Table Of Contents
- About the editors
- About the book
- This eBook can be cited
- Mathematics & Religion in Ancient Greece and Medieval Islam: John Lennart Berggren
- Mechanics and Imagination in Ancient Greek Astronomy: Sphairopoiїa as Image and Tool: James Evans
- Sphairopoiїa in Mathematics and Philosophy of Nature
- Sphairopoiïa in Art and Education
- Sphairopoiїa and Gnomonics
- Some Ancient Planetariums
- Some Details of Ancient Greek Lunar Theory
- The Lunar Anomaly in the Antikythera Mechanism
- Sphairopoiїa as Tool of Discovery
- Alexandrian Astronomy in the 2nd Century AD: Ptolemy and his Times: Anne Tihon
- I. Ptolemy
- His Sources
- His instruments
- His collaborators
- His official position
- His colleagues
- Philosophical and religious ideas
- II. Contemporary astronomy: the papyrus Fouad Inv 267A
- III. Survival of Ptolemy in Antiquity
- Appendix. Ptolemy’s works
- (1) Almagest
- (2) Planetary Hypotheses
- (3) Phaseis
- (4) Handy Tables
- Note on a passage of the Arabic translation of Ptolemy’s Planetary Hypotheses: Sébastien Moureau
- Isis, Sarapis, Cyrus and John: Between Healing Gods and Thaumaturgical Saints: Laurent Bricault
- Sarapis of Canopus
- Isis of Menouthis
- Cyrus and John
- The Song of Orpheus in the Argonautica and the Theogonic Library of Apollonius: Marco Antonio Santamaria
- Imitation and aesthetic appreciation in Hellenistic poetry
- The Song of Orpheus in the Argonautica by Apollonius
- Narration in reported speech
- Themes of the Cosmogony
- The tripartite division of the world into earth, sky and sea
- The “single form” preceding the separation
- Separation through the work of strife
- The birth of the mountains and rivers
- The first divine couple, Ophion and Eurynome, and their defeat at the hands of Cronus
- Zeus’ future power
- Conclusion: a symphony of voices
- Paradox and the Marvellous in Greek Poetry of the Imperial Period: Luis Arturo Guichard
- Between literature and science, poetry and prose, Alexandria and Rome: the case of Dionysius’ Periegesis of the Known World: Jane Lucy Lightfoot
- 1. Literature
- 2. Geography
- 3. Author and narrator
- Lucian’s Podagra, Asclepius and Galen. The popularisation of medicine in the second century AD: María Paz de Hoz
- Medical knowledge and literature
- Medicine and Religion
- Did physicians learn anything from Asclepius?
- Conclusion: popularisation of medicine
- Christian Paideia in Early Imperial Alexandria: Clelia Martínez Maza
- “When I scan the circling spirals of the stars, no longer do I touch earth with my feet”: Juan Luis García Alonso
- Nonnus’ natural histories: anything to do with Dionysus?: Laura Miguélez-Cavero
- 1. Books 1–12: Rhetorical prelude
- a. Zeus undergoes several animal metamorphoses
- b. Rhea/Cibele’s power over animals, especially lions
- c. Animal shapes on his maternal side
- 2. Adult Dionysus: Animals as a fictional and literary resource
- 3. Usurpers as spurious animal masters and false lions
- 4. Elephantastic: India as land of Elephants
- 5. What about the sea? Marine creatures and didactic poetry
- Greek Poetry in Late Antique Alexandria: between Culture and Religion: Gianfranco Agosti
- John the Baptist
- True Miracles
- Dangerous statues
- Index locorum
- Index rerum notabilium
This book is the outcome of, on the one hand, the conference “Imperial Alexandria: Interactions between Science, Religion and Literature”, held at Salamanca University in October 2011, and, on the other, the activities of the research project FFI2011-29180 – Interacciones entre ciencia, religión y literatura en el Mediterráneo grecorromano (Interactions between science, religion and literature in the Graeco-Roman Mediterranean), which is hosted by that same university and financed by Spain’s Ministry of Science and Innovation (MICINN), which also funded the ancillary processes arranged for these purposes (FFI2010-10326-E).
This conference convened a group of experts from different fields to address the interrelationship between science, religion and literature in imperial times in the Graeco-Roman world, and especially in Alexandria, situating it within the context of the long tradition of knowledge that had been consolidating itself in this city, above all during the Hellenistic era. The encounter’s main aim was therefore to create a forum for interdisciplinary reflection on “the Alexandrian model” of knowledge in imperial times and its background, being attended by philologists and historians specialising in different types of texts (literary, scientific and religious), whose study requires an interdisciplinary approach; the overriding aim was to open a gateway to the understanding of the texts and the cultural expressions of the time, with priority being given to the notion of contact and the relationship between science, religion and literature, and explore new pathways in the focus on each subject in order to gain a better understanding of the spirit, way of thinking and moral and religious values of a particularly important era in the development of ancient culture.
The focal point of our study has been a highly significant period within this context and one that witnessed major changes, namely, the imperial era, understanding this to be the chronological arc that sweeps from the end of the first century BC (the annexation of Egypt ← 7 | 8 → as a Roman province in 30 BC is the standard date for the beginning of the period) through to the end of the third century AD, when widespread social upheaval in Alexandria, its decline as an economic power and the pressure exerted by the barbarian tribes on the Empire’s frontiers clearly signalled the end of an era that was confirmed by the founding of Constantinople in AD 324/330. It is a period in which Greek and Latin cultures introduced a new dynamic of communication that would last at least until the sixth century, based on the Roman Empire’s efficient administrative network. A period, furthermore, in which prestigious cultural centres such as Alexandria and Rome coexisted alongside Greek cities, which were becoming increasingly richer and more refined, in the Mediterranean and Asia Minor. In terms of the history of culture, there is a displacement of the ancient centres of power toward other new ones modelled on Hellenistic Alexandria. Yet what’s more, and this is the period’s main feature, there is a transformation in the forms of knowledge based on the myriad subjects of learning that had developed a remarkable level of specialisation in the Hellenistic era, as well as in the specific way such learning circulated and was expressed. In the long run, this transformation of knowledge would lead to a new specialisation that coincides largely with the definitions of each branch of knowledge that survive through to Late Antiquity and even the Middle Ages. The manner in which the three aforementioned spheres interrelate or distance themselves from each other is one of the keys for understanding the fundamentals of culture during that period, yet it is a subject that has never been the focus of a book-lenght study. This conference, therefore, sought to centre the discussion on the dynamics of relationship, appropriation, prestige and critique that exists between different ways of thinking and expression: science, religion and literature.
The actual content of the papers presented did indeed show us that it is extremely difficult to make a very neat temporal delimitation, even when certain chronological boundaries may be valid, and that a book on Alexandria in imperial times needs to be based on the notion of Alexandrian tradition, which is what truly gives consistency to the topics addressed. Further still, it confirms our initial impression that the axis forming the relationships between science, re ← 8 | 9 → ligion and literature apparent in many of the texts from the imperial era produced in Alexandria and in other intellectual centres in the Graeco-Roman Mediterranean is precisely a common tradition, the same cultural unity to which the idiosyncrasies of each sphere of knowledge and the diversity of local traditions are subordinated.
We are pleased to see that our initial hypothesis has turned out to be valid; that is, the relationship between science, religion and literature in imperial Alexandria is effectively a key element for understanding the texts of the time, and that this hypothesis has enabled specialists from different fields to explain aspects of their own type of text. The reader will not find it difficult to identify in each one of the papers gathered in this book a focus and type of resources that are specifically literary, religious or scientific, but they all pursue a greater understanding of the text by referring to at least one of the other two areas of knowledge. We trust this volume will help to illustrate the complex relationships between these three spheres and between them and an imperial culture whose roots are firmly embedded in Hellenistic Alexandria.
We would like to thank the contributors to the volume for attending this very lively conference and for their fine work on the papers; the Department of Classical Philology and the Philology Faculty at Salamanca for hosting the conference; Peter Lang and the editor of the IRIS series for publishing the work; our former student Aitor Blanco for his collaboration on a preliminary english translation of two of the papers, and the Spanish Ministry of Science and Innovation for funding both the conference and the publication of the book.
The Editors ← 9 | 10 → ← 10 | 11 →
In his classic study of religion and human psychology, The Varieties of Religious Experience, William James makes the point that in speaking of religion one has to begin with the realization that one is speaking of a collective, and the word does not stand for ‘any single principle or essence.’1 James goes on to distinguish between two manifestations of religion: the institutional and the personal. And he says at the outset that he will largely be silent relative to the first of these two forms, the institutional, and will focus almost entirely on the second, the personal. This latter aspect he describes as “the feelings, acts, and experiences of individual men in their solitude, so far as they apprehend themselves to stand in relation to whatever they may consider the divine.” In this lecture both the institutional and personal manifestations of religion will enter, but I stress James’s mention of the personal form because it reminds us that under the rubric of ‘religion’ there are phenomena that do not have any direct connection with institutions.
It may happen, however, that the institutional and the personal aspects are very closely linked. Indeed, although it seems that the earliest known connection between religion and mathematics in ancient Greece arose from ‘the feelings, acts, and experiences’ of Pythagoras (ca. 572–497 BC) his teachings are known only through later writings stemming from the Pythagorean school. And the reports of the life of Pythagoras indicate that he worked within some sort of institutional setting, a group of individuals who considered themselves a group and who had a developed form of doctrine and discipline. But it is also the case that later Pythagoreanism manifested itself primarily as a personal attitude towards the cosmos. ← 11 | 12 →
At the heart of this attitude is the belief that the basis of all existence is number. As Aristotle writes in Metaphysics I, 5, the Pythagoreans “supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.”
This belief has obviously had great scientific significance, but it also had a moral significance because the Pythagoreans believed that one can know the character of things by knowing the numbers associated with them. The commentator, Iamblichus, around the end of the third century A. D., wrote in his Theology of Arithmetic that mathematics is the key to understanding all of nature. And by this he meant, as his illustrations show, not the technical use of mathematics in the astronomy of the Almagest but insight into nature to be gained by a metaphorical interpretation of the numbers found in the heavens.
A much earlier writer, Philolaus, a contemporary of Socrates, argued2 that all matter is composed of limiters (numbers, shapes, etc.) and unlimiteds (e. g. the four elements and continua such as space and time). These “are not combined in a haphazard way but are subject to a ‘fitting together’ or ‘harmonia,’ which can be described mathematically.”
Philolaus’s primary example of such a harmonia of limiters and unlimiteds is a musical scale, in which the continuum of sound is limited according to whole number ratios, so that the octave, fifth, and fourth are defined by the ratios 2: 1, 3: 2 and 4: 3, respectively, Thus limits form harmony from unlimited sounds. Since the whole world is structured according to number, we only gain knowledge of the world insofar as we grasp these numbers. “This numerical essence of things,” Philolaus argues, “is eternal; it is a unique and divine nature, the knowledge of which does not belong to man.”3
The Greek view of number was expressed by a variety of ancient writers, but that of the Pythagorean Nicomachus (ca. 100 A. D.) is typical. “Number is a defined [or ‘limited’] multitude or a collection of units ….”4 There was, then, only the monad, the begetter of num ← 12 | 13 → bers, to employ one of Iamblichus’s metaphors, and the whole numbers 2, 3, …. Numbers begin with ‘two’, Iamblichus’s ‘dyad.’ And Aristotle wrote (Metaphysics A.5) that for the Pythagoreans the numbers fell into two classes, the odd and even. The metaphorical use of numbers is, in this connection, exemplified by the Pythagoreans’ pairing of this dichotomy with another, that of male and female, so that odd numbers represent the male and even numbers the female. Thus, the sum of the first even (2) and the first odd (3) numbers, represents marriage. And the fact that odd plus even makes odd becomes, in their interpretation of odd as masculine and even as feminine, a correlate of the domination of the male over the female.5
But another of Philolaus’s limiters, shapes, could also, in Pythagorean thought, be thought of numerically. This they did by arranging pebbles to produce certain figures, Hence “figured numbers”. The simplest were triangular numbers, containing 3, 6, 10, … points.6 Ten, for example, was the Pythagorean ‘decad’ and a symbol for the cosmos. Of the number 10, Plato’s nephew, and successor at the Academy, Speusippus, points out, in his Pythagorean Numbers, that the decad contains the sum of all the numbers whose ratios describe harmonic musical sounds. These geometric representations of certain classes of numbers resulted in names, such as ‘square’ numbers, which are still used to refer to them.7 Speusippus’s work also contains discussions of solid numbers, and one can find in the writings of both Nicomachus and Theon of Smyrna extensive discussions of plane and solid numbers.8 ← 13 | 14 →
Even within the Pythagorean tradition, however, such scholars as Burkert and Knorr believe that these polygonal representations of numbers led to a number of significant theorems – e. g. the fact that any square (such as 9) can be represented as the sum of a certain number of odd numbers beginning with the unit (in this case 1, 3, 5). Using this fact together with the pebble arrangements, the Pythagoreans arrived at the well-known Pythagorean triples, i. e. three whole numbers, such as 3, 4, and 5 that can be the sides of a right-angled triangle. The fact that a geometric property, such as the kind of angles in a triangle, could force the arithmetic property of a square being equal to the sum of two other squares, demonstrated dramatically the numerical basis of reality. As Burkert puts it, “The suspicion remains that the theorem had more than a mathematical significance in Pythagoras’ school, and that the numbers involved seemed in a cryptic way meaningful.”9 Burkert goes on to point out that the Pythagorean triple that occurs constantly in ancient testimony on this point, the (3, 4, 5) triple would be highly significant for the Pythagoreans since, as we have said, 3 is a male number, 4 a female number, and 5 (the sum of a male – 3 – and female – 2 – numbers) is the number of marriage.
Burkert points out, quite properly, that although this is certainly thinking about numbers, it is not the kind of thinking we associate with Greek mathematics. In his words,
What we find among the Pythagoreans is amazement and ‘reverence’ for certain numbers and their properties and interrelations. ‘Even’ and ‘odd’ are united in ‘marriage’: and to them [the Pythagoreans] this means that cosmic forces are at work.10
The relationships between mathematics and religion in the Greek world were not, however, confined to Pythagorean doctrine. The numbers referred to above, the simple ratios limiting the harmonious sounds, appear also in early Greek temple architecture. For example, the design of the temple of Zeus in Olympia, completed in 456 B. C. E., ← 14 | 15 → was governed by the ratio of 1:2, starting from two-foot-wide tiles and progressing by successive doublings to a distance of 16 feet between the columns.11
More complex ratios were used in temples as well, For example, when the architects Ictinus and Callicrates built the Parthenon in Athens in the years 447–432 they used the ratio of the two smallest square numbers, 9:4, to determine the whole building.12 So, the ratios 81:36:16 are equal to the ratios of length : breadth : height and both ratios 81 : 36 and 36:16 are equal to 9:4. And the ratio of 3:2, whose squares produce the ratio 9:4, governs the harmonious sounds of the Pythagorean fifth. Architecture was indeed, as Goethe put it, ‘frozen music’.
Almost a century before the Parthenon, though, one finds that ca. 540 B. C. E. the temple of Apollo in Corinth was built with the same kind of proportion, i. e. A:B=B:C (which the Greeks called the ‘geometric mean’ and we call the ‘golden mean’), between lengths A and C. It is the earliest known temple with a clear proportion length : breadth = breadth : height.
This same ratio appears again as “the mathematical foundation of one of the most famous Greek temples, the Tholos13 in the sanctuary of Athena at Delphi.”14 Built during the decade 380–370 BC, the building has the property that its 20 outer columns are spaced around its circular base to form a regular icosagon15. (The connection between the regular icosagon and the geometric mean is made clear in Book IV of Euclid’s Elements.) Moreover, each of the 20 columns of the building has 20 grooves, so each column recreates in small the design of the whole. And each column is 20 feet high.16 ← 15 | 16 →
We have referred to Greek cosmology in connection with Philolaus and we return to the topic now. In Philolaus’s work we find the claim that the celestial bodies (which included a counter earth and a central fire) are divine. Plato, although he did not share all the details of Philolaus’s cosmology, also believed that the celestial bodies were divine.17 And Aristotle, too, argued in De Caelo that the substance that fills the spheres beyond that of the moon, namely the aether, is divine.
This belief in the divinity of the celestial led the Athenians to try Anaxagoras for impiety for stating that the sun was a red hot mass of metal,18 an early example of a conflict between religious and scientific cosmology.
For a number of centuries following Aristotle, a new style seems to enter Greek science, and that was the deductive, tersely logical style that one associates with the great figures of ancient Greek mathematics: Euclid, Archimedes and Apollonius. For example, Euclid, in his treatise on the celestial sphere, The Phaenomena [of the Heavens], says nothing about divinity. The treatise begins by marshalling arguments for believing that the cosmos is spherical, starting with the sentence “The fixed stars are seen always rising from the same place and setting in the same place. ….”19 And the first proposition is a proof that “The Earth is in the middle of the cosmos.” Nor does Archimedes say anything about the gods or divinity in his Arenarius, a work in which he calculates the size of the cosmos. Finally, in Geminus’s Introduction to the Phenomena, written for the educated layman probably sometime during the first century BC, there is no hint of anything divine about the heavens. Geminus begins with “The ← 16 | 17 → circle of the signs is divided into 12 parts …”20 and never departs from this straightforward, narrative tone.
The situation changes, however, when we come to the greatest of the Greek astronomers, Claudius Ptolemy, who worked during the second century AD. Certainly anyone who has read any significant part of the Almagest will know that Ptolemy was a virtuoso in technical astronomy and complex mathematical arguments.
However, he begins his Almagest in a philosophical vein, with an approving quotation of Aristotle’s statement that theoretical philosophy has three branches: theology, mathematics, and physics. Unlike Aristotle, however, Ptolemy argues that the primary subject of these three is not theology. (He says that, like physics, theology “should be called ‘guesswork’ rather than knowledge”21). Rather, Ptolemy “stated [in his introduction to the Almagest] that what is mathematical preserves the divine nature which is the subject matter of theology …” He went on to say that only mathematics, whose “subject matter falls, as it were, in the middle between the other two” can provide “unshakable knowledge to its devotees provided one approaches it rigorously.”22
This view of mathematical argument as a source of certainty also influenced the much later writer, Proclus, who, with a nod to Euclid, wrote an Elements of Theology in which his arguments were modeled on those in mathematics.
Ptolemy tells us in the Almagest that the heavenly bodies are divine.23 And they were moved by a ‘first cause,’ which can be thought of, in Ptolemy’s words, as “an invisible and motionless deity.”24 For this reason Ptolemy viewed mathematics as a propaedeutic to theology, since it could provide certain knowledge about things (the ← 17 | 18 → heavenly bodies) that shared some essential attributes (e. g. eternal and unchanging) with the subject of theology.25
Complementing Ptolemy’s belief in the divine nature of the heavens was his belief in an ethical role for astronomy, which, in exhibiting the eternal, unchanging and rational movements of the divine celestial bodies, provided a visible ideal model for human behavior. As he put it:
As regard to virtuous conduct in practical actions and character, this science [astronomy], above all things, could make men see clearly; from the constancy, order, symmetry and calm which are associated with the divine, it makes its followers lovers of the divine beauty, accustoming them and reforming their natures, as it were, to a similar spiritual state.26
Nor is this sort of reasoning limited to the preface to the Almagest. In fact, in Ptolemy’s treatise on music, his Harmonics, we find that the Almagest was part of a larger program. As Liba Taub put it, in this largely mathematical treatise
Ptolemy’s task … was to identify the analogous structures and relationships present in music, in the heavens, and in the human soul; the same fundamental mathematical relationships underlie and define the Good in each type of matter.27
In this work, again, Ptolemy’s underlying ethical motivation comes to the fore when he writes:
It was because he [Pythagoras] understood this fact that Pythagoras advised people that when they arose at dawn, before setting off on any activity, they should apply themselves to music and to soothing melody … and so make their souls well-attuned and concordant for the actions of the day.28
Indeed, the ratios at the root of harmonious melodies could even affect the gods themselves, for (as he also wrote) “the fact that the ← 18 | 19 → gods are invoked with music and melody of some sort … shows that we desire them to listen to our prayers with kindly gentleness.”29
After this examination of religion and the mathematical sciences in the Greek world we turn to the medieval Islamic world, where mathematics played a number of important roles in religion. And these roles, in turn, provided support to the mathematicians in justifying their pursuits in a society that was grounded on religious faith.
But it must be said at the start that these roles occasioned some considerable controversy in Muslim society, and opinion on the value, or even propriety, of study of such foreign sciences30 as mathematics and philosophy was divided. On the one hand, much of the support for the acquisition of ancient Greek and Indian works in the sciences and philosophy came from caliphs, ministers of state, and prominent families.31 And they could cite, in support of their patronage, the Muslim tradition that quoted Muh.ammad as urging his followers to “Seek knowledge, even in China.”
In the first half of the ninth century, al-Kindī, scion of a distinguished family and one of the great intellects of Arabic literature, wrote extensively on a range of scientific and philosophical subjects. Of those among his contemporaries who attacked philosophy in the name of religion, al-Kindī said that they themselves were “without religion.”32 (Although, as a Muslim, al-Kindī could not share Ptolemy’s view of the divinity of the celestial bodies, he did say that celestial bodies are rational entities, who move in circles to obey and worship God.)
But, despite support among a number of the elite, the controversy over foreign learning continued. And, because the issue of religion and the exact sciences in medieval Islam has been so oversimplified in a number of the modern media, it is well to examine ← 19 | 20 → the various shades of opinion in this controversy. For example, in the century following al-Kindī, an Iranian mathematician and astronomer, al-Sijzī, wrote of men living in his town who thought it lawful to kill mathematicians.33 Yet, al-Sijzī lived at a time, the second half of the tenth century, when the study of geometry was flourishing and the sciences were supported by the kings of the Buyid dynasty, who ruled what is now Iran and much of Iraq.
Elsewhere, however, the Yemini legal scholar al-Aṣbaḥī wrote that,
The times of prayer are not to be found by the degrees on an astrolabe nor by calculation using astronomers. They are to be found only by direct observation … The astronomers took their knowledge from Euclid and the Sindhind, and from Aristotle and other philosophers, all of them infidels.34
Such sharp attacks provoked equally sharp replies. Thus, the 11th-century Central Asian polymath and scientist, al-Bīrūnī, wrote of people like al-Aṣbaḥī as follows: The extremist … would stamp the sciences as atheistic and would proclaim that they lead people astray – in order to make ignoramuses, like him, hate the sciences.”
All of these incidents, pro and con, come from the eastern caliphate, but one can cite similar ambivalence in the western part of the Muslim world, Spain and North Africa. Thus, the contemporary of al-Bīrūnī, the historian Sācid al-Andalusī, from Almería, relates how, the Andalusian caliph, al-Ḥakam ibn ‘Abd al-Raḥmān, “brought from Baghdad and Egypt the best of their scientific works and their most valuable publications whether new or old.” However, al-Ḥakam died in 977 AD, when his son was still a child. So, one of his officials, ‘Abdullah b. Muḥammad al-Qahtaqnī, usurped power and, as Said tells it,
His first action … was to seize the libraries of … al-Ḥakam…. he showed these books to his entourage of theologians and ordered them to take from them all ← 20 | 21 → those dealing with the ancient sciences of logic, astronomy and other fields, saving only the books on medicine and mathematics.35
Intermediate to these positions was that of a number of eminent Muslim scholars who, while not condemning a study of the foreign sciences (as they were called), held the view that excessive study of nonreligious areas could lead to the neglect of one’s obligations to the religious community Islam. Thus the famous 9th-century physician, Abū Bakr al-Razī, said that he studied mathematics only to the extent that it was absolutely necessary. He avoided, he tells us, the path of the “so-called philosophers who devote their whole lives to studying geometrical superfluities.”36 A similar thought is found in the Prolegomena of the great scholar Ibn Khaldūn in the 14th century.
But, al-Bīrūnī also replied to these ‘moderate’ views in referring to
[…] people who discard the sciences and … persecute the custodians of learning. The extremist among them would stamp the sciences as atheistic … [but] the rude and stubborn critic …, who calls himself impartial, would listen to scientific discourses, but … would come forth with what he considers to be great wisdom and ask, ‘What is the benefit of these sciences?’. He does not know the virtue that distinguishes mankind from all sorts of the animal kind. It is knowledge, in general, which is pursued by man and which is pursued for the sake of knowledge.37
A variation on this theme is the passage from the famous theologian al-Ghazālī who wrote in his Revival of the Religious Sciences that
[…] the study of the sciences of Euclid, the Almagest, and the subtleties of arithmetic and geometry … render the mind more acute and strengthen the soul, and yet we refrain from them for one reason: they are among the presuppositions of the ancient sciences and these latter include those sciences, beside arithmetic and geometry, that entail the acceptance of dangerous doctrines. Even if geometry and arithmetic do not contain notions that are harmful to religious beliefs, we nevertheless fear that one might be attracted through them to doctrines that are dangerous. ← 21 | 22 →
We have gone into the historical background of the sciences and religion in Islam at some length because we feel that the literature on the topic, especially coverage in the electronic media, is too often tendentious, either overemphasizing periods and places where there was a strong bias against science or portraying the whole of Islamic history as a paradigm of what societal support for science should be. Historical truth is local.
The one generalization that does hold is, in spite of a continuing debate the mathematical sciences were widely cultivated in the medieval Islamic world and often interacted significantly with the religion of Islam. Three such sciences are arithmetic, geometry, and astronomy.
It is well-known that our decimal, positional system of arithmetic came to the West from the Islamic world, where an important application of arithmetic was the calculation of both zakāt and legacies. (Zakāt is the community’s share of the individual’s wealth, payable each year at a set rate.) For example, in his Supplement of Arithmetic, the eleventh-century mathematician Abu Manṣūr al-Baghdādī calculated the gradual diminution, over three years, of a sum of 7,586 dirhams, assuming an annual rate of taxation of 1 in 40. (The dirham was divided into 40 fulūs, the plural of fals).
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- Bern, Berlin, Bruxelles, Frankfurt am Main, New York, Oxford, Wien, 2014. 324 pp., num. coloured and b/w ill.