scholarly journals Early Texts on Hindu-Arabic Calculation

2001 ◽  
Vol 14 (1-2) ◽  
pp. 13-38 ◽  
Author(s):  
Menso Folkerts
Keyword(s):  
New York ◽  
Fifteenth Century ◽  
Twelfth Century ◽  
Decimal Place ◽  
Latin Translation ◽  
Place Value ◽  
Detailed Knowledge ◽  
The West ◽  
Value System

This article describes how the decimal place value system was transmitted from India via the Arabs to the West up to the end of the fifteenth century. The arithmetical work of al-Khwārizmī's, ca. 825, is the oldest Arabic work on Indian arithmetic of which we have detailed knowledge. There is no known Arabic manuscript of this work; our knowledge of it is based on an early reworking of a Latin translation. Until some years ago, only one fragmentary manuscript of this twelfth-century reworking was known (Cambridge, UL, Ii.6.5). Another manuscript that transmits the complete text (New York, Hispanic Society of America, HC 397/726) has made possible a more exact study of al-Khwārizmī's work. This article gives an outline of this manuscript's contents and discusses some characteristics of its presentation.

scholarly journals On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought

2015 ◽  
pp. 7 ◽  
Author(s):  
Sören Stenlund
Keyword(s):  
Sixteenth Century ◽  
Decimal Place ◽  
Place Value ◽  
Late Nineteenth Century ◽  
Value System ◽  
Early Modernity ◽  
Modern Physics ◽  
Ontological Sense ◽  
Modern Mathematics ◽  
Algebraic Symbolism

The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolism and started to use the word ‘symbolic’ in the relevant, non-ontological sense. This approach has played an important role for many of the great inventions in modern mathematics such as the introduction of the decimal place-value system of numeration, Descartes’ analytic geometry, and Leibniz’s infinitesimal calculus. It was also central for the rigorization movement in mathematics in the late nineteenth century, as well as for the mathematics of modern physics in the 20th century.However, the nature of symbolic mathematics has been concealed and confused due to the strong influence of the heritage from the Euclidean and Aristotelian traditions. This essay sheds some light on what has been concealed by approaching some of the crucial issues from a historical perspective. Furthermore, I argue that the conception of modern mathematics as symbolic mathematics was essential to Wittgenstein’s approach to the foundations and nature of mathematics. This connection between Wittgenstein’s thought and symbolic mathematics provides the resources for countering the still prevalent view that he defended an uttrely idiosyncratic conception, disconnected from the progress of serious science. Instead, his project can be seen as clarifying ideas that have been crucial to the development of mathematics since early modernity.

From Middle Horizon cord-keeping to the rise of Inka khipus in the central Andes

Antiquity ◽  
2014 ◽  
Vol 88 (339) ◽  
pp. 205-221 ◽  
Author(s):  
Gary Urton
Keyword(s):  
Number System ◽  
Central Andes ◽  
Decimal Place ◽  
Place Value ◽  
Middle Horizon ◽  
Value System ◽  
Intermediate Period ◽  
Andean South America ◽  
Ams Dating ◽  
Descendant Communities

Recording devices formed of knotted cords, known askhipus, are a well-known feature of imperial administration among the Inka of Andean South America. The origins and antecedents of this recording system are, however, much less clearly documented. Important insights into that ancestry are offered by a group of eight khipus dating from the later part of the Middle Horizon period (AD 600–1000), probably used by the pre-Inka Wari culture of the central Andes. This article reports the AMS dating of four of these early khipus. A feature of the Middle Horizon khipus is the clustering of knots in groups of five, suggesting that they were produced by a people with a base five number system. Later, Inka khipus were organised instead around a decimal place-value system. Hence the Inka appear to have encountered the base five khipus among Wari descendant communities late in the Middle Horizon or early in the Late Intermediate period (AD 1000–1450), subsequently adapting them to a decimal system.

Liber de causis

2018 ◽  
Author(s):  
Hannes Jarka-sellers
Keyword(s):  
Twelfth Century ◽  
Ninth Century ◽  
The Other ◽  
Natural Source ◽  
Latin Translation ◽  
Source Text ◽  
Medieval Philosophy ◽  
The West ◽  
Other Hand ◽  
The One

The Liber de causis (Book of Causes) is a short treatise on Neoplatonist metaphysics, composed in Arabic by an unknown author probably in the ninth century in Baghdad. Through its twelfth-century Latin translation, it greatly influenced mature medieval philosophy in the West. Drawing heavily on the Greek Neoplatonist Proclus, the Liber de causis represents a development of late Neoplatonism along two lines. On the one hand, the author modifies and simplifies Proclus’ theory of causes to accord more closely with the three-part division of ultimate causes advanced by the founder of Neoplatonism, Plotinus. On the other hand, the author introduces some of the metaphysical principles of Qu’ranic or biblical monotheism. The result is a metaphysically provocative reinterpretation of Neoplatonist thought which, because it seemed to accommodate Platonist philosophy to the medieval worldview, made the Liber de causis a natural source text for medieval philosophers.

Utopia’s Moorish Inspiration: Thomas More’s Reading of Ibn Ṭufayl

2018 ◽  
Vol 41 (3) ◽  
Author(s):  
Daniel Regnier
Keyword(s):  
Twelfth Century ◽  
The Self ◽  
Latin Translation ◽  
Thomas More ◽  
Philosophical Novel ◽  
Ibn Tufayl

A promising but neglected precedent for Thomas More’s Utopia is to be found in Ibn Ṭufayl’s Ibn Ḥayy Yaqẓān. This twelfth-century Andalusian philosophical novel describing the self-education and enlightenment of a feral child on an island, while certainly a precedent for the European Bildungsroman, also arguably qualifies as a utopian text. It is possible that More had access to Pico de la Mirandola’s Latin translation of Ibn Ḥayy Yaqẓān. This study consists of a review of historical and philological evidence that More may have read Ibn Ḥayy Yaqẓān and a comparative reading of More’s and Ṭufayl’s two famous works. I argue that there are good reasons to see in Ibn Ḥayy Yaqẓān a source for More’s Utopia and that in certain respects we can read More’s Utopia as a response to Ṭufayl’s novel. L’Ibn Ḥayy Yaqẓān d’Ibn Ṭufayl consiste en un précédent incontournable mais négligé à l’Utopie de More. Ce récit philosophique andalou du douzième siècle décrivant l’auto-formation et l’éveil d’un enfant sauvage sur une île peut être considéré comme un texte utopique, bien qu’il soit certainement un précédent pour le Bildungsroman européen. Thomas More pourrait avoir lu l’Ibn Ḥayy Yaqẓān, puisqu’il a pu avoir accès à la traduction latine qu’en a fait Pic de la Miradolle. Cette étude examine les données historiques et philologiques permettant de poser que More a probablement lu cet ouvrage, et propose une lecture comparée de l’Ibn Ḥayy Yaqẓān et de l’Utopie de More. On y avance qu’il y a non seulement de bonnes raisons de considérer l’Ibn Ḥayy Yaqẓān d’Ibn Ṭufayl comme une source de l’Utopie de More, mais qu’il est aussi possible à certains égards de lire l’Utopie comme une réponse à l’Ibn Ḥayy Yaqẓān.

Gerald H. Thayer's ornithological work in St Vincent and the Grenadines, Lesser Antilles

2018 ◽  
Vol 45 (1) ◽  
pp. 21-39 ◽  
Author(s):  
James W. Wiley
Keyword(s):  
New York ◽  
New York City ◽  
West Indies ◽  
The United States ◽  
Lesser Antilles ◽  
American Museum ◽  
The West ◽  
Comparative Zoology ◽  
North And South America ◽  
North And South

Gerald Handerson Thayer (1883–1939) was an artist, writer and naturalist who worked in North and South America, Europe and the West Indies. In the Lesser Antilles, Thayer made substantial contributions to the knowledge and conservation of birds in St Vincent and the Grenadines. Thayer observed and collected birds throughout much of St Vincent and on many of the Grenadines from January 1924 through to December 1925. Although he produced a preliminary manuscript containing interesting distributional notes and which is an early record of the region's ornithology, Thayer never published the results of his work in the islands. Some 413 bird and bird egg specimens have survived from his work in St Vincent and the Grenadines and are now housed in the American Museum of Natural History (New York City) and the Museum of Comparative Zoology (Cambridge, Massachusetts). Four hundred and fifty eight specimens of birds and eggs collected by Gerald and his father, Abbott, from other countries are held in museums in the United States.

Mafias on the Move

2011 ◽  
Author(s):  
Federico Varese
Keyword(s):  
United States ◽  
New York ◽  
Organized Crime ◽  
The United States ◽  
The West ◽  
Market Expansion ◽  
The North ◽  
Economic Transformations ◽  
At Will

Organized crime is spreading like a global virus as mobs take advantage of open borders to establish local franchises at will. That at least is the fear, inspired by stories of Russian mobsters in New York, Chinese triads in London, and Italian mafias throughout the West. As this book explains, the truth is more complicated. The author has spent years researching mafia groups in Italy, Russia, the United States, and China, and argues that mafiosi often find themselves abroad against their will, rather than through a strategic plan to colonize new territories. Once there, they do not always succeed in establishing themselves. The book spells out the conditions that lead to their long-term success, namely sudden market expansion that is neither exploited by local rivals nor blocked by authorities. Ultimately the inability of the state to govern economic transformations gives mafias their opportunity. In a series of matched comparisons, the book charts the attempts of the Calabrese 'Ndrangheta to move to the north of Italy, and shows how the Sicilian mafia expanded to early twentieth-century New York, but failed around the same time to find a niche in Argentina. The book explains why the Russian mafia failed to penetrate Rome but succeeded in Hungary. A pioneering chapter on China examines the challenges that triads from Taiwan and Hong Kong find in branching out to the mainland. This book is both a compelling read and a sober assessment of the risks posed by globalization and immigration for the spread of mafias.

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