Cinggis-qan (d. 1227) and their successors created the largest empire in history, and although the Mongol hordes have been most famous for rapine, pillage, war, and conquest, their overall reputation has recently achieved a well-deserved and long-awaited rehabilitation, based on Mongol achievements in many other areas than empire building. A new generation of scholars (led by Jack Weatherford) now recognizes that the Mongols, when they were not conquering and setting up empires and states, were often busy spreading cultural, technological and even scientific goods from one part of the world to the other, everything from food to philosophy and medicinals and medical lore, as well as achievements of science and technology.
Paul Buell discusses the transmission of Arabic medicine to China as attested for example in the Huihui yaofang 回回藥方 (HHYF), “Muslim Medicinal Recipes”, or perhaps better, “Western Medicinal Recipes”, so much is after all Greek. It is a unique document one that is Arabic Medicine on the surface but in fact shows many other influences, not just that of mainstream Arabic Medicine.
In “Art and Mathematics, Two Different Paths to the same Truth”, Patricia Radelet-de Grave analyses the classifications of Arabic abstract designs made by Hermann Weyl (1885–1955) and Andreas Speiser (1885–1970) based on the symmetries that organise them. For example, it is about abstract designs of Alhambra fortress in Muslim Spain (thirteenth-fourteenth centuries), which belong to a tradition of geometric motifs that goes back to ancient Egypt. The work of classification of groups made by Weyl and Speiser contributed largely to the spreading out of group theory in twentieth century mathematics.
The notions of group and of symmetry are deeply connected. A symmetry group is the set of all geometrical transformations under which the group remains unchanged or invariant. The fundamental mathematical idea of Arab-Islamic designs is indeed “invariance”, which means that motifs remains the same after a transformation in the plane: displacement, rotation or reflection. Radelet-de Grave argues that they were the product of a deep mathematical reflection, observing that all possible transformations of certain symmetry groups can be found in Arab geometric designs.
Marouane ben Miled analyses the impact of grammar in the emergence of algebra as a formal language in Arabic mathematics. He refers to the use of mathematics in Arabic grammar and lexicography in the eighth century. If Roshdi Rashed showed how al-Khalīl (eighth century) used combinatorial mathematical results to produce all the possible entries of a dictionary, submitting them to a phonological study, ben Miled asks himself how grammar methods were used in mathematics. He explains that al-Khawārizmī’s Algebra (written between 813 and 833) consists of a syntactical construction followed by geometrical and arithmetical interpretations. Algebra, a formal language where geometrical and arithmetical concepts, constructions and propositions of the Ancients meet, acts as a common empty language where both arithmetic and geometry find expression. Ben Miled focuses on the use of the rule of qiyās (analogy)—which occupies a central position in Arabic grammar and in Islamic juridical science—by al-Khawārizmī in his Algebra.
In his article “Ibn al-Haytham: between Mathematics and Physics”, Rashed explains, in a more detailed manner, the meaning of the combination between mathematics and physics that emerges in the works of Ibn al-Haytham. In astronomy, Ibn al-Haytham, having found contradictions in Ptolemy, established a totally geometrical celestial kinematics, independent of cosmological considerations and of Aristotelian dynamics. The result was a model of the apparent motion of the “seven planets” halfway between Ptolemy and Kepler. In optics, Ibn al-Haytham reformed the optics of Euclid and Ptolemy, which was a geometry of perception, and modified the doctrine of the Islamic Aristotelian philosophers of Islam, who considered the forms perceived by the eye as “totalities” transmitted by the objects under the effect of light. He separated the theory of vision from the theory of light and established experimentally that light propagates independently of vision from illuminated objects onto the eye in straight lines and, he assumed, with great speed. In so doing, he founded a totally geometrical optics. The advances he accomplished in astronomy and optics were similar: he mathematised these disciplines and combined this mathematisation with the ideas of the physical phenomena.
The purpose of this article is to show that the materialistic views of the Arab historian Ibn Khaldūn (1332–1406) expressed in his book known as the Muqaddima (“Introduction”), although geographically and chronologically far from seventeenth—eighteenth centuries’ Europe, anticipated similar intersections between materialism of nature and materialism of society (Descartes, Hobbes, Locke, Hume). Particularly we intend to analyse the meaning of a key-notion in Ibn Khaldūn’s historiography: the notion of “muṭābaqa”. This word literally means “coincidence”, “correspondence”, “conformity” between superimposable entities. In the field of historiography Ibn Khaldūn uses this word with the meaning of coincidence between historical events (waqāʾiʿ) and conditions or circumstances (aḥwāl). We analyse the notion of muṭābaqa as a microcosm of intersections between two great fields: the “system” of classical Arab culture and Khaldūn’s new materialistic conception of history. The latter, in its turn, lies in a zone of intersection between the natural and the social sciences. In our conclusion we highlight that the finalistic and aprioristic aporia inherent in the historical law of muṭābaqa is a most fertile and creative element in Khaldūn’s philosophy of history.
Anas Ghrab, in his “La musique parmi les sciences dans les textes arabes médiévaux”, analyses the position occupied by music in the Arab-Islamic system of knowledge. In conformity with the Aristotelian pattern, before acquiring the status of an autonomous discipline, music was considered by most of the Arab authors as part of the mathematical sciences. Aristotelian philosophers like al-Fārābī (878-950) and Avicenna (980-1037), relying upon Euclid and Ptolemy, observed that music shared elements with physics, because of the physical nature of sounds. In this respect Ghrab highlights another aspect of the relationship between different branches of mathematics and between mathematics and physics in classical Islam, a subject dealt with by Masoumi-Hamedani in this volume. He also refers to the influence of classical Islam on later research in music by the European scholarship of the Renaissance and beyond.
The aim of this article is to trace the history of the conceptual and historical relations between two groups of scientific disciplines, the mathematical sciences and the physical sciences, during the Islamic period. In so doing, Hossein Masoumi Hamedani wants to show how sophisticated this relations were and how the acknowledgement of the existence of some disciplines with both a mathematical and a physical aspect created a deep cleavage within the Aristotelian conception of science. The Author discusses the different reactions of mathematicians and physicists of the classical Islamic period to this situation and finally investigates Ibn al-Haytham’s idea that a combination of the method of physics and of the method of mathematics is necessary in treating problems pertaining to optics, and particularly to light and vision.
Patricia Radelet-de Grave shows that the notion of “invariance”, which she discusses also in her article “Art and Mathematics, Two Different Paths to the same Truth” with reference to symmetry groups, was essential also to the emergence of a crucial notion of modern physics, namely Galilean relativity which says that the fundamental laws of physics are invariant in all frames of reference moving with constant velocity with respect to each other. Galileo (1564–1642) demonstrated it by carrying out various experiments on a ship. The prehistory of the notion of invariance, essential to this principle can be found in Arab designs, although their invariance does not refer to transformations in the physical space but in the geometric plane. The notion of invariance has been applied subsequently by Huygens (1629–1695) to obtain the laws of collisions, by Lorenz (1853–1928) to obtain the coordinate transformations for space-time and by Einstein (1879–1955) to formulate special relativity then general relativity. Relying upon her analysis of the origin of invariance in Arab geometric designs, Radelet-de Grave advances a general hypothesis of philosophy of science, according to which fundamental scientific ideas are perennial and universal.