbach, Georg von) (1423–61) among others. Among the Latin translations of Ibn alHaytham's works by Gerard of Cremona (c. 1114–87) is a treatise on dawn and twilight, Liber de crepusculis, that is no longer attributed to Ibn alHaytham.Richard LorchAdditional ReadingA good general survey of Ibn alHaytham's work is A.I. Sabra, “Ibn alHaytham,” in Dictionary of Scientific Biography, vol. 6 (1972), pp. 189–210. The introductions to the following all contain some biographical material: The Optics of Ibn alHaytham: Books I–III, On Direct Vision, trans. by A.I. Sabra, 2 vol. (1989); J.P. Hogendijk, Ibn alHaytham's Completion of the Conics (1985); and Y. Tzvi Langermann, Ibn alHaytham's On the Configuration of the World (1990).For the text of nine of Ibn alHaytham's mathematical works, with translation and commentary, as well as the theory of the two Ibn alHaythams, see vol. 2 of Roshdi Rashed, Les Mathématiques infinitésimales du IXe au XIe siécle (1993). For a different view of this theory and for a continuation of the author's study of Ibn alHaytham, see A.I. Sabra, “One Ibn alHaytham or Two? An Exercise in Reading the Biobibliographical Sources,” Zeitschrift für Geschichte der ArabischIslamischen Wissenschaften, 12:1–50 (1998).Richard Lorch
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