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Greco-Roman (Mid- and Neo-Platonic, and Aristotelian) texts translated by the Kindi school were commented, redacted and developed substantially by Islamic intellectuals, who also built upon Persian and Indian mathematical systems, astronomy, algebra, trigonometry and medicine. The Samanid dynasty in the eastern part of Persia, Greater Khorasan and Central Asia as well as the Buyid dynasty in the western part of Persia and Iraq provided a thriving atmosphere for scholarly and cultural development. Under the Samanids, Bukhara rivaled Baghdad as a cultural capital of the Islamic world. There, the study of the Quran and the Hadith thrived. Philosophy, Fiqh and theology (kalaam) were further developed, most noticeably by Avicenna and his opponents. Al-Razi and Al-Farabi had provided methodology and knowledge in medicine and philosophy. Avicenna had access to the great libraries of Balkh, Khwarezm, Gorgan, Rey, Isfahan and Hamadan. Various texts (such as the 'Ahd with Bahmanyar) show that he debated philosophical points with the greatest scholars of the time. Aruzi Samarqandi describes how before Avicenna left Khwarezm he had met Al-Biruni (a famous scientist and astronomer), Abu Nasr Iraqi (a renowned mathematician), Abu Sahl Masihi (a respected philosopher) and Abu al-Khayr Khammar (a great physician). Biography
Early life and education
Avicenna was born in in the village of Afshana in Transoxiana to a family of Persian stock. The village was near the Samanid capital of Bukhara, which was his mother's hometown. His father Abd Allah was a native of the city of Balkh in Tukharistan. | [
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An official of the Samanid bureaucracy, he had served as the governor of a village of the royal estate of Harmaytan (near Bukhara) during the reign of Nuh II (). Avicenna also had a younger brother. A few years later, the family settled in Bukhara, a centre of learning, which attracted many scholars. It was there that Avicenna was educated, which early on was seemingly administered by his father. Although both Avicenna's father and brother had converted to Ismailism, he himself did not follow the faith. He was instead an adherent of the Hanafi school, which was also followed by the Samanids. Avicenna was first schooled in the Quran and literature, and by the age of 10, he had memorised the entire Quran. He was later sent by his father to an Indian greengrocer, who taught him arithmetic. Afterwards, he was schooled in Jurisprudence by the Hanafi jurist Ismail al-Zahid. Some time later, Avicenna's father invited the physician and philosopher Abu Abdallah al-Natili to their house to educate Avicenna. Together, they studied the Isagoge of Porphyry (died 305) and possibly the Categories of Aristotle (died 322 BC) as well. After Avicenna had read the Almagest of Ptolemy (died 170) and Euclid's Elements, Natili told him to continue his research independently. By the time Avicenna was eighteen, he was well-educated in Greek sciences. Although Avicenna only mentions Natili as his teacher in his autobiography, he most likely had other teachers as well, such as the physicians Abu Mansur Qumri and Abu Sahl al-Masihi. | [
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Career
In Bukhara and Gurganj
At the age of seventeen, Avicenna was made a physician of Nuh II. By the time Avicenna was at least 21 years old, his father died. He was subsequently given an administrative post, possibly succeeding his father as the governor of Harmaytan. Avicenna later moved to Gurganj, the capital of Khwarazm, which he reports that he did due to "necessity". The date he went to the place is uncertain, as he reports that he served the Khwarazmshah (ruler) of the region, the Ma'munid Abu al-Hasan Ali. The latter ruled from 997 to 1009, which indicates that Avicenna moved sometime during that period. He may have moved in 999, the year which the Samanid state fell after the Turkic Qarakhanids captured Bukhara and imprisoned the Samanid ruler Abd al-Malik II. Due to his high position and strong connection with the Samanids, Avicenna may have found himself in an unfavorable position after the fall of his suzerain. It was through the minister of Gurganj, Abu'l-Husayn as-Sahi, a patron of Greek sciences, that Avicenna entered into the service of Abu al-Hasan Ali. Under the Ma'munids, Gurganj became a centre of learning, attracting many prominent figures, such as Avicenna and his former teacher Abu Sahl al-Masihi, the mathematician Abu Nasr Mansur, the physician Ibn al-Khammar, and the philologist al-Tha'alibi. In Gurgan
Avicenna later moved due to "necessity" once more (in 1012), this time to the west. There he travelled through the Khurasani cities of Nasa, Abivard, Tus, Samangan and Jajarm. | [
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He was planning to visit the ruler of the city of Gurgan, the Ziyarid Qabus (), a cultivated patron of writing, whose court attracted many distinguished poets and scholars. However, when Avicenna eventually arrived, he discovered that the ruler had been dead since the winter of 1013. Avicenna then left Gurgan for Dihistan, but returned after becoming ill. There he met Abu 'Ubayd al-Juzjani (died 1070) who became his pupil and companion. Avicenna stayed briefly in Gurgan, reportedly serving Qabus' son and successor Manuchihr () and resided in the house of a patron. In Ray and Hamadan
In , Avicenna went to the city of Ray, where he entered into the service of the Buyid amir (ruler) Majd al-Dawla () and his mother Sayyida Shirin, the de facto ruler of the realm. There he served as the physician at the court, treating Majd al-Dawla, who was suffering from melancholia. Avicenna reportedly later served as the "business manager" of Sayyida Shirin in Qazvin and Hamadan, though details regarding this tenure are unclear. During his period, Avicenna finished his Canon of Medicine, and started writing his Book of Healing. In 1015, during Avicenna's stay in Hamadan, he participated in a public debate, as was custom for newly arrived scholars in western Iran at that time. The purpose of the debate was to examining one's reputation against a prominent local resident. The person whom Avicenna debated against was Abu'l-Qasim al-Kirmani, a member of the school of philosophers of Baghdad. | [
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The debate became heated, resulting in Avicenna accusing Abu'l-Qasim of lack of basic knowledge in logic, while Abu'l-Qasim accused Avicenna of impoliteness. After the debate, Avicenna sent a letter to the Baghdad Peripatetics, asking if Abu'l-Qasim's claim that he shared the same opinion as them was true. Abu'l-Qasim later retaliated by writing a letter to an unknown person, in which he made accusations so serious, that Avicenna wrote to a deputy of Majd al-Dawla, named Abu Sa'd, to investigate the matter. The accusation made towards Avicenna may have been the same as he had received earlier, in which he was accused by the people of Hamadan of copying the stylistic structures of the Quran in his Sermons on Divine Unity. The seriousness of this charge, in the words of the historian Peter Adamson, "cannot be underestimated in the larger Muslim culture." Not long afterwards, Avicenna shifted his allegiance to the rising Buyid amir Shams al-Dawla (the younger brother of Majd al-Dawla), which Adamson suggests was due to Abu'l-Qasim also working under Sayyida Shirin. Avicenna had been called upon by Shams al-Dawla to treat him, but after the latters campaign in the same year against his former ally, the Annazid ruler Abu Shawk (), he forced Avicenna to become his vizier. Although Avicenna would sometimes clash with Shams al-Dawla's troops, he remained vizier until the latter died of colic in 1021. | [
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Avicenna was asked by Shams al-Dawla's son and successor Sama' al-Dawla () stay as vizier, but instead went into hiding with his patron Abu Ghalib al-Attar, to wait for better opportunities to emerge. It was during this period that Avicenna was secretly in contact with Ala al-Dawla Muhammad (), the Kakuyid ruler of Isfahan and uncle of Sayyida Shirin. During his stay at Attar's home that Avicenna completed his Book of Healing, writing fifty pages a day. The Buyid court in Hamadan, particularly the Kurdish vizier Taj al-Mulk, suspected Avicenna of correspondence with Ala al-Dawla, and as result had the house of Attar ransacked and Avicenna imprisoned in the fortress of Fardajan, outside Hamadan. Juzjani blames one of Avicenna's informers for his capture. Avicenna was imprisoned in four months, until Ala al-Dawla captured Hamadan, thus putting an end to Sama al-Dawla's reign. In Isfahan
Avicenna was subsequently released, and went to Isfahan, where he was well received by Ala al-Dawla. In the words of Juzjani, the Kakuyid ruler gave Avicenna "the respect and esteem which someone like him deserved." Adamson also says that Avicenna's service under Ala al-Dawla "proved to be the most stable period of his life." Avicenna served as the advisor, if not vizier of Ala al-Dawla, accompanying him in many of his military expeditions and travels. Avicenna dedicated two Persian works to him, a philosophical treatise named Danish-nama-yi Ala'i ("Book of Science for Ala"), and a medical treatise about the pulse. | [
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During the brief occupation of Isfahan by the Ghaznavids in January 1030, Avicenna and Ala al-Dawla relocated to the southwestern Iranian region of Khuzistan, where they stayed until the death of the Ghaznavid ruler Mahmud (), which occurred two months later. It was seemingly when Avicenna returned to Isfahan that he started writing his Pointers and Reminders. In 1037, while Avicenna was accompanying Ala al-Dawla to a battle near Isfahan, he was hit by a severe colic, which he had been constantly suffering from throughout his life. He died shortly afterwards in Hamadan, where he was buried. Philosophy
Avicenna wrote extensively on early Islamic philosophy, especially the subjects logic, ethics and metaphysics, including treatises named Logic and Metaphysics. Most of his works were written in Arabic—then the language of science in the Middle East—and some in Persian. Of linguistic significance even to this day are a few books that he wrote in nearly pure Persian language (particularly the Danishnamah-yi 'Ala', Philosophy for Ala' ad-Dawla'). Avicenna's commentaries on Aristotle often criticized the philosopher, encouraging a lively debate in the spirit of ijtihad. Avicenna's Neoplatonic scheme of "emanations" became fundamental in the Kalam (school of theological discourse) in the 12th century. His Book of Healing became available in Europe in partial Latin translation some fifty years after its composition, under the title Sufficientia, and some authors have identified a "Latin Avicennism" as flourishing for some time, paralleling the more influential Latin Averroism, but suppressed by the Parisian decrees of 1210 and 1215. | [
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Avicenna's psychology and theory of knowledge influenced William of Auvergne, Bishop of Paris and Albertus Magnus, while his metaphysics influenced the thought of Thomas Aquinas. Metaphysical doctrine
Early Islamic philosophy and Islamic metaphysics, imbued as it is with Islamic theology, distinguishes more clearly than Aristotelianism between essence and existence. Whereas existence is the domain of the contingent and the accidental, essence endures within a being beyond the accidental. The philosophy of Avicenna, particularly that part relating to metaphysics, owes much to al-Farabi. The search for a definitive Islamic philosophy separate from Occasionalism can be seen in what is left of his work. Following al-Farabi's lead, Avicenna initiated a full-fledged inquiry into the question of being, in which he distinguished between essence (Mahiat) and existence (Wujud). He argued that the fact of existence cannot be inferred from or accounted for by the essence of existing things, and that form and matter by themselves cannot interact and originate the movement of the universe or the progressive actualization of existing things. Existence must, therefore, be due to an agent-cause that necessitates, imparts, gives, or adds existence to an essence. To do so, the cause must be an existing thing and coexist with its effect. Avicenna's consideration of the essence-attributes question may be elucidated in terms of his ontological analysis of the modalities of being; namely impossibility, contingency and necessity. Avicenna argued that the impossible being is that which cannot exist, while the contingent in itself (mumkin bi-dhatihi) has the potentiality to be or not to be without entailing a contradiction. | [
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When actualized, the contingent becomes a 'necessary existent due to what is other than itself' (wajib al-wujud bi-ghayrihi). Thus, contingency-in-itself is potential beingness that could eventually be actualized by an external cause other than itself. The metaphysical structures of necessity and contingency are different. Necessary being due to itself (wajib al-wujud bi-dhatihi) is true in itself, while the contingent being is 'false in itself' and 'true due to something else other than itself'. The necessary is the source of its own being without borrowed existence. It is what always exists. The Necessary exists 'due-to-Its-Self', and has no quiddity/essence (mahiyya) other than existence (wujud). Furthermore, It is 'One' (wahid ahad) since there cannot be more than one 'Necessary-Existent-due-to-Itself' without differentia (fasl) to distinguish them from each other. Yet, to require differentia entails that they exist 'due-to-themselves' as well as 'due to what is other than themselves'; and this is contradictory. However, if no differentia distinguishes them from each other, then there is no sense in which these 'Existents' are not one and the same. Avicenna adds that the 'Necessary-Existent-due-to-Itself' has no genus (jins), nor a definition (hadd), nor a counterpart (nadd), nor an opposite (did), and is detached (bari) from matter (madda), quality (kayf), quantity (kam), place (ayn), situation (wad) and time (waqt). | [
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Avicenna's theology on metaphysical issues (ilāhiyyāt) has been criticized by some Islamic scholars, among them al-Ghazali, Ibn Taymiyya and Ibn al-Qayyim. While discussing the views of the theists among the Greek philosophers, namely Socrates, Plato and Aristotle in Al-Munqidh min ad-Dalal ("Deliverance from Error"), al-Ghazali noted that the Greek philosophers "must be taxed with unbelief, as must their partisans among the Muslim philosophers, such as Avicenna and al-Farabi and their likes." He added that "None, however, of the Muslim philosophers engaged so much in transmitting Aristotle's lore as did the two men just mentioned. [...] The sum of what we regard as the authentic philosophy of Aristotle, as transmitted by al-Farabi and Avicenna, can be reduced to three parts: a part which must be branded as unbelief; a part which must be stigmatized as innovation; and a part which need not be repudiated at all." Argument for God's existence
Avicenna made an argument for the existence of God which would be known as the "Proof of the Truthful" (Arabic: burhan al-siddiqin). Avicenna argued that there must be a "necessary existent" (Arabic: wajib al-wujud), an entity that cannot not exist and through a series of arguments, he identified it with the Islamic conception of God. Present-day historian of philosophy Peter Adamson called this argument one of the most influential medieval arguments for God's existence, and Avicenna's biggest contribution to the history of philosophy. | [
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Al-Biruni correspondence
Correspondence between Avicenna (with his student Ahmad ibn 'Ali al-Ma'sumi) and Al-Biruni has survived in which they debated Aristotelian natural philosophy and the Peripatetic school. Abu Rayhan began by asking Avicenna eighteen questions, ten of which were criticisms of Aristotle's On the Heavens. Theology
Avicenna was a devout Muslim and sought to reconcile rational philosophy with Islamic theology. His aim was to prove the existence of God and His creation of the world scientifically and through reason and logic. Avicenna's views on Islamic theology (and philosophy) were enormously influential, forming part of the core of the curriculum at Islamic religious schools until the 19th century. Avicenna wrote a number of short treatises dealing with Islamic theology. These included treatises on the prophets (whom he viewed as "inspired philosophers"), and also on various scientific and philosophical interpretations of the Quran, such as how Quranic cosmology corresponds to his own philosophical system. In general these treatises linked his philosophical writings to Islamic religious ideas; for example, the body's afterlife. There are occasional brief hints and allusions in his longer works, however, that Avicenna considered philosophy as the only sensible way to distinguish real prophecy from illusion. He did not state this more clearly because of the political implications of such a theory, if prophecy could be questioned, and also because most of the time he was writing shorter works which concentrated on explaining his theories on philosophy and theology clearly, without digressing to consider epistemological matters which could only be properly considered by other philosophers. | [
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Later interpretations of Avicenna's philosophy split into three different schools; those (such as al-Tusi) who continued to apply his philosophy as a system to interpret later political events and scientific advances; those (such as al-Razi) who considered Avicenna's theological works in isolation from his wider philosophical concerns; and those (such as al-Ghazali) who selectively used parts of his philosophy to support their own attempts to gain greater spiritual insights through a variety of mystical means. It was the theological interpretation championed by those such as al-Razi which eventually came to predominate in the madrasahs. Avicenna memorized the Quran by the age of ten, and as an adult, he wrote five treatises commenting on suras from the Quran. One of these texts included the Proof of Prophecies, in which he comments on several Quranic verses and holds the Quran in high esteem. Avicenna argued that the Islamic prophets should be considered higher than philosophers. Avicenna is generally understood to have been aligned with the Sunni Hanafi school of thought. Avicenna studied Hanafi law, many of his notable teachers were Hanafi jurists, and he served under the Hanafi court of Ali ibn Mamun. Avicenna said at an early age that he remained "unconvinced" by Ismaili missionary attempts to convert him. Medieval historian Ẓahīr al-dīn al-Bayhaqī (d. 1169) also believed Avicenna to be a follower of the Brethren of Purity. Thought experiments
While he was imprisoned in the castle of Fardajan near Hamadhan, Avicenna wrote his famous "floating man"—literally falling man—a thought experiment to demonstrate human self-awareness and the substantiality and immateriality of the soul. | [
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Avicenna believed his "Floating Man" thought experiment demonstrated that the soul is a substance, and claimed humans cannot doubt their own consciousness, even in a situation that prevents all sensory data input. The thought experiment told its readers to imagine themselves created all at once while suspended in the air, isolated from all sensations, which includes no sensory contact with even their own bodies. He argued that, in this scenario, one would still have self-consciousness. Because it is conceivable that a person, suspended in air while cut off from sense experience, would still be capable of determining his own existence, the thought experiment points to the conclusions that the soul is a perfection, independent of the body, and an immaterial substance. The conceivability of this "Floating Man" indicates that the soul is perceived intellectually, which entails the soul's separateness from the body. Avicenna referred to the living human intelligence, particularly the active intellect, which he believed to be the hypostasis by which God communicates truth to the human mind and imparts order and intelligibility to nature. Following is an English translation of the argument:
However, Avicenna posited the brain as the place where reason interacts with sensation. Sensation prepares the soul to receive rational concepts from the universal Agent Intellect. The first knowledge of the flying person would be "I am," affirming his or her essence. That essence could not be the body, obviously, as the flying person has no sensation. | [
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Thus, the knowledge that "I am" is the core of a human being: the soul exists and is self-aware. Avicenna thus concluded that the idea of the self is not logically dependent on any physical thing, and that the soul should not be seen in relative terms, but as a primary given, a substance. The body is unnecessary; in relation to it, the soul is its perfection. In itself, the soul is an immaterial substance. The Canon of Medicine
Avicenna authored a five-volume medical encyclopedia: The Canon of Medicine (Al-Qanun fi't-Tibb). It was used as the standard medical textbook in the Islamic world and Europe up to the 18th century. The Canon still plays an important role in Unani medicine. Liber Primus Naturalium
Avicenna considered whether events like rare diseases or disorders have natural causes. He used the example of polydactyly to explain his perception that causal reasons exist for all medical events. This view of medical phenomena anticipated developments in the Enlightenment by seven centuries. The Book of Healing
Earth sciences
Avicenna wrote on Earth sciences such as geology in The Book of Healing. While discussing the formation of mountains, he explained:
Philosophy of science
In the Al-Burhan (On Demonstration) section of The Book of Healing, Avicenna discussed the philosophy of science and described an early scientific method of inquiry. He discussed Aristotle's Posterior Analytics and significantly diverged from it on several points. Avicenna discussed the issue of a proper methodology for scientific inquiry and the question of "How does one acquire the first principles of a science?" | [
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He asked how a scientist would arrive at "the initial axioms or hypotheses of a deductive science without inferring them from some more basic premises?" He explained that the ideal situation is when one grasps that a "relation holds between the terms, which would allow for absolute, universal certainty". Avicenna then added two further methods for arriving at the first principles: the ancient Aristotelian method of induction (istiqra), and the method of examination and experimentation (tajriba). Avicenna criticized Aristotelian induction, arguing that "it does not lead to the absolute, universal, and certain premises that it purports to provide." In its place, he developed a "method of experimentation as a means for scientific inquiry." Logic
An early formal system of temporal logic was studied by Avicenna. Although he did not develop a real theory of temporal propositions, he did study the relationship between temporalis and the implication. Avicenna's work was further developed by Najm al-Dīn al-Qazwīnī al-Kātibī and became the dominant system of Islamic logic until modern times. Avicennian logic also influenced several early European logicians such as Albertus Magnus and William of Ockham. Avicenna endorsed the law of non-contradiction proposed by Aristotle, that a fact could not be both true and false at the same time and in the same sense of the terminology used. He stated, "Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned." | [
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Physics
In mechanics, Avicenna, in The Book of Healing, developed a theory of motion, in which he made a distinction between the inclination (tendency to motion) and force of a projectile, and concluded that motion was a result of an inclination (mayl) transferred to the projectile by the thrower, and that projectile motion in a vacuum would not cease. He viewed inclination as a permanent force whose effect is dissipated by external forces such as air resistance. The theory of motion presented by Avicenna was probably influenced by the 6th-century Alexandrian scholar John Philoponus. Avicenna's is a less sophisticated variant of the theory of impetus developed by Buridan in the 14th century. It is unclear if Buridan was influenced by Avicenna, or by Philoponus directly. In optics, Avicenna was among those who argued that light had a speed, observing that "if the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite." He also provided a wrong explanation of the rainbow phenomenon. Carl Benjamin Boyer described Avicenna's ("Ibn Sīnā") theory on the rainbow as follows:
In 1253, a Latin text entitled Speculum Tripartitum stated the following regarding Avicenna's theory on heat:
Psychology
Avicenna's legacy in classical psychology is primarily embodied in the Kitab al-nafs parts of his Kitab al-shifa (The Book of Healing) and Kitab al-najat (The Book of Deliverance). These were known in Latin under the title De Anima (treatises "on the soul"). | [
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Notably, Avicenna develops what is called the Flying Man argument in the Psychology of The Cure I.1.7 as defence of the argument that the soul is without quantitative extension, which has an affinity with Descartes's cogito argument (or what phenomenology designates as a form of an "epoche"). Avicenna's psychology requires that connection between the body and soul be strong enough to ensure the soul's individuation, but weak enough to allow for its immortality. Avicenna grounds his psychology on physiology, which means his account of the soul is one that deals almost entirely with the natural science of the body and its abilities of perception. Thus, the philosopher's connection between the soul and body is explained almost entirely by his understanding of perception; in this way, bodily perception interrelates with the immaterial human intellect. In sense perception, the perceiver senses the form of the object; first, by perceiving features of the object by our external senses. This sensory information is supplied to the internal senses, which merge all the pieces into a whole, unified conscious experience. This process of perception and abstraction is the nexus of the soul and body, for the material body may only perceive material objects, while the immaterial soul may only receive the immaterial, universal forms. The way the soul and body interact in the final abstraction of the universal from the concrete particular is the key to their relationship and interaction, which takes place in the physical body. The soul completes the action of intellection by accepting forms that have been abstracted from matter. | [
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This process requires a concrete particular (material) to be abstracted into the universal intelligible (immaterial). The material and immaterial interact through the Active Intellect, which is a "divine light" containing the intelligible forms. The Active Intellect reveals the universals concealed in material objects much like the sun makes colour available to our eyes. Other contributions
Astronomy and astrology
Avicenna wrote an attack on astrology titled Resāla fī ebṭāl aḥkām al-nojūm, in which he cited passages from the Quran to dispute the power of astrology to foretell the future. He believed that each planet had some influence on the earth, but argued against astrologers being able to determine the exact effects. Avicenna's astronomical writings had some influence on later writers, although in general his work could be considered less developed than Alhazen or Al-Biruni. One important feature of his writing is that he considers mathematical astronomy as a separate discipline to astrology. He criticized Aristotle's view of the stars receiving their light from the Sun, stating that the stars are self-luminous, and believed that the planets are also self-luminous. He claimed to have observed Venus as a spot on the Sun. This is possible, as there was a transit on 24 May 1032, but Avicenna did not give the date of his observation, and modern scholars have questioned whether he could have observed the transit from his location at that time; he may have mistaken a sunspot for Venus. He used his transit observation to help establish that Venus was, at least sometimes, below the Sun in Ptolemaic cosmology, i.e. | [
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the sphere of Venus comes before the sphere of the Sun when moving out from the Earth in the prevailing geocentric model. He also wrote the Summary of the Almagest, (based on Ptolemy's Almagest), with an appended treatise "to bring that which is stated in the Almagest and what is understood from Natural Science into conformity". For example, Avicenna considers the motion of the solar apogee, which Ptolemy had taken to be fixed. Chemistry
Avicenna was first to derive the attar of flowers from distillation and used steam distillation to produce essential oils such as rose essence, which he used as aromatherapeutic treatments for heart conditions. Unlike al-Razi, Avicenna explicitly disputed the theory of the transmutation of substances commonly believed by alchemists:
Four works on alchemy attributed to Avicenna were translated into Latin as:
was the most influential, having influenced later medieval chemists and alchemists such as Vincent of Beauvais. However, Anawati argues (following Ruska) that the de Anima is a fake by a Spanish author. Similarly the Declaratio is believed not to be actually by Avicenna. The third work (The Book of Minerals) is agreed to be Avicenna's writing, adapted from the Kitab al-Shifa (Book of the Remedy). Avicenna classified minerals into stones, fusible substances, sulfurs and salts, building on the ideas of Aristotle and Jabir. The epistola de Re recta is somewhat less sceptical of alchemy; Anawati argues that it is by Avicenna, but written earlier in his career when he had not yet firmly decided that transmutation was impossible. Poetry
Almost half of Avicenna's works are versified. | [
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His poems appear in both Arabic and Persian. As an example, Edward Granville Browne claims that the following Persian verses are incorrectly attributed to Omar Khayyám, and were originally written by Ibn Sīnā:
Legacy
Classical Islamic civilization
Robert Wisnovsky, a scholar of Avicenna attached to the McGill University, says that "Avicenna was the central figure in the long history of the rational sciences in Islam, particularly in the fields of metaphysics, logic and medicine" but that his works didn't only have an influence in these "secular" fields of knowledge alone, as "these works, or portions of them, were read, taught, copied, commented upon, quoted, paraphrased and cited by thousands of post-Avicennian scholars—not only philosophers, logicians, physicians and specialists in the mathematical or exact sciences, but also by those who specialized in the disciplines of ʿilm al-kalām (rational theology, but understood to include natural philosophy, epistemology and philosophy of mind) and usūl al-fiqh (jurisprudence, but understood to include philosophy of law, dialectic, and philosophy of language)." Middle Ages and Renaissance
As early as the 14th century when Dante Alighieri depicted him in Limbo alongside the virtuous non-Christian thinkers in his Divine Comedy such as Virgil, Averroes, Homer, Horace, Ovid, Lucan, Socrates, Plato and Saladin. Avicenna has been recognized by both East and West, as one of the great figures in intellectual history. | [
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George Sarton, the author of The History of Science, described Avicenna as "one of the greatest thinkers and medical scholars in history" and called him "the most famous scientist of Islam and one of the most famous of all races, places, and times". He was one of the Islamic world's leading writers in the field of medicine. Along with Rhazes, Abulcasis, Ibn al-Nafis and al-Ibadi, Avicenna is considered an important compiler of early Muslim medicine. He is remembered in the Western history of medicine as a major historical figure who made important contributions to medicine and the European Renaissance. His medical texts were unusual in that where controversy existed between Galen and Aristotle's views on medical matters (such as anatomy), he preferred to side with Aristotle, where necessary updating Aristotle's position to take into account post-Aristotelian advances in anatomical knowledge. Aristotle's dominant intellectual influence among medieval European scholars meant that Avicenna's linking of Galen's medical writings with Aristotle's philosophical writings in the Canon of Medicine (along with its comprehensive and logical organisation of knowledge) significantly increased Avicenna's importance in medieval Europe in comparison to other Islamic writers on medicine. His influence following translation of the Canon was such that from the early fourteenth to the mid-sixteenth centuries he was ranked with Hippocrates and Galen as one of the acknowledged authorities, ("prince of physicians"). Modern reception
In present-day Iran, Afghanistan and Tajikistan, he is considered a national icon, and is often regarded as among the greatest Persians. A monument was erected outside the Bukhara museum. | [
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The Avicenna Mausoleum and Museum in Hamadan was built in 1952. Bu-Ali Sina University in Hamadan (Iran), the biotechnology Avicenna Research Institute in Tehran (Iran), the ibn Sīnā Tajik State Medical University in Dushanbe, Ibn Sina Academy of Medieval Medicine and Sciences at Aligarh, India, Avicenna School in Karachi and Avicenna Medical College in Lahore, Pakistan, Ibn Sina Balkh Medical School in his native province of Balkh in Afghanistan, Ibni Sina Faculty Of Medicine of Ankara University Ankara, Turkey, the main classroom building (the Avicenna Building) of the Sharif University of Technology, and Ibn Sina Integrated School in Marawi City (Philippines) are all named in his honour. His portrait hangs in the Hall of the Avicenna Faculty of Medicine in the University of Paris. There is a crater on the Moon named Avicenna and a mangrove genus. In 1980, the Soviet Union, which then ruled his birthplace Bukhara, celebrated the thousandth anniversary of Avicenna's birth by circulating various commemorative stamps with artistic illustrations, and by erecting a bust of Avicenna based on anthropological research by Soviet scholars. Near his birthplace in Qishlak Afshona, some north of Bukhara, a training college for medical staff has been named for him. On the grounds is a museum dedicated to his life, times and work. The Avicenna Prize, established in 2003, is awarded every two years by UNESCO and rewards individuals and groups for their achievements in the field of ethics in science. | [
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The aim of the award is to promote ethical reflection on issues raised by advances in science and technology, and to raise global awareness of the importance of ethics in science. The Avicenna Directories (2008–15; now the World Directory of Medical Schools) list universities and schools where doctors, public health practitioners, pharmacists and others, are educated. The original project team stated "Why Avicenna? Avicenna ... was ... noted for his synthesis of knowledge from both east and west. He has had a lasting influence on the development of medicine and health sciences. The use of Avicenna's name symbolises the worldwide partnership that is needed for the promotion of health services of high quality." In June 2009, Iran donated a "Persian Scholars Pavilion" to United Nations Office in Vienna which is placed in the central Memorial Plaza of the Vienna International Center. The "Persian Scholars Pavilion" at United Nations in Vienna, Austria is featuring the statues of four prominent Iranian figures. Highlighting the Iranian architectural features, the pavilion is adorned with Persian art forms and includes the statues of renowned Iranian scientists Avicenna, Al-Biruni, Zakariya Razi (Rhazes) and Omar Khayyam. The 1982 Soviet film Youth of Genius () by recounts Avicenna's younger years. The film is set in Bukhara at the turn of the millennium. In Louis L'Amour's 1985 historical novel The Walking Drum, Kerbouchard studies and discusses Avicenna's The Canon of Medicine. | [
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In his book The Physician (1988) Noah Gordon tells the story of a young English medical apprentice who disguises himself as a Jew to travel from England to Persia and learn from Avicenna, the great master of his time. The novel was adapted into a feature film, The Physician, in 2013. Avicenna was played by Ben Kingsley. List of works
The treatises of Avicenna influenced later Muslim thinkers in many areas including theology, philology, mathematics, astronomy, physics and music. His works numbered almost 450 volumes on a wide range of subjects, of which around 240 have survived. In particular, 150 volumes of his surviving works concentrate on philosophy and 40 of them concentrate on medicine. His most famous works are The Book of Healing, and The Canon of Medicine. Avicenna wrote at least one treatise on alchemy, but several others have been falsely attributed to him. His Logic, Metaphysics, Physics, and De Caelo, are treatises giving a synoptic view of Aristotelian doctrine, though Metaphysics demonstrates a significant departure from the brand of Neoplatonism known as Aristotelianism in Avicenna's world; Arabic philosophers have hinted at the idea that Avicenna was attempting to "re-Aristotelianise" Muslim philosophy in its entirety, unlike his predecessors, who accepted the conflation of Platonic, Aristotelian, Neo- and Middle-Platonic works transmitted into the Muslim world. The Logic and Metaphysics have been extensively reprinted, the latter, e.g., at Venice in 1493, 1495 and 1546. | [
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Some of his shorter essays on medicine, logic, etc., take a poetical form (the poem on logic was published by Schmoelders in 1836). Two encyclopedic treatises, dealing with philosophy, are often mentioned. The larger, Al-Shifa' (Sanatio), exists nearly complete in manuscript in the Bodleian Library and elsewhere; part of it on the De Anima appeared at Pavia (1490) as the Liber Sextus Naturalium, and the long account of Avicenna's philosophy given by Muhammad al-Shahrastani seems to be mainly an analysis, and in many places a reproduction, of the Al-Shifa'. A shorter form of the work is known as the An-najat (Liberatio). The Latin editions of part of these works have been modified by the corrections which the monastic editors confess that they applied. There is also a (hikmat-al-mashriqqiyya, in Latin Philosophia Orientalis), mentioned by Roger Bacon, the majority of which is lost in antiquity, which according to Averroes was pantheistic in tone. Avicenna's works further include:
Sirat al-shaykh al-ra'is (The Life of Avicenna), ed. and trans. WE. Gohlman, Albany, NY: State University of New York Press, 1974. (The only critical edition of Avicenna's autobiography, supplemented with material from a biography by his student Abu 'Ubayd al-Juzjani. A more recent translation of the Autobiography appears in D. Gutas, Avicenna and the Aristotelian Tradition: Introduction to Reading Avicenna's Philosophical Works, Leiden: Brill, 1988; second edition 2014.) Al-isharat wa al-tanbihat (Remarks and Admonitions), ed. | [
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S. Dunya, Cairo, 1960; parts translated by S.C. Inati, Remarks and Admonitions, Part One: Logic, Toronto, Ont. : Pontifical Institute for Mediaeval Studies, 1984, and Ibn Sina and Mysticism, Remarks and Admonitions: Part 4, London: Kegan Paul International, 1996. Al-Qanun fi'l-tibb (The Canon of Medicine), ed. I. a-Qashsh, Cairo, 1987. (Encyclopedia of medicine.) manuscript, Latin translation, Flores Avicenne, Michael de Capella, 1508, Modern text. Ahmed Shawkat Al-Shatti, Jibran Jabbur. Risalah fi sirr al-qadar (Essay on the Secret of Destiny), trans. G. Hourani in Reason and Tradition in Islamic Ethics, Cambridge: Cambridge University Press, 1985. Danishnama-i 'ala'i (The Book of Scientific Knowledge), ed. and trans. P. Morewedge, The Metaphysics of Avicenna, London: Routledge and Kegan Paul, 1973. Kitab al-Shifa''' (The Book of Healing). (Avicenna's major work on philosophy. He probably began to compose al-Shifa' in 1014, and completed it in 1020.) Critical editions of the Arabic text have been published in Cairo, 1952–83, originally under the supervision of I. Madkour. Kitab al-Najat (The Book of Salvation), trans. F. Rahman, Avicenna's Psychology: An English Translation of Kitab al-Najat, Book II, Chapter VI with Historical-philosophical Notes and Textual Improvements on the Cairo Edition, Oxford: Oxford University Press, 1952. (The psychology of al-Shifa'.) | [
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(Digital version of the Arabic text)
Risala fi'l-Ishq (A Treatise on Love). Translated by Emil L. Fackenheim. Persian works
Avicenna's most important Persian work is the Danishnama-i 'Alai (, "the Book of Knowledge for [Prince] 'Ala ad-Daulah"). Avicenna created new scientific vocabulary that had not previously existed in Persian. The Danishnama covers such topics as logic, metaphysics, music theory and other sciences of his time. It has been translated into English by Parwiz Morewedge in 1977. The book is also important in respect to Persian scientific works.Andar Danesh-e Rag (, "On the Science of the Pulse") contains nine chapters on the science of the pulse and is a condensed synopsis. Persian poetry from Avicenna is recorded in various manuscripts and later anthologies such as Nozhat al-Majales. | [
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See also
Al-Qumri (possibly Avicenna's teacher)
Abdol Hamid Khosro Shahi (Iranian theologian)
Mummia (Persian medicine)
Namesakes of Ibn Sina
Ibn Sina Academy of Medieval Medicine and Sciences in Aligarh
Avicenna Bay in Antarctica
Avicenna (crater) on the far side of the Moon
Avicenna Cultural and Scientific Foundation
Avicenne Hospital in Paris, France
Avicenna International College in Budapest, Hungary
Avicenna Mausoleum (complex dedicated to Avicenna) in Hamadan, Iran
Avicenna Research Institute in Tehran, Iran
Avicenna Tajik State Medical University in Dushanbe, Tajikistan
Bu-Ali Sina University in Hamedan, Iran
Ibn Sina Peak – named after the Scientist, on the Kyrgyzstan–Tajikistan border
Ibn Sina Foundation in Houston, Texas
Ibn Sina Hospital, Baghdad, Iraq
Ibn Sina Hospital, Istanbul, Turkey
Ibn Sina Medical College Hospital, Dhaka, Bangladesh
Ibn Sina University Hospital of Rabat-Salé at Mohammed V University in Rabat, Morocco
Ibne Sina Hospital, Multan, Punjab, Pakistan
International Ibn Sina Clinic, Dushanbe, Tajikistan
Philosophy
Eastern philosophy
Iranian philosophy
Islamic philosophy
Contemporary Islamic philosophy
Science in the medieval Islamic world
List of scientists in medieval Islamic world
Sufi philosophy
Science and technology in Iran
Ancient Iranian medicine
List of pre-modern Iranian scientists and scholars
References
Sources cited
Further reading
Encyclopedic articles
(PDF version)
Avicenna entry by Sajjad H. Rizvi in the Internet Encyclopedia of Philosophy Primary literature
For an old list of other extant works, C. Brockelmann's Geschichte der arabischen Litteratur (Weimar 1898), vol. i. pp. 452–458. (XV. | [
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W.; G. W. T.)
For a current list of his works see A. Bertolacci (2006) and D. Gutas (2014) in the section "Philosophy". Avicenne: Réfutation de l'astrologie. Edition et traduction du texte arabe, introduction, notes et lexique par Yahya Michot. Préface d'Elizabeth Teissier (Beirut-Paris: Albouraq, 2006) . William E. Gohlam (ed. ), The Life of Ibn Sina. A Critical Edition and Annotated Translation, Albany, State of New York University Press, 1974. For Ibn Sina's life, see Ibn Khallikan's Biographical Dictionary, translated by de Slane (1842); F. Wüstenfeld's Geschichte der arabischen Aerzte und Naturforscher (Göttingen, 1840). Madelung, Wilferd and Toby Mayer (ed. and tr. ), Struggling with the Philosopher: A Refutation of Avicenna's Metaphysics. A New Arabic Edition and English Translation of Shahrastani's Kitab al-Musara'a. Secondary literature
This is, on the whole, an informed and good account of the life and accomplishments of one of the greatest influences on the development of thought both Eastern and Western. ... It is not as philosophically thorough as the works of D. Saliba, A.M. Goichon, or L. Gardet, but it is probably the best essay in English on this important thinker of the Middle Ages. (Julius R. Weinberg, The Philosophical Review, Vol. 69, No. 2, Apr. 1960, pp. | [
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255–259)
This is a distinguished work which stands out from, and above, many of the books and articles which have been written in this century on Avicenna (Ibn Sīnā) (980–1037). It has two main features on which its distinction as a major contribution to Avicennan studies may be said to rest: the first is its clarity and readability; the second is the comparative approach adopted by the author. ... (Ian Richard Netton, Journal of the Royal Asiatic Society, Third Series, Vol. 4, No. 2, July 1994, pp. 263–264)
Y.T. Langermann (ed. ), Avicenna and his Legacy. A Golden Age of Science and Philosophy, Brepols Publishers, 2010,
For a new understanding of his early career, based on a newly discovered text, see also: Michot, Yahya, Ibn Sînâ: Lettre au vizir Abû Sa'd. Editio princeps d'après le manuscrit de Bursa, traduction de l'arabe, introduction, notes et lexique (Beirut-Paris: Albouraq, 2000) . This German publication is both one of the most comprehensive general introductions to the life and works of the philosopher and physician Avicenna (Ibn Sīnā, d. 1037) and an extensive and careful survey of his contribution to the history of science. Its author is a renowned expert in Greek and Arabic medicine who has paid considerable attention to Avicenna in his recent studies. ... (Amos Bertolacci, Isis, Vol. 96, No. 4, December 2005, p. 649)
Shaikh al Rais Ibn Sina (Special number) 1958–59, Ed. | [
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] |
Hakim Syed Zillur Rahman, Tibbia College Magazine, Aligarh Muslim University, Aligarh, India. Medicine
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External links
Avicenna (Ibn-Sina) on the Subject and the Object of Metaphysics with a list of translations of the logical and philosophical works and an annotated bibliography
980s births
1037 deaths
10th-century Iranian people
11th-century astronomers
11th-century Persian writers
11th-century philosophers
Alchemists of medieval Islam
Aristotelian philosophers
Burials in Iran
Buyid viziers
Classical humanists
Critics of atheism
Cultural critics
Epistemologists
Founders of philosophical traditions
Iranian music theorists
Islamic philosophers
Transoxanian Islamic scholars
Logicians
People from Bukhara Region
Pharmacologists of medieval Iran
Medieval Persian poets
Medieval Persian writers
Metaphysicians
Moral philosophers
Musical theorists of medieval Islam
Ontologists
People from Khorasan
Persian physicists
Philosophers of ethics and morality
Philosophers of logic
Philosophers of mind
Philosophers of psychology
Philosophers of religion
Philosophers of science
Physicians of medieval Islam
Samanid scholars
Unani medicine
Medieval Persian philosophers
Iranian logicians
Iranian ethicists
People who memorized the Quran
Samanid officials | [
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Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C. ), though analysis as a formal concept is a relatively recent development. The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses. As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name). Applications
Science
The field of chemistry uses analysis in three ways: to identify the components of a particular chemical compound (qualitative analysis), to identify the proportions of components in a mixture (quantitative analysis), and to break down chemical processes and examine chemical reactions between elements of matter. For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples. A matrix can have a considerable effect on the way a chemical analysis is conducted and the quality of its results. Analysis can be done manually or with a device. | [
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Types of Analysis:
A) Qualitative Analysis: It is concerned with which components are in a given sample or compound. Example: Precipitation reaction
B) Quantitative Analysis: It is to determine the quantity of individual component present in a given sample or compound. Example: To find concentration by uv-spectrophotometer. Isotopes
Chemists can use isotope analysis to assist analysts with issues in anthropology, archeology, food chemistry, forensics, geology, and a host of other questions of physical science. Analysts can discern the origins of natural and man-made isotopes in the study of environmental radioactivity. Business
Financial statement analysis – the analysis of the accounts and the economic prospects of a firm
Fundamental analysis – a stock valuation method that uses financial analysis
Gap analysis – involves the comparison of actual performance with potential or desired performance of an organization
Business analysis – involves identifying the needs and determining the solutions to business problems
Price analysis – involves the breakdown of a price to a unit figure
Market analysis – consists of suppliers and customers, and price is determined by the interaction of supply and demand
Technical analysis – the study of price action in securities markets in order to forecast future prices
Opportunity analysis – consists of customers trends within the industry, customer demand and experience determine purchasing behavior
Computer science
Requirements analysis – encompasses those tasks that go into determining the needs or conditions to meet for a new or altered product, taking account of the possibly conflicting requirements of the various stakeholders, such as beneficiaries or users. | [
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Competitive analysis (online algorithm) – shows how online algorithms perform and demonstrates the power of randomization in algorithms
Lexical analysis – the process of processing an input sequence of characters and producing as output a sequence of symbols
Object-oriented analysis and design – à la Booch
Program analysis (computer science) – the process of automatically analysing the behavior of computer programs
Semantic analysis (computer science) – a pass by a compiler that adds semantical information to the parse tree and performs certain checks
Static code analysis – the analysis of computer software that is performed without actually executing programs built from that
Structured systems analysis and design methodology – à la Yourdon
Syntax analysis – a process in compilers that recognizes the structure of programming languages, also known as parsing
Worst-case execution time – determines the longest time that a piece of software can take to run
Economics
Agroecosystem analysis
Input–output model if applied to a region, is called Regional Impact Multiplier System
Engineering
Analysts in the field of engineering look at requirements, structures, mechanisms, systems and dimensions. Electrical engineers analyse systems in electronics. Life cycles and system failures are broken down and studied by engineers. It is also looking at different factors incorporated within the design. Intelligence
The field of intelligence employs analysts to break down and understand a wide array of questions. Intelligence agencies may use heuristics, inductive and deductive reasoning, social network analysis, dynamic network analysis, link analysis, and brainstorming to sort through problems they face. Military intelligence may explore issues through the use of game theory, Red Teaming, and wargaming. | [
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Signals intelligence applies cryptanalysis and frequency analysis to break codes and ciphers. Business intelligence applies theories of competitive intelligence analysis and competitor analysis to resolve questions in the marketplace. Law enforcement intelligence applies a number of theories in crime analysis. Linguistics
Linguistics explores individual languages and language in general. It breaks language down and analyses its component parts: theory, sounds and their meaning, utterance usage, word origins, the history of words, the meaning of words and word combinations, sentence construction, basic construction beyond the sentence level, stylistics, and conversation. It examines the above using statistics and modeling, and semantics. It analyses language in context of anthropology, biology, evolution, geography, history, neurology, psychology, and sociology. It also takes the applied approach, looking at individual language development and clinical issues. Literature
Literary criticism is the analysis of literature. The focus can be as diverse as the analysis of Homer or Freud. While not all literary-critical methods are primarily analytical in nature, the main approach to the teaching of literature in the west since the mid-twentieth century, literary formal analysis or close reading, is. This method, rooted in the academic movement labelled The New Criticism, approaches texts – chiefly short poems such as sonnets, which by virtue of their small size and significant complexity lend themselves well to this type of analysis – as units of discourse that can be understood in themselves, without reference to biographical or historical frameworks. | [
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This method of analysis breaks up the text linguistically in a study of prosody (the formal analysis of meter) and phonic effects such as alliteration and rhyme, and cognitively in examination of the interplay of syntactic structures, figurative language, and other elements of the poem that work to produce its larger effects. Mathematics
Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors. Florian Cajori explains in A History of Mathematics (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:
The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in [appended to] Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it." The analytic method is not conclusive, unless all operations involved in it are known to be reversible. | [
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To remove all doubt, the Greeks, as a rule, added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions. James Gow uses a similar argument as Cajori, with the following clarification, in his A Short History of Greek Mathematics (1884):
The synthetic proof proceeds by shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded. The Greeks distinguished theoretic from problematic analysis. A theoretic analysis is of the following kind. To prove that A is B, assume first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be known a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible, then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem. Problematic analysis is applied in all cases where it is proposed to construct a figure which is assumed to satisfy a given condition. The problem is then converted into some theorem which is involved in the condition and which is proved synthetically, and the steps of this synthetic proof taken backwards are a synthetic solution of the problem. | [
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Music
Musical analysis – a process attempting to answer the question "How does this music work?" Musical Analysis is a study of how the composers use the notes together to compose music. Those studying music will find differences with each composer's musical analysis, which differs depending on the culture and history of music studied. An analysis of music is meant to simplify the music for you. Schenkerian analysis
Schenkerian analysis is a collection of music analysis that focuses on the production of the graphic representation. This includes both analytical procedure as well as the notational style. Simply put, it analyzes tonal music which includes all chords and tones within a composition. Philosophy
Philosophical analysis – a general term for the techniques used by philosophers
Philosophical analysis refers to the clarification and composition of words put together and the entailed meaning behind them. Philosophical analysis dives deeper into the meaning of words and seeks to clarify that meaning by contrasting the various definitions. It is the study of reality, justification of claims, and the analysis of various concepts. Branches of philosophy include logic, justification, metaphysics, values and ethics. If questions can be answered empirically, meaning it can be answered by using the senses, then it is not considered philosophical. Non-philosophical questions also include events that happened in the past, or questions science or mathematics can answer. Analysis is the name of a prominent journal in philosophy. Psychotherapy
Psychoanalysis – seeks to elucidate connections among unconscious components of patients' mental processes
Transactional analysis
Transactional analysis is used by therapists to try to gain a better understanding of the unconscious. | [
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It focuses on understanding and intervening human behavior. Policy
Policy analysis – The use of statistical data to predict the effects of policy decisions made by governments and agencies
Policy analysis includes a systematic process to find the most efficient and effective option to address the current situation. Qualitative analysis – The use of anecdotal evidence to predict the effects of policy decisions or, more generally, influence policy decisions
Signal processing
Finite element analysis – a computer simulation technique used in engineering analysis
Independent component analysis
Link quality analysis – the analysis of signal quality
Path quality analysis
Fourier analysis
Statistics
In statistics, the term analysis may refer to any method used
for data analysis. | [
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Among the many such methods, some are:
Analysis of variance (ANOVA) – a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts
Boolean analysis – a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis
Cluster analysis – techniques for finding groups (called clusters), based on some measure of proximity or similarity
Factor analysis – a method to construct models describing a data set of observed variables in terms of a smaller set of unobserved variables (called factors)
Meta-analysis – combines the results of several studies that address a set of related research hypotheses
Multivariate analysis – analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis
Principal component analysis – transformation of a sample of correlated variables into uncorrelated variables (called principal components), mostly used in exploratory data analysis
Regression analysis – techniques for analysing the relationships between several predictive variables and one or more outcomes in the data
Scale analysis (statistics) – methods to analyse survey data by scoring responses on a numeric scale
Sensitivity analysis – the study of how the variation in the output of a model depends on variations in the inputs
Sequential analysis – evaluation of sampled data as it is collected, until the criterion of a stopping rule is met
Spatial analysis – the study of entities using geometric or geographic properties
Time-series analysis – methods that attempt to understand a sequence of data points spaced apart at uniform time intervals
Other
Aura analysis – a technique in which supporters of the method claim that the body's aura, or energy field is analysed
Bowling analysis – Analysis of the performance of cricket players
Lithic analysis – the analysis of stone tools using basic scientific techniques
Lithic analysis is most often used by archeologists in determining which types of tools were used at a given time period pertaining to current artifacts discovered. | [
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Protocol analysis – a means for extracting persons' thoughts while they are performing a task
See also
Formal analysis
Metabolism in biology
Methodology
Scientific method
References
External links
Abstraction
Critical thinking skills
Emergence
Empiricism
Epistemological theories
Intelligence
Mathematical modeling
Metaphysics of mind
Methodology
Ontology
Philosophy of logic
Rationalism
Reasoning
Research methods
Scientific method
Theory of mind | [
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Augustin-Jean Fresnel ( ; ; or ; ; 10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric (purely refractive) stepped lens, first proposed by Count Buffon and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors. By expressing Huygens's principle of secondary waves and Young's principle of interference in quantitative terms, and supposing that simple colors consist of sinusoidal waves, Fresnel gave the first satisfactory explanation of diffraction by straight edges, including the first satisfactory wave-based explanation of rectilinear propagation. Part of his argument was a proof that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. By further supposing that light waves are purely transverse, Fresnel explained the nature of polarization, the mechanism of chromatic polarization, and the transmission and reflection coefficients at the interface between two transparent isotropic media. Then, by generalizing the direction-speed-polarization relation for calcite, he accounted for the directions and polarizations of the refracted rays in doubly-refractive crystals of the biaxial class (those for which Huygens's secondary wavefronts are not axisymmetric). | [
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The period between the first publication of his pure-transverse-wave hypothesis, and the submission of his first correct solution to the biaxial problem, was less than a year. Later, he coined the terms linear polarization, circular polarization, and elliptical polarization, explained how optical rotation could be understood as a difference in propagation speeds for the two directions of circular polarization, and (by allowing the reflection coefficient to be complex) accounted for the change in polarization due to total internal reflection, as exploited in the Fresnel rhomb. Defenders of the established corpuscular theory could not match his quantitative explanations of so many phenomena on so few assumptions. Fresnel had a lifelong battle with tuberculosis, to which he succumbed at the age of 39. Although he did not become a public celebrity in his lifetime, he lived just long enough to receive due recognition from his peers, including (on his deathbed) the Rumford Medal of the Royal Society of London, and his name is ubiquitous in the modern terminology of optics and waves. After the wave theory of light was subsumed by Maxwell's electromagnetic theory in the 1860s, some attention was diverted from the magnitude of Fresnel's contribution. In the period between Fresnel's unification of physical optics and Maxwell's wider unification, a contemporary authority, Humphrey Lloyd, described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the domain of physical science, Newton's system of the universe alone excepted." | [
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Early life
Family
Augustin-Jean Fresnel (also called Augustin Jean or simply Augustin), born in Broglie, Normandy, on 10 May 1788, was the second of four sons of the architect Jacques Fresnel (1755–1805) and his wife Augustine, née Mérimée (1755–1833). In 1790, following the Revolution, Broglie became part of the département of Eure. The family moved twice – in 1789/90 to Cherbourg, and in 1794 to Jacques's home town of Mathieu, where Madame Fresnel would spend 25 years as a widow, outliving two of her sons. The first son, Louis (1786–1809), was admitted to the École Polytechnique, became a lieutenant in the artillery, and was killed in action at Jaca, Spain, the day before his 23rd birthday. The third, Léonor (1790–1869), followed Augustin into civil engineering, succeeded him as secretary of the Lighthouse Commission, and helped to edit his collected works. The fourth, Fulgence Fresnel (1795–1855), became a noted linguist, diplomat, and orientalist, and occasionally assisted Augustin with negotiations. Fulgence died in Bagdad in 1855 having led a mission to explore Babylon. Léonor apparently was the only one of the four who married. Their mother's younger brother, Jean François "Léonor" Mérimée (1757–1836), father of the writer Prosper Mérimée (1803–1870), was a paint artist who turned his attention to the chemistry of painting. | [
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He became the Permanent Secretary of the École des Beaux-Arts and (until 1814) a professor at the École Polytechnique, and was the initial point of contact between Augustin and the leading optical physicists of the day . Education
The Fresnel brothers were initially home-schooled by their mother. The sickly Augustin was considered the slow one, not inclined to memorization; but the popular story that he hardly began to read until the age of eight is disputed. At the age of nine or ten he was undistinguished except for his ability to turn tree-branches into toy bows and guns that worked far too well, earning himself the title l'homme de génie (the man of genius) from his accomplices, and a united crackdown from their elders. In 1801, Augustin was sent to the École Centrale at Caen, as company for Louis. But Augustin lifted his performance: in late 1804 he was accepted into the École Polytechnique, being placed 17th in the entrance examination. As the detailed records of the École Polytechnique begin in 1808, we know little of Augustin's time there, except that he made few if any friends and – in spite of continuing poor health – excelled in drawing and geometry: in his first year he took a prize for his solution to a geometry problem posed by Adrien-Marie Legendre. | [
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Graduating in 1806, he then enrolled at the École Nationale des Ponts et Chaussées (National School of Bridges and Roads, also known as "ENPC" or "École des Ponts"), from which he graduated in 1809, entering the service of the Corps des Ponts et Chaussées as an ingénieur ordinaire aspirant (ordinary engineer in training). Directly or indirectly, he was to remain in the employment of the "Corps des Ponts" for the rest of his life. Religious formation
Augustin Fresnel's parents were Roman Catholics of the Jansenist sect, characterized by an extreme Augustinian view of original sin. Religion took first place in the boys' home-schooling. In 1802, Mme Fresnel reportedly said:
Augustin remained a Jansenist. He indeed regarded his intellectual talents as gifts from God, and considered it his duty to use them for the benefit of others. Plagued by poor health, and determined to do his duty before death thwarted him, he shunned pleasures and worked to the point of exhaustion. According to his fellow engineer Alphonse Duleau, who helped to nurse him through his final illness, Fresnel saw the study of nature as part of the study of the power and goodness of God. He placed virtue above science and genius. Yet in his last days he needed "strength of soul," not against death alone, but against "the interruption of discoveries… of which he hoped to derive useful applications." | [
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Jansenism is considered heretical by the Roman Catholic Church , and this may be part of the explanation why Fresnel, in spite of his scientific achievements and his royalist credentials, never gained a permanent academic teaching post; his only teaching appointment was at the Athénée in the winter of 1819–20. Be that as it may, the brief article on Fresnel in the old Catholic Encyclopedia does not mention his Jansenism, but describes him as "a deeply religious man and remarkable for his keen sense of duty." Engineering assignments
Fresnel was initially posted to the western département of Vendée. There, in 1811, he anticipated what became known as the Solvay process for producing soda ash, except that recycling of the ammonia was not considered. That difference may explain why leading chemists, who learned of his discovery through his uncle Léonor, eventually thought it uneconomic. About 1812, Fresnel was sent to Nyons, in the southern département of Drôme, to assist with the imperial highway that was to connect Spain and Italy. It is from Nyons that we have the first evidence of his interest in optics. On 15 May 1814, while work was slack due to Napoleon's defeat, Fresnel wrote a "P.S." to his brother Léonor, saying in part:
As late as 28 December he was still waiting for information, but he had received Biot's memoir by 10 February 1815. (The Institut de France had taken over the functions of the French Académie des Sciences and other académies in 1795. | [
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In 1816 the Académie des Sciences regained its name and autonomy, but remained part of the institute.) In March 1815, perceiving Napoleon's return from Elba as "an attack on civilization", Fresnel departed without leave, hastened to Toulouse and offered his services to the royalist resistance, but soon found himself on the sick list. Returning to Nyons in defeat, he was threatened and had his windows broken. During the Hundred Days he was placed on suspension, which he was eventually allowed to spend at his mother's house in Mathieu. There he used his enforced leisure to begin his optical experiments. Contributions to physical optics
Historical context: From Newton to Biot
The appreciation of Fresnel's reconstruction of physical optics might be assisted by an overview of the fragmented state in which he found the subject. In this subsection, optical phenomena that were unexplained or whose explanations were disputed are named in bold type. The corpuscular theory of light, favored by Isaac Newton and accepted by nearly all of Fresnel's seniors, easily explained rectilinear propagation: the corpuscles obviously moved very fast, so that their paths were very nearly straight. The wave theory, as developed by Christiaan Huygens in his Treatise on Light (1690), explained rectilinear propagation on the assumption that each point crossed by a traveling wavefront becomes the source of a secondary wavefront. Given the initial position of a traveling wavefront, any later position (according to Huygens) was the common tangent surface (envelope) of the secondary wavefronts emitted from the earlier position. | [
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As the extent of the common tangent was limited by the extent of the initial wavefront, the repeated application of Huygens's construction to a plane wavefront of limited extent (in a uniform medium) gave a straight, parallel beam. While this construction indeed predicted rectilinear propagation, it was difficult to reconcile with the common observation that wavefronts on the surface of water can bend around obstructions, and with the similar behavior of sound waves – causing Newton to maintain, to the end of his life, that if light consisted of waves it would "bend and spread every way" into the shadows. Huygens's theory neatly explained the law of ordinary reflection and the law of ordinary refraction ("Snell's law"), provided that the secondary waves traveled slower in denser media (those of higher refractive index). The corpuscular theory, with the hypothesis that the corpuscles were subject to forces acting perpendicular to surfaces, explained the same laws equally well, albeit with the implication that light traveled faster in denser media; that implication was wrong, but could not be directly disproven with the technology of Newton's time or even Fresnel's time . Similarly inconclusive was stellar aberration—that is, the apparent change in the position of a star due to the velocity of the earth across the line of sight (not to be confused with stellar parallax, which is due to the displacement of the earth across the line of sight). Identified by James Bradley in 1728, stellar aberration was widely taken as confirmation of the corpuscular theory. | [
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But it was equally compatible with the wave theory, as Euler noted in 1746 – tacitly assuming that the aether (the supposed wave-bearing medium) near the earth was not disturbed by the motion of the earth. The outstanding strength of Huygens's theory was his explanation of the birefringence (double refraction) of "Iceland crystal" (transparent calcite), on the assumption that the secondary waves are spherical for the ordinary refraction (which satisfies Snell's law) and spheroidal for the extraordinary refraction (which does not). In general, Huygens's common-tangent construction implies that rays are paths of least time between successive positions of the wavefront, in accordance with Fermat's principle. In the special case of isotropic media, the secondary wavefronts must be spherical, and Huygens's construction then implies that the rays are perpendicular to the wavefront; indeed, the law of ordinary refraction can be separately derived from that premise, as Ignace-Gaston Pardies did before Huygens. Although Newton rejected the wave theory, he noticed its potential to explain colors, including the colors of "thin plates" (e.g., "Newton's rings", and the colors of skylight reflected in soap bubbles), on the assumption that light consists of periodic waves, with the lowest frequencies (longest wavelengths) at the red end of the spectrum, and the highest frequencies (shortest wavelengths) at the violet end. | [
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In 1672 he published a heavy hint to that effect, but contemporary supporters of the wave theory failed to act on it: Robert Hooke treated light as a periodic sequence of pulses but did not use frequency as the criterion of color, while Huygens treated the waves as individual pulses without any periodicity; and Pardies died young in 1673. Newton himself tried to explain colors of thin plates using the corpuscular theory, by supposing that his corpuscles had the wavelike property of alternating between "fits of easy transmission" and "fits of easy reflection", the distance between like "fits" depending on the color and the medium and, awkwardly, on the angle of refraction or reflection into that medium. More awkwardly still, this theory required thin plates to reflect only at the back surface, although thick plates manifestly reflected also at the front surface. It was not until 1801 that Thomas Young, in the Bakerian Lecture for that year, cited Newton's hint, and accounted for the colors of a thin plate as the combined effect of the front and back reflections, which reinforce or cancel each other according to the wavelength and the thickness. Young similarly explained the colors of "striated surfaces" (e.g., gratings) as the wavelength-dependent reinforcement or cancellation of reflections from adjacent lines. He described this reinforcement or cancellation as interference. Neither Newton nor Huygens satisfactorily explained diffraction—the blurring and fringing of shadows where, according to rectilinear propagation, they ought to be sharp. | [
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Newton, who called diffraction "inflexion", supposed that rays of light passing close to obstacles were bent ("inflected"); but his explanation was only qualitative. Huygens's common-tangent construction, without modifications, could not accommodate diffraction at all. Two such modifications were proposed by Young in the same 1801 Bakerian Lecture: first, that the secondary waves near the edge of an obstacle could diverge into the shadow, but only weakly, due to limited reinforcement from other secondary waves; and second, that diffraction by an edge was caused by interference between two rays: one reflected off the edge, and the other inflected while passing near the edge. The latter ray would be undeviated if sufficiently far from the edge, but Young did not elaborate on that case. These were the earliest suggestions that the degree of diffraction depends on wavelength. Later, in the 1803 Bakerian Lecture, Young ceased to regard inflection as a separate phenomenon, and produced evidence that diffraction fringes inside the shadow of a narrow obstacle were due to interference: when the light from one side was blocked, the internal fringes disappeared. But Young was alone in such efforts until Fresnel entered the field. | [
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Huygens, in his investigation of double refraction, noticed something that he could not explain: when light passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second; but when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. This discovery gave Newton another reason to reject the wave theory: rays of light evidently had "sides". Corpuscles could have sides (or poles, as they would later be called); but waves of light could not, because (so it seemed) any such waves would need to be longitudinal (with vibrations in the direction of propagation). Newton offered an alternative "Rule" for the extraordinary refraction, which rode on his authority through the 18th century, although he made "no known attempt to deduce it from any principles of optics, corpuscular or otherwise." In 1808, the extraordinary refraction of calcite was investigated experimentally, with unprecedented accuracy, by Étienne-Louis Malus, and found to be consistent with Huygens's spheroid construction, not Newton's "Rule". | [
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Malus, encouraged by Pierre-Simon Laplace, then sought to explain this law in corpuscular terms: from the known relation between the incident and refracted ray directions, Malus derived the corpuscular velocity (as a function of direction) that would satisfy Maupertuis's "least action" principle. But, as Young pointed out, the existence of such a velocity law was guaranteed by Huygens's spheroid, because Huygens's construction leads to Fermat's principle, which becomes Maupertuis's principle if the ray speed is replaced by the reciprocal of the particle speed! The corpuscularists had not found a force law that would yield the alleged velocity law, except by a circular argument in which a force acting at the surface of the crystal inexplicably depended on the direction of the (possibly subsequent) velocity within the crystal. Worse, it was doubtful that any such force would satisfy the conditions of Maupertuis's principle. In contrast, Young proceeded to show that "a medium more easily compressible in one direction than in any direction perpendicular to it, as if it consisted of an infinite number of parallel plates connected by a substance somewhat less elastic" admits spheroidal longitudinal wavefronts, as Huygens supposed. But Malus, in the midst of his experiments on double refraction, noticed something else: when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like one of the two rays emerging from a calcite crystal. | [
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It was Malus who coined the term polarization to describe this behavior, although the polarizing angle became known as Brewster's angle after its dependence on the refractive index was determined experimentally by David Brewster in 1815. Malus also introduced the term plane of polarization. In the case of polarization by reflection, his "plane of polarization" was the plane of the incident and reflected rays; in modern terms, this is the plane normal to the electric vibration. In 1809, Malus further discovered that the intensity of light passing through two polarizers is proportional to the squared cosine of the angle between their planes of polarization (Malus's law), whether the polarizers work by reflection or double refraction, and that all birefringent crystals produce both extraordinary refraction and polarization. As the corpuscularists started trying to explain these things in terms of polar "molecules" of light, the wave-theorists had no working hypothesis on the nature of polarization, prompting Young to remark that Malus's observations "present greater difficulties to the advocates of the undulatory theory than any other facts with which we are acquainted." Malus died in February 1812, at the age of 36, shortly after receiving the Rumford Medal for his work on polarization. In August 1811, François Arago reported that if a thin plate of mica was viewed against a white polarized backlight through a calcite crystal, the two images of the mica were of complementary colors (the overlap having the same color as the background). | [
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The light emerging from the mica was "depolarized" in the sense that there was no orientation of the calcite that made one image disappear; yet it was not ordinary ("unpolarized") light, for which the two images would be of the same color. Rotating the calcite around the line of sight changed the colors, though they remained complementary. Rotating the mica changed the saturation (not the hue) of the colors. This phenomenon became known as chromatic polarization. Replacing the mica with a much thicker plate of quartz, with its faces perpendicular to the optic axis (the axis of Huygens's spheroid or Malus's velocity function), produced a similar effect, except that rotating the quartz made no difference. Arago tried to explain his observations in corpuscular terms. In 1812, as Arago pursued further qualitative experiments and other commitments, Jean-Baptiste Biot reworked the same ground using a gypsum lamina in place of the mica, and found empirical formulae for the intensities of the ordinary and extraordinary images. The formulae contained two coefficients, supposedly representing colors of rays "affected" and "unaffected" by the plate – the "affected" rays being of the same color mix as those reflected by amorphous thin plates of proportional, but lesser, thickness. Arago protested, declaring that he had made some of the same discoveries but had not had time to write them up. In fact the overlap between Arago's work and Biot's was minimal, Arago's being only qualitative and wider in scope (attempting to include polarization by reflection). | [
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But the dispute triggered a notorious falling-out between the two men. Later that year, Biot tried to explain the observations as an oscillation of the alignment of the "affected" corpuscles at a frequency proportional to that of Newton's "fits", due to forces depending on the alignment. This theory became known as mobile polarization. To reconcile his results with a sinusoidal oscillation, Biot had to suppose that the corpuscles emerged with one of two permitted orientations, namely the extremes of the oscillation, with probabilities depending on the phase of the oscillation. Corpuscular optics was becoming expensive on assumptions. But in 1813, Biot reported that the case of quartz was simpler: the observable phenomenon (now called optical rotation or optical activity or sometimes rotary polarization) was a gradual rotation of the polarization direction with distance, and could be explained by a corresponding rotation (not oscillation) of the corpuscles. Early in 1814, reviewing Biot's work on chromatic polarization, Young noted that the periodicity of the color as a function of the plate thickness – including the factor by which the period exceeded that for a reflective thin plate, and even the effect of obliquity of the plate (but not the role of polarization)—could be explained by the wave theory in terms of the different propagation times of the ordinary and extraordinary waves through the plate. But Young was then the only public defender of the wave theory. | [
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In summary, in the spring of 1814, as Fresnel tried in vain to guess what polarization was, the corpuscularists thought that they knew, while the wave-theorists (if we may use the plural) literally had no idea. Both theories claimed to explain rectilinear propagation, but the wave explanation was overwhelmingly regarded as unconvincing. The corpuscular theory could not rigorously link double refraction to surface forces; the wave theory could not yet link it to polarization. The corpuscular theory was weak on thin plates and silent on gratings; the wave theory was strong on both, but under-appreciated. Concerning diffraction, the corpuscular theory did not yield quantitative predictions, while the wave theory had begun to do so by considering diffraction as a manifestation of interference, but had only considered two rays at a time. Only the corpuscular theory gave even a vague insight into Brewster's angle, Malus's law, or optical rotation. Concerning chromatic polarization, the wave theory explained the periodicity far better than the corpuscular theory, but had nothing to say about the role of polarization; and its explanation of the periodicity was largely ignored. And Arago had founded the study of chromatic polarization, only to lose the lead, controversially, to Biot. Such were the circumstances in which Arago first heard of Fresnel's interest in optics. Rêveries
Fresnel's letters from later in 1814 reveal his interest in the wave theory, including his awareness that it explained the constancy of the speed of light and was at least compatible with stellar aberration. | [
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Eventually he compiled what he called his rêveries (musings) into an essay and submitted it via Léonor Mérimée to André-Marie Ampère, who did not respond directly. But on 19 December, Mérimée dined with Ampère and Arago, with whom he was acquainted through the École Polytechnique; and Arago promised to look at Fresnel's essay. In mid 1815, on his way home to Mathieu to serve his suspension, Fresnel met Arago in Paris and spoke of the wave theory and stellar aberration. He was informed that he was trying to break down open doors ("il enfonçait des portes ouvertes"), and directed to classical works on optics. Diffraction
First attempt (1815)
On 12 July 1815, as Fresnel was about to leave Paris, Arago left him a note on a new topic:
Fresnel would not have ready access to these works outside Paris, and could not read English. But, in Mathieu – with a point-source of light made by focusing sunlight with a drop of honey, a crude micrometer of his own construction, and supporting apparatus made by a local locksmith – he began his own experiments. His technique was novel: whereas earlier investigators had projected the fringes onto a screen, Fresnel soon abandoned the screen and observed the fringes in space, through a lens with the micrometer at its focus, allowing more accurate measurements while requiring less light. Later in July, after Napoleon's final defeat, Fresnel was reinstated with the advantage of having backed the winning side. He requested a two-month leave of absence, which was readily granted because roadworks were in abeyance. | [
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On 23 September he wrote to Arago, beginning "I think I have found the explanation and the law of colored fringes which one notices in the shadows of bodies illuminated by a luminous point." In the same paragraph, however, Fresnel implicitly acknowledged doubt about the novelty of his work: noting that he would need to incur some expense in order to improve his measurements, he wanted to know "whether this is not useless, and whether the law of diffraction has not already been established by sufficiently exact experiments." He explained that he had not yet had a chance to acquire the items on his reading lists, with the apparent exception of "Young's book", which he could not understand without his brother's help. Not surprisingly, he had retraced many of Young's steps. In a memoir sent to the institute on 15 October 1815, Fresnel mapped the external and internal fringes in the shadow of a wire. He noticed, like Young before him, that the internal fringes disappeared when the light from one side was blocked, and concluded that "the vibrations of two rays that cross each other under a very small angle can contradict each other…" But, whereas Young took the disappearance of the internal fringes as confirmation of the principle of interference, Fresnel reported that it was the internal fringes that first drew his attention to the principle. | [
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To explain the diffraction pattern, Fresnel constructed the internal fringes by considering the intersections of circular wavefronts emitted from the two edges of the obstruction, and the external fringes by considering the intersections between direct waves and waves reflected off the nearer edge. For the external fringes, to obtain tolerable agreement with observation, he had to suppose that the reflected wave was inverted; and he noted that the predicted paths of the fringes were hyperbolic. In the part of the memoir that most clearly surpassed Young, Fresnel explained the ordinary laws of reflection and refraction in terms of interference, noting that if two parallel rays were reflected or refracted at other than the prescribed angle, they would no longer have the same phase in a common perpendicular plane, and every vibration would be cancelled by a nearby vibration. He noted that his explanation was valid provided that the surface irregularities were much smaller than the wavelength. On 10 November, Fresnel sent a supplementary note dealing with Newton's rings and with gratings, including, for the first time, transmission gratings – although in that case the interfering rays were still assumed to be "inflected", and the experimental verification was inadequate because it used only two threads. As Fresnel was not a member of the institute, the fate of his memoir depended heavily on the report of a single member. The reporter for Fresnel's memoir turned out to be Arago (with Poinsot as the other reviewer). On 8 November, Arago wrote to Fresnel:
Fresnel was troubled, wanting to know more precisely where he had collided with Young. | [
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Concerning the curved paths of the "colored bands", Young had noted the hyperbolic paths of the fringes in the two-source interference pattern, corresponding roughly to Fresnel's internal fringes, and had described the hyperbolic fringes that appear on the screen within rectangular shadows. He had not mentioned the curved paths of the external fringes of a shadow; but, as he later explained, that was because Newton had already done so. Newton evidently thought the fringes were caustics. Thus Arago erred in his belief that the curved paths of the fringes were fundamentally incompatible with the corpuscular theory. Arago's letter went on to request more data on the external fringes. Fresnel complied, until he exhausted his leave and was assigned to Rennes in the département of Ille-et-Vilaine. At this point Arago interceded with Gaspard de Prony, head of the École des Ponts, who wrote to Louis-Mathieu Molé, head of the Corps des Ponts, suggesting that the progress of science and the prestige of the Corps would be enhanced if Fresnel could come to Paris for a time. He arrived in March 1816, and his leave was subsequently extended through the middle of the year. Meanwhile, in an experiment reported on 26 February 1816, Arago verified Fresnel's prediction that the internal fringes were shifted if the rays on one side of the obstacle passed through a thin glass lamina. Fresnel correctly attributed this phenomenon to the lower wave velocity in the glass. Arago later used a similar argument to explain the colors in the scintillation of stars. | [
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Fresnel's updated memoir was eventually published in the March 1816 issue of Annales de Chimie et de Physique, of which Arago had recently become co-editor. That issue did not actually appear until May. In March, Fresnel already had competition: Biot read a memoir on diffraction by himself and his student Claude Pouillet, containing copious data and arguing that the regularity of diffraction fringes, like the regularity of Newton's rings, must be linked to Newton's "fits". But the new link was not rigorous, and Pouillet himself would become a distinguished early adopter of the wave theory. "Efficacious ray", double-mirror experiment (1816)
On 24 May 1816, Fresnel wrote to Young (in French), acknowledging how little of his own memoir was new. But in a "supplement" signed on 14 July and read the next day, Fresnel noted that the internal fringes were more accurately predicted by supposing that the two interfering rays came from some distance outside the edges of the obstacle. To explain this, he divided the incident wavefront at the obstacle into what we now call Fresnel zones, such that the secondary waves from each zone were spread over half a cycle when they arrived at the observation point. The zones on one side of the obstacle largely canceled out in pairs, except the first zone, which was represented by an "efficacious ray". This approach worked for the internal fringes, but the superposition of the efficacious ray and the direct ray did not work for the external fringes. | [
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The contribution from the "efficacious ray" was thought to be only partly canceled, for reasons involving the dynamics of the medium: where the wavefront was continuous, symmetry forbade oblique vibrations; but near the obstacle that truncated the wavefront, the asymmetry allowed some sideways vibration towards the geometric shadow. This argument showed that Fresnel had not (yet) fully accepted Huygens's principle, which would have permitted oblique radiation from all portions of the front. In the same supplement, Fresnel described his well-known double mirror, comprising two flat mirrors joined at an angle of slightly less than 180°, with which he produced a two-slit interference pattern from two virtual images of the same slit. A conventional double-slit experiment required a preliminary single slit to ensure that the light falling on the double slit was coherent (synchronized). In Fresnel's version, the preliminary single slit was retained, and the double slit was replaced by the double mirror – which bore no physical resemblance to the double slit and yet performed the same function. This result (which had been announced by Arago in the March issue of the Annales) made it hard to believe that the two-slit pattern had anything to do with corpuscles being deflected as they passed near the edges of the slits. But 1816 was the "Year Without a Summer": crops failed; hungry farming families lined the streets of Rennes; the central government organized "charity workhouses" for the needy; and in October, Fresnel was sent back to Ille-et-Vilaine to supervise charity workers in addition to his regular road crew. | [
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According to Arago,
Fresnel's letters from December 1816 reveal his consequent anxiety. To Arago he complained of being "tormented by the worries of surveillance, and the need to reprimand…" And to Mérimée he wrote: "I find nothing more tiresome than having to manage other men, and I admit that I have no idea what I'm doing." Prize memoir (1818) and sequel
On 17 March 1817, the Académie des Sciences announced that diffraction would be the topic for the biannual physics Grand Prix to be awarded in 1819. The deadline for entries was set at 1 August 1818 to allow time for replication of experiments. Although the wording of the problem referred to rays and inflection and did not invite wave-based solutions, Arago and Ampère encouraged Fresnel to enter. In the fall of 1817, Fresnel, supported by de Prony, obtained a leave of absence from the new head of the Corp des Ponts, Louis Becquey, and returned to Paris. He resumed his engineering duties in the spring of 1818; but from then on he was based in Paris, first on the Canal de l'Ourcq, and then (from May 1819) with the cadastre of the pavements. On 15 January 1818, in a different context (revisited below), Fresnel showed that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. | [
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His method was similar to the phasor representation, except that the "forces" were plane vectors rather than complex numbers; they could be added, and multiplied by scalars, but not (yet) multiplied and divided by each other. The explanation was algebraic rather than geometric. Knowledge of this method was assumed in a preliminary note on diffraction, dated 19 April 1818 and deposited on 20 April, in which Fresnel outlined the elementary theory of diffraction as found in modern textbooks. He restated Huygens's principle in combination with the superposition principle, saying that the vibration at each point on a wavefront is the sum of the vibrations that would be sent to it at that moment by all the elements of the wavefront in any of its previous positions, all elements acting separately . For a wavefront partly obstructed in a previous position, the summation was to be carried out over the unobstructed portion. In directions other than the normal to the primary wavefront, the secondary waves were weakened due to obliquity, but weakened much more by destructive interference, so that the effect of obliquity alone could be ignored. For diffraction by a straight edge, the intensity as a function of distance from the geometric shadow could then be expressed with sufficient accuracy in terms of what are now called the normalized Fresnel integrals:
The same note included a table of the integrals, for an upper limit ranging from 0 to 5.1 in steps of 0.1, computed with a mean error of 0.0003, plus a smaller table of maxima and minima of the resulting intensity. | [
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In his final "Memoir on the diffraction of light", deposited on 29 July and bearing the Latin epigraph "Natura simplex et fecunda" ("Nature simple and fertile"), Fresnel slightly expanded the two tables without changing the existing figures, except for a correction to the first minimum of intensity. For completeness, he repeated his solution to "the problem of interference", whereby sinusoidal functions are added like vectors. He acknowledged the directionality of the secondary sources and the variation in their distances from the observation point, chiefly to explain why these things make negligible difference in the context, provided of course that the secondary sources do not radiate in the retrograde direction. Then, applying his theory of interference to the secondary waves, he expressed the intensity of light diffracted by a single straight edge (half-plane) in terms of integrals which involved the dimensions of the problem, but which could be converted to the normalized forms above. With reference to the integrals, he explained the calculation of the maxima and minima of the intensity (external fringes), and noted that the calculated intensity falls very rapidly as one moves into the geometric shadow. The last result, as Olivier Darrigol says, "amounts to a proof of the rectilinear propagation of light in the wave theory, indeed the first proof that a modern physicist would still accept." | [
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For the experimental testing of his calculations, Fresnel used red light with a wavelength of 638nm, which he deduced from the diffraction pattern in the simple case in which light incident on a single slit was focused by a cylindrical lens. For a variety of distances from the source to the obstacle and from the obstacle to the field point, he compared the calculated and observed positions of the fringes for diffraction by a half-plane, a slit, and a narrow strip – concentrating on the minima, which were visually sharper than the maxima. For the slit and the strip, he could not use the previously computed table of maxima and minima; for each combination of dimensions, the intensity had to be expressed in terms of sums or differences of Fresnel integrals and calculated from the table of integrals, and the extrema had to be calculated anew. The agreement between calculation and measurement was better than 1.5% in almost every case. Near the end of the memoir, Fresnel summed up the difference between Huygens's use of secondary waves and his own: whereas Huygens says there is light only where the secondary waves exactly agree, Fresnel says there is complete darkness only where the secondary waves exactly cancel out. The judging committee comprised Laplace, Biot, and Poisson (all corpuscularists), Gay-Lussac (uncommitted), and Arago, who eventually wrote the committee's report. Although entries in the competition were supposed to be anonymous to the judges, Fresnel's must have been recognizable by the content. | [
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There was only one other entry, of which neither the manuscript nor any record of the author has survived. That entry (identified as "no.1") was mentioned only in the last paragraph of the judges' report, noting that the author had shown ignorance of the relevant earlier works of Young and Fresnel, used insufficiently precise methods of observation, overlooked known phenomena, and made obvious errors. In the words of John Worrall, "The competition facing Fresnel could hardly have been less stiff." We may infer that the committee had only two options: award the prize to Fresnel ("no. 2"), or withhold it. The committee deliberated into the new year. Then Poisson, exploiting a case in which Fresnel's theory gave easy integrals, predicted that if a circular obstacle were illuminated by a point-source, there should be (according to the theory) a bright spot in the center of the shadow, illuminated as brightly as the exterior. This seems to have been intended as a reductio ad absurdum. Arago, undeterred, assembled an experiment with an obstacle 2mm in diameter – and there, in the center of the shadow, was Poisson's spot. The unanimous report of the committee, read at the meeting of the Académie on 15 March 1819, awarded the prize to "the memoir marked no. 2, and bearing as epigraph: Natura simplex et fecunda." At the same meeting, after the judgment was delivered, the president of the Académie opened a sealed note accompanying the memoir, revealing the author as Fresnel. | [
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The award was announced at the public meeting of the Académie a week later, on 22 March. Arago's verification of Poisson's counter-intuitive prediction passed into folklore as if it had decided the prize. That view, however, is not supported by the judges' report, which gave the matter only two sentences in the penultimate paragraph. Neither did Fresnel's triumph immediately convert Laplace, Biot, and Poisson to the wave theory, for at least four reasons. First, although the professionalization of science in France had established common standards, it was one thing to acknowledge a piece of research as meeting those standards, and another thing to regard it as conclusive. Second, it was possible to interpret Fresnel's integrals as rules for combining rays. Arago even encouraged that interpretation, presumably in order to minimize resistance to Fresnel's ideas. Even Biot began teaching the Huygens-Fresnel principle without committing himself to a wave basis. Third, Fresnel's theory did not adequately explain the mechanism of generation of secondary waves or why they had any significant angular spread; this issue particularly bothered Poisson. Fourth, the question that most exercised optical physicists at that time was not diffraction, but polarization – on which Fresnel had been working, but was yet to make his critical breakthrough. Polarization
Background: Emissionism and selectionism
An emission theory of light was one that regarded the propagation of light as the transport of some kind of matter. While the corpuscular theory was obviously an emission theory, the converse did not follow: in principle, one could be an emissionist without being a corpuscularist. | [
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This was convenient because, beyond the ordinary laws of reflection and refraction, emissionists never managed to make testable quantitative predictions from a theory of forces acting on corpuscles of light. But they did make quantitative predictions from the premises that rays were countable objects, which were conserved in their interactions with matter (except absorbent media), and which had particular orientations with respect to their directions of propagation. According to this framework, polarization and the related phenomena of double refraction and partial reflection involved altering the orientations of the rays and/or selecting them according to orientation, and the state of polarization of a beam (a bundle of rays) was a question of how many rays were in what orientations: in a fully polarized beam, the orientations were all the same. This approach, which Jed Buchwald has called selectionism, was pioneered by Malus and diligently pursued by Biot. Fresnel, in contrast, decided to introduce polarization into interference experiments. Interference of polarized light, chromatic polarization (1816–21)
In July or August 1816, Fresnel discovered that when a birefringent crystal produced two images of a single slit, he could not obtain the usual two-slit interference pattern, even if he compensated for the different propagation times. A more general experiment, suggested by Arago, found that if the two beams of a double-slit device were separately polarized, the interference pattern appeared and disappeared as the polarization of one beam was rotated, giving full interference for parallel polarizations, but no interference for perpendicular polarizations . | [
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These experiments, among others, were eventually reported in a brief memoir published in 1819 and later translated into English. In a memoir drafted on 30 August 1816 and revised on 6 October, Fresnel reported an experiment in which he placed two matching thin laminae in a double-slit apparatus – one over each slit, with their optic axes perpendicular – and obtained two interference patterns offset in opposite directions, with perpendicular polarizations. This, in combination with the previous findings, meant that each lamina split the incident light into perpendicularly polarized components with different velocities – just like a normal (thick) birefringent crystal, and contrary to Biot's "mobile polarization" hypothesis. Accordingly, in the same memoir, Fresnel offered his first attempt at a wave theory of chromatic polarization. When polarized light passed through a crystal lamina, it was split into ordinary and extraordinary waves (with intensities described by Malus's law), and these were perpendicularly polarized and therefore did not interfere, so that no colors were produced (yet). But if they then passed through an analyzer (second polarizer), their polarizations were brought into alignment (with intensities again modified according to Malus's law), and they would interfere. This explanation, by itself, predicts that if the analyzer is rotated 90°, the ordinary and extraordinary waves simply switch roles, so that if the analyzer takes the form of a calcite crystal, the two images of the lamina should be of the same hue (this issue is revisited below). | [
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But in fact, as Arago and Biot had found, they are of complementary colors. To correct the prediction, Fresnel proposed a phase-inversion rule whereby one of the constituent waves of one of the two images suffered an additional 180° phase shift on its way through the lamina. This inversion was a weakness in the theory relative to Biot's, as Fresnel acknowledged, although the rule specified which of the two images had the inverted wave. Moreover, Fresnel could deal only with special cases, because he had not yet solved the problem of superposing sinusoidal functions with arbitrary phase differences due to propagation at different velocities through the lamina. He solved that problem in a "supplement" signed on 15 January 1818 (mentioned above). In the same document, he accommodated Malus's law by proposing an underlying law: that if polarized light is incident on a birefringent crystal with its optic axis at an angle θ to the "plane of polarization", the ordinary and extraordinary vibrations (as functions of time) are scaled by the factors cosθ and sinθ, respectively. Although modern readers easily interpret these factors in terms of perpendicular components of a transverse oscillation, Fresnel did not (yet) explain them that way. Hence he still needed the phase-inversion rule. He applied all these principles to a case of chromatic polarization not covered by Biot's formulae, involving two successive laminae with axes separated by 45°, and obtained predictions that disagreed with Biot's experiments (except in special cases) but agreed with his own. | [
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Fresnel applied the same principles to the standard case of chromatic polarization, in which one birefringent lamina was sliced parallel to its axis and placed between a polarizer and an analyzer. If the analyzer took the form of a thick calcite crystal with its axis in the plane of polarization, Fresnel predicted that the intensities of the ordinary and extraordinary images of the lamina were respectively proportional to
where is the angle from the initial plane of polarization to the optic axis of the lamina, is the angle from the initial plane of polarization to the plane of polarization of the final ordinary image, and is the phase lag of the extraordinary wave relative to the ordinary wave due to the difference in propagation times through the lamina. The terms in are the frequency-dependent terms and explain why the lamina must be thin in order to produce discernible colors: if the lamina is too thick, will pass through too many cycles as the frequency varies through the visible range, and the eye (which divides the visible spectrum into only three bands) will not be able to resolve the cycles. From these equations it is easily verified that for all so that the colors are complementary. Without the phase-inversion rule, there would be a plus sign in front of the last term in the second equation, so that the -dependent term would be the same in both equations, implying (incorrectly) that the colors were of the same hue. These equations were included in an undated note that Fresnel gave to Biot, to which Biot added a few lines of his own. | [
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If we substitute
and
then Fresnel's formulae can be rewritten as
which are none other than Biot's empirical formulae of 1812, except that Biot interpreted and as the "unaffected" and "affected" selections of the rays incident on the lamina. If Biot's substitutions were accurate, they would imply that his experimental results were more fully explained by Fresnel's theory than by his own. Arago delayed reporting on Fresnel's works on chromatic polarization until June 1821, when he used them in a broad attack on Biot's theory. In his written response, Biot protested that Arago's attack went beyond the proper scope of a report on the nominated works of Fresnel. But Biot also claimed that the substitutions for and and therefore Fresnel's expressions for and were empirically wrong because when Fresnel's intensities of spectral colors were mixed according to Newton's rules, the squared cosine and sine functions varied too smoothly to account for the observed sequence of colors. That claim drew a written reply from Fresnel, who disputed whether the colors changed as abruptly as Biot claimed, and whether the human eye could judge color with sufficient objectivity for the purpose. On the latter question, Fresnel pointed out that different observers may give different names to the same color. Furthermore, he said, a single observer can only compare colors side by side; and even if they are judged to be the same, the identity is of sensation, not necessarily of composition. | [
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Fresnel's oldest and strongest point – that thin crystals were subject to the same laws as thick ones and did not need or allow a separate theory – Biot left unanswered. Arago and Fresnel were seen to have won the debate. Moreover, by this time Fresnel had a new, simpler explanation of his equations on chromatic polarization. Breakthrough: Pure transverse waves (1821)
In the draft memoir of 30 August 1816, Fresnel mentioned two hypotheses – one of which he attributed to Ampère – by which the non-interference of orthogonally-polarized beams could be explained if polarized light waves were partly transverse. But Fresnel could not develop either of these ideas into a comprehensive theory. As early as September 1816, according to his later account, he realized that the non-interference of orthogonally-polarized beams, together with the phase-inversion rule in chromatic polarization, would be most easily explained if the waves were purely transverse, and Ampère "had the same thought" on the phase-inversion rule. But that would raise a new difficulty: as natural light seemed to be unpolarized and its waves were therefore presumed to be longitudinal, one would need to explain how the longitudinal component of vibration disappeared on polarization, and why it did not reappear when polarized light was reflected or refracted obliquely by a glass plate. Independently, on 12 January 1817, Young wrote to Arago (in English) noting that a transverse vibration would constitute a polarization, and that if two longitudinal waves crossed at a significant angle, they could not cancel without leaving a residual transverse vibration. | [
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Young repeated this idea in an article published in a supplement to the Encyclopædia Britannica in February 1818, in which he added that Malus's law would be explained if polarization consisted in a transverse motion. Thus Fresnel, by his own testimony, may not have been the first person to suspect that light waves could have a transverse component, or that polarized waves were exclusively transverse. And it was Young, not Fresnel, who first published the idea that polarization depends on the orientation of a transverse vibration. But these incomplete theories had not reconciled the nature of polarization with the apparent existence of unpolarized light; that achievement was to be Fresnel's alone. In a note that Buchwald dates in the summer of 1818, Fresnel entertained the idea that unpolarized waves could have vibrations of the same energy and obliquity, with their orientations distributed uniformly about the wave-normal, and that the degree of polarization was the degree of non-uniformity in the distribution. Two pages later he noted, apparently for the first time in writing, that his phase-inversion rule and the non-interference of orthogonally-polarized beams would be easily explained if the vibrations of fully polarized waves were "perpendicular to the normal to the wave"—that is, purely transverse. But if he could account for lack of polarization by averaging out the transverse component, he did not also need to assume a longitudinal component. | [
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It was enough to suppose that light waves are purely transverse, hence always polarized in the sense of having a particular transverse orientation, and that the "unpolarized" state of natural or "direct" light is due to rapid and random variations in that orientation, in which case two coherent portions of "unpolarized" light will still interfere because their orientations will be synchronized. It is not known exactly when Fresnel made this last step, because there is no relevant documentation from 1820 or early 1821 (perhaps because he was too busy working on lighthouse-lens prototypes; see below). But he first published the idea in a paper on "Calcul des teintes…" ("calculation of the tints…"), serialized in Arago's Annales for May, June, and July 1821. In the first installment, Fresnel described "direct" (unpolarized) light as "the rapid succession of systems of waves polarized in all directions", and gave what is essentially the modern explanation of chromatic polarization, albeit in terms of the analogy between polarization and the resolution of forces in a plane, mentioning transverse waves only in a footnote. The introduction of transverse waves into the main argument was delayed to the second installment, in which he revealed the suspicion that he and Ampère had harbored since 1816, and the difficulty it raised. He continued:
According to this new view, he wrote, "the act of polarization consists not in creating these transverse movements, but in decomposing them into two fixed perpendicular directions and in separating the two components". | [
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While selectionists could insist on interpreting Fresnel's diffraction integrals in terms of discrete, countable rays, they could not do the same with his theory of polarization. For a selectionist, the state of polarization of a beam concerned the distribution of orientations over the population of rays, and that distribution was presumed to be static. For Fresnel, the state of polarization of a beam concerned the variation of a displacement over time. That displacement might be constrained but was not static, and rays were geometric constructions, not countable objects. The conceptual gap between the wave theory and selectionism had become unbridgeable. The other difficulty posed by pure transverse waves, of course, was the apparent implication that the aether was an elastic solid, except that, unlike other elastic solids, it was incapable of transmitting longitudinal waves. The wave theory was cheap on assumptions, but its latest assumption was expensive on credulity. If that assumption was to be widely entertained, its explanatory power would need to be impressive. Partial reflection (1821)
In the second installment of "Calcul des teintes" (June 1821), Fresnel supposed, by analogy with sound waves, that the density of the aether in a refractive medium was inversely proportional to the square of the wave velocity, and therefore directly proportional to the square of the refractive index. | [
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For reflection and refraction at the surface between two isotropic media of different indices, Fresnel decomposed the transverse vibrations into two perpendicular components, now known as the s and p components, which are parallel to the surface and the plane of incidence, respectively; in other words, the s and p components are respectively square and parallel to the plane of incidence. For the s component, Fresnel supposed that the interaction between the two media was analogous to an elastic collision, and obtained a formula for what we now call the reflectivity: the ratio of the reflected intensity to the incident intensity. The predicted reflectivity was non-zero at all angles. The third installment (July 1821) was a short "postscript" in which Fresnel announced that he had found, by a "mechanical solution", a formula for the reflectivity of the p component, which predicted that the reflectivity was zero at the Brewster angle. So polarization by reflection had been accounted for – but with the proviso that the direction of vibration in Fresnel's model was perpendicular to the plane of polarization as defined by Malus. (On the ensuing controversy, see Plane of polarization.) The technology of the time did not allow the s and p reflectivities to be measured accurately enough to test Fresnel's formulae at arbitrary angles of incidence. But the formulae could be rewritten in terms of what we now call the reflection coefficient: the signed ratio of the reflected amplitude to the incident amplitude. | [
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Then, if the plane of polarization of the incident ray was at 45° to the plane of incidence, the tangent of the corresponding angle for the reflected ray was obtainable from the ratio of the two reflection coefficients, and this angle could be measured. Fresnel had measured it for a range of angles of incidence, for glass and water, and the agreement between the calculated and measured angles was better than 1.5° in all cases. Fresnel gave details of the "mechanical solution" in a memoir read to the Académie des Sciences on 7 January 1823. Conservation of energy was combined with continuity of the tangential vibration at the interface. The resulting formulae for the reflection coefficients and reflectivities became known as the Fresnel equations. The reflection coefficients for the s and p polarizations are most succinctly expressed as
and
where and are the angles of incidence and refraction; these equations are known respectively as Fresnel's sine law and Fresnel's tangent law. By allowing the coefficients to be complex, Fresnel even accounted for the different phase shifts of the s and p components due to total internal reflection. This success inspired James MacCullagh and Augustin-Louis Cauchy, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a complex refractive index. The same technique is applicable to non-metallic opaque media. With these generalizations, the Fresnel equations can predict the appearance of a wide variety of objects under illumination – for example, in computer graphics . | [
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Circular and elliptical polarization, optical rotation (1822)
In a memoir dated 9 December 1822, Fresnel coined the terms linear polarization (French: polarisation rectiligne) for the simple case in which the perpendicular components of vibration are in phase or 180° out of phase, circular polarization for the case in which they are of equal magnitude and a quarter-cycle (±90°) out of phase, and elliptical polarization for other cases in which the two components have a fixed amplitude ratio and a fixed phase difference. He then explained how optical rotation could be understood as a species of birefringence. Linearly-polarized light could be resolved into two circularly-polarized components rotating in opposite directions. If these components propagated at slightly different speeds, the phase difference between them – and therefore the direction of their linearly-polarized resultant – would vary continuously with distance. These concepts called for a redefinition of the distinction between polarized and unpolarized light. Before Fresnel, it was thought that polarization could vary in direction, and in degree (e.g., due to variation in the angle of reflection off a transparent body), and that it could be a function of color (chromatic polarization), but not that it could vary in kind. Hence it was thought that the degree of polarization was the degree to which the light could be suppressed by an analyzer with the appropriate orientation. Light that had been converted from linear to elliptical or circular polarization (e.g., by passage through a crystal lamina, or by total internal reflection) was described as partly or fully "depolarized" because of its behavior in an analyzer. | [
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After Fresnel, the defining feature of polarized light was that the perpendicular components of vibration had a fixed ratio of amplitudes and a fixed difference in phase. By that definition, elliptically or circularly polarized light is fully polarized although it cannot be fully suppressed by an analyzer alone. The conceptual gap between the wave theory and selectionism had widened again. Total internal reflection (1817–23)
By 1817 it had been discovered by Brewster, but not adequately reported, that plane-polarized light was partly depolarized by total internal reflection if initially polarized at an acute angle to the plane of incidence. Fresnel rediscovered this effect and investigated it by including total internal reflection in a chromatic-polarization experiment. With the aid of his first theory of chromatic polarization, he found that the apparently depolarized light was a mixture of components polarized parallel and perpendicular to the plane of incidence, and that the total reflection introduced a phase difference between them. Choosing an appropriate angle of incidence (not yet exactly specified) gave a phase difference of 1/8 of a cycle (45°). Two such reflections from the "parallel faces" of "two coupled prisms" gave a phase difference of 1/4 of a cycle (90°). These findings were contained in a memoir submitted to the Académie on 10 November 1817 and read a fortnight later. An undated marginal note indicates that the two coupled prisms were later replaced by a single "parallelepiped in glass"—now known as a Fresnel rhomb. | [
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This was the memoir whose "supplement", dated January 1818, contained the method of superposing sinusoidal functions and the restatement of Malus's law in terms of amplitudes. In the same supplement, Fresnel reported his discovery that optical rotation could be emulated by passing the polarized light through a Fresnel rhomb (still in the form of "coupled prisms"), followed by an ordinary birefringent lamina sliced parallel to its axis, with the axis at 45° to the plane of reflection of the Fresnel rhomb, followed by a second Fresnel rhomb at 90° to the first. In a further memoir read on 30 March, Fresnel reported that if polarized light was fully "depolarized" by a Fresnel rhomb – now described as a parallelepiped – its properties were not further modified by a subsequent passage through an optically rotating medium or device. The connection between optical rotation and birefringence was further explained in 1822, in the memoir on elliptical and circular polarization. This was followed by the memoir on reflection, read in January 1823, in which Fresnel quantified the phase shifts in total internal reflection, and thence calculated the precise angle at which a Fresnel rhomb should be cut in order to convert linear polarization to circular polarization. For a refractive index of 1.51, there were two solutions: about 48.6° and 54.6°. Double refraction
Background: Uniaxial and biaxial crystals; Biot's laws
When light passes through a slice of calcite cut perpendicular to its optic axis, the difference between the propagation times of the ordinary and extraordinary waves has a second-order dependence on the angle of incidence. | [
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If the slice is observed in a highly convergent cone of light, that dependence becomes significant, so that a chromatic-polarization experiment will show a pattern of concentric rings. But most minerals, when observed in this manner, show a more complicated pattern of rings involving two foci and a lemniscate curve, as if they had two optic axes. The two classes of minerals naturally become known as uniaxal and biaxal—or, in later literature, uniaxial and biaxial. In 1813, Brewster observed the simple concentric pattern in "beryl, emerald, ruby &c." The same pattern was later observed in calcite by Wollaston, Biot, and Seebeck. Biot, assuming that the concentric pattern was the general case, tried to calculate the colors with his theory of chromatic polarization, and succeeded better for some minerals than for others. In 1818, Brewster belatedly explained why: seven of the twelve minerals employed by Biot had the lemniscate pattern, which Brewster had observed as early as 1812; and the minerals with the more complicated rings also had a more complicated law of refraction. In a uniform crystal, according to Huygens's theory, the secondary wavefront that expands from the origin in unit time is the ray-velocity surface—that is, the surface whose "distance" from the origin in any direction is the ray velocity in that direction. | [
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In calcite, this surface is two-sheeted, consisting of a sphere (for the ordinary wave) and an oblate spheroid (for the extraordinary wave) touching each other at opposite points of a common axis—touching at the north and south poles, if we may use a geographic analogy. But according to Malus's corpuscular theory of double refraction, the ray velocity was proportional to the reciprocal of that given by Huygens's theory, in which case the velocity law was of the form
where and were the ordinary and extraordinary ray velocities according to the corpuscular theory, and was the angle between the ray and the optic axis. By Malus's definition, the plane of polarization of a ray was the plane of the ray and the optic axis if the ray was ordinary, or the perpendicular plane (containing the ray) if the ray was extraordinary. In Fresnel's model, the direction of vibration was normal to the plane of polarization. Hence, for the sphere (the ordinary wave), the vibration was along the lines of latitude (continuing the geographic analogy); and for the spheroid (the extraordinary wave), the vibration was along the lines of longitude. On 29 March 1819, Biot presented a memoir in which he proposed simple generalizations of Malus's rules for a crystal with two axes, and reported that both generalizations seemed to be confirmed by experiment. For the velocity law, the squared sine was replaced by the product of the sines of the angles from the ray to the two axes (Biot's sine law). | [
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And for the polarization of the ordinary ray, the plane of the ray and the axis was replaced by the plane bisecting the dihedral angle between the two planes each of which contained the ray and one axis (Biot's dihedral law). Biot's laws meant that a biaxial crystal with axes at a small angle, cleaved in the plane of those axes, behaved nearly like a uniaxial crystal at near-normal incidence; this was fortunate because gypsum, which had been used in chromatic-polarization experiments, is biaxial. First memoir and supplements (1821–22)
Until Fresnel turned his attention to biaxial birefringence, it was assumed that one of the two refractions was ordinary, even in biaxial crystals. But, in a memoir submitted on 19 November 1821, Fresnel reported two experiments on topaz showing that neither refraction was ordinary in the sense of satisfying Snell's law; that is, neither ray was the product of spherical secondary waves. The same memoir contained Fresnel's first attempt at the biaxial velocity law. For calcite, if we interchange the equatorial and polar radii of Huygens's oblate spheroid while preserving the polar direction, we obtain a prolate spheroid touching the sphere at the equator. A plane through the center/origin cuts this prolate spheroid in an ellipse whose major and minor semi-axes give the magnitudes of the extraordinary and ordinary ray velocities in the direction normal to the plane, and (said Fresnel) the directions of their respective vibrations. The direction of the optic axis is the normal to the plane for which the ellipse of intersection reduces to a circle. | [
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So, for the biaxial case, Fresnel simply replaced the prolate spheroid with a triaxial ellipsoid, which was to be sectioned by a plane in the same way. In general there would be two planes passing through the center of the ellipsoid and cutting it in a circle, and the normals to these planes would give two optic axes. From the geometry, Fresnel deduced Biot's sine law (with the ray velocities replaced by their reciprocals). The ellipsoid indeed gave the correct ray velocities (although the initial experimental verification was only approximate). But it did not give the correct directions of vibration, for the biaxial case or even for the uniaxial case, because the vibrations in Fresnel's model were tangential to the wavefront—which, for an extraordinary ray, is not generally normal to the ray. This error (which is small if, as in most cases, the birefringence is weak) was corrected in an "extract" that Fresnel read to the Académie a week later, on 26 November. Starting with Huygens's spheroid, Fresnel obtained a 4th-degree surface which, when sectioned by a plane as above, would yield the wave-normal velocities for a wavefront in that plane, together with their vibration directions. For the biaxial case, he generalized the equation to obtain a surface with three unequal principal dimensions; this he subsequently called the "surface of elasticity". But he retained the earlier ellipsoid as an approximation, from which he deduced Biot's dihedral law. Fresnel's initial derivation of the surface of elasticity had been purely geometric, and not deductively rigorous. | [
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His first attempt at a mechanical derivation, contained in a "supplement" dated 13 January 1822, assumed that (i) there were three mutually perpendicular directions in which a displacement produced a reaction in the same direction, (ii) the reaction was otherwise a linear function of the displacement, and (iii) the radius of the surface in any direction was the square root of the component, in that direction, of the reaction to a unit displacement in that direction. The last assumption recognized the requirement that if a wave was to maintain a fixed direction of propagation and a fixed direction of vibration, the reaction must not be outside the plane of those two directions. In the same supplement, Fresnel considered how he might find, for the biaxial case, the secondary wavefront that expands from the origin in unit time—that is, the surface that reduces to Huygens's sphere and spheroid in the uniaxial case. He noted that this "wave surface" (surface de l'onde) is tangential to all possible plane wavefronts that could have crossed the origin one unit of time ago, and he listed the mathematical conditions that it must satisfy. But he doubted the feasibility of deriving the surface from those conditions. | [
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In a "second supplement", Fresnel eventually exploited two related facts: (i) the "wave surface" was also the ray-velocity surface, which could be obtained by sectioning the ellipsoid that he had initially mistaken for the surface of elasticity, and (ii) the "wave surface" intersected each plane of symmetry of the ellipsoid in two curves: a circle and an ellipse. Thus he found that the "wave surface" is described by the 4th-degree equation
where and are the propagation speeds in directions normal to the coordinate axes for vibrations along the axes (the ray and wave-normal speeds being the same in those special cases). Later commentators put the equation in the more compact and memorable form
Earlier in the "second supplement", Fresnel modeled the medium as an array of point-masses and found that the force-displacement relation was described by a symmetric matrix, confirming the existence of three mutually perpendicular axes on which the displacement produced a parallel force. Later in the document, he noted that in a biaxial crystal, unlike a uniaxial crystal, the directions in which there is only one wave-normal velocity are not the same as those in which there is only one ray velocity. Nowadays we refer to the former directions as the optic axes or binormal axes, and the latter as the ray axes or biradial axes . Fresnel's "second supplement" was signed on 31 March 1822 and submitted the next day – less than a year after the publication of his pure-transverse-wave hypothesis, and just less than a year after the demonstration of his prototype eight-panel lighthouse lens . | [
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Second memoir (1822–26)
Having presented the pieces of his theory in roughly the order of discovery, Fresnel needed to rearrange the material so as to emphasize the mechanical foundations; and he still needed a rigorous treatment of Biot's dihedral law. He attended to these matters in his "second memoir" on double refraction, published in the Recueils of the Académie des Sciences for 1824; this was not actually printed until late 1827, a few months after his death. In this work, having established the three perpendicular axes on which a displacement produces a parallel reaction, and thence constructed the surface of elasticity, he showed that Biot's dihedral law is exact provided that the binormals are taken as the optic axes, and the wave-normal direction as the direction of propagation. As early as 1822, Fresnel discussed his perpendicular axes with Cauchy. Acknowledging Fresnel's influence, Cauchy went on to develop the first rigorous theory of elasticity of non-isotropic solids (1827), hence the first rigorous theory of transverse waves therein (1830) — which he promptly tried to apply to optics. The ensuing difficulties drove a long competitive effort to find an accurate mechanical model of the aether. Fresnel's own model was not dynamically rigorous; for example, it deduced the reaction to a shear strain by considering the displacement of one particle while all others were fixed, and it assumed that the stiffness determined the wave velocity as in a stretched string, whatever the direction of the wave-normal. | [
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But it was enough to enable the wave theory to do what selectionist theory could not: generate testable formulae covering a comprehensive range of optical phenomena, from mechanical assumptions. Photoelasticity, multiple-prism experiments (1822)
In 1815, Brewster reported that colors appear when a slice of isotropic material, placed between crossed polarizers, is mechanically stressed. Brewster himself immediately and correctly attributed this phenomenon to stress-induced birefringence — now known as photoelasticity. In a memoir read in September 1822, Fresnel announced that he had verified Brewster's diagnosis more directly, by compressing a combination of glass prisms so severely that one could actually see a double image through it. In his experiment, Fresnel lined up seven 45°-90°-45° prisms, short side to short side, with their 90° angles pointing in alternating directions. Two half-prisms were added at the ends to make the whole assembly rectangular. The prisms were separated by thin films of turpentine (térébenthine) to suppress internal reflections, allowing a clear line of sight along the row. When the four prisms with similar orientations were compressed in a vise across the line of sight, an object viewed through the assembly produced two images with perpendicular polarizations, with an apparent spacing of 1.5mm at one metre. | [
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At the end of that memoir, Fresnel predicted that if the compressed prisms were replaced by (unstressed) monocrystalline quartz prisms with matching directions of optical rotation, and with their optic axes aligned along the row, an object seen by looking along the common optic axis would give two images, which would seem unpolarized when viewed through an analyzer but, when viewed through a Fresnel rhomb, would be polarized at ±45° to the plane of reflection of the rhomb (indicating that they were initially circularly polarized in opposite directions). This would show directly that optical rotation is a form of birefringence. In the memoir of December 1822, in which he introduced the term circular polarization, he reported that he had confirmed this prediction using only one 14°-152°-14° prism and two glass half-prisms. But he obtained a wider separation of the images by replacing the glass half-prism with quartz half-prisms whose rotation was opposite to that of the 14°-152°-14° prism. He added in passing that one could further increase the separation by increasing the number of prisms. Reception
For the supplement to Riffault's translation of Thomson's System of Chemistry, Fresnel was chosen to contribute the article on light. The resulting 137-page essay, titled De la Lumière (On Light), was apparently finished in June 1821 and published by February 1822. With sections covering the nature of light, diffraction, thin-film interference, reflection and refraction, double refraction and polarization, chromatic polarization, and modification of polarization by reflection, it made a comprehensive case for the wave theory to a readership that was not restricted to physicists. | [
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To examine Fresnel's first memoir and supplements on double refraction, the Académie des Sciences appointed Ampère, Arago, Fourier, and Poisson. Their report, of which Arago was clearly the main author, was delivered at the meeting of 19 August 1822. Then, in the words of Émile Verdet, as translated by Ivor Grattan-Guinness:
Whether Laplace was announcing his conversion to the wave theory – at the age of 73 – is uncertain. Grattan-Guinness entertained the idea. Buchwald, noting that Arago failed to explain that the "ellipsoid of elasticity" did not give the correct planes of polarization, suggests that Laplace may have merely regarded Fresnel's theory as a successful generalization of Malus's ray-velocity law, embracing Biot's laws. In the following year, Poisson, who did not sign Arago's report, disputed the possibility of transverse waves in the aether. Starting from assumed equations of motion of a fluid medium, he noted that they did not give the correct results for partial reflection and double refraction – as if that were Fresnel's problem rather than his own – and that the predicted waves, even if they were initially transverse, became more longitudinal as they propagated. In reply Fresnel noted, inter alia, that the equations in which Poisson put so much faith did not even predict viscosity. | [
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The implication was clear: given that the behavior of light had not been satisfactorily explained except by transverse waves, it was not the responsibility of the wave-theorists to abandon transverse waves in deference to pre-conceived notions about the aether; rather, it was the responsibility of the aether modelers to produce a model that accommodated transverse waves. According to Robert H. Silliman, Poisson eventually accepted the wave theory shortly before his death in 1840. Among the French, Poisson's reluctance was an exception. According to Eugene Frankel, "in Paris no debate on the issue seems to have taken place after 1825. Indeed, almost the entire generation of physicists and mathematicians who came to maturity in the 1820s – Pouillet, Savart, Lamé, Navier, Liouville, Cauchy – seem to have adopted the theory immediately." Fresnel's other prominent French opponent, Biot, appeared to take a neutral position in 1830, and eventually accepted the wave theory – possibly by 1846 and certainly by 1858. In 1826, the British astronomer John Herschel, who was working on a book-length article on light for the Encyclopædia Metropolitana, addressed three questions to Fresnel concerning double refraction, partial reflection, and their relation to polarization. The resulting article, titled simply "Light", was highly sympathetic to the wave theory, although not entirely free of selectionist language. It was circulating privately by 1828 and was published in 1830. Meanwhile, Young's translation of Fresnel's De la Lumière was published in installments from 1827 to 1829. | [
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George Biddell Airy, the former Lucasian Professor at Cambridge and future Astronomer Royal, unreservedly accepted the wave theory by 1831. In 1834, he famously calculated the diffraction pattern of a circular aperture from the wave theory, thereby explaining the limited angular resolution of a perfect telescope . By the end of the 1830s, the only prominent British physicist who held out against the wave theory was Brewster, whose objections included the difficulty of explaining photochemical effects and (in his opinion) dispersion. A German translation of De la Lumière was published in installments in 1825 and 1828. The wave theory was adopted by Fraunhofer in the early 1820s and by Franz Ernst Neumann in the 1830s, and then began to find favor in German textbooks. The economy of assumptions under the wave theory was emphasized by William Whewell in his History of the Inductive Sciences, first published in 1837. In the corpuscular system, "every new class of facts requires a new supposition," whereas in the wave system, a hypothesis devised in order to explain one phenomenon is then found to explain or predict others. In the corpuscular system there is "no unexpected success, no happy coincidence, no convergence of principles from remote quarters"; but in the wave system, "all tends to unity and simplicity." Hence, in 1850, when Foucault and Fizeau found by experiment that light travels more slowly in water than in air, in accordance with the wave explanation of refraction and contrary to the corpuscular explanation, the result came as no surprise. | [
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Lighthouses and the Fresnel lens
Fresnel was not the first person to focus a lighthouse beam using a lens. That distinction apparently belongs to the London glass-cutter Thomas Rogers, whose first lenses, 53cm in diameter and 14cm thick at the center, were installed at the Old Lower Lighthouse at Portland Bill in 1789. Further samples were installed in about half a dozen other locations by 1804. But much of the light was wasted by absorption in the glass. Nor was Fresnel the first to suggest replacing a convex lens with a series of concentric annular prisms, to reduce weight and absorption. In 1748, Count Buffon proposed grinding such prisms as steps in a single piece of glass. In 1790, the Marquis de Condorcet suggested that it would be easier to make the annular sections separately and assemble them on a frame; but even that was impractical at the time. These designs were intended not for lighthouses, but for burning glasses. Brewster, however, proposed a system similar to Condorcet's in 1811, and by 1820 was advocating its use in British lighthouses. Meanwhile, on 21 June 1819, Fresnel was "temporarily" seconded by the Commission des Phares (Commission of Lighthouses) on the recommendation of Arago (a member of the Commission since 1813), to review possible improvements in lighthouse illumination. The commission had been established by Napoleon in 1811 and placed under the Corps des Ponts – Fresnel's employer. | [
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By the end of August 1819, unaware of the Buffon-Condorcet-Brewster proposal, Fresnel made his first presentation to the commission, recommending what he called lentilles à échelons (lenses by steps) to replace the reflectors then in use, which reflected only about half of the incident light. One of the assembled commissioners, Jacques Charles, recalled Buffon's suggestion, leaving Fresnel embarrassed for having again "broken through an open door". But, whereas Buffon's version was biconvex and in one piece, Fresnel's was plano-convex and made of multiple prisms for easier construction. With an official budget of 500 francs, Fresnel approached three manufacturers. The third, François Soleil, produced the prototype. Finished in March 1820, it had a square lens panel 55cm on a side, containing 97 polygonal (not annular) prisms – and so impressed the Commission that Fresnel was asked for a full eight-panel version. This model, completed a year later in spite of insufficient funding, had panels 76cm square. In a public spectacle on the evening of 13 April 1821, it was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete. Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by Saint-Gobain, giving eight rotating beams – to be seen by mariners as a periodic flash. Above and behind each main panel was a smaller, sloping bull's-eye panel of trapezoidal outline with trapezoidal elements. | [
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