Ibn al-Haytham

Abū ʿAlī al-Ḥasan ibn al-Haytham — known in Latin Europe as Alhazen — was born in Basra, Iraq, around 965 and died in Cairo, Egypt, around 1040.¹ He was a mathematician and astronomer who made significant contributions to the principles of optics and to the use of scientific experiments.¹ He was educated in Basra and Baghdad.² The UNESCO Courier describes him as a scholar of many disciplines — mathematics, physics, mechanics, astronomy, philosophy, and medicine.³

Among Arab scholars he was called the “Second Ptolemy” (Baṭlamyūs Thānī).³ With al-Bīrūnī (973–1048) and Ibn Sīnā (980–1037) he was one of the leading Muslim scholars of the 10th–11th centuries.³ He is sometimes called al-Baṣrī, meaning from the city of Basra in Iraq, and sometimes al-Miṣrī, meaning that he came from Egypt.⁴ He seems to have written around 92 works, of which over 55 have survived⁴; by his own testimony he wrote 25 works on the mathematical sciences and 44 works on physics and metaphysics.³

While Ibn al-Haytham was a young boy growing up in Basra, the Fatimids conquered the Nile Valley in 969 and founded the city of Cairo as the capital of their new empire.⁴ He did not devote himself to academic study at a young age: he trained for what might best be described as a civil-service job and was appointed a minister for Basra and the surrounding region.⁴ In time he became increasingly unhappy with his deep studies of religion, and made the decision to devote himself entirely to the study of science, which he found most clearly described in the writings of Aristotle.⁴

According to one version of his life, told by the 13th-century historian Ibn al-Qifṭī (d. 1248), Ibn al-Haytham was invited to Egypt by the Fatimid caliph al-Ḥākim — who reigned 996–1021 and is known as “the Mad Caliph” — to demonstrate his claim that he could regulate the Nile.¹ Al-Ḥākim requested that Ibn al-Haytham come to Egypt to carry out his proposal, and appointed him to head an engineering team which would undertake the task.⁴

After personally reconnoitering near the southern border of Egypt, Ibn al-Haytham confessed his inability to engineer such a project.¹ As the team travelled up the Nile, he realized that his idea of regulating the water with large constructions would not work⁴; Tbakhi and Amr specify that the scheme was to regulate the river's flow by building a dam south of Aswan.² Although still given an official position by the caliph, he began to fear for his life, feigned madness, and was confined to his own home until the end of al-Ḥākim's caliphate¹; he was stripped of his possessions and books and kept under house arrest for about ten years, until al-Ḥākim's death in 1021.² Ibn al-Qifṭī reports that he then earned a living in Egypt largely by copying manuscripts, and claimed to possess a manuscript in Ibn al-Haytham's handwriting from 1040.¹ After his release he lived near the Azhar Mosque in Cairo — in a domed building, a qubbah — teaching mathematics and physics, writing science texts, and making money by copying texts.⁴²

The surviving accounts must be handled with care: most of the biographical data on Ibn al-Haytham comes from the writings of the 13th-century Muslim historian Ibn al-Qifṭī (1172–1248), and the stories related to his life are often contradictory.² A different report says that after failing in his mission to regulate the Nile, Ibn al-Haytham fled from Egypt to Syria; this seems unlikely, for other reports make it certain that he was in Egypt in 1038.⁴ Britannica notes that it has recently been plausibly argued that there were two Ibn al-Haythams: al-Ḥasan ibn al-Ḥasan, the mathematician who wrote on optics, and Muḥammad ibn al-Ḥasan, the astronomer-philosopher who wrote the autobiography and the works in the first and second lists.¹ His own autobiography, written in 1027, survives — but it says nothing of the events of his life and concentrates on his intellectual development.⁴

Ibn al-Haytham's most important work is the Kitāb al-Manāẓir, the Book of Optics.¹ The seven-volume work is considered by many to be his most important contribution⁴, and it deals, in seven volumes, with an experimental and mathematical study of the properties of light.³ Tbakhi and Amr state that it was written while he was incarcerated, between 1011 and 1021, and that it has been ranked alongside Isaac Newton's Principia Mathematica as one of the most influential books ever written in physics.² It reached Latin Europe as Opticae thesaurus Alhazeni: MacTutor dates the Latin translation to 1270⁴, while Britannica places an anonymous translation probably early in the 13th century¹ and the UNESCO Courier says it was translated anonymously in the 12th/13th century.³

Book I establishes the study of light and vision, making clear that the investigation will rest on experimental evidence rather than abstract theory.⁴ Book II discusses visual perception, while Book III examines the conditions necessary for good vision and how errors in vision are caused.⁴ In Book IV he gave experimental proof of the specular reflection of accidental as well as essential light, a complete formulation of the laws of reflection, and a description of the construction and use of a copper instrument for measuring reflections from plane, spherical, cylindrical, and conical mirrors.⁴ Book V contains Alhazen's problem; Book VI examines errors in vision due to reflection; and the final book, Book VII, examines refraction.⁴ The work also contains a detailed investigation of refraction, including experiments involving angles of incidence and deviation.¹

The Optics appears to have been neglected in the East until the commentary on it by the mathematician Kamāl al-Dīn Abuʾl Ḥasan Muḥammad ibn al-Ḥasan al-Fārisī (d. 1320).¹ In the West, a Latin translation of it — sometimes literal and sometimes interpretative — was made by an unknown scholar, probably early in the 13th century.¹ The 1572 Latin printed edition, prepared by Friedrich Risner, presents Alhazen's seven books of optics together with Witelo's Perspectiva, and adds Risner's own commentaries on Alhazen.⁵ The work had a major influence on 13th-century thinkers such as Roger Bacon and on later scientists such as the astronomer Johannes Kepler (1571–1630).¹

The central claim of the Optics is 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.¹ MacTutor calls this the first correct explanation of vision, showing that light is reflected from an object into the eye.⁴ The model overturned the ancient emission theory of Euclid and Ptolemy, although the book shows some influence from Ptolemy's 2nd-century Optics.¹

In Book I Ibn al-Haytham makes it clear that his investigation of light will be based on experimental evidence rather than on abstract theory, and he notes that light is the same irrespective of its source — sunlight, light from a fire, or light reflected from a mirror are all of the same nature.⁴ In the introduction of the Optics he declares that his method will rest on criticising premises and exercising caution in drawing conclusions, and that in all that he judges he will seek the truth and not be swayed by opinion.⁴ Ansari identifies the main feature of his method as the design of experiment in order to test a hypothesis, rather than using experiment merely for observation or discovery as his predecessors did.³ Tbakhi and Amr describe his working method as a repeating cycle of observation, hypothesis, experimentation, and the need for independent verification.²

His investigation of refraction included experiments involving angles of incidence and deviation¹, and refraction is correctly explained in the Optics by light's moving slower in denser media.¹ His other optical works include Ḍawʾ al-qamar (On the Light of the Moon), al-Hāla wa-qaws quzaḥ (On the Halo and the Rainbow), Ṣūrat al-kusūf (On the Shape of the Eclipse, which includes a discussion of the camera obscura), and al-Ḍawʾ (A Discourse on Light).¹ MacTutor credits him as the first person to mention the camera obscura, whose use his studies of optics led him to propose.⁴ In Tbakhi and Amr's account he is known for the earliest use of the camera obscura and pinhole camera, and he carried out the first experiments on the dispersion of light into its constituent colors.²

He dealt at length with the theory of shadows, eclipses, and the rainbow, attempted to explain binocular vision, and gave a correct explanation of the apparent increase in size of the Sun and the Moon when near the horizon.² His study of refraction led him to propose that the atmosphere has a finite depth of about 15 km, and he explained twilight by refraction of sunlight once the Sun was less than 19° below the horizon.⁴ The Discourse on Light and the tracts On the Light of Stars, On the Light of the Moon, and On the Halo and the Rainbow are the main sources from which his working method can be deduced.³ He is considered by some to be the founder of psychophysics and experimental psychology, for his pioneering work on the psychology of visual perception.²

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 — is stated and solved in the Optics by means of conic sections.¹ The problem, for which he is best remembered, is usually posed as: 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.⁴ It appears in Book V, where drawing lines from two points in the plane of a circle that meet at a point on the circumference making equal angles with the normal leads to an equation of the fourth degree.² Huygens later reformulated the problem, found a good solution, and Vincenzo Riccati and then Saladini simplified and improved it.⁴

The problem led Ibn al-Haytham to derive the earliest formula for the sum of fourth powers and, by using an early proof by mathematical induction, to develop a method for determining the general formula for the sum of any integral powers.² In number theory he solved problems involving congruences using what is now called Wilson's theorem.⁴ In his Analysis and Synthesis he was the first to realize that every even perfect number is of the form 2^(n−1)(2^n−1), where 2^n−1 is prime, but he was not able to prove the result successfully; it was proved later, in the 18th century, by Euler.² Rashed claims that Ibn al-Haytham was the first to state the converse of Euclid's perfect-number theorem, though the statement does not appear explicitly in his work; his attempt to prove it in Analysis and Synthesis was not entirely successful, yet Rashed calls it a deliberate attempt to characterise the set of perfect numbers.⁴

Beyond mirrors, he wrote a work on the area of lunes — crescents formed from two intersecting circles — and then wrote the first of two treatises on squaring the circle using lunes; the promised second treatise never appeared, suggesting he realized he could not solve the problem.⁴ His Maqāla fī tamām Kitāb al-Makhrūṭāt (Completion of the Conics) is an attempt to reconstruct the lost eighth book of Apollonius's Conics (c. 200 BC).¹ In his Ḥall shukūk fī Kitāb Uqlīdis (Solution of the Difficulties of Euclid's Elements) he investigated particular cases of Euclid's theorems, offered alternative constructions, and replaced some indirect proofs with direct proofs.¹ In his Sharḥ muṣādarāt Kitāb Uqlīdis (Commentary on the Premises of Euclid's Elements) he based his treatment of parallel lines on equidistant lines rather than Euclid's definition of lines that never meet.¹

Ibn al-Haytham's most famous astronomical work is Hayʾat al-ʿālam (On the Configuration of the World), a nontechnical description of how the abstract mathematical models of Ptolemy's Almagest can be understood according to the natural philosophy of his time.¹ In this popular work, intended for the layman, he completely accepts Ptolemy's views without question.⁴ There were several Latin translations of the Configuration, a book which influenced Georg Peuerbach (1423–61) among others.¹

A later work, al-Shukūk ʿalā Baṭlamyūs (Doubts concerning Ptolemy), written between 1025 and 1028, criticizes the Almagest along with Ptolemy's Planetary Hypotheses and Optics.¹² 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.² The Model of the Motions of Each of the Seven Planets, written in 1038, was an important book on astronomy; the surviving manuscript was only recently discovered, with much of it still missing, so the work has not yet been published in modern times.²

Popular accounts often credit Ibn al-Haytham with more than the sources document; the three most common exaggerations are audited below against the record.¹⁴²

Three passages are given below in the wording preserved in the sources: the method promised in the introduction of the Optics⁴, the account of concentrated solar heating in the Discourse of the Concave Spherical Mirror⁷, and the geocentric picture of the earth at rest in On the Configuration of the World.²

His optical writings influenced many Western intellectuals such as Roger Bacon, John Pecham, Witelo, and Johannes Kepler.² The Optics had a major influence on 13th-century thinkers such as Roger Bacon and on later scientists such as Kepler (1571–1630).¹ In the East, the book had been taken up again through the commentary of Kamāl al-Dīn al-Fārisī (d. 1320).¹ The first real appreciation of the action of a lens — in particular the ability of a convex form to produce a magnified image of an object — appears to be credited to Ibn al-Haytham.²

Modern astronomy commemorates him in the sky: the lunar crater Alhazen, 34.65 km in diameter and centred at 15.91° N, 71.83° E on the Moon, had its name adopted by the IAU in 1935, in honour of “Abū Ali Al-Hasan Ibn Al Haitham; Iraqi mathematician”.⁸ Main-belt asteroid (59239) Alhazen was discovered at Gnosca on 7 February 1999 by S. Sposetti, and the name was suggested by P. Venzi.⁹ The naming citation describes him as an astronomer, mathematician, doctor, philosopher, and physicist whose work mainly dealt with the study of the visual phenomenon and with optical geometry.⁹ The Gazetteer itself records his dates as 987–1038, at odds with the c. 965–c. 1040 dates given by Britannica.⁸¹

In 2015, during the International Year of Light, Ibn al-Haytham was celebrated at UNESCO as a pioneer of modern optics.³ UNESCO hosted an international conference about the Islamic Golden Age of science and the legacy of Ibn al-Haytham, calling him one of the inventors of modern optics, on 14–15 September 2015.⁶ The celebration coincided with the 1,000th anniversary of the publication of his Kitāb al-Manāẓir (Book of Optics).⁶ UNESCO describes him as considered the father of modern optics, a scholar who pioneered scientific experimental methodology.⁶