Invention -that single leap of a human mind that gives us all we create. Yet we make a mistake when we call a telephone or a light bulb an invention, says John Lienhard. In truth, light bulbs, airplanes, steam engines-these objects are the end results, the fruits, of vast aggregates of invention. They are not invention itself. In How Invention Begins, Lienhard reconciles the ends of invention with the individual leaps upon which they are built, illuminating the vast web of individual inspirations that lie behind whole technologies. He traces, for instance, the way in which thousands of people applied their combined inventive genius to airplanes, railroad engines, and automobiles. As he does so, it becomes clear that a collective desire, an upwelling of fascination, a spirit of the times-a Zeitgeist -laid its hold upon inventors. The thing they all sought to create was speed itself. Likewise, Lienhard shows that when we trace the astonishingly complex technology of printing books, we come at last to that which we desire from books-the knowledge, the learning, that they provide. Can we speak of speed or education as inventions? To do so, he concludes, is certainly no greater a stretch than it is to call radio or the telephone an "invention." Throughout this marvelous volume, Lienhard illuminates these processes, these webs of insight or inspiration, by weaving a fabric of anecdote, history, and technical detail-all of which come together to provide a full and satisfying portrait of the true nature of invention.

As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers.

This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine.

The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging."

The book offers a collection of essays on various aspects of Leibniz's scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz's logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz's scientific works through modern mathematical tools, and compare Leibniz's results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz's work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz's researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

Intended for undergraduate mathematics students and teachers, How it All Began provides an introduction to the history of various branches of mathematics, the lives of the mathematicians, and the challenges they faced_which helped lead them to their mathematical discoveries. Written in a slightly more technical style than typical histories of mathematics, this book brings the 'characters' of mathematics to life while prompting analysis into the meaning and practice of their mathematical discoveries. How it All Began explores the great Greek legacy, Indian arithmetic, Integral Calculus, the Analytic Geometry of Rene Descartes, Differential Calculus, the Non-Commutative Algebra of Hamilton, the arithmetization of analysis, and the beginnings of Algebra. Using a topical organization method, How it All Began is a perfect supplement to standard mathematics texts and classroom instruction focused on specific subject matter.

"This work is an enormously significant contribution to the history of mathematics. No other work surveys the vast landscape of Mesopotamian mathematics from a position of the modern understanding of the past, incorporating the latest scholarship and yet still managing to be so accessible to nonspecialists. Robson's book is an outstanding guide that can be consulted by anyone interested in the field."--Duncan J. Melville, St. Lawrence University

"A very significant contribution to the history of ancient mathematics, and to the history of mathematics in general. I anticipate this book will be very, very useful to readers outside the field and general readers, because it is very clearly and incisively written, it gives clear indications about where to find the primary sources, and it summarizes previous historiography very effectively. There is no comparable book."--Serafina Cuomo, Birkbeck College, London

"A truly exciting and highly readable intellectual history of ancient Iraq. Eleanor Robson's "Mathematics in Ancient Iraq" is destined to become a classic. The book will have a wide readership among people interested in Near Eastern archaeology, the origins of writing, the history of education, and the history of science. This is truly a magnificent read."--Gary Urton, Harvard University

"This is a wholly original work, the first to integrate all the recent work from the history of mathematics in this area with archaeological scholarship. The result is a remarkably rich portrayal of mathematics in ancient Iraq. The breadth of coverage is striking, both in chronological terms but also in broad intellectual ones. The book is very well written and handsomely illustrated."--JeremyGray, The Open University

An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. It was also the era of new math. Introduced to US schools in the late 1950s and 1960s, the new math was a curricular answer to Cold War fears of American intellectual inadequacy. In the age of Sputnik and increasingly sophisticated technological systems and machines, math class came to be viewed as a crucial component of the education of intelligent, virtuous citizens who would be able to compete on a global scale. In this history, Christopher J. Phillips examines the rise and fall of the new math as a marker of the period's political and social ferment. Neither the new math curriculum designers nor its diverse legions of supporters concentrated on whether the new math would improve students' calculation ability. Rather, they felt the new math would train children to think in the right way, instilling in students a set of mental habits that might better prepare them to be citizens of modern society a world of complex challenges, rapid technological change, and unforeseeable futures. While Phillips grounds his argument in shifting perceptions of intellectual discipline and the underlying nature of mathematical knowledge, he also touches on long-standing debates over the place and relevance of mathematics in liberal education. And in so doing, he explores the essence of what it means to be an intelligent American by the numbers.

Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue importatn nineteenth century ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics - algebra, geometry, number theory, analysis, logic, and set theory - with narratives to show how they are linked.
Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecher, and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics.

The mathematician John Pell was a member of that golden generation of scientists Boyle, Wren, Hooke, and others which came together in the early Royal Society. Although he left a huge body of manuscript materials, he has remained an extraordinarily neglected figure, whose papers have never been properly explored. This book, the first ever full-length study of Pell, presents an in-depth account of his life and mathematical thinking, based on a detailed study of his manuscripts. It not only restores to his proper place in history a figure who was one of the leading mathematicians of his day; it also brings to life a strange, appealing, but awkward character, whose failure to publish his discoveries was caused by powerful scruples. In addition, this book shows that the range of Pell's interests extended far beyond mathematics. He was a key member of the circle of the 'intelligencer' Samuel Hartlib; he prepared translations of works by Descartes and Comenius; in the 1650s he served as Cromwell's envoy to Switzerland; and in the last part of his life he was an active member of the Royal Society, interested in the whole range of its activities. The study of Pell's life and thought thus illuminates many different aspects of 17th-century intellectual life. The book is in three parts. The first is a detailed biography of Pell; the second is an extended essay on his mathematical work; the third is a richly annotated edition of his correspondence with Sir Charles Cavendish. This correspondence, which has often been cited by scholars but has never been published in full, is concerned not only with mathematics but also with optics, philosophy, and many other subjects; conducted mainly while Pell was in the Netherlands and Cavendish was also on the Continent, it is an unusually fascinating example of the correspondence that flourished in the 17th-century 'Republic of letters'. This book will be an essential resource not only for historians of mathematics, science, and philosophy, but also for intellectual and cultural historians of early modern Europe.

First published in 1202, Fibonacci 's Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.

Aryabhata (sometimes spelled as Aryabhatta) was one of the greatest mathematician and astronomer of the classical world. He not only had enormous influence in India but across the world. He was only 23 years old when he wrote the Aryabhatiya. It consisted of this findings including astronomical constants and the sine table, mathematics, the reckoning of time (movement of heavenly bodies) and about the cosmos. He was the one to calculate the value of Pi, observed solar and lunar eclipses, calculated the summation of series of squares and cubes, determined the area of a triangle, defined cosine, versine and inverse sine. He is credited for finding how long it took the earth to spin on its axis, the length of the year and coming up with the heliocentric model and much more.

Unfortunately, many of us do not even know who Aryabhata is. Sadly, not much is even known about his life, where he came from, about his parentage or even his name for that matter. This book discovers and evaluates the life and works of the world's most important and forgotten mathematician and astronomer. Find out who Aryabhata was and what he did?

Topics covered in the "Life and Works of Aryabhata"
Who was Aryabhata?
World's greatest mathematicians
Indian mathematicians
Ancient Indian mathematics
Indian mathematics
Introduction to Aryabhata
Name and place of birth of Aryabhata
Taregna - The (birth) place of Aryabhata
The works of Aryabhata
The Arya-Siddhanta
Who invented Pi?
Approximation of Pi by others and Aryabhata
Aryabhata was not the first to use zero
The real story of zero
History of algebra
Aryabhata and algebra
Aryabhata and trigonometry
Indian astronomy and Aryabhata
Astronomical observations of Aryabhata
Heliocentrism and Aryabhata
References and further reading

A meticulously researched history on the development of American mathematics in the three decades following World War I As the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? The New Era in American Mathematics, 1920-1950 explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the twentieth century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European emigres fled to the shores of the United States. Drawing from extensive archival and primary-source research, Parshall uncovers the key players in American mathematics who worked together to effect change and she looks at their research output over the course of three decades. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress. And she uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Throughout, she considers how geopolitical circumstances shifted the course of the discipline. Examining how the American mathematical community asserted itself on the international stage, The New Era in American Mathematics, 1920-1950 shows the way one nation became the focal point for the field.

2013 Reprint of 1931 edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Frank Plumpton Ramsey (1903-1930) was a British mathematician who also made significant and precocious contributions in philosophy and economics before his death at the age of 26. He was a close friend of Ludwig Wittgenstein, and was instrumental in translating Wittgenstein's "Tractatus Logico-Philosophicus" into English, and in persuading Wittgenstein to return to philosophy and to Cambridge. This volume collects Ramsey's most important papers. Contents: The foundations of mathematics.--Mathematical logic.--On a problem of formal logic.--Universals.--Note on the preceding paper.--Facts and propositions.--Truth and probability.--Further considerations.--Last papers.

The book begins with a discussion of Benjamin Peirce's linear associative algebra and then considers this and other early influences on the logic of is son, C. S. Peirce. A discussion of the early algebraic logicians such as Boole, Jevons and De Morgan follows, culminating in a detailed analysis of C. S. Peirce's seminal paper "Description of a Notation for the Logic of Relatives." His further developments of the 1880s, including quantificational logic are also traced. At the end of his life, Peirce looked to his graphical logic system - the existential graphs - to provide the logic of the future.

The Author investigated 30,000 years writing-history of humanity in his previous book Signs Letters Alphabet. This book ads to his investigation everything he could find about numbers and number writing in our history. The ancient numerals: the dot, line, a line perpendicular to it (I) and a long line. Every one of these signs marked its own local value. Thus, we can write every number with different arrangements of these four signs. The reader can compare the 17,000-year-old numeral pictured on the front of this book (written on the cave's wall in Lascaux) with the 19th century signs seen on the inside of this back cover. The earliest found dot-line numeral so far is around 30,000 years old. Finds with such recordings get more numerous as we approach our time. This method was used, unchanged, in Ancient Egypt through its history, in China, by the Mayans, by the Aramaic culture in Middle East, the Eskimos and even in the salt mines of Transylvanian until the start of 20th century. Everybody did it, because there was no other kind of number-writing. We are no exception either. Our "Arabic" number-writing has a Palaeolithic origin also, except that the signs became over-ornamented in India, changing to "cifra" (adornment, ciphers), before arriving in Europe. The Palaeolithic calculator had two basic signs: dot and line. The lines could be drawn in the sand as in Egypt or even somewhere in Africa today. The dots could be pebbles, marbles, kernels or shells. The very fast calculator, with wires and beads on them is still used world wide, its name and form varies from abacus (Latin) to soroban (Japan) or from schoti Russia) to suan pan (China).

Mathematics originates with intuition. But intuition alone can only go so far and formalism develops to handle the more difficult problems. Formalism, however, has its inherent dangers. There are three types of formalism. Type I formalism, exemplified in the work of Euler, is basically heuristic reasoning, the use of familiar reasoning in areas where the reasoning might not or ought not apply. The results include startling successes, and also theorems admitting exceptions. Type II formalism, associated with names like Bolzano, Cauchy, and Weierstrass, attempts to clarify the situation by means of precise definitions of the terms used. Type III formalism, the axiomatic method, leaves the fundamental concepts undefined, but offers precise rules for their use. Such precision deserts intuition and one pays the price. Most dramatically, the formal definitions of Type II formalism allow for the construction of monsters - bizarre counterexamples that exhibit behaviour inconsistent with existing intuition. The initially repellant nature of these "monsters" leads to dissatisfaction that is only dispelled by their growing familiarity and applicability. The present book covers the history of formalism in mathematics from Euclid through the 20th century. It should be of interest to advanced mathematics students, anyone who teaches mathematics, and anyone generally interested in the foundation of mathematics.

For the first time, the early eighteenth century biographical notices of Sir Isaac Newton have been compiled into one convenient volume. Eminent Newtonian scholar Rupert Hall brings together the five biographies on Newton from this period and includes commentary on each translation. The centerpiece of the volume is a new translation of Paolo Frisi's 1778 biography, which was the first such work on Newton ever published. This comprehensive work also includes the biographies of Newton by Fontenelle (1727), Thomas Birch (1738), Charles Hutton (1795), and John Conduitt, as well as a bibliography of Newton's works. This book is a valuable addition to the works on Newton and will be of extreme interest to historians of science, Newtonian scholars, and general readers with an interest in the history of one of the world's greatest scientific geniuses.

This challenging book argues that a new way of speaking of mathematics and describing it emerged at the end of the sixteenth century. Leading mathematicians like Hariot, Stevin, Galileo, and Cavalieri began referring to their field in terms drawn from the exploration accounts of Columbus and Magellan. As enterprising explorers in search of treasures of knowledge, these mathematicians described themselves as sailing the treacherous seas of mathematics, facing shipwreck on the shoals of paradox, and seeking shelter and refuge on the shores of geometrical demonstrations. Mathematics, formerly praised for its logic, clarity, and inescapable truths, was for them a hazardous voyage in inhospitable geometrical lands.
Significantly, many of the same practitioners who promoted the vision of mathematics as heroic exploration also played central roles in developing the most important mathematical innovation of the period--the infinitesimal methods. This was no coincidence: the heroic tales of exploration and discovery helped shape a new form of mathematical practice, complete with new questions, new acceptable answers, and new standards of evidence. It was this new vision of mathematics as a grand adventure that allowed for the development of the new techniques that led to the Newtonian calculus.
In demonstrating this, the book moves from real voyages to imaginary ones, from the coasts of the Canadian Arctic to the tropical forests of Guyana, and from the inner structure of matter to the intricacies of the mathematical continuum. Throughout, a common rhetoric and imagery of exploration and discovery run like a thread through these diverse elements and bind them together.

Code 19 provides a powerful evidence for God's existence, as expected, envisioned or demanded by some philosophers and scientists, such as Galileo Galilei, Isaac Newton, Gottfried Leibniz, David Hume, Paul Dirac, and Carl Sagan.Code 19 was hidden in the 74th chapter of the Quran The Hidden, for 19x74 (1406) lunar years, and was discovered in 1974 by my colleague, Dr. Rashad Khalifa, an Egyptian-American biochemist. The number 19 has been a major controversy since its discovery and the number has realized all its assigned functions according to the prophetic verses of Chapter 74.Because of the implications of his discovery of the Secret, as well as his strong criticism of the sectarian teachings based on Hadith and Sunna, Rashad was declared a heretic/apostate by leading Sunni scholars from 38 countries who held an emergency conference in Saudi Arabia in 1989 to discuss the Salman Rushdie controversy. While Rushdi survived, Rashad was assassinated in this Masjid in January 31, 1990, by a terrorist group linked to al-Qaeda. The author of this book also received similar fatwa, yet he has escaped several assassination attempts, so far.Code 19, which was also discovered in the original portions of the Old Testament by Judah ben Samuel in 11th century, is simple to understand but impossible to imitate.Code 19 has little to do with numerology, since its literary-numerical (LitNu) pattern can be verified or falsified through scientific inquiry. It is radically different from the pattern demonstrated in The Bible Code, which has no statistical value.Unlike regular metaphysical or paranormal claims, Code 19 can be verified or falsified by virtually anyone, since the Arabic version of the Quran is available everywhere. Besides, for the most part, the reader does not need to know Arabic but only two eyes to see, an ability to count, a critical mind, and an open mind and heart to witness extraordinary signs as the fulfillment of a great prophecy.This discovery has created a paradigm change among those who witness it: instead of joining a religious bandwagon by blindly believing a holy story or hearsay, we must be critical thinkers; we must question everything and seek truth through knowledge. The code suggests a "Copernican revolution" in theology of religions. Instead of Krishna-centered, or Jesus-centered, or Muhammad-centered religions we must turn to the original center, to the God-centered model. The message of rational monotheism has sparked an ongoing controversy in countries with Muslim-majority populations, e.g., Egypt, Pakistan, Malaysia, Saudi Arabia, Turkey, etc. Internet forums are filled with heated debates regarding this code.The improbability and impossibility of the numerical structure of the Quran being produced by a medieval Arab genius becomes evident when we consider the following factors: It includes simple elements of the Quran and goes deeper to an interlocking system of complex numerical patterns and relationships. It involves not only frequencies of letters and words but also the numerical values of letters. It involves not only an intricate numerical pattern but also a huge set of data consisting of units with multiple functions, such as letters that are also digits, words that are also numbers. The nemeroliteral aspect of the Quran were not known by the adherents of the Quran until late 1960s and especially, 1974. The literary aspect of the Quran has received praises from many literary giants throughout centuries. The scientific accuracy of Quranic statements on various fields has been immaculate. Muhammad was one of the busiest and greatest social and political reformists in human history. The timing of the discovery of the code is precise and prophetic. A series of prophetic events regarding the code has been fulfilled.

One of the most imaginative mathematicians of the nineteenth century, Sir William Rowan Hamilton (1805-1865) changed the course of modern algebra with his discovery of quaternions in 1843. Although Hamilton's work was largely theoretical, his ideas came to have invaluable practical applications with the advent of quantum mechanics in the twentieth century. In this acclaimed biography, Thomas L. Hankins brings together the many aspects of Hamilton's life and work--from his significant contributions to mathematics, optics, and mechanics to his passion for metaphysics, poetry, and politics--fully portraying the brilliant man whose faith and idealism guided him in everything he did.

Thomas Harriot (1560-1621) was a pioneer in both the figurative and literal sense. Navigational adviser and loyal friend to Sir Walter Ralegh, Harriot took part in the first expedition to colonize Virginia. Not only was he responsible for getting Ralegh's ships safely to harbor in the New World, once there he became the first European to acquire a working knowledge of an indigenous language (he also began a lifelong love of tobacco, which may have been his undoing). Harriot's abilities were seemingly unlimited and nearly awe-inspiring. He was the first to use a telescope to map the moon's craters, and, independently of Galileo, discovered and recorded sunspots. He preceded Newton (whose fame eclipsed his) in his discovery of the properties of the prism. He was arguably the best mathematician of his age, and one of the finest experimental scientists of all time. Yet Harriot has traditionally remained a tantalizingly elusive character. He had no close family to pass down records, and few of his letters survive. Most importantly, he never published his scientific discoveries, and half a century after his death he had all but been forgotten. In recent decades, many (self-styled "Harrioteers") have become obsessed with restoring to Harriot his right place, but Robyn Arianrhod's biography is the first actually to do this, and she has done it the only way it can be done: through his science. Using Harriot's re-discovered manuscripts, Arianrhod illuminates the full extent of his achievements in science and physics, expertly guiding us through what makes them original and important, and the story behind them. Because he hadn't yet polished them for publication, Harriot's papers also proffer unique insight into the scientific process itself. Though his thinking depended on a more natural, intuitive approach than those who followed him, Harriot laid the foundations of what in Newton's time would become modern physics. Arianrhod's biography offers the human face of scientific discovery, a lived example of the way in which science actually progresses. Set against the backdrop of the Elizabethan world with all of its dramas and creative tensions-Harriot's years almost exactly overlap those of Shakespeare's-this biography gives proper due to one of history's most remarkable minds.

Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: * Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics * Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. * Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested

Reprint. Paperback. 387 pp. Diophantus of Alexandria, sometimes called "the father of algebra," was an Alexandrian mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations, many of which are now lost. In studying Arithmetica, Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of diophantine equations ("diophantine geometry") and of diophantine approximations remain important areas of mathematical research. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation. Heath's work is one of the standard books in the field.

Based on extensive research in Sanskrit sources, "Mathematics in India" chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.

Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. "Mathematics in India" provides a rich and complex understanding of the Indian mathematical tradition.

**Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" ("Interdisciplinary Science Reviews" 28, 2003, 1-13).