Ibn al-Haytham, known in Latin as Alhazen (c. 965 – c. 1040), was a prominent mathematician, astronomer, and physicist during the Islamic Golden Age, originating from the region now identified as Iraq. Acknowledged as "the father of modern optics," he made substantial advancements, particularly in the foundational principles of optics and the understanding of visual perception. His seminal publication, Kitāb al-Manāẓir (Arabic: كتاب المناظر, 'Book of Optics'), composed between 1011 and 1021, has been preserved through a Latin translation. During the Scientific Revolution, Alhazen's writings were frequently referenced by notable figures such as Galileo Galilei, René Descartes, Johannes Kepler, and Christiaan Huygens.
Ibn al-Haytham, Latinized as Alhazen (c. 965 – c. 1040), was a mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled Kitāb al-Manāẓir (Arabic: كتاب المناظر, 'Book of Optics'), written during 1011–1021, which survived in a Latin edition. The works of Alhazen were frequently cited during the Scientific Revolution by Galileo Galilei, René Descartes, Johannes Kepler, and Christiaan Huygens.
Ibn al-Haytham pioneered the accurate demonstration of vision as an intromissive process, rather than extramissive, and posited that visual perception originates in the brain, citing its subjective nature and susceptibility to individual experience. He articulated the principle of least time for refraction, a concept that subsequently evolved into Fermat's principle. His research significantly advanced catoptrics and dioptrics through detailed investigations into reflection, refraction, and the characteristics of images generated by light rays. As an early advocate for empirical validation, Ibn al-Haytham asserted that hypotheses require substantiation through experiments based on verifiable procedures or rigorous mathematical reasoning, thereby establishing himself as a precursor to the scientific method five centuries prior to Renaissance scientists; consequently, he is occasionally recognized as the world's "first true scientist." Furthermore, he was a polymath, contributing to philosophy, theology, and medicine.
Born in Basra, Ibn al-Haytham spent the majority of his prolific career in Cairo, the Fatimid capital, where he sustained himself by composing numerous treatises and instructing members of the aristocracy. He is occasionally identified by the byname al-Baṣrī, referencing his birthplace, or al-Miṣrī ('the Egyptian'). Abu'l-Hasan Bayhaqi referred to Al-Haytham as the "Second Ptolemy," while John Peckham designated him "The Physicist." Ibn al-Haytham's work laid the groundwork for the contemporary discipline of physical optics.
Biography
Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Alhazen) was born around 965 CE into a family of either Arab or Persian descent in Basra, Iraq, then a component of the Buyid emirate. Initially, his intellectual pursuits were directed towards religious studies and community service. Confronted by the era's diverse and often contradictory religious perspectives, he eventually distanced himself from theological engagement, turning instead to the rigorous study of mathematics and science. He served as a vizier in his hometown of Basra, achieving renown for his expertise in applied mathematics, notably demonstrated by his efforts to manage the Nile's inundations.
Following his return to Cairo, he was assigned an administrative role. His inability to successfully execute this responsibility incurred the displeasure of Caliph Al-Hakim, reportedly compelling him to remain in seclusion until the caliph's demise in 1021, at which point his confiscated assets were restored. According to anecdotal accounts, Alhazen simulated insanity and was subjected to house arrest during this interval. It was during this period that he authored his significant work, the Book of Optics. Alhazen resided in Cairo, specifically in the vicinity of the renowned University of al-Azhar, sustaining himself through his literary endeavors until his death around 1040 CE. A manuscript of Apollonius's Conics, inscribed in Ibn al-Haytham's own hand, is preserved in Aya Sofya (MS Aya Sofya 2762, 307 fob., dated Safar 415 A.H. [1024]).
His students included Sorkhab (Sohrab), a Persian scholar from Semnan, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince.
Book of Optics
Alhazen's most renowned contribution is his seven-volume optical treatise, Kitab al-Manazir (Book of Optics), composed between 1011 and 1021. Within this work, Ibn al-Haytham was the first to articulate that vision results from light reflecting off an object and subsequently entering the eyes, and to assert that visual processing takes place in the brain, citing the subjective nature of perception and its modulation by individual experience.
The Optics was translated into Latin by an anonymous scholar during the late 12th or early 13th century.
This treatise garnered considerable acclaim throughout the Middle Ages. The Latin rendition, De aspectibus, was subsequently translated into Italian vernacular towards the close of the 14th century, appearing under the title De li aspecti.
The work was published by Friedrich Risner in 1572 under the title Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus, which translates to 'Treasury of Optics: seven books by the Arab Alhazen, first edition; by the same, on twilight and the height of clouds'. Risner is credited with introducing the name variant "Alhazen"; prior to his publication, the scholar was recognized in the Western world as Alhacen. In 1834, E. A. Sedillot discovered Alhazen's geometric treatises within the Bibliothèque nationale in Paris. A. Mark Smith has cataloged a total of 18 complete or nearly complete manuscripts, alongside five fragments, distributed across 14 distinct repositories, notably including holdings at the Bodleian Library in Oxford and the library in Bruges.
Optical Theories
Classical antiquity was characterized by two predominant theories of vision. The emission theory, advocated by scholars such as Euclid and Ptolemy, posited that vision occurred through the eye's emission of light rays. Conversely, the intromission theory, championed by Aristotle and his disciples, proposed that physical forms from an object entered the eye. Earlier Islamic scholars, including al-Kindi, primarily based their arguments on Euclidean, Galenic, or Aristotelian frameworks. Ptolemy's Optics exerted the most significant influence on Alhazen's Book of Optics, while Galen's descriptions informed the anatomical and physiological understanding of the eye. Alhazen's notable contribution was the formulation of a comprehensive theory that integrated elements from Euclid's mathematical ray arguments, Galen's medical insights, and Aristotle's intromission concepts. His intromission theory, aligning with al-Kindi but diverging from Aristotle, asserted 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". This proposition presented a challenge: explaining the formation of a coherent image from numerous independent radiation sources, especially given that every point on an object would theoretically project rays to every point on the eye.
Alhazen sought a mechanism where each point on an object would correspond uniquely to a single point on the eye. He endeavored to address this by positing that the eye exclusively perceived perpendicular rays originating from the object; specifically, for any given point on the eye, only the ray arriving directly, without refraction by other ocular components, would be registered. Employing a physical analogy, he contended that perpendicular rays possessed greater strength than oblique rays: just as a ball thrown directly at a board might shatter it, while an obliquely thrown ball would merely deflect, perpendicular rays were more potent than refracted rays, and thus, only these perpendicular rays were perceived by the eye. Given that only one perpendicular ray could enter the eye at any specific point, and all such rays would converge conically towards the eye's center, this model enabled him to resolve the issue of multiple rays from a single object point reaching the eye. By prioritizing only perpendicular rays, a one-to-one correspondence was established, thereby eliminating the perceptual ambiguity. Subsequently, in Book Seven of the Optics, he proposed that other rays would undergo refraction within the eye and be perceived as if perpendicular. His arguments concerning perpendicular rays, however, do not adequately elucidate why only perpendicular rays were perceived, nor do they explain why weaker oblique rays would not be perceived, albeit with reduced intensity. Furthermore, his later assertion that refracted rays would be perceived as if perpendicular lacks compelling support. Nevertheless, despite these inherent weaknesses, no other contemporary theory offered such comprehensive scope, and its influence, particularly in Western Europe, was profound. Alhazen's De Aspectibus (Book of Optics) directly or indirectly stimulated extensive optical research and development from the 13th to the 17th centuries. Kepler's subsequent theory of the retinal image, which successfully resolved the problem of point correspondence between object and eye, was directly predicated upon Alhazen's foundational conceptual framework.
Through empirical experimentation, Alhazen demonstrated the rectilinear propagation of light. He conducted numerous experiments involving lenses, mirrors, refraction, and reflection. His analytical approach to reflection and refraction involved the separate consideration of the vertical and horizontal components of light rays.
Alhazen conducted extensive investigations into the mechanisms of sight, ocular anatomy, intraocular image formation, and the broader visual system. In a 1996 article published in Perception, Ian P. Howard contended that numerous discoveries and theoretical frameworks, historically ascribed to Western European scholars centuries later, should instead be credited to Alhazen. For instance, he articulated principles that later, in the 19th century, would be formalized as Hering's law of equal innervation. Furthermore, Alhazen provided a description of vertical horopters six centuries prior to Aguilonius, a formulation that more closely aligns with contemporary definitions than Aguilonius's own. His research on binocular disparity was subsequently replicated by Panum in 1858. While acknowledging Alhazen's significant contributions, Craig Aaen-Stockdale has advised caution, particularly when evaluating Alhazen's work independently of Ptolemy, a scholar with whom Alhazen was profoundly conversant. Although Alhazen rectified a notable error in Ptolemy's understanding of binocular vision, his overall exposition bore considerable resemblance to Ptolemy's, who had also endeavored to elucidate the phenomenon now known as Hering's law. Fundamentally, Alhazen's optical theories constituted an elaboration and expansion upon Ptolemy's foundational work.
Drawing upon the scholarship of Lejeune and Sabra, Raynaud provided a more exhaustive analysis of Ibn al-Haytham's contributions to binocular vision, demonstrating that concepts such as correspondence, homonymous diplopia, and crossed diplopia were integral to Ibn al-Haytham's optical framework. However, diverging from Howard's perspective, Raynaud elucidated why Ibn al-Haytham did not delineate a circular horopter and argued that, through his experimental reasoning, Ibn al-Haytham approached the discovery of Panum's fusional area more closely than that of the Vieth-Müller circle. Nevertheless, Ibn al-Haytham's theory of binocular vision encountered two primary limitations: a failure to acknowledge the retina's crucial role and, notably, the absence of experimental inquiry into ocular pathways.
Alhazen's most distinctive contribution lay in his progression from describing the eye's anatomical structure to analyzing how this anatomy would function as an optical system. His experimental insights into pinhole projection seemingly informed his contemplation of image inversion within the eye, a phenomenon he endeavored to circumvent. He posited that light rays impinging perpendicularly upon the lens (which he termed the 'glacial humor') underwent further outward refraction upon exiting this humor, thereby ensuring that the resultant image reached the optic nerve at the posterior of the eye in an upright orientation. Adhering to Galen's view, Alhazen considered the lens to be the primary receptive organ for sight, though certain aspects of his writings suggest an incipient recognition of the retina's involvement.
Alhazen's comprehensive synthesis of light and vision conformed to the Aristotelian framework, offering an exhaustive and logically coherent description of the visual process.
His investigations in catoptrics, the branch of optics concerned with mirrors, primarily focused on spherical and parabolic mirrors, alongside the phenomenon of spherical aberration. He observed that the ratio between the angle of incidence and the angle of refraction is not constant, and he also explored the magnifying capabilities of lenses.
The Law of Reflection
Alhazen is recognized as the first physicist to articulate a comprehensive statement of the law of reflection. He was also the first to postulate that the incident ray, the reflected ray, and the normal to the reflective surface all reside within a single plane, which is perpendicular to the reflecting plane itself.
Alhazen's Problem
In Book V of his Book of Optics, Alhazen explored catoptrics, introducing what is now recognized as Alhazen's problem, a concept initially articulated by Ptolemy in 150 AD. This problem involves identifying a point on the circumference of a circle where lines drawn from two given points in the plane intersect, forming equal angles with the normal at that specific point. Conceptually, this is analogous to determining the precise location on a circular billiard table's edge where a cue ball, aimed from one point, must strike to rebound and hit a second target ball. Optically, its primary application is to ascertain the reflection point on a spherical mirror for light originating from a source to reach an observer's eye. This inquiry culminates in a fourth-degree equation. Alhazen's pursuit of this solution led him to formulate a method for summing fourth powers, expanding upon the previously established formulas for sums of squares and cubes. His methodology possesses the potential for generalization to calculate the sum of any integral powers, although he did not explicitly extend it beyond the fourth power, likely because this was sufficient for his calculation of a paraboloid's volume. He applied this result on sums of integral powers to perform an early form of integration, utilizing the formulas for sums of integral squares and fourth powers to compute the volume of a paraboloid. Alhazen ultimately resolved the problem through the application of conic sections and a rigorous geometric proof. However, his solution was notably extensive and intricate, potentially posing comprehension challenges for mathematicians encountering it via Latin translations. Subsequently, mathematicians employed Descartes' analytical techniques to further investigate the problem. An algebraic solution was eventually achieved in 1965 by actuary Jack M. Elkin, with additional solutions presented in 1989 by Harald Riede and in 1997 by Oxford mathematician Peter M. Neumann. More recently, researchers at Mitsubishi Electric Research Laboratories (MERL) have successfully extended Alhazen's problem to encompass general rotationally symmetric quadric mirrors, including hyperbolic, parabolic, and elliptical configurations.
Camera Obscura
While the camera obscura was recognized by the ancient Chinese and documented by the Han Chinese polymath Shen Kuo in his 1088 C.E. scientific treatise, Dream Pool Essays, and its fundamental principles were discussed by Aristotle in his Problems, Alhazen's writings provided the inaugural comprehensive description and initial analytical examination of the device.
Ibn al-Haytham primarily employed the camera obscura for observing partial solar eclipses. In his essay, he documented his observation of the sun's crescent shape during an eclipse. The introductory passage states: "The image of the sun at the time of the eclipse, unless it is total, demonstrates that when its light passes through a narrow, round hole and is cast on a plane opposite to the hole it takes on the form of a moonsickle."
Alhazen's findings are acknowledged for their foundational significance in the historical development of the camera obscura; however, this particular treatise holds broader importance across various other domains.
Historically, ancient and medieval optics were bifurcated into the study of vision, termed 'optics proper,' and the investigation of light properties and luminous rays, known as 'burning mirrors.' Ibn al-Haytham's treatise, On the shape of the eclipse, represents a pioneering effort to integrate these two distinct scientific disciplines.
Ibn al-Haytham's discoveries frequently emerged from the convergence of mathematical rigor and empirical experimentation, a characteristic exemplified by his work On the shape of the eclipse. Beyond facilitating broader study of partial solar eclipses, this treatise significantly advanced the comprehension of camera obscura functionality. It constitutes a physico-mathematical investigation into image formation within the camera obscura, wherein Ibn al-Haytham adopted an experimental methodology, systematically varying the aperture's size and shape, the camera's focal length, and the light source's form and intensity to ascertain his findings.
Within his writings, Alhazen elucidated the phenomenon of image inversion within the camera obscura. He further distinguished that the image closely resembles the source when the aperture is small, yet can deviate significantly from the source when the aperture is large. These conclusions were derived through a meticulous point analysis of the image.
Refractometer
Alhazen, in the seventh tract of his *Book of Optics*, detailed an experimental apparatus designed to explore various refraction phenomena. This device aimed to ascertain the relationships among the angle of incidence, the angle of refraction, and the angle of deflection, representing a modification of a similar instrument previously employed by Ptolemy.
Unconscious Inference
Alhazen articulated the concept of unconscious inference within his discourse on color perception. He posited that the inferential process distinguishing color from initial sensation occurs more rapidly than for other visible characteristics (excluding light), noting that this "time is so short as not to be clearly apparent to the beholder." This implies that the perception of color and form transpires at a different location. Alhazen further elaborated that visual information must reach the central nerve cavity for subsequent processing, stating:
the sentient organ does not perceive the forms emanating from visible objects until it has been influenced by these forms. Consequently, it does not apprehend color as color or light as light until it has been affected by the respective forms of color or light. The influence exerted upon the sentient organ by the form of color or light constitutes a specific alteration, and such alteration necessarily unfolds over time. It is during the interval in which the form propagates from the sentient organ's surface to the cavity of the common nerve, and subsequently, that the sensitive faculty, inherent throughout the sentient body, will perceive color as color. Therefore, the ultimate perception of color and light by the sentient entity occurs at a point in time subsequent to the form's arrival from the sentient organ's surface to the common nerve's cavity.
Color Constancy
Alhazen elucidated the phenomenon of color constancy by noting that an object's color modifies the light it reflects. He proposed that the inherent quality of light and the object's color become intermingled, and that the visual system subsequently differentiates between them. In Book II, Chapter 3, he states:
Furthermore, light does not traverse from a colored object to the eye independently of its color, nor does the form of color transmit from the colored object to the eye without accompanying light. Neither the form of light nor that of color, as they exist within the colored object, can propagate except in a combined state, and the ultimate sentient faculty can only perceive them as intermingled. Despite this, the sentient faculty discerns that the visible object possesses luminosity, and that the light observed within the object is distinct from its color, recognizing these as two separate properties.
Other Contributions
Alhazen's Kitab al-Manazir (Book of Optics) details numerous experimental observations and demonstrates how he employed these findings to elucidate specific optical phenomena through mechanical analogies. His projectile experiments led him to conclude that only perpendicular impacts possessed sufficient force to penetrate surfaces, while oblique strikes typically resulted in deflection. To illustrate refraction from a less dense to a denser medium, for instance, he utilized the mechanical analogy of an iron ball hurled at a thin slate covering a large aperture in a metal sheet. A perpendicular throw would shatter the slate and pass through, whereas an oblique throw, despite equal force and distance, would not. He further applied this principle to explain the discomfort caused by intense, direct light, drawing a mechanical parallel: Alhazen correlated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The resolution to the issue of multiple rays entering the eye was found in prioritizing the perpendicular ray, as only one such ray from each point on an object's surface could effectively penetrate the eye.
Sudanese psychologist Omar Khaleefa has contended that Alhazen merits recognition as the founder of experimental psychology, citing his groundbreaking contributions to the psychology of visual perception and optical illusions. Khaleefa additionally proposed that Alhazen should be regarded as the "founder of psychophysics," a sub-discipline and antecedent to modern psychology. However, despite Alhazen's numerous subjective accounts concerning vision, no evidence supports his use of quantitative psychophysical techniques, and this particular claim has been refuted.
Alhazen proposed an explanation for the Moon illusion, a phenomenon that significantly influenced the scientific discourse of medieval Europe. Numerous scholars reiterated theories attempting to resolve the apparent discrepancy in the Moon's size, which seems larger when near the horizon compared to its appearance higher in the sky. Alhazen contested Ptolemy's refraction theory, reframing the problem as one of perceived, rather than actual, magnification. He posited that assessing an object's distance relies on the presence of an unbroken series of intervening elements between the object and the observer. When the Moon is elevated in the sky, the absence of intervening objects leads to its perception as being closer. The apparent size of an object, despite having a constant angular dimension, fluctuates with its perceived distance. Consequently, the Moon seems closer and smaller when high in the sky, but more distant and larger when on the horizon. Influenced by Alhazen's explanation, works by Roger Bacon, John Pecham, and Witelo progressively established the Moon illusion as a psychological phenomenon, leading to the rejection of the refraction theory by the 17th century. While Alhazen frequently receives credit for the perceived distance explanation, he was not its originator. Cleomedes (c. 2nd century) presented this perspective (alongside refraction) and attributed it to Posidonius (c. 135 – c. 51 BCE). Ptolemy might also have proposed this explanation in his Optics, though the relevant text remains ambiguous. Alhazen's treatises enjoyed broader dissemination during the Middle Ages compared to those of his predecessors, likely accounting for his widespread recognition.
Scientific Method
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. 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.
A notable characteristic of Alhazen's optical investigations involves a systematic and methodological dependence on experimentation (i'tibar) (Arabic: اختبار) and rigorous controlled testing. Furthermore, his experimental protocols were founded upon the integration of classical physics (ilm tabi'i) with mathematics (ta'alim), particularly geometry. This integrated mathematical-physical methodology for experimental science underpinned the majority of his assertions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and established his theories concerning vision, light, and color, alongside his investigations into catoptrics and dioptrics (the respective studies of light reflection and refraction).
Matthias Schramm asserted that 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." G. J. Toomer, however, voiced reservations concerning Schramm's perspective, partly due to the fact that in 1964, the Book of Optics had not been entirely translated from Arabic, leading Toomer to worry that isolated passages could be interpreted anachronistically without proper context. While recognizing Alhazen's significant contributions to the advancement of experimental methodologies, Toomer contended that Alhazen's work should not be evaluated independently of other Islamic and ancient scholars. Toomer concluded his assessment by stating that a comprehensive evaluation of Schramm's assertion—that Ibn al-Haytham was the genuine progenitor of modern physics—would necessitate further translation of Alhazen's corpus and a thorough examination of his impact on subsequent medieval authors.
Other Works on Physics
Optical Treatises
Alhazen authored numerous other treatises on optics, in addition to the seminal Book of Optics, notably his Risala fi l-Daw' (Treatise on Light). His research encompassed the characteristics of luminance, rainbows, eclipses, twilight, and moonlight. The experimental foundation for his theories on catoptrics was established through investigations involving mirrors and the refractive properties of interfaces between air, water, and various geometric forms of glass, such as cubes, hemispheres, and quarter-spheres.
Celestial Physics
In his Epitome of Astronomy, Alhazen explored the physics of the celestial domain, asserting that Ptolemaic models should be interpreted as representations of physical objects rather than mere abstract hypotheses. This implied the feasibility of constructing physical models where, for instance, celestial bodies would not intersect. The proposition of mechanical models for the geocentric Ptolemaic system "significantly advanced the ultimate acceptance of the Ptolemaic system among Western Christians." Nevertheless, Alhazen's insistence on grounding astronomy in tangible physical entities was crucial, as it rendered astronomical hypotheses "subject to the principles of physics," thereby allowing for their critique and refinement based on these principles.
He also authored Maqala fi daw al-qamar, which translates to On the Light of the Moon.
Mechanics
Alhazen's writings included discussions on theories concerning the motion of bodies.
Astronomical Works
On the Configuration of the World
Within his treatise On the Configuration of the World, Alhazen provided an elaborate account of Earth's physical structure:
The Earth, in its entirety, constitutes a spherical body whose center coincides with the center of the cosmos. It remains stationary at the world's core, immovably fixed, exhibiting no translational or rotational motion, but perpetually at rest.
This volume offers a non-technical elucidation of Ptolemy's Almagest. Its subsequent translations into Hebrew and Latin during the 13th and 14th centuries significantly impacted astronomers, including Georg von Peuerbach, throughout the European Middle Ages and Renaissance.
Doubts Concerning Ptolemy
Alhazen's work, Al-Shukūk ‛alā Batlamyūs, alternatively rendered as Doubts Concerning Ptolemy or Aporias against Ptolemy, published between 1025 and 1028, presented a critique of Ptolemy's Almagest, Planetary Hypotheses, and Optics. In this treatise, Alhazen highlighted numerous inconsistencies within these works, particularly in the field of astronomy. While Ptolemy's Almagest focused on mathematical theories of planetary motion, the Hypotheses addressed Ptolemy's conception of the planets' actual physical arrangement. Ptolemy himself conceded that his theoretical models and proposed configurations were not always congruent, asserting that this discrepancy was acceptable as long as it did not lead to observable errors. However, Alhazen delivered particularly sharp criticism regarding the intrinsic contradictions within Ptolemy's corpus. He contended that certain mathematical constructs introduced by Ptolemy into astronomy, notably the equant, failed to adhere to the physical prerequisite of uniform circular motion. Alhazen further underscored the illogicality of correlating actual physical movements with abstract mathematical points, lines, and circles:
Ptolemy posited an arrangement (hay'a) that is physically impossible. The fact that this arrangement, in his imagination, generates the observed planetary motions does not absolve him from the error inherent in his assumed configuration, as the actual motions of the planets cannot arise from an arrangement that is impossible to exist... Merely conceiving a celestial circle and imagining a planet moving within it does not, in itself, induce the planet's motion.
Following his identification of these issues, Alhazen seemingly aimed to reconcile the contradictions he observed in Ptolemy's work in a subsequent publication. Alhazen posited the existence of a "true configuration" of the planets, which he believed Ptolemy had not fully comprehended. His objective was to refine and complete Ptolemy's system, rather than to entirely supersede it. Within Doubts Concerning Ptolemy, Alhazen articulated his perspectives on the inherent challenges in acquiring scientific knowledge and emphasized the imperative to critically evaluate established authorities and theories.
The pursuit of truth is an intrinsic objective; however, he cautioned that truths are inherently subject to uncertainties, and even esteemed scientific authorities, such as Ptolemy, whom he held in high regard, are not infallible.
He posited that the critical evaluation of existing theories, a central theme of this work, is critically important for the advancement of scientific knowledge.
Model of the Motions of Each of the Seven Planets
Alhazen authored The Model of the Motions of Each of the Seven Planets around c. 1038. Only a single damaged manuscript of this work has been discovered, with merely its introduction and the initial section, which addresses the theory of planetary motion, remaining intact. The complete work originally comprised a second section dedicated to astronomical calculation and a third section on astronomical instruments. Building upon the critiques presented in his Doubts on Ptolemy, Alhazen developed a novel, geometry-centric planetary model. This model elucidated planetary motions through the principles of spherical geometry, infinitesimal geometry, and trigonometry. While maintaining a geocentric cosmology and presuming uniformly circular celestial motions—necessitating the incorporation of epicycles to account for observed phenomena—he successfully dispensed with Ptolemy's equant. Fundamentally, his model did not aim to offer a causal explanation for these motions; instead, it focused on delivering a comprehensive geometric description capable of elucidating observed planetary movements without the internal inconsistencies present in Ptolemy's framework.
Other astronomical works
Alhazen produced a total of twenty-five astronomical treatises, categorized into several groups. One group addressed technical subjects like the Exact Determination of the Meridian. A second collection focused on precise astronomical observation, while a third explored diverse astronomical problems and inquiries, including the precise location of the Milky Way. Notably, Alhazen undertook the first systematic endeavor to assess the Milky Way's parallax, integrating both Ptolemy's observational data and his own findings. His analysis led him to conclude that the Milky Way's parallax was significantly smaller than that of the Moon, suggesting its nature as a celestial body rather than an atmospheric phenomenon. While others had previously posited that the Milky Way was not an atmospheric phenomenon, Alhazen was the first to provide a quantitative analysis supporting this assertion. The fourth category comprises ten works dedicated to astronomical theory, encompassing the previously mentioned Doubts and Model of the Motions.
Mathematical works
In the field of mathematics, Alhazen advanced upon the works of Euclid and Thabit ibn Qurra, pioneering the foundational connections between algebra and geometry. He also contributed significantly to the study of conic sections and number theory.
He derived a formula for the summation of the first 100 natural numbers, substantiating this formula with a geometric proof.
Geometry
Alhazen investigated the Euclidean parallel postulate, recognized as the fifth postulate in Euclid's Elements. His approach involved a proof by contradiction, effectively integrating the concept of motion into geometric reasoning. He also formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld subsequently designated as the "Ibn al-Haytham–Lambert quadrilateral". However, Omar Khayyam criticized this methodology, noting Aristotle's prior condemnation of incorporating motion into geometry.
Within elementary geometry, Alhazen endeavored to resolve the classical problem of squaring the circle by employing the areas of lunes (crescent-shaped figures), though he ultimately abandoned this intractable challenge. The pair of lunes constructed from a right triangle—by erecting a semicircle inward on the hypotenuse and outward on each of the other two sides—are specifically termed the lunes of Alhazen; notably, their combined area precisely equals that of the original triangle.
Number theory
Alhazen's contributions to number theory encompass his investigations into perfect numbers. Within his treatise Analysis and Synthesis, he potentially became the first to articulate the proposition that every even perfect number adheres to the form 2n−1(2n − 1), provided that 2n − 1 is a prime number. However, he did not succeed in proving this assertion; the proof was subsequently provided by Euler in the 18th century, and the result is now recognized as the Euclid–Euler theorem.
Alhazen addressed problems concerning congruences by employing principles now identified as Wilson's theorem. In his work Opuscula, Alhazen examined the resolution of systems of congruences and presented two distinct general solution methodologies. The first, termed the canonical method, incorporated Wilson's theorem, whereas his second approach utilized a variant of the Chinese remainder theorem.
Calculus
Alhazen successfully derived the sum formula for the fourth power, employing a methodology applicable to determining the sum for any integral power. This technique was subsequently utilized to calculate the volume of a paraboloid. Notably, he was able to ascertain the integral formula for any polynomial, even without formulating a generalized expression.
Additional Contributions
The Influence of Melodies on Animal Psyches
Alhazen authored a Treatise on the Influence of Melodies on the Souls of Animals; however, no extant copies of this work are known. The treatise seemingly explored the responsiveness of animals to music, investigating, for instance, whether a camel's gait would accelerate or decelerate in response to melodies.
Engineering Endeavors
Regarding his engineering career, historical accounts indicate that Alhazen was summoned to Egypt by the Fatimid Caliph, Al-Hakim bi-Amr Allah, with the mandate to manage the Nile River's annual flooding. He conducted an exhaustive scientific investigation into the Nile's inundation patterns and subsequently devised plans for constructing a dam at the location of the contemporary Aswan Dam. Nevertheless, his subsequent fieldwork revealed the project's impracticality, leading him to simulate insanity to evade potential punitive measures from the Caliph.
Philosophical Contributions
Within his Treatise on Place, Alhazen challenged Aristotle's assertion that nature inherently resists a vacuum. He employed geometric principles to argue that place (al-makan) constitutes an imagined three-dimensional void situated between the internal surfaces of an encompassing entity. Abd-el-latif, an adherent of Aristotle's philosophical concept of place, subsequently critiqued Alhazen's work in Fi al-Radd 'ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham's place), specifically faulting its geometric interpretation of place.
Alhazen further explored the perception of space and its epistemological ramifications in his seminal work, the Book of Optics. By "linking the visual apprehension of space to preceding corporeal experiences, Alhazen definitively repudiated the inherent intuitiveness of spatial perception and, consequently, the independent nature of vision. Lacking concrete concepts of distance and magnitude for comparative analysis, visual input provides minimal information regarding these attributes."
Theological Perspectives
Alhazen was a Muslim, with the majority of sources identifying him as a Sunni and an adherent of the Ash'ari school of thought. According to Ziauddin Sardar, several prominent Muslim scientists, including Ibn al-Haytham and Abū Rayhān al-Bīrūnī, who were instrumental in pioneering the scientific method, were themselves followers of the Ashʿari school of Islamic theology. Consistent with other Ashʿarites who maintained that faith, or taqlid, should be exclusively directed towards Islam and not towards ancient Hellenistic authorities, Ibn al-Haytham's conviction that taqlid ought to apply solely to the prophets of Islam and not to any other figures underpinned a significant portion of his scientific skepticism and critical stance against Ptolemy and other ancient scholars, as articulated in his works Doubts Concerning Ptolemy and Book of Optics.
Alhazen authored a treatise on Islamic theology, wherein he examined prophethood and formulated a framework of philosophical criteria to identify false claimants during his era. Additionally, he composed a work titled Finding the Direction of Qibla by Calculation, which mathematically addressed the determination of the Qibla, the direction towards which Muslim prayers (salat) are offered.
Occasional allusions to theological concepts or religious sentiments are present within his technical writings, for instance, in Doubts Concerning Ptolemy:
Truth is pursued for its intrinsic value... The discovery of truth is arduous, and its path is challenging. For truths are often veiled in obscurity... Nevertheless, God has not shielded the scientist from error nor protected science from deficiencies and imperfections. Had this been otherwise, scientists would exhibit no divergence of opinion on any scientific matter...
From The Winding Motion:
Based on the assertions of the esteemed Shaykh, it is evident that he accepts Ptolemy's pronouncements entirely, not through reliance on demonstration or empirical proof, but by sheer imitation (taqlid); this approach mirrors how scholars of prophetic tradition place their faith in Prophets, may God's blessings be upon them. However, this method diverges from how mathematicians place their trust in experts within the demonstrative sciences.
Concerning the relationship between objective truth and the divine:
My continuous pursuit of knowledge and truth led me to the conviction that the most effective path to attaining divine illumination and proximity to God lies in the quest for truth and understanding.
Legacy
Alhazen made substantial contributions across optics, number theory, geometry, astronomy, and natural philosophy. His optical research is particularly recognized for introducing a novel emphasis on experimental methodology.
Alhazen's seminal work, Kitab al-Manazir (Book of Optics), gained prominence in the Muslim world, primarily, though not exclusively, via the thirteenth-century commentary by Kamāl al-Dīn al-Fārisī, titled Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir. In al-Andalus, al-Mu'taman ibn Hūd, an eleventh-century prince of the Banu Hud dynasty of Zaragossa and author of a significant mathematical text, utilized this work. A Latin translation of the Kitab al-Manazir likely emerged in the late twelfth or early thirteenth century. This translation profoundly influenced numerous scholars in Christian Europe, including Roger Bacon, Robert Grosseteste, Witelo, Giambattista della Porta, Leonardo da Vinci, Galileo Galilei, Christiaan Huygens, René Descartes, and Johannes Kepler. Concurrently, within the Islamic world, Alhazen's intellectual heritage was further developed by the Persian scientist Kamal al-Din al-Farisi (d. c. 1320), who 'reformed' his Optics in his own work, Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics). Alhazen is believed to have authored up to 200 books, with only 55 extant today. Some of his optical treatises are preserved solely through their Latin translations. During the medieval period, his cosmological texts were translated into Latin, Hebrew, and other languages.
H. J. J. Winter, a British historian of science, summarized Ibn al-Haytham's significance in the history of physics by stating:
Following Archimedes' demise, no truly eminent physicist emerged until Ibn al-Haytham. Consequently, if our focus remains solely on the history of physics, a protracted period exceeding twelve hundred years transpired, during which the Golden Age of Greece transitioned into the era of Muslim Scholasticism, and the experimental ethos of antiquity's most distinguished physicist was rekindled in the Arab scholar from Basra.
Despite only one commentary on Alhazen's optical works surviving from the Islamic Middle Ages, Geoffrey Chaucer references his contributions in The Canterbury Tales:
The lunar impact crater Alhazen and asteroid 59239 Alhazen are named in his honor. Furthermore, the Aga Khan University (Pakistan) established "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology" as an endowed chair in recognition of Alhazen's legacy.
The impact crater Alhazen on the Moon is named in his honour, as was the asteroid 59239 Alhazen. 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".
The 2015 International Year of Light commemorated the millennium anniversary of Ibn Al-Haytham's optical works.
In 2014, the episode "Hiding in the Light" from Cosmos: A Spacetime Odyssey, hosted by Neil deGrasse Tyson, highlighted Ibn al-Haytham's achievements. Alfred Molina provided the voice for Ibn al-Haytham in this episode.
More than four decades prior, Jacob Bronowski featured Alhazen's work in a comparable television documentary and its accompanying book, The Ascent of Man. In episode 5, titled The Music of the Spheres, Bronowski asserted his belief that Alhazen represented "the one really original scientific mind that Arab culture produced," whose optical theory remained unsurpassed until the era of Isaac Newton and Gottfried Wilhelm Leibniz.
UNESCO designated 2015 as the International Year of Light, with its Director-General, Irina Bokova, recognizing Ibn al-Haytham as 'the father of optics'. This initiative aimed, among other objectives, to commemorate Ibn Al-Haytham's contributions to optics, mathematics, and astronomy. An international campaign, developed by the 1001 Inventions organization and titled 1001 Inventions and the World of Ibn Al-Haytham, showcased his work through interactive exhibits, workshops, and live shows. This campaign collaborated with science centers, science festivals, museums, educational institutions, and digital and social media platforms. Additionally, the campaign produced and distributed the short educational film, "1001 Inventions and the World of Ibn Al-Haytham."
Ibn al-Haytham is depicted on the 10,000 dinar banknote of the Iraqi dinar, from the 2003 series.
List of works
Medieval biographers attribute over 200 works to Alhazen across diverse fields, with at least 96 scientific treatises identified. While most of his compositions are no longer extant, more than 50 have partially endured. Approximately half of these surviving works address mathematics, 23 focus on astronomy, and 14 pertain to optics, alongside a limited number on other topics. Although not all extant works have undergone scholarly examination, a selection of those that have been studied is presented subsequently.
Lost Works
- A Compendium of Optics Derived from the Works of Euclid and Ptolemy, Supplemented with Concepts from Ptolemy's Absent First Discourse
- Treatise on Burning Mirrors
- Treatise on the Nature of Sight and the Mechanism of Vision
Notes
Notes
References
Sources
Primary
Primary
Secondary
- Works by Ibn al-Haytham at Open Library
- Langermann, Y. Tzvi (2007). "Ibn al-Haytham: Abū ʿAlī al-Ḥasan ibn al-Ḥasan." In Thomas Hockey et al. (eds.), The Biographical Encyclopedia of Astronomers. New York: Springer, pp. 556–5567. ISBN 978-0-387-31022-0."Biography from the BBC." Archived from the original on 11 February 2006. Retrieved 16 September 2008.Çavkanî: Arşîva TORÎma Akademî
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