Alhazen

Ibn al-Haytham (Alhazen)
Born	(965-07-01)July 1, 965 CE[1] (354 AH)[2] Basra, Buyid Emirate
Died	March 6, 1040(1040-03-06) (aged 74)[1] (430 AH)[3] Cairo, Egypt, Fatimid Caliphate
Residence	Basra Cairo
Fields	Optics Astronomy Mathematics
Known for	Book of Optics Doubts Concerning Ptolemy Alhazen's problem Horopter Moon illusion and contributions to experimental science scientific methodology visual perception empirical theory of perception
Influences	Aristotle Euclid Ptolemy
Influenced	Averroes Roger Bacon Witelo

Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Arabic: أبو علي، الحسن بن الحسن بن الهيثم‎), frequently referred to as Ibn al-Haytham (Arabic: ابن الهيثم, Latinized as Alhazen^{[Notes 1]} or Alhacen; c. 965 – c. 1040) was an Arab^[4] scientist, polymath, mathematician, astronomer and philosopher who made significant contributions to the principles of optics, astronomy, mathematics, visual perception and the scientific method. He also wrote insightful commentaries on works by Aristotle, Ptolemy and the Ancient Greek mathematician Euclid.^[5]

He has been described as the father of modern optics, experimental physics and scientific methodology^[6][7][8][9] and could also claim to be the first theoretical physicist.^[7] In medieval Europe, he was nicknamed Ptolemaeus Secundus ("Ptolemy the Second")^[10] or simply called "The Physicist".^[11] He is also sometimes called al-Basri (Arabic: البصري) after Basra, his birthplace.^[12]

According to one version of his biography,^[13] al-Haytham, overconfident about the practical application of his mathematical knowledge, assumed he could regulate the floods of the Nile. Having been ordered to do so by Al-Hakim bi-Amr Allah, the sixth ruler of the Fatimid caliphate, he quickly realised its impossibility. Fearing for his life, he feigned madness^[1][14] and was placed under house arrest. Once Al-Hakim had died, he was able to prove that he was not mad and for the rest of his life made money copying texts while writing mathematical works and teaching.^[15]

Overview

Biography

Born c. 965 in Basra, which was then part of the Buyid emirate,^[1] to an Arab family,^[16][17] he lived mainly in Cairo, Egypt, dying there at age 74.^[10] During the Islamic Golden Age, Basra was a "key beginning of learning",^[18] and he was educated there and in Baghdad, the capital of the Abbasid Caliphate, and the focus of the "high point of Islamic civilization".^[18] During his time in Basra, he trained for government work and became Minister for the area.^[12]

One account of his career has him called to Egypt by Al-Hakim bi-Amr Allah, ruler of the Fatimid Caliphate, to regulate the flooding of the Nile, a task requiring an early attempt at building a dam at the present site of the Aswan Dam.^[19] After deciding the scheme was impractical and fearing the caliph's anger, he feigned madness. He was kept under house arrest from 1011 until al-Hakim's death in 1021.^[20] During this time, he wrote his influential Book of Optics. After his house arrest ended, he wrote scores of other treatises on physics, astronomy and mathematics. He later traveled to Islamic Spain. During this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine, and practical experiments.

Some biographers have claimed that Alhazen fled to Syria, ventured into Baghdad later in his life, or was in Basra when he pretended to be insane. In any case, he was in Egypt by 1038.^[12] Accounts state that during his time in Cairo he lived near and studied at the Al-Azhar Mosque.^[21]

Among his students were Sorkhab (Sohrab), a Persian from Iran's Semnan who was his student for over 3 years, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian scientist who learned mathematics from Alhazan.^[22]

Legacy

Alhazen made significant improvements in optics, physical science, and the scientific method. Alhazen's work on optics is credited with contributing a new emphasis on experiment.

His main work, Kitab al-Manazir (Book of Optics) had little direct influence in the Islamic Middle East, being known mainly through a thirteenth-century commentary by Kamāl al-Dīn al-Fārisī, the Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir.^[23] In Islamic Spain it was used by the eleventh-century mathematician, al-Mu'taman ibn Hūd, and a Latin translation was produced in the thirteenth century.^[24][25] Through this translation, Alhazen exerted a great influence on Western science: for example, on the work of Roger Bacon, who cites him by name.^[26] His research in catoptrics (the study of optical systems using mirrors) centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the problem known as "Alhazen's problem".^[27] Meanwhile in the Islamic world, Alhazen's work influenced Averroes' writings on optics,^[28] and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (died ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).^[29] Alhazen wrote as many as 200 books, although only 55 have survived, and many of those have not yet been translated from Arabic.^{[citation needed]} Some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages. The crater Alhazen on the Moon is named in his honour,^[30] as was the asteroid 59239 Alhazen.^[31] In honour of Alhazen, the Aga Khan University (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".^[32] Alhazen, by the name Ibn al-Haytham, is featured on the obverse of the Iraqi 10,000-dinar banknote issued in 2003,^[33] and on 10-dinar notes from 1982. A research facility that UN weapons inspectors suspected of conducting chemical and biological weapons research in Saddam Hussein's Iraq was also named after him.^[33][34]

Book of Optics

Alhazen's most famous work is his seven-volume treatise on optics Kitab al-Manazir (Book of Optics), written from 1011 to 1021.

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.^[35] It was printed by Friedrich Risner in 1572, with the title Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus (English : Optics treasure: Arab Alhazeni seven books, published for the first time: The book of the Twilight of the clouds and ascensions).^[36] Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen, which is the correct transcription of the Arabic name.^[37] This work enjoyed a great reputation during the Middle Ages. Works by Alhazen on geometric subjects were discovered in the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot. Other manuscripts are preserved in the Bodleian Library at Oxford and in the library of Leiden.

Theory of vision

Two major theories on vision prevailed in classical antiquity. The first theory, the emission theory, was supported by such thinkers as Euclid and Ptolemy, who believed that sight worked by the eye emitting rays of light. The second theory, the intromission theory supported by Aristotle and his followers, had physical forms entering the eye from an object. Previous Islamic writers (such as al-Kindi) had argued essentially on Euclidean, Galenist, or Aristotelian lines; Alhazen's achievement was to come up with a theory which successfully combined parts of the mathematical ray arguments of Euclid, the medical tradition of Galen, and the intromission theories of Aristotle. Alhazen's intromission theory followed al-Kindi (and broke with Aristotle) in asserting that "from each point of every colored body, illuminated by any light, issue light and color along every straight line that can be drawn from that point".^[38] This however left him with the problem of explaining how a coherent image was formed from many independent sources of radiation; in particular, every point of an object would send rays to every point on the eye. What Alhazen needed was for each point on an object to correspond to one point only on the eye.^[38] He attempted to resolve this by asserting that only perpendicular rays from the object would be perceived by the eye; for any one point on the eye, only the ray which reached it directly, without being refracted by any other part of the eye, would be perceived. He argued using a physical analogy that perpendicular rays were stronger than oblique rays; in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye. As there was only one perpendicular ray that would enter the eye at any one point, and all these rays would converge on the centre of the eye in a cone, this allowed him to resolve the problem of each point on an object sending many rays to the eye; if only the perpendicular ray mattered, then he had a one-to-one correspondence and the confusion could be resolved.^[39] He later asserted (in book seven of the Optics) that other rays would be refracted through the eye and perceived as if perpendicular.^[40]

His arguments regarding perpendicular rays do not clearly explain why only perpendicular rays were perceived; why would the weaker oblique rays not be perceived more weakly?^[41] His later argument that refracted rays would be perceived as if perpendicular does not seem persuasive.^[42] However, despite its weaknesses, no other theory of the time was so comprehensive, and it was enormously influential, particularly in Western Europe: "Directly or indirectly, his De Aspectibus inspired much of the activity in optics which occurred between the 13th and 17th centuries." ^[43] Kepler's later theory of the retinal image (which resolved the problem of the correspondence of points on an object and points in the eye) built directly on the conceptual framework of Alhazen.^[43]

Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection.^[27] He was the first to consider separately the vertical and horizontal components of reflected and refracted light rays, which was an important step in understanding optics geometrically.^[44]

The camera obscura was known to the Chinese, and Aristotle had discussed the principle behind it in his Problems, however it is Alhazen's work which contains the first clear description^[45] and early analysis^[46] of the device.

Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the visual system. Ian P. Howard argued in a 1996 Perception article that Alhazen should be credited with many discoveries and theories which were previously attributed to Western Europeans writing centuries later. For example, he described what became in the 19th century Hering's law of equal innervation; he had a description of vertical horopters which predates Aguilonius by 600 years and is actually closer to the modern definition than Aguilonius's; and his work on binocular disparity was repeated by Panum in 1858.^[47] Craig Aaen-Stockdale, while agreeing that Alhazen should be credited with many advances, has expressed some caution, especially when considering Alhazen in isolation from Ptolemy, who Alhazen was extremely familiar with. Alhazen corrected a significant error of Ptolemy regarding binocular vision, but otherwise his account is very similar; Ptolemy also attempted to explain what is now called Hering's law.^[48] In general, Alhazen built on and expanded the optics of Ptolemy.^[49][50] In a more detailed account of Ibn al-Haytham's contribution to the study of binocular vision based on Lejeune^[51] and Sabra,^[13] Raynaud^[52] showed that the concepts of correspondence, homonymous and crossed diplopia were in place in Ibn al-Haytham's optics. But contrary to Howard, he explained why Ibn al-Haytham did not give the circular figure of the horopter and why, by reasoning experimentally, he was in fact closer to the discovery of Panum's fusional area than that of the Vieth-Müller circle. In this regard, Ibn al-Haytham's theory of binocular vision faced two main limits: the lack of recognition of the role of the retina, and obviously the lack of an experimental investigation of ocular tracts.

Alhazen's most original contribution was that after describing how he thought the eye was anatomically constructed, he went on to consider how this anatomy would behave functionally as an optical system.^[53] His understanding of pinhole projection from his experiments appears to have influenced his consideration of image inversion in the eye,^[54] which he sought to avoid.^[55] He maintained that the rays that fell perpendicularly on the lens (or glacial humor as he called it) were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye.^[56] He followed Galen in believing that the lens was the receptive organ of sight, although some of his work hints that he thought the retina was also involved.^[57]

Scientific method

“	The duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and,.. attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.	”
—Alhazen, [13]

An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (i'tibar)(Arabic: إختبار) and controlled testing in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics (ilm tabi'i) with mathematics (ta'alim; geometry in particular). This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics (the study of the refraction of light).^[29] Bradley Steffens in his book Ibn Al-Haytham: First Scientist has argued that Alhazen's approach to testing and experimentation made an important contribution to the scientific method. According to Matthias Schramm, Alhazen:

was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the moonlight through two small apertures onto a screen diminishes constantly as one of the apertures is gradually blocked up.^[58]

G. J. Toomer expressed some skepticism regarding Schramm's view, arguing that caution is needed to avoid reading anachronistically particular passages in Alhazen's very large body of work, and while acknowledging Alhazen's importance in developing experimental techniques, argued that he should not be considered in isolation from other Islamic and ancient thinkers.^[59]

Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by Ptolemy in 150 AD. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in order to carom off the edge of the table and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree.^[12][60] This eventually led Alhazen to derive a formula for the sum of fourth powers, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid.^[61] Alhazen eventually solved the problem using conic sections and a geometric proof. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation. Later mathematicians used Descartes' analytical methods to analyse the problem,^[62] with a new solution being found in 1997 by the Oxford mathematician Peter M. Neumann.^[63] Recently, Mitsubishi Electric Research Laboratories (MERL) researchers Amit Agrawal, Yuichi Taguchi and Srikumar Ramalingam solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.^[64] They showed that the mirror reflection point can be computed by solving an eighth degree equation in the most general case. If the camera (eye) is placed on the axis of the mirror, the degree of the equation reduces to six.^[65] Alhazen's problem can also be extended to multiple refractions from a spherical ball. Given a light source and a spherical ball of certain refractive index, the closest point on the spherical ball where the light is refracted to the eye of the observer can be obtained by solving a tenth degree equation.^[65]

Other contributions

The Book of Optics describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with projectiles, and a description of his conclusions is: "it was only the impact of perpendicular projectiles on surfaces which was forceful enough to enable them to penetrate whereas the oblique ones were deflected. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw would break the slate and pass through, whereas an oblique one with equal force and from an equal distance would not."^[66] He also used this result to explain how intense, direct light hurts the eye, using a mechanical analogy: "Alhazen associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray since there could only be one such ray from each point on the surface of the object which could penetrate the eye."^[66]

Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered be the "founder of experimental psychology", for his pioneering work on the psychology of visual perception and optical illusions.^[67] Khaleefa has also argued that Alhazen should also be considered the "founder of psychophysics", a subdiscipline and precursor to modern psychology.^[67] Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.^[48]

Alhazen offered an explanation of the Moon illusion, an illusion that played an important role in the scientific tradition of medieval Europe.^[68] Many authors repeated explanations that attempted to solve the problem of the Moon appearing larger near the horizon than it does when higher up in the sky, a debate that is still unresolved. Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Alhazen's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with the refraction theory being rejected in the 17th century.^[69] Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. Cleomedes (c. 2nd century) gave this account (in addition to refraction), and he credited it to Posidonius (c. 135-50 BC).^[70] Ptolemy may also have offered this explanation in his Optics, but the text is obscure.^[71] Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.

Other works on physics

Optical treatises

Besides the Book of Optics, Alhazen wrote several other treatises on the same subject, including his Risala fi l-Daw’ (Treatise on Light). He investigated the properties of luminance, the rainbow, eclipses, twilight, and moonlight. Experiments with mirrors and magnifying lenses provided the foundation for his theories on catoptrics.^[72]

In his treatise Mizan al-Hikmah (Balance of Wisdom), Alhazen discussed the density of the atmosphere and related it to altitude. He also studied atmospheric refraction.^[27]

Celestial physics

Alhazen discussed the physics of the celestial region in his Epitome of Astronomy, arguing that Ptolemaic models needed to be understood in terms of physical objects rather than abstract hypotheses; in other words that it should be possible to create physical models where (for example) none of the celestial bodies would collide with each other. The suggestion of mechanical models for the Earth centred Ptolemaic model "greatly contributed to the eventual triumph of the Ptolemaic system among the Christians of the West". Alhazen's determination to root astronomy in the realm of physical objects was important however, because it meant astronomical hypotheses "were accountable to the laws of physics", and could be criticised and improved upon in those terms.^[73]

In Mizan al-Hikmah (Balance of Wisdom), Alhazen discussed the theories of attraction between masses.^[27] He also wrote Maqala fi daw al-qamar (On the Light of the Moon).

Mechanics

In his work, Alhazen discussed theories on the motion of a body.^[72] In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he used geometry in an attempt to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body.^[74]

Astronomical works

On the Configuration of the World

In his On the Configuration of the World Alhazen presented a detailed description of the physical structure of the earth:

The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its [the world's] middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.^[75]

The book is a non-technical explanation of Ptolemy's Almagest, which was eventually translated into Hebrew and Latin in the 13th and 14th centuries and subsequently had an influence on astronomers such as Georg von Peuerbach^[1] during the European Middle Ages and Renaissance.^[76][77]

Doubts Concerning Ptolemy

In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts Concerning Ptolemy or Aporias against Ptolemy, published at some time between 1025 and 1028, Alhazen criticized Ptolemy's Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works, particularly in astronomy. Ptolemy's Almagest concerned mathematical theories regarding the motion of the planets, whereas the Hypotheses concerned what Ptolemy thought was the actual configuration of the planets. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works.^[78] He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the equant, failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:^[79]

Ptolemy assumed an arrangement (hay'a) that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist... [F]or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.^[80][81]

Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work. Alhazen's belief was that there was a "true configuration" of the planets which Ptolemy had failed to grasp; his intention was to complete and repair Ptolemy's system, not to replace it completely.^[78]

In the Doubts Concerning Ptolemy Alhazen set out his views on the difficulty of attaining scientific knowledge and the need to question existing authorities and theories:

Truth is sought for itself [but] the truths, [he warns] are immersed in uncertainties [and the scientific authorities (such as Ptolemy, whom he greatly respected) are] not immune from error...^[13]

He held that the criticism of existing theories—which dominated this book—holds a special place in the growth of scientific knowledge.

Model of the Motions of Each of the Seven Planets

Alhazen's The Model of the Motions of Each of the Seven Planets was written c. 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his Doubts on Ptolemy, Alhazen described a new, geometry based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of epicycles to explain observed motion, but he managed to eliminate Ptolemy's equant. In general, his model made no attempt to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description which could be used to explain observed motions, without the contradictions inherent in Ptolemy's model.^[82]

Other astronomical works

Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as Exact Determination of the Meridian, a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the Milky Way; Alhazen argued for a distant location, based on the fact that it does not move in relation to the fixed stars.^[83] The fourth group consists of ten works on astronomical theory, including the Doubts and Model of the Motions discussed above.^[84]

Mathematical works

In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on "the beginnings of the link between algebra and geometry."^[85]

Geometry

In geometry, Alhazen developed analytical geometry and the link between algebra and geometry.^[85] He developed a formula for adding the first 100 natural numbers, using a geometric proof to prove the formula.^[86]

Alhazen explored the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction,^[87] and in effect introducing the concept of motion into geometry.^[88] He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral".^[89] His theorems on quadrilaterals, including the Lambert quadrilateral, were the first theorems on elliptical geometry and hyperbolic geometry. These theorems, along with his alternative postulates, such as Playfair's axiom, can be seen as marking the beginning of non-Euclidean geometry. His work had a considerable influence on its development among the later Persian geometers Omar Khayyám and Nasīr al-Dīn al-Tūsī, and the European geometers Witelo, Gersonides, and Alfonso.^[90]

In elementary geometry, Alhazen attempted to solve the problem of squaring the circle using the area of lunes (crescent shapes), but later gave up on the impossible task.^[12] The two lunes formed from a right triangle by erecting a semicircle on each of the triangle's sides, inward for the hypotenuse and outward for the other two sides, are known as the lunes of Alhazen; they have the same total area as the triangle itself.^[91]

Number theory

His contributions to number theory include his work on perfect numbers. In his Analysis and Synthesis, Alhazen may have been the first to state that every even perfect number is of the form 2ⁿ⁻¹(2ⁿ − 1) where 2ⁿ − 1 is prime, but he was not able to prove this result successfully (Euler later proved it in the 18th century).^[12]

Alhazen solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem.^[12]

Other works

Influence of Melodies on the Souls of Animals

Alhazen also wrote a Treatise on the Influence of Melodies on the Souls of Animals, although no copies have survived. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace.

Engineering

In engineering, one account of his career as a civil engineer has him summoned to Egypt by the Fatimid Caliph, Al-Hakim bi-Amr Allah, to regulate the flooding of the Nile River. He carried out a detailed scientific study of the annual inundation of the Nile River, and he drew plans for building a dam, at the site of the modern-day Aswan Dam. His field work, however, later made him aware of the impracticality of this scheme, and he soon feigned madness so he could avoid punishment from the Caliph.^[92]

Philosophy

In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he used geometry in an attempt to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body.^[74] Abd-el-latif, a supporter of Aristotle's philosophical view of place, later criticized the work in Fi al-Radd ‘ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham’s place) for its geometrization of place.^[74]

Alhazen also discussed space perception and its epistemological implications in his Book of Optics. In "tying the visual perception of space to prior bodily experience, Alhacen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for correlation, sight can tell us next to nothing about such things."^[93]

Theology

Alhazen was a devout Muslim, though it is uncertain which branch of Islam he followed. He may have been either a follower of the orthodox Ash'ari school of Sunni Islamic theology according to Ziauddin Sardar^[94] and Lawrence Bettany^[95] (and opposed to the views of the Mu'tazili school),^[95] a follower of the Mu'tazili school of Islamic theology according to Peter Edward Hodgson,^[96] or a follower of Shia Islam possibly according to A. I. Sabra.^[97]

Alhazen wrote a work on Islamic theology, in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time.^[98] He also wrote a treatise entitled Finding the Direction of Qibla by Calculation, in which he discussed finding the Qibla, where Salat prayers are directed towards, mathematically.^[99]

He wrote in his Doubts Concerning Ptolemy:

Truth is sought for its own sake ... Finding the truth is difficult, and the road to it is rough. For the truths are plunged in obscurity. ... God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science...^[100]

In The Winding Motion, Alhazen further wrote:

From the statements made by the noble Shaykh, it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation (taqlid); that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences.^[101]

Alhazen described his theology:

I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge.^[102]

List of works

According to medieval biographers, Alhazen wrote more than 200 works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects.^[103] Not all his surviving works have yet been studied, but some of the ones that have are given below.^[84][99]

1. Book of Optics
2. Analysis and Synthesis
3. Balance of Wisdom
4. Corrections to the Almagest
5. Discourse on Place
6. Exact Determination of the Pole
7. Exact Determination of the Meridian
8. Finding the Direction of Qibla by Calculation
9. Horizontal Sundials
10. Hour Lines
11. Doubts Concerning Ptolemy
12. Maqala fi'l-Qarastun
13. On Completion of the Conics
14. On Seeing the Stars
15. On Squaring the Circle
16. On the Burning Sphere
17. On the Configuration of the World
18. On the Form of Eclipse
19. On the Light of Stars
20. On the Light of the Moon
21. On the Milky Way
22. On the Nature of Shadows
23. On the Rainbow and Halo
24. Opuscula
25. Resolution of Doubts Concerning the Almagest
26. Resolution of Doubts Concerning the Winding Motion
27. The Correction of the Operations in Astronomy
28. The Different Heights of the Planets
29. The Direction of Mecca
30. The Model of the Motions of Each of the Seven Planets
31. The Model of the Universe
32. The Motion of the Moon
33. The Ratios of Hourly Arcs to their Heights
34. The Winding Motion
35. Treatise on Light
36. Treatise on Place
37. Treatise on the Influence of Melodies on the Souls of Animals^[104]

Notes

References

Sources

Further reading

Primary

• Sabra, A. I., ed. (1983), The Optics of Ibn al-Haytham, Books I-II-III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables, Kuwait: National Council for Culture, Arts and Letters 
• Sabra, A. I., ed. (2002), The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV-V: On Reflection and Images Seen by Reflection. 2 vols, Kuwait: The National Council for Culture, Arts and Letters 
• Sabra, A. I., trans. (1989), The Optics of Ibn al-Haytham. Books I-II-III: On Direct Vision. English Translation and Commentary. 2 vols, Studies of the Warburg Institute, vol. 40, London: The Warburg Institute, University of London, ISBN 0-85481-072-2, OCLC 165564751 165564771 180528350 180528355 180528359 21530166 230045836 24910015 59836570 
• Smith, A. Mark, ed. and trans. (2001), "Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's De aspectibus, the Medieval Latin Version of Ibn al-Haytham's Kitāb al-Manāzir, 2 vols.", written at Philadelphia, Transactions of the American Philosophical Society (Philadelphia: American Philosophical Society) 91 (4-5), ISBN 0-87169-914-1, OCLC 47168716 
• Smith, A. Mark, ed. and trans. (2006), "Alhacen on the Principles of Reflection: A Critical Edition, with English Translation and Commentary, of Books 4 and 5 of Alhacen's De Aspectibus, the Medieval Latin version of Ibn-al-Haytham's Kitāb al-Manāzir, 2 vols", Transactions of the American Philosophical Society (Philadelphia: American Philosophical Soc.) 96 (2–3), ISBN 0-87169-962-1, OCLC 123464885 185359947 185359957 219328717 219328739 70078653 

Secondary

• Graham, Mark. How Islam Created the Modern World. Amana Publications, 2006.
• Omar, Saleh Beshara (June 1975), Ibn al-Haytham and Greek optics: a comparative study in scientific methodology, PhD Dissertation, University of Chicago, Department of Near Eastern Languages and Civilizations 
• Saliba, George (2007), Islamic Science and the Making of the European Reneissance, MIT Press, ISBN 0-262-19557-7 
• Belting, Hans, Afterthoughts on Alhazen’s Visual Theory and Its Presence in the Pictorial Theory of Western Perspective, in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies In the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp. 19–42.
• Siegfried Zielinski & Franziska Latell, How One Sees, in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies In the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp. 19–42.

External links

• Langermann, Y. Tzvi (2007). "Ibn al‐Haytham: Abū ʿAlī al‐Ḥasan ibn al‐Ḥasan". In Thomas Hockey et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 556–7. ISBN 978-0-387-31022-0.  (PDF version)
• Sabra, A. I. (2008) [1970–80]. "Ibn Al-Haytham, Abū ʿAlī Al-Ḥasan Ibn Al-Ḥasan". Complete Dictionary of Scientific Biography. Encyclopedia.com. 
• Ibn al-Haytham on two Iraqi banknotes
• The Miracle of Light – a UNESCO article on Ibn al-Haytham
• Biography from Malaspina Global Portal
• Short biographies on several "Muslim Heroes and Personalities" including Ibn al-Haytham
• Biography from ioNET via the Wayback Machine
• Biography from the BBC via the Wayback Machine
• Biography from Trinity College (Connecticut)
• Biography from Molecular Expressions
• The First True Scientist from BBC News
• Over the Moon From The UNESCO Courier on the occasion of the International Year of Astronomy 2009

v t e Astronomy in medieval Islam Astronomers 8th c. Ahmad Nahavandi Al-Fadl ibn Naubakht Ibrāhīm al-Fazārī and his son Mashallah ibn Athari Yaʿqūb ibn Ṭāriq 9th c. Abu Ma'shar al-Balkhi Abu Said Gorgani Al-Farghānī Al-Kindi Al-Mahani Al-Ḥajjāj ibn Yūsuf ibn Maṭar Al-Marwazi Ali ibn Isa al-Asturlabi Banu Musa Iranshahri Khālid ibn ʿAbd al‐Malik Al-Khwārizmī Sahl ibn Bishr Thābit ibn Qurra 10th c. Abd al-Rahman al-Sufi Al-Adami and Ibn al-Adami Abu-Mahmud Khojandi Abū Ja'far al-Khāzin Abū Sahl al-Qūhī Abū al-Wafā' Būzjānī Ahmad ibn Yusuf Al-Battani Alchabitius Al-Nayrizi Al-Saghani Ibn Yunus Ibrahim ibn Sinan 11th c. Abu Nasr Mansur Al-Bīrūnī Al-Zarqālī Alhazen Avicenna Ibn al-Saffar Kushyar ibn Labban Said Al-Andalusi Sijzi 12th c. Al-Bitruji Al-Kharaqī Al-Khazini Al-Samaw'al Abu al-Salt Anvari Ibn al-Kammad Jabir ibn Aflah Omar Khayyám Sharaf al-Dīn al-Ṭūsī 13th c. Ibn al-Banna' al-Marrakushi Ibn al‐Ha'im al‐Ishbili Jamal ad-Din Muhyi al-Dīn al-Maghribī Nasir al-Din al-Tusi Qutb al-Din al-Shirazi Shams al-Dīn al-Samarqandī Zakariya al-Qazwini Ibn Abi al-Shukr Mu'ayyad al-Din al-'Urdi Athīr al-Dīn al-Abharī Muhammad ibn Abi Bakr al‐Farisi 14th c. Ibn al-Shatir Shams al-Dīn Abū Abd Allāh al-Khalīlī Abū al‐ʿUqūl 15th c. Ali Qushji ʿAbd al‐Wājid Jamshīd al-Kāshī Qāḍī Zāda al-Rūmī Ulugh Beg Sibt al-Mardini Ibn al-Majdi 'Abd al-'Aziz al-Wafa'i 16th c. Al-Birjandi Bahāʾ al-dīn al-ʿĀmilī Piri Reis Taqi al-Din Muhammad ibn Ma'ruf Works ʿAjā'ib al-makhlūqāt wa gharā'ib al-mawjūdāt Arabic star names Book of Optics Encyclopedia of the Brethren of Purity Islamic calendar Star chart Tabula Rogeriana The Book of Healing Zij: Alfonsine tables Almanac Astronomical catalog Book of Fixed Stars Star catalogue Toledan Tables Trigonometry table Zij-i Ilkhani Zij-i-Sultani Sullam al-sama' Instruments Alidade Analog computer Aperture Armillary sphere Astrolabe Astronomical clock Celestial globe Compass Compass rose Dioptra Equatorial ring Equatorium Globe Graph paper Magnifying glass Mural instrument Navigational astrolabe Nebula Planisphere Quadrant Sextant Shadow square Spherical astrolabe Sundial Telescope Triquetrum Concepts Almucantar Apogee Astrophysics Axial tilt Azimuth Celestial mechanics Celestial spheres Circular orbit Deferent and epicycle Earth's rotation Eccentricity Ecliptic Elliptic orbit Equant Galaxy Geocentrism Gravitational potential energy Gravity Heliocentrism Inertia Islamic cosmology Moonlight Multiverse Muslim views on astrology Obliquity Parallax Precession Qibla Salat times Specific gravity Spherical Earth Starlight Sublunary sphere Sunlight Supernova Temporal finitism Trepidation Triangulation Tusi-couple Universe Centers Al-Azhar University House of Knowledge House of Wisdom Islamic observatories Istanbul observatory of Taqi al-Din Madrasah Maragheh observatory Observatory Research institute Samarkand observatory Umayyad Mosque University of Al-Karaouine Influences Babylonian astronomy Egyptian astronomy Hellenistic astronomy Indian astronomy Influenced Byzantine astronomy Chinese astronomy European astronomy Indian astronomy

v t e Mathematics in medieval Islam Mathematicians 9th century 'Abd al-Hamīd ibn Turk Sind ibn Ali Al-Abbās ibn Said al-Jawharī Al-Ḥajjāj ibn Yūsuf ibn Maṭar Al-Kindi Al-Mahani Banū Mūsā Hunayn ibn Ishaq Muḥammad ibn Mūsā al-Khwārizmī Thābit ibn Qurra Na'im ibn Musa Sahl ibn Bishr Habash al-Hasib al-Marwazi 10th century Abd al-Rahman al-Sufi Abū al-Wafā' al-Būzjānī Abū Ja'far al-Khāzin Abū Kāmil Shujāʿ ibn Aslam Abu'l-Hasan al-Uqlidisi Abu-Mahmud Khojandi Ahmad ibn Yusuf Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus Ibrahim ibn Sinan Muhammad ibn Jābir al-Harrānī al-Battānī Sinan ibn Thabit Al-Isfahani Abu-Mahmud Khojandi Nazif ibn Yumn Abū Sahl al-Qūhī 11th century Abū Ishāq Ibrāhīm al-Zarqālī Abu Nasr Mansur Abū Rayḥān al-Bīrūnī Alhazen Ibn Muʿādh al-Jayyānī Al-Karaji Al-Sijzi Alī ibn Ahmad al-Nasawī Avicenna Ibn Tahir al-Baghdadi Kushyar ibn Labban Yusuf al-Mu'taman ibn Hud 12th century Al-Khazini Ibn Yahyā al-Maghribī al-Samaw'al Omar Khayyám Jabir ibn Aflah Abu Bakr al-Hassar 13th century Muhyi al-Dīn al-Maghribī Nasīr al-Dīn al-Tūsī Shams al-Dīn al-Samarqandī Sharaf al-Dīn al-Tūsī Ibn al‐Ha'im al‐Ishbili Ibn Abi al-Shukr 14th century Yaʿīsh ibn Ibrāhīm al-Umawī Ibn al-Banna' al-Marrakushi Ibn al-Shatir Kamāl al-Dīn Fārisī Al-Khalili Qotb al-Din Shirazi Ahmad al-Qalqashandi 15th century Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī Ali Qushji Jamshīd al-Kāshī Qāḍī Zāda al-Rūmī Ulugh Beg Ibn al-Majdi 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi al-Din Ibn Hamza al-Maghribi Ibn Ghazi al-Miknasi Treatises Almanac Book of Fixed Stars Book of Optics De Gradibus Encyclopedia of the Brethren of Purity Tables of Toledo Tabula Rogeriana The Compendious Book on Calculation by Completion and Balancing The Book of Healing Zij Zij-i Ilkhani Zij-i-Sultani Concepts Alhazen's problem Centers Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Istanbul observatory of Taqi al-Din Madrasah Maktab Maragheh observatory University of Al-Karaouine Influences Babylonian mathematics Greek mathematics Indian mathematics Influenced Byzantine mathematics European mathematics Indian mathematics

v t e Islamic philosophy Fields Alchemy Aqidah (theology) 'Aql (intellect) Cosmology astrology medieval astronomy Eschatology Ethics Kalam (dialectic) Fiqh (jurisprudence) Logic Metaphysics Natural philosophy (physics) Peace Madrasah (education) Medieval science Medieval psychology Sufism (mysticism) Schools Early Farabism Avicennism Averroism Illuminationism Sufi cosmology metaphysics Transcendent theosophy Traditionalist Contemporary Concepts ʻAṣabīya Ḥāl Iʻjaz ʼIjtihād ʻlm ʻIrfān Ijmāʿ Maslaha Nafs Qadar Qiyās Shūrā Tawḥīd Ummah   Philosophers by century (CE) 9th–10th Al-Kindi Ali ibn Sahl Rabban al-Tabari Abu al-Abbas Iranshahri Zakariya Razi Apharabius Abu Hatim al-Razi Al Amiri Ikhwan al-Safa Abu Sulayman Sijistani Ibn Masarrah Abu Yaqub al-Sijistani 11th Al-Ghazali Ibn Miskawayh Avicenna Ibn Hazm Bahmanyar Mu'ayyad fi'l-Din al-Shirazi Nasir Khusraw 12th Abu'l-Barakāt al-Baghdādī Afdal al-Din Kashani Ahi Evren Ahmad Yasavi Ayn-al-Quzat Averroes Ibn Tufail Omar Khayyám Suhrawardi Shams Tabrizi 13th Hajji Bektash Wali Jalal ad-Din Muhammad Rumi Ibn Sab’in Ibn Arabi al-Abharī Nasir al-Din Tusi Ibn Taymiyyah Qutb al-Din al-Shirazi 14th–16th Ibn Khaldun Yunus Emre Hajji Bayram Jalaladdin Davani Aziz Mahmud Hudayi Qadi Mir Husayn al-Maybudi 17th–19th Mir Damad Mir Fendereski Mulla Sadra Mohsen Fayz Kashani Abd al-Razzaq Lahiji Mujaddid Alf-i-Sani Rajab Ali Tabrizi Qazi Sa’id Qumi Shah Waliullah Hādī Sabzavārī 20th–present Muhammad Husayn Tabatabaei Muhammad Iqbal Gohar Shahi Mohammad Baqir al-Sadr René Guénon Frithjof Schuon Martin Lings Hossein Nasr Naquib al-Attas Abdolkarim Soroush Gholamhossein Ebrahimi Dinani Taha Abdurrahman

v t e Medicine in the medieval Islamic world Physicians 7th century Al-Harith ibn Kalada and his son Abu Hafsa Yazid Bukhtishu Masarjawaih Ibn Abi Ramtha al-Tamimi Rufaida Al-Aslamia Ibn Uthal 8th century Bukhtishu family Ja'far al-Sadiq 9th century Albubather Bukhtishu family Jabril ibn Bukhtishu Jābir ibn Hayyān Hunayn ibn Ishaq and his son Yahya ibn Sarafyun Al-Kindi Masawaiyh Sabur ibn Sahl Ali ibn Sahl Rabban al-Tabari Al-Ruhawi Yuhanna ibn Bukhtishu Salmawaih ibn Bunan 10th century Qusta ibn Luqa Abu ul-Ala Shirazi Abul Hasan al-Tabari Al-Natili Qumri Abu Zayd al-Balkhi Isaac Israeli ben Solomon Ali ibn Abbas al-Majusi Abu Sahl 'Isa ibn Yahya al-Masihi Muvaffak Muhammad ibn Zakariya al-Razi Ibn Juljul Al-Zahrawi Ibn al-Jazzar Al-Kaŝkarī Ibn Abi al-Ashʿath Ibn al-Batriq Ibrahim ibn Baks 11th century Abu Ubaid Juzjani Alhazen Ali ibn Ridwan Avicenna Ephraim ibn al-Za'faran Ibn al-Wafid Abdollah ibn Bukhtishu Ibn Butlan Ibn al-Kattani Ibn Jazla Masawaih al-Mardini Yusuf al-Ilaqi Ibn Al-Thahabi Ibn Abi Sadiq Ali ibn Isa al-Kahhal 12th century Abu al-Bayan ibn al-Mudawwar Ahmad ibn Farrokh Ibn Hubal Zayn al-Din Gorgani Maimonides Serapion the Younger Ibn Zuhr Ya'qub ibn Ishaq al-Israili Abu Jafar ibn Harun of Trujillo Averroes Ibn Tufail Al-Ghafiqi Ibn Abi al-Hakam Abu'l-Barakāt al-Baghdādī Samauʼal Al-Maghribī Ibn al-Tilmīdh Ibn Jumay‘ 13th century Sa'ad al-Dawla Al-Shahrazuri Rashidun al-Suri Amin al-Din Rashid al-Din Vatvat Avraham son of Rambam Da'ud Abu al-Fadl Al-Dakhwar Ibn Abi Usaibia Joseph ben Judah of Ceuta Abd al-Latif al-Baghdadi (medieval writer) Ibn al-Nafis Zakariya al-Qazwini Najib ad-Din-e-Samarqandi Qotb al-Din Shirazi Ibn al-Quff 14th century Muhammad ibn Mahmud Amuli Al-Nagawri Aqsara'i Zayn-e-Attar Mansur ibn Ilyas Jaghmini Mas‘ud ibn Muhammad Sijzi Najm al-Din Mahmud ibn Ilyas al-Shirazi Nakhshabi Sadid al-Din al-Kazaruni Yusuf ibn Ismail al-Kutubi Ibn al-Khatib Rashid-al-Din Hamadani 15th century Abu Sa'id al-Afif Muhammad Ali Astarabadi Husayni Isfahani Burhan-ud-din Kermani Şerafeddin Sabuncuoğlu Muhammad ibn Yusuf al-Harawi Nurbakhshi Shaykh Muhammad ibn Thaleb 16th century Hakim-e-Gilani Abul Qasim ibn Mohammed al-Ghassani Taqi al-Din Muhammad ibn Ma'ruf Dawud al-Antaki Concepts Psychology Ophthalmology Works The Canon of Medicine Anatomy Charts of the Arabs The Book of Healing Book of the Ten Treatises of the Eye De Gradibus Al-Tasrif Zakhireye Khwarazmshahi Adab al-Tabib Centers Bimaristan Nur al-Din Bimaristan Al-'Adudi Influences Ancient Greek medicine Influenced Medical Renaissance Ibn Sina Academy of Medieval Medicine and Sciences

Authority control WorldCat VIAF: 90038995 LCCN: n81027793 ISNI: 0000 0001 1774 221X GND: 118648160 SUDOC: 08612756X BNF: cb12028218d NKC: xx0083904

Persondata
Name	al-Haytham, Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn
Alternative names	Alhacen; Alhazen; al-Basri
Short description	Scientist
Date of birth	965
Place of birth	Basra, Islamic Empire
Date of death	c. 1040
Place of death	Cairo, Egypt