The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter.

With mathematical reconstructions and philosophical arguments I show that Toomer's 1973 paper never contained any conclusive evidence for his claims that Hipparchus had a 3438'-based chord table, and that the Indians used that table to compute their sine tables. Recalculating Toomer's reconstructions with a 3600' radius -- i.e. the radius of the chord table in Ptolemy's Almagest, expressed in 'minutes' instead of 'degrees' -- generates Hipparchan-like ratios similar to those produced by a 3438' radius. It is therefore possible that the (...) radius of Hipparchus's chord table was 3600', and that the Indians independently constructed their 3438'-based sine table. (shrink)

This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew (...) how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof. (shrink)

Very Short Introductions: Brilliant, Sharp, Inspiring Ancient Greece is often considered to be the birthplace of science and medicine, and the explanation of natural phenomena without recourse to supernatural causes. These early natural philosophers - lovers of wisdom concerning nature - sought to explain the order and composition of the world, and how we come to know it. They were particularly interested in what exists and how it is ordered: ontology and cosmology. They were also concerned with how we (...) come to know (epistemology) and how best to live (ethics). At the same time, the scientific thinkers of early Greece and Rome were also influenced by ideas from other parts of the world, and incorporated aspects of Egyptian, Babylonian, and Indian science and mathematics in their studies. In this Very Short Introduction Liba Taub gives an overview of the major developments in early science between the 8th century BC and 6th century AD. Focussing on Greece and Rome, Taub challenges a number of modern misconceptions about science in the classical world, which has often been viewed with a modern lens and by modern scientists, such as the misconception that little empirical work was conducted, or that the Romans did not 'do' science, unlike the Greeks. Beginning with the scientific notions of Thales, Pythagoras, Parmenides and other Presocratics, she moves on to Plato and Aristotle, before considering Hellenistic science, the influence of the Stoics and Epicurean ideas, and the works of Pliny the Elder, Eratosthenes, and Ptolemy. In her sweeping discussion, Taub explores the richness and creativity of ideas concerning the natural world and its function in the ancient world, and the influence these ideas have had on later centuries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. (shrink)

This book offers an engaging and comprehensive introduction to scientific theories, and the evolution of science and mathematics through the centuries. It discusses the history of scientific thought and ideas and the intricate dynamic between new scientific discoveries, scientists, culture, and societies. Through stories and historical accounts, the volume illustrates the human engagement and preoccupation with science and the interpretation of natural phenomena. It highlights key scientific breakthroughs from the ancient to later ages, giving us accounts of the (...) work of ancient Greek and Indian mathematicians and astronomers as well as of the work of modern scientists like Descartes, Newton, Planck, Mendel and many more. The author also discusses the vast advancements which have been made in the exploration of space, matter, and genetics and their relevance in the advancement of the scientific tradition. He provides great insights into the process of scientific experimentation and the relationship between science and mathematics. He also shares amusing anecdotes of scientists and their interactions with the world around them. Detailed and accessible, this book will be of great interest to students and researchers of science, mathematics, the philosophy of science, science and technology studies, and history. It will also be useful for general readers who are interested in the history of scientific discoveries and ideas. (shrink)

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of (...) Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal. (shrink)

This paper explains how mathematical computation can be constructed from weaker recursive patterns typical of natural languages. A thought experiment is used to describe the formalization of computational rules, or arithmetical axioms, using only orally-based natural language capabilities, and motivated by two accomplishments of ancient Indian mathematics and linguistics. One accomplishment is the expression of positional value using versified Sanskrit number words in addition to orthodox inscribed numerals. The second is Pāṇini’s invention, around the fifth century BCE, (...) of a formal grammar for spoken Sanskrit, expressed in oral verse extending ordinary Sanskrit, and using recursive methods rediscovered in the twentieth century. The Sanskrit positional number compounds and Pāṇini’s formal system are construed as linguistic grammaticalizations relying on tacit cognitive models of symbolic form. The thought experiment shows that universal computation can be constructed from natural language structure and skills, and shows why intentional capabilities needed for language use play a role in computation across all media. The evolution of writing and positional number systems in Mesopotamia is used to transfer the thought experiment of “oral arithmetic” to inscribed computation. The thought experiment and historical evidence combine to show how and why mathematical computation is a cognitive technology extending generic symbolic skills associated with language structure, usage, and change. (shrink)

Ancient allures the postmodern social subject trapped in the strangeness of time—the time after the end of history. For that time-beaten subject ancient is the unconscious of coherence, predictability, and certainty. Or perhaps that ancient is a glory fled. Whatsoever, ancient is generally sacralized—irrespective of the type of socialization that happened in the past—and journey to the ancient is often deemed to be a pilgrimage. When ideas of the ancient in their individuality and totality (...) inter alia become the natural intellectual resource for rebuilding postmodern societies, discriminative ingenuity becomes an essential faculty. Any uncritical reverence of the ancient becomes antithetical to modern social and political values, inviting the risk of reproducing inequities of the past. This article problematizes such uncritical dependence on the ancient using Ancient Indian Jurisprudence, which has been looked up on as a repository of moral and legal values, as a case in point. It meditates from the experiences and perspectives of an imaginary ‘teaching subject’ on the many pitfalls and possibilities of the ancient as it builds a framework of teaching and learning, and a representative scheme of evaluation for Ancient Indian Jurisprudence. (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we (...) go through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

Ancient Indian Coins. Osmund Bopearachchi and Wilfried Pieper., Brepols, Turnhout 1998. 289 pp. + 59 plates. €88. ISBN 2-503-50730-1 Uygur Buddhist Literature. Johan Elverskog., Brepols, Turnhout 1997. 154 pp. €43. ISBN 2-503-50544-9.

Four modes of language acquisition and communication are presented translating ancient Indian expressions on human consciousness, mind, their form, structure and function clubbing with the Sabdabrahma theory of language acquisition and communication. The modern scientific understanding of such an insight is discussed. . A flowchart of language processing in humans will be given. A gross model of human language acquisition, comprehension and communication process forming the basis to develop software for relevantmind-machine modeling will be presented. The implications of (...) such a model to artificial intelligence and cognitive sciences will be discussed. The essential nature and necessity of a physics, communication engineering , biophysical and biochemical insight as both complementary and supplementary to using mathematical and computational methods in delineating the theory of language processing in humans is put forward. (shrink)

The article is the first exploration of Mārganāṭyam, a new tradition in the performing arts of modern India, created from the beginning of the XXI century by an outstanding researcher of musical, theatrical and dance culture, Kalamandalam Piyal Bhattacharya and his students. It is based on the many years of the author’s personal observations, interaction, interviews and discussions with the participants of “Chidakash Kalalay. Centre of Art and Divinity”, an artistic community based on the direct transfer of knowledge and skills (...) from teacher to students, which has developed around Piyal. The features of the method of reconstruction of the ancient Indian theater, the flexible application of the legacy of the past in modern conditions are under study. Particular attention is paid to the artistic interpretation and comprehension of the Indian philosophical heritage, and above all the concepts and worldview of Nyaya and Vedanta systems, transferring them to the space of scenic images. The presented material demonstrates that an integrated approach to the artistic heritage, a metatheater, combined with individual pedagogical unfold of the personality of the artists, creates the possibility of recreating the long-vanished tradition and complex philosophical issues in a way that is well understood today, relevant and reflects the essential needs of modern creators and viewers of the Indian theater at large. (shrink)

Proceedings of the seminar organized by Centre of Advanced Study in Sanskrit, University of Pune in 2007.

Contributed articles on eighteen Indic philosophers and grammarians flourishing between 400 B.C. to 1600 A.D.

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.

A drink called surā is the alcoholic drink mentioned in our oldest Indian text, the Ṛg Veda, and people continued to make a drink called surā for millennia. This article uses the methodology of the comparative study of fermentation methods in order to make sense of the earliest descriptions of surā brewing processes. Surā was brewed in a semi-solid state, using malts for saccharification, perhaps also with a complex microbial ferment starter as one sees elsewhere in Asia today. Surā (...) was not distilled. Understanding this has philological value: if surā was brewed with this process, we can better understand certain words associated with surā in Vedic texts, e.g., the drink called parisrut, certain material objects, and certain processes. Although brewing instructions are varied and may reflect several modes of brewing, and although the process in surviving descriptions may have been ritually inflected to highlight resemblances with soma pressing, I argue we can still get a sense of the basic method of brewing. These are some of the earliest detailed descriptions of brewing a grain drink that, con- sidered in the long term, has similarities with both Mesopotamian brewing and East Asian methods. (shrink)

It remains only to remark that, what I, the survivor through, get called is in some measure a matter of semantical preference. And Sanskrit terms that might, sometimes, be rendered “consciousness” in English — like ‘citta’, or ‘caitanya’, or ‘cetana’, for instance — could serve, and do, solong as one stays mindful of the facts — that they are terms for what I am, surviving through my being conscious, and my not being so, and not merely for what I am, (...) when conscious.What seems to me of deep significance, though, is that other terms — like ‘ātman’, ‘puru $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{s}$$ a’, ‘sāk $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{s}$$ in’, and even ‘'jīvātman’ — far more often get used for what I'm talking of here; and that none of these obviously, or, indeed, ever need mean ‘consciousness’.6. (shrink)

In the last century and in the first decades of the present century the historians of India laid stress on the isolation of the subcontinent by the mountains and seas surrounding her on all sides and cutting her off as a separate universe. The progress of modern research has shown how mistaken this view was. We now see the true facts much more clearly than ever. The mountain barriers, though formidable at many points, are broken by gaps which have always (...) allowed a considerable intercourse across the frontiers on the northwest as well as the northeast and at some points due north as well. By her position in the center of the littoral of the Indian Ocean, India enjoyed ample facilities for communication by sea with the countries lying to her west and east, and we now know that she and her neighbors availed themselves of these facilities from time immemorial. The Indian Ocean was navigated freely from very early, even prehistoric, times, and there was a series of lively maritime exchanges—migratory, commercial, and cultural—among the peoples of Africa, India, and Indonesia, or more generally Southeast Asia. Western Asia and the lands adjoining the Levant also took, from the beginning, a prominent part in this commerce of goods and ideas between India and the world. It is the aim of this paper to trace briefly the ancient contacts between India and the Western countries to the time when the rise and spread of Islam and the Islamic impact on India ushered in a new epoch. (shrink)

Unknown to most Western psychologists, ancient Indian scriptures contain very rich, empirically derived psychological theories that are, however, intertwined with religious and philosophical content. This article represents our attempt to extract the psychological theory of cognition and consciousness from a prominent ancient Indian thought system: Samkhya-Yoga. We derive rather broad hypotheses from this approach that may complement and extend Western mainstream theorizing. These hypotheses address an ancient personality theory, the effects of practicing the applied part (...) of Samkhya-Yoga on normal and extraordinary cognition, as well as different ways of perceiving reality. We summarize empirical evidence collected in diverse fields of research that allows for making judgments about the hypotheses, and suggest more specific hypotheses to be examined in future research. We conclude that the existing evidence for the hypotheses is substantial but that there are still considerable gaps in theory and research to be filled. Theories of cognition contained in the ancient Indian systems have the potential to modify and complement existing Western mainstream accounts of cognition. In particular, they might serve as a basis for arriving at more comprehensive theories for several research areas that, so far, lack strong theoretical grounding, such as meditation research or research on aspects of consciousness. (shrink)

This book studies the history of intercultural human rights. It examines the foundational elements of human rights in the East and the West and provides a comparative analysis of the independent streams of thought originating from the two different geographic spaces. It traces the genesis of the idea of human rights back to ancient Indian and Greco-Roman texts, especially concepts such as the Rigvedic universal moral law, the Upanishadic narratives, the Romans' model of governance, the rule of law, (...) and administration of justice. It also looks at Cicero's concept of rights and duties which focuses on quality of compassion and fair play, and Seneca's expositions on mercy, empathy, justice and checks on the arbitrary exercise of power. An important contribution, this book fills a significant gap in the study of human rights. It will be useful for students and researchers of political science, ancient history, religion and civilizations, philosophy, history, human rights, governance, law, sociology, and South Asian studies. The book also caters to general readers interested in the history of human rights. (shrink)

For scholars of ancient Indian religions, the wandering mendicants who left home and family for a celibate life and the search for liberation represent an enigma. The Vedic religion, centered on the married household, had no place for such a figure. Much has been written about the Indian ascetic but hardly any scholarly attention has been paid to the married householder with wife and children, generally referred to in Sanskrit as grhastha: "the stay-at-home." The institution of the (...) householder is viewed implicitly as posing little historical problems with regard to its origin or meaning. This volume problematizes the figure of the householder within ancient Indian culture and religion. It shows that the term grhastha is a neologism and is understandable only in its opposition to the ascetic who goes away from home (pravrajita). Through a thorough and comprehensive analysis of a wide range of inscriptions and texts, ranging from the Vedas, Dharmasastras, Epics, and belle lettres to Buddhist and Jain texts and texts on governance and erotics, this volume analyses the meanings, functions, and roles of the householder from the earliest times unti about the fifth century CE. The central finding of these studies is that the householder bearing the name grhastha is not simply a married man with a family but someone dedicated to the same or similar goals as an ascetic while remaining at home and performing the economic and ritual duties incumbent on him. The grhastha is thus not a generic householder, for whom there are many other Sanskrit terms, but a religiously charged concept that is intended as a full-fledged and even superior alternative to the concept of a religious renouncer. (shrink)

The ‘deontic orientation’ thesis—that is, the claim that ancient Indian legal theory is orientated or focussed towards duty to the exclusion of other jural operators—features prominently in the discourse of ancient Indian law. In contrast, contemporary legal systems tend to employ a variety of other jural operators also, including right, liberty, power, and so forth. Theorists like Wesley Hohfeld even assert that these operators are elemental, and hence not reducible to other operators. This disparity may be (...) addressed from various evaluational and conceptual standpoints. I address instead a more basic question: is the disparity real? Does a scrutiny of legal treatises factually validate the deontic orientation thesis? I contend that the thesis is factually not sustainable, and that legal treatises of ancient India do display a sophisticated conception of non-deontic operators. To this end I undertake a scrutiny of Kauṭilya’s Arthaśāstra, to determine the treatise’s use of non-deontic operators, and whether it treats them as entities in their own standing as opposed to derivatives or outcomes of the deontic. (shrink)

불교와 자이나교 양쪽에서 전하고 있는 파에시 논쟁 문헌에 등장하는 수많은 비유 중에서 특히 도박 관련 비유에 나타난 고대 인도 문화의 놀이 문화와 번역 용어 문제를 중점적으로 분석하였다. 파에시 논쟁 문헌에 등장하는 갖가지 비유들은 실제로 그 논쟁이 이루어졌던 당시에 논쟁의 상호 당사자들은 너무도 잘 알고 있던 내용일 것이라는 점은 미루어 짐작할 수 있다. 이 논문에서 필자는 파에시 논쟁 문헌에서 나오는 “악카 놀이”는 고대부터 인도에서 행해진 놀이 방법의 하나로 추정되며, 악카는 나무 열매라고 밝힌다. 따라서 이를 단순히 주사위 또는 주사위 놀이라고 통칭하여 번역하는 (...) 것은 적절하지 못하다고 주장한다. 필자는 고대 인도의 유흥 문화의 일종으로서 도박의 수단이 되기도 하였던 악카 놀이는 그대로 음역하여 사용하는 것이 합당하다고 보았다. 이것은 일찍이 한역 원칙 중 음역해야 한다고 보았던 5불번(不翻) 가운데 차방무고(此方無故) 또는 차토무고(此土無故)에 해당한다. 인도에는 있지만 이 지역에 없는 나무 열매를 지칭하는 고유명사이기 때문이다. 논쟁에서 비유를 사용하는 목적은 보다 더 용이하게 자신의 주장을 입증하는 데 있다. 그러나 만약에 논쟁의 상대방이 그 뜻을 알아채지 못하거나 이해할 수도 없는 비유를 사용한다면 헛된 일이 될 것이며, 논쟁에서도 패배하고 말 것이다. 고대 인도에서 보편적으로 행해졌던 유흥 문화에 속하는 악카 놀이에 대한 이해가 없이 악카라는 단어를 현대적으로 풀어서 번역하는 것은 신중을 기해야 할 것이다. 왜냐하면 그 용어 하나에 대한 번역에 그치지 않고 그와 관련된 앞뒤 내용의 의미 전달에도 실패하고 마는 결과를 초래하기 때문이다. (shrink)