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Islamic Golden Age
|Name:||Abū ‘Alī al-Ḥasan ibn al-Ḥasan ibn al-Haytham|
|Title:||Ibn al-Haytham and Alhacen|
|Main interests:||Anatomy, Astronomy, Engineering, Mathematics, Mechanics, Medicine, Optics, Ophthalmology, Philosophy, Physics, Psychology, Science|
|works:||Book of Optics, Analysis and Synthesis, Balance of Wisdom, Discourse on Place, Doubts concerning Ptolemy, Maqala fi'l-qarastun, On the Configuration of the World, Opuscula, The Model of the Motions, The Resolution of Doubts, Treatise on Light, Treatise on Place|
|Influences:||Aristotle, Euclid, Ptolemy, Banū Mūsā, Thabit, al-Kindi, Ibn Sahl, al-Quhi|
|Influenced:||Al-Khazini, al-Farisi, Maragheh school, Bacon, Peckham, Witelo, Cardano, Fermat, Kepler, Snell, Descartes, Huygens, etc.
Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Arabic: أبو علي الحسن بن الحسن بن الهيثم, Latinized: Alhacen or (deprecated) Alhazen) (965 – 1039), was an Arab or Persian Muslim polymath who made significant contributions to the principles of optics, as well as to anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, physics, psychology, visual perception, and to science in general with his introduction of the scientific method. He is sometimes called al-Basri (Arabic: البصري), after his birthplace in the city of Basra in Iraq (Mesopotamia), then ruled by the Buyid dynasty of Persia.
Ibn al-Haytham is regarded as the father of optics for his influential The Book of Optics, which correctly explained and proved the modern intromission theory of visual perception, and for his experiments on optics, including experiments on lenses, mirrors, refraction, reflection, and the dispersion of light into its constituent colors. He studied binocular vision and the moon illusion, speculated on the finite speed, rectilinear propagation and electromagnetic aspects of light, and argued that rays of light are streams of energy particles travelling in straight lines.
Described as the first scientist, Ibn al-Haytham brought about the process of scientific method due to his constant doubt on the human being’s ability to understand nature’s works systematically and properly. Bradley Steffens of Ibn al-Haytham: First Scientist states that al-Haytham wrote in his book The Book of Optics, “When inquiry concerns subtle matters, perplexity grows, views diverge, opinions vary, conclusions differ, and certainty becomes difficult to obtain. The premises are gleaned from the senses, and the senses, which are our tools, are not immune from error.” The scientific method was a route to establish the validity of the observations, hypotheses, and conclusions on scientific matters.
Due to his quantitative, empirical and experimental approach to physics and science, he is considered the pioneer of the modern scientific method and of experimental physics, and some have described him as the "first scientist" for this reason.
He is also considered by some to be the founder of psychophysics and experimental psychology for his experimental approach to the psychology of visual perception,</ref> and a pioneer of the philosophical field of phenomenology. His The Book of Optics has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books ever written in the history of physics.
Among his other achievements, Ibn al-Haytham described the pinhole camera and invented the camera obscura (a precursor to the modern camera), discovered Fermat's principle of least time and the law of inertia (known as Newton's first law of motion), discovered the concept of momentum (part of Newton's second law of motion), described the attraction between masses and was aware of the magnitude of acceleration due to gravity at a distance, discovered that the heavenly bodies were accountable to the laws of physics, presented the earliest critique and reform of the Ptolemaic model, first stated Wilson's theorem in number theory, pioneered analytic geometry, formulated and solved Alhazen's problem geometrically, developed and proved the earliest general formula for infinitesimal and integral calculus using mathematical induction, and in his optical research laid the foundations for the later development of telescopic astronomy, as well as for the microscope and the use of optical aids in Renaissance art.
Ab_ ‘Al_ al-Hasan ibn al-Hasan ibn al-Haytham was born in the Arab city of Basra, Iraq (Mesopotamia), then part of the Buyid dynasty of Persia, and he probably died in Cairo, Egypt. Known in the West as Alhacen or Alhazen, Ibn al-Haytham was born in 965 in Basra, and was educated there and in Baghdad.
Most families choosing to educate their children were wealthy, which afforded their tuition fees to the teachers. Ibn al-Haytham was one of few such children, who in his early years, was educated at a mosque in Basra–the Basran mosque was an important area for religious practice as well as a center for education.
Ibn al-Haytham’s course in life took him through several turning points, as will be discussed later. One account of his career has him summoned to Egypt by the mercurial caliph Hakim to regulate the flooding of the Nile. After his fieldwork made him aware of the impracticality of this scheme, and fearing the caliph's anger, he feigned madness. He was kept under house arrest until al-Hakim's death in 1021. During this time, he wrote a part or all of his influential The Book of Optics and scores of other important treatises on physics and mathematics. He later traveled to Spain and, during this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine, and the development of scientific methods—on all of which he has left several outstanding books.
As a devout Muslim, Ibn al-Haytham spent a large portion of his life understanding and serving his God. While still a student, he studied theology and applied his learning to the problems of Islamic sects at that time. At that time, and even till today, two major sects of Islam, the Shi’ah and the Sunnah argued over the rightful successor of the Prophet Muhammad. As Bradley Steffens of Ibn al-Haytham: First Scientist states, “The disagreements between the Sunnah, the Shi’ah, and other Muslim sects, such as the Sufi and Mu’tazilah, troubled young Ibn al-Haytham.” Al-Haytham concluded, after ardently studying the various religious systems, that the differences in the sects were not in their religious doctrine, but in their backgrounds. This conclusion disappointed him greatly because it did not bring him any closer than he already was to understanding the works of God.
After this period in his life, Ibn al-Haytham moved on to study the works of the philosopher, Aristotle. In his autobiography, he said, “When I discovered what Aristotle had done, I became engrossed in my desire to understand philosophy wholeheartedly.” Indulging into philosophy, he read many of Aristotle’s works, and started summarizing and eventually even commenting on his works.
Turning Points in Life
Ibn al-Haytham did not stick only to the study of philosophy–he discovered his talent for mathematics, and began to delve into the works of the Greek mathematician, Euclid, and later studied works of Archimedes and Ptolemy, summarizing their famous works.
As Ibn al-Haytham worked on such treatises, his life took a new direction. Possibly due to his wealthy family and his father’s high position in the government of Basra, Ibn al-Haytham was appointed vizier, or high official. Some historians believe his role was as a Financial Minister, while others thought he had been a civil engineer in charge of projects for the public–these speculations were made due to the fact that he had written some books on finance as well as civil engineering. If he were indeed a civil engineer, it is known that Ibn al-Haytham has shown interest in hydrodynamics and even written books on canals and dams. However, this appointment, Ibn al-Haytham feared, would prove as a hindrance, since he would have much less time to spend on his own interests in the sciences.
At around this time, Ibn al-Haytham suffered from some mental illness–it is still under discussion whether or not he faked his illness, but it convinced other government officials to remove him from the position. Steffens stated, “From what is known about his personality and beliefs, it also would have been out of character for Ibn al-Haytham to mislead government officials. He often said that pursuing the truth was most important thing in life. … On the other hand, his writings show no signs of mental instability. Furthermore, it is possible that his passion for pure learning was so intense that it drove him to perpetrate his scheme.”
However, Ibn al-Haytham was still not left to his work as his life took a turn again–sometime in 1010, a messenger of Al-Hakim Bi-amr Allah, the sixth ruler of the Fatimid dynasty of Egypt, gave him the message that Al-Hakim wanted to discuss Ibn al-Haytham’s plans (that he had perhaps had as a civil engineering high official at Basra) for building a dam for taming the Nile River. Ibn al-Haytham knows better to have refused an offer by this erratic ruler, though it again interrupted his pursuit of interests in the sciences. He left for Cairo to meet Al-Hakim in late 1010, and arrived there early in 1011. In one account of what happened once he got there, he met with Al-Hakim himself and discussed his plans, after which the ruler was very disappointed and ridiculed his plan. Ibn al-Haytham may have fled to Syria to escape any punishment planned for him. Another account told that Al-Hakim was very pleased with the plan, and allotted all his resources for this project. In this case, Ibn al-Haytham decided to build the dam in the segment of the river in the village of al-Janadil near Aswan, where it will be adequate for the formation of a lake behind the dam. Once he surveyed the area, however, he found that it is impossible to construct a dam with the resources he had. He decided to abandon the project and flee without informing the ruler, but al-Hakim actually proposed that he be made an officer in his government. Ibn al-Haytham took the position with a feeling of reserve, still fearing that the erratically young ruler may change his mind and punish him. This position in the government proved even more time consuming than his position in Basra, and some historians suggest he may have had mental illness in this period, for real, or faked. The ruler was not to be fooled this instance, and Ibn al-Haytham was placed under house arrest for ten years, only to be freed when Al-Hakim mysteriously disappeared the tenth year after Ibn al-Haytham’s imprisonment.
During these ten years under house arrest, Ibn al-Haytham had none of his possessions. Yet, many scholars say he must have written or created at least a part of his most famous books, The Book of Optics and demonstrations to test his hypotheses. After his release, historians say he supported himself by making copies of manuscripts and selling them. Ibn al-Haytham may have also been a teacher in Cairo. A historian, Ali ibn Zayd al-Bayhaqi, shares a story that reveals the attitude Ibn al-Haytham expressed towards learning. Steffens summarizes the story saying, “A Syrian nobleman named Surkhab came to Ibn al-Haytham and asked it he could study with him. Ibn al-Haytham agreed to tutor the nobleman but demanded one hundred dinars a month for payment. The price was high, but Surkhab did not hesitate to pay the fee. For three years the Syrian studied with Ibn al-Haytham. At the end of this time, his education complete, Surkhab bid his tutor farewell. Ibn al-Haytham asked the nobleman to wait a moment. “You deserve this money all the more,” Ibn al-Haytham said, returning all 3,600 dinars to Surkhab, “since I just wished to test your sincerity and, when I saw that for the sake of learning you cared little for money, I devoted full attention towards you education. Do remember that, in any righteous cause, it is not good to accept a return, a bribe, or a gift.””
Ibn al-Haytham was a pioneer in optics, astronomy, engineering, mathematics, physics, and psychology. His optical writings influenced many Western intellectuals such as Roger Bacon, John Pecham, Witelo, and Johannes Kepler.
Yasmeen M. Faruqi writes:
"In seventeenth century Europe the problems formulated by Ibn al-Haytham (965-1041) became known as “Alhazen’s problem.” [...] Al-Haytham’s contributions to geometry and number theory went well beyond the Archimedean tradition. Al-Haytham also worked on analytical geometry and the beginnings of the link between algebra and geometry. Subsequently, this work led in pure mathematics to the harmonious fusion of algebra and geometry that was epitomised by Descartes in geometric analysis and by Newton in the calculus. Al-Haytham was a scientist who made major contributions to the fields of mathematics, physics and astronomy during the latter half of the tenth century."
According to medieval biographers, Ibn al-Haytham 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 areas of science. Not all of his surviving works have yet been studied, but some of his most important ones are described below. These include:
- Book of Optics (1021)
- Analysis and Synthesis
- Balance of Wisdom
- Discourse on Place
- Maqala fi'l-qarastun
- Doubts concerning Ptolemy (1028)
- On the Configuration of the World
- The Model of the Motions of Each of the Seven Planets (1038)
- The Resolution of Doubts
- Treatise on Light
- Treatise on Place
Rosanna Gorini wrote the following on Ibn al-Haytham's introduction of the scientific method:
"According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable."
Roshdi Rashed wrote the following on Ibn al-Haytham:
"His work on optics, which includes a theory of vision and a theory of light, is considered by many to be his most important contribution, setting the scene for developments well into the seventeenth century. His contributions to geometry and number theory go well beyond the archimedean tradition. And by promoting the use of experiments in scientific research, al-Haytham played an important part in setting the scene for modern science."
Ibn al-Haytham developed rigorous experimental methods of controlled scientific testing in order to verify theoretical hypotheses and substantiate inductive conjectures. Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:
- Statement of problem
- Formulation of hypothesis
- Testing of hypothesis using experimentation
- Analysis of experimental results
- Interpretation of data and formulation of conclusion
- Publication of findings
In The Model of the Motions, Ibn al-Haytham also describes an early version of Occam's razor, where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the cosmological hypotheses that cannot be observed from Earth.
Ibn al-Haytham was one of the most eminent physicists, whose developments in optics and the scientific method were particularly outstanding. Ibn al-Haytham's work on optics is credited with contributing a new emphasis on experiment. His influence on physical sciences in general, and on optics in particular, has been held in high esteem and, in fact, ushered in a new era in optical research, both in theory and practice. The scientific method is considered to be so fundamental to modern science that some—especially philosophers of science and practicing scientists—consider earlier inquiries into nature to be pre-scientific. Due to its importance in the history of science, some have considered his development of the scientific method to be the most important scientific development of the second millennium.
"Ibn-al-Haitham (Alhazen, 965-1039 C.E.) was one of the greatest physicists of all time. He made experimental contributions of the highest order in optics. He enunciated that a ray of light, in passing through a medium, takes the path which is the easier and 'quicker'. In this he was anticipating Fermat's Principle of Least Time by many centuries. He enunciated the law of inertia, later to become Newton's first law of motion. Part V of Roger Bacon's "Opus Majus" is practically an annotation to Ibn al Haitham's Optics."
George Sarton, the "father of the history of science," wrote in the Introduction to the History of Science:
"[Ibn al-Haytham] was not only the greatest Muslim physicist, but by all means the greatest of mediaeval times."
"Ibn Haytham's writings reveal his fine development of the experimental faculty. His tables of corresponding angles of incidence and refraction of light passing from one medium to another show how closely he had approached discovering the law of constancy of ratio of sines, later attributed to Snell. He accounted correctly for twilight as due to atmospheric refraction, estimating the sun's depression to be 19 degrees below the horizon, at the commencement of the phenomenon in the mornings or at its termination in the evenings."
Robert S. Elliot wrote the following on the Book of Optics:
"Alhazen was one of the ablest students of optics of all times and published a seven-volume treatise on this subject which had great celebrity throughout the medieval period and strongly influenced Western thought, notably that of Roger Bacon and Kepler. This treatise discussed concave and convex mirrors in both cylindrical and spherical geometries, anticipated Fermat's law of least time, and considered refraction and the magnifying power of lenses. It contained a remarkably lucid description of the optical system of the eye, which study led Alhazen to the belief that light consists of rays which originate in the object seen, and not in the eye, a view contrary to that of Euclid and Ptolemy."
The Biographical Dictionary of Scientists wrote the following on Ibn al-Haytham::
"He was probably the greatest scientist of the Middle Ages and his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler."
The Latin translation of his main work, Kitab al-Manazir, exerted a great influence upon Western science: for example, on the work of Roger Bacon, who cites him by name, and on Kepler. It brought about a great progress in experimental methods. His research in catoptrics centered on spherical and parabolic mirrors and spherical aberration. He made the important 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 important problem known as Alhazen's problem.
The list of his books runs to 200 or so, yet very few of the books have survived. Even his monumental treatise on optics survived only through its Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages.
The Alhazen crater on the Moon was named in his honour. Ibn al-Haytham is also featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003. The asteroid "59239 Alhazen" was also named in his honour, while Iran's largest laser research facility, located in the Atomic Energy Organization of Iran headquarters in Tehran, is named after him as well.
Book of Optics
His seven-volume treatise on optics, Kitab al-Manazir (Book of Optics) (written from 1011 to 1021), which has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books ever written in physics, drastically transformed the understanding of light and vision. In classical antiquity, there were two major theories on vision. 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. Ibn al-Haytham argued on the basis of common observations (such as the eye being dazzled or even injured if we look at a very bright light) and logical arguments (such as how a ray could proceeding from the eyes reach the distant stars the instant after we open our eye) to maintain that we cannot see by rays being emitted from the eye, nor through physical forms entering the eye. He instead developed a highly successful theory which explained the process of vision as rays of light proceeding to the eye from each point on an object, which he proved through the use of experimentation.
Ibn al-Haytham proved that rays of light travel in straight lines, and carried out a number of experiments with lenses, mirrors, refraction, and reflection. He was also the first to reduce reflected and refracted light rays into vertical and horizontal components, which was a fundamental development in geometric optics. He also discovered a result similar to Snell's law of sines, but did not quantify it and derive the law mathematically. Ibn al-Haytham is also credited with the invention of the camera obscura and pinhole camera. Optics was translated into Latin by an unknown scholar at the end of the twelfth century or the beginning of the thirteenth century. 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 . 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. This work enjoyed a great reputation during the Middle Ages. Works by Alhacen on geometrical 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. Ibn al-Haytham's optical studies were influential in a number of later developments, including the telescope, which laid the foundations of telescopic astronomy, as well as of the modern camera, the microscope, and the use of optical aids in Renaissance art.
Other treatises on optics
Besides the Book of Optics, Ibn al-Haytham wrote a number of other treatises on optics. His Risala fi l-Daw’ (Treatise on Light) is a supplement to his Kitab al-Manazir (Book of Optics). The text contained further investigations on the properties of luminance and its radiant dispersion through various transparent and translucent media. He also carried out further observations, investigations and examinations on the anatomy of the eye, the camera obscura and pinhole camera, illusions in visual perception, the meteorology of the rainbow and the density of the atmosphere, various celestial phenomena (including the eclipse, twilight, and moonlight), refraction, catoptrics, dioptrics, spherical and parabolic mirrors, and magnifying lenses.
In his treatise, Mizan al-Hikmah (Balance of Wisdom), Ibn al-Haytham discussed the density of the atmosphere and related it to altitude. He also studied atmospheric refraction. He discovered that the twilight only ceases or begins when the Sun is 19° below the horizon and attempted to measure the height of the atmosphere on that basis.
Astrophysics, celestial mechanics, and statics
Ibn al-Haytham's Mizan al-Hikmah (Balance of Wisdom) dealt with statics, astrophysics, and celestial mechanics. He discussed the theory of attraction between masses, and it seems that he was also aware of the magnitude of acceleration due to gravity at a distance.
His Maqala fi'l-qarastun is a treatise on centers of gravity. Little is currently known about the work, except for what is known through the later works of al-Khazini in the twelfth century. In this treatise, Ibn al-Haytham formulated the theory that the heaviness of bodies varies with their distance from the center of the Earth.
Dynamics and kinematics
In the dynamics and kinematics fields of mechanics, Ibn al-Haytham's Risala fi’l-makan (Treatise on Place) discussed theories on the motion of a body. He maintained that a body moves perpetually unless an external force stops it or changes its direction of motion. This was a precursor to the law of inertia later stated by Galileo Galilei in the sixteenth century and now known as Newton's first law of motion.
Doubts concerning Ptolemy
In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts concerning Ptolemy or Aporias against Ptolemy, written between 1025 and 1028, Ibn al-Haytham criticized many of Ptolemy's works, including the Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works. 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 wrote a scathing critique of the physical reality of Ptolemy's astronomical system, noting the absurdity of relating actual physical motions to imaginary mathematical points, lines, and circles:
"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."
In his Aporias against Ptolemy, Ibn al-Haytham also commented on the difficulty of attaining scientific knowledge:
"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..."
He held that the criticism of existing theories—which dominated this book—holds a special place in the growth of scientific knowledge:
"Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus 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, applying his mind to the core and margins of its content, 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."
On the Configuration of the World
In his On the Configuration of the World, despite his criticisms directed towards Ptolemy, Ibn al-Haytham continued to accept the physical reality of the geocentric model of the universe, presenting a detailed description of the physical structure of the celestial spheres in his On the Configuration of the World:
"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."
While he attempted to discover the physical reality behind Ptolemy's mathematical model, he developed the concept of a single orb (falak) for each component of Ptolemy's planetary motions. This work was eventually translated into Hebrew and Latin in the thirteenth and fourteenth centuries and subsequently had an important influence during the European Middle Ages and Renaissance.
The Model of the Motions
Ibn al-Haytham's The Model of the Motions of Each of the Seven Planets, written in 1038, was an important book on astronomy. The surviving manuscript of this work has only recently been discovered, with much of it still missing, hence the work has not yet been published in modern times. Following on from his Doubts on Ptolemy and The Resolution of Doubts, Ibn al-Haytham described the first non-Ptolemaic model in The Model of the Motions. His reform excluded cosmology, as he developed a systematic study of celestial kinematics that was completely geometric. This in turn led to innovative developments in infinitesimal geometry.
His reformed model was the first to reject the equant and eccentrics, free celestial kinematics from cosmology, and reduce physical entities to geometrical entities. The model also propounded the Earth's rotation about its axis, and the centres of motion were geometrical points without any physical significance, like Johannes Kepler's model centuries later.
In the text, Ibn al-Haytham also describes an early version of Occam's razor, where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the cosmological hypotheses that cannot be observed from Earth.
In engineering, one account of his career as a civil engineer has him summoned to Egypt by the mercurial caliph Hakim to regulate the flooding of the Nile. His fieldwork, however, later made him aware of the impracticality of this scheme.
In mathematics, Ibn al-Haytham builds on the mathematical works of Euclid and Thabit ibn Qurra, and goes on to systemize infinitesimal calculus, conic sections, number theory, and analytic geometry after linking algebra to geometry.
His work on catoptrics in Book V of the Book of Optics contains the important problem known as Alhazen's problem. 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 leads to an equation of the fourth degree. This eventually led Ibn al-Haytham to derive the earliest formula for the sum of fourth powers; and by using an early proof by mathematical induction, he developed a method for determining the general formula for the sum of any integral powers. This was fundamental to the development of infinitesimal and integral calculus.
While Ibn al-Haytham solved the problem using conic sections and a geometric proof, Alhazen's problem remained influential in Europe, as later mathematicians such as Christiaan Huygens, James Gregory, Guillaume de l'Hôpital, Isaac Barrow and many others attempted to find an algebraic solution to the problem, using various methods including analytic methods of geometry and derivation by complex numbers. Mathematicians were not able to find an algebraic solution to the problem until the end of the twentieth century.
In geometry, Ibn al-Haytham developed analytical geometry by establishing the linkage between algebra and geometry. Ibn al-Haytham also discovered a formula for adding the first 100 natural numbers (which may later have been intuited by Carl Friedrich Gauss as a youth). Ibn al-Haytham used a geometric proof to prove the formula. His attempted proof of the parallel postulate was also similar to the Lambert quadrilateral and Playfair's axiom in the eighteenth century.
In elementary geometry, Ibn al-Haytham attempted to solve the problem of squaring the circle using the area of lunes, but later gave up on the impossible task. Ibn al-Haytham also tackled other problems in elementary (Euclidean) and advanced (Apollonian and Archimedean) geometry, some of which he was the first to solve.
His contributions to number theory includes his work on perfect numbers. In his Analysis and Synthesis, Ibn al-Haytham was the first to realize 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 eighteenth century).
Ibn al-Haytham solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Ibn al-Haytham 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.
Book of Optics
In philosophy, Ibn al-Haytham is considered a pioneer of phenomenology. He articulated a relationship between the physical and observable world and that of intuition, psychology and mental functions. His theories regarding knowledge and perception, linking the domains of science and religion, led to a philosophy of existence based on the direct observation of reality from the observer's point of view. Much of his thought on phenomenology was not further developed until the twentieth century.
Ibn al-Haytham's Risala fi’l-makan (Treatise on Place) presents a critique of Aristotle's concept of place (topos). Aristotle's Physics stated that the place of something is the two-dimensional boundary of the containing body that is at rest and is in contact with what it contains. Ibn al-Haytham disagreed and demonstrated that place (al-makan) is the imagined three-dimensional void between the inner surfaces of the containing body. He showed that place was akin to space, foreshadowing René Descartes's concept of place in the Extensio in the seventeenth century.
Following on from his Treatise on Place, Ibn al-Haytham's Qawl fi al-Makan (Discourse on Place) was an important treatise which presents geometrical demonstrations for his geometrization of place, in opposition to Aristotle's philosophical concept of place, which Ibn al-Haytham rejected on mathematical grounds. 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.
Ibn al-Haytham is said to have been a supporter of the Ash'ari school of Islamic theology, and opposed to the views of the Mu'tazili school, though he may have been a Mu'tazili supporter himself at some point in his life.
Book of Optics
In the Book of Optics, Ibn al-Haytham was the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. He explained possible errors in vision in detail, and as an example described how a small child with less experience may have more difficulty interpreting what he or she sees. He also gave an example of how an adult can make mistakes in vision due to experience that suggests that one is seeing one thing, when one is really seeing something else.
At a scientific conference in February 2007, Charles M. Falco argued that Ibn al-Haytham's work on optics may have influenced the use of optical aids by Renaissance artists. Falco said that his and David Hockney's examples of Renaissance art "demonstrate a continuum in the use of optics by artists from c. 1430, arguably initiated as a result of Ibn al-Haytham's influence, until today."
- Islamic science
- Scientific method
- History of science
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- ↑ Hamarneh 1972.
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- ↑ Charles M. Falco, 2007, Ibn al-Haytham and the Origins of Modern Image Analysis. Plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, 12–15 February 2007. Sharjah, United Arab Emirates (U.A.E.). Retrieved February 11, 2009.
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- Smith, John D. 1992. The Remarkable Ibn al-Haytham. The Mathematical Gazette. 76:475:189-198.
- Steffens, Bradley. 2006. Ibn al-Haytham: First Scientist. Greensboro, NC: Morgan Reynolds Publishing. ISBN 1599350246.
- Wade, Nicholas J. and Finger, Stanley. 2001. The eye as an optical instrument: from camera obscura to Helmholtz's perspective. Perception. 30:10:1157-1177.
- Falco, Charles M. 2007. Ibn al-Haytham and the Origins of Modern Image Analysis. The International Conference on Information Sciences, Signal Processing and its Applications. Sharjah, United Arab Emirates (U.A.E.). Retrieved February 11, 2009.
- Omar, Saleh Beshara. 1975. Ibn al-Haytham and Greek optics: a comparative study in scientific methodology. Chicago, IL: PhD Dissertation, Univ. of Chicago, Dept. of Near Eastern Languages and Civilizations.
All links retrieved March 30, 2014.
- Abu Ali al-Hasan ibn al-Haytham – MacTutor.
- Alhazen (ca. 965-1039) – Science World.
- Alhazen (Abu Ali al Hassan ibn al Haitham) (c. 965-c. 1040) – The Internet Encyclopedia of Science.
- The Miracle of Light - a UNESCO article on Ibn Haitham.
- A Polymath in the 10th century – Roshdi Rashed. Science. 297:2002:773.
- "Ibn al-Haytham: Brief life of an Arab mathematician" – Sabra, A.I.
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