Project proposal: Indian theoretical sciences discussion forum
Raj Chakrabarti, PhD
Research Scientist, Chemical Physics
Department of Chemistry
Princeton University
Dated: 9/10/07
Abstract: This proposal outlines plans for a discussion forum on the history of Indian theoretical sciences. Recent work in this area indicates that in both mathematics and linguistics, ancient and medieval Indian scientists made certain seminal discoveries several centuries before their Western counterparts, to whom these findings are currently attributed. The proper placement of these discoveries within the context of the broader history of science would have considerable impact on modern science education, both in India and the West, due to the vastly different epistemological approaches underlying
these two schools of thought. The aim of the discussion forum is to assemble, both over the internet and locally in the Princeton/New York area, a panel of scholars and experts who will examine existing literature on this subject, critically compare Indian and European discoveries, and ultimately publish original commentary. Progress toward this goal will be measured by several milestones, including editing the online encylopedia Wikipedia, drafting an article contrasting Greek and Indian scientific philosophy, and assembling a suggested curriculum for Indian science education within universities.
I. Educational backdrop
In the year 2000, the International Task Force on Higher Education and Society prepared a report describing challenges facing higher education in developing countries (Ahmad et al., 2000). India figured prominently within the list of countries where educational reform was deemed essential. The continued development of an advanced infrastructure for higher education was considered by this global task force to be a prerequisite for the economic development of these nations in the 21st century.
More than 6 years later, there is increasing interest in overhauling aspects of the educational system in developing nations like India (Neelakanthan2007), as the economic resources needed to accomplish this ambitious task rapidly become available. The details of this proposed academic restructuring must be carefully considered from various perspectives. Certainly, it is essential to fashion an educational infrastructure that can reach the rural majority of the nation’s population (Bartning and Chakrabarti 2007). However, at this critical juncture, it is particularly important to ensure that Indian higher education is not fashioned entirely in the image of western, eurocentric models, given the popular belief that countries like India are impoverished not only economically but also intellectually (Sinha2000). In truth, many of these nations have distinguished histories of intellectual achievement, stunted by a history of colonization.
Among developing countries, India is uniquely qualified to teach its own indigenous developments due to its well-known status as the source of many Eastern schools of thought. Possible results of such efforts include the formulation of a national attitude toward science and technology that is fully consistent with the prevailing traditional culture. But for such an effect to take root, the history of Indian intellectual achievements that have modern-day technological relevance must be clarified. The need in this area is perhaps greatest in the development of curricula pertaining to the natural or theoretical sciences. The dominant albeit misguided attitude toward this subject is that eastern intellectual traditions focus primarily on metaphysics and religious philosophy, with very little emphasis on the hard sciences. Recently, the extent of historical Indian developments in the theoretical sciences - particularly in math, linguistics and the foundations of computer science – have been hotly debated (Raju2007; Joseph1994; Bhate and Kak 1993). These developments challenge the traditional conception of Indian thought as metaphysical. The outcome of these debates – in the West as well as in the East – could affect whether Indian universities and schools choose to accept these developments as factually accurate and include them within their curricula.
The present discussion forum will aim to increase awareness about and ultimately contribute to the resolution of several debates surrounding Indian achievements in the theoretical sciences, and their continued relevance to modern-day science. Educational implications in both India and the West will be an ongoing theme.
II. Subject matter and focus
A. Medieval infinite series / calculus (math); engineered properties of Sanskrit (lingustics/computer science)
The subject matter discussed within the forum will focus on Indian mathematics and linguistics history. In the area of mathematics, we will emphasize developments in the medieval period associated with foundations of infinite series and the calculus. Several of the most important infinite series expansions for trigonometric functions – including the sine, cosine and arctangent – were discovered in India several centuries before they surfaced in Europe (Roy1990; Katz1995; Pingree2003; Rajagopal1986), and recent work makes a compelling case that some of these developments may have even been transmitted to the immediate predecessors of Newton and Leibniz, thus possibly contributing to the development of European calculus (Raju2007). Although there is extensive documentation of the transmission of ancient Indian mathematics (e.g., the decimal place numeral system and algebra) to the Arab world and subsequently to Europe (Ifrah 2000), medieval developments (and possible transmission) have received much less attention, until recently.
For example, these recent studies contend that the medieval Indian monograph Yuktibhasa should possibly be considered the world’s first calculus text (Raju2001). However, various scholars have protested this interpretation, claiming that without development of a complete theory of differentiation and integration, or the fundamental theorem of calculus, the content of these manuscripts cannot be equated with the discovery of calculus (Wiki2007a, Bressoud 2002). Perhaps the biggest point of contention is the possible transmission of these seminal ideas from India to Europe (Raju2007). Two important questions in this area that we will aim to answer are: 1) what factors, and prior mathematical developments, made this early development of infinite series possible; and 2) to precisely what extent do these resemble the corresponding European developments?
The linguistics segment of the forum will focus on the properties of the Sanskrit language that rendered it particularly useful for the communication of mathematical results. Sanskrit is generally accepted as the first attempt at an engineered language, possessing several properties of efficiency and precision that are remarkably similar to those implemented in artificial computer languages some 2,500 years later (Briggs1985; Bhate and Kak 1993). Properties that will be discussed include, but are not limited to, the generative grammar of Sanskrit and its relationship to the Backus normal form of modern day programming languages (Backus1959; Ingerman1967). A critical analysis will be made of the extent to which Sanskrit grammar is context free (Chomsky1956), compared to modern synthetic languages. Possible shortcomings of Sanskrit in this regard will also be considered. Particular attention will be paid to the application of these linguistic developments to early and medieval Indian mathematics (Staal1995).
The initial discussions in both these areas will be structured around a critical reading of the writings of Raju, Sinha and Kak. The reading list below references some of the most important of these writings.
B. Indian scientific epistemology: empiricism, engineering
In discussing these theoretical issues, emphasis will be placed on the engineering approach to mathematics that was predominant in India during the medieval period. For example, Indian achievements in infinite series were often motivated by the astronomical problem of predicting the motion of the planets (Pingree1978; Pingree1996; Kak2000), and scientists developed sophisticated techniques to improve the numerical accuracy of their calculations of these motions. Indeed, the factors motivating the development of the Indian calculus are not unlike those commonly held to be responsible for the development of Western calculus, namely Newton’s desire to formulate and solve the problems of mechanics.
However, the point will be made that this engineering approach to mathematics in India dates back to ancient times, in stark contrast to the formal approach that dominated mathematics in the West (Anglin1994) during the same time period, with the types of applied/computational approaches common in India (Plofker1996) becoming popular only after the advent of computer technology in the 20th century.
Another crucial point of departure between Indian and Western scientific epistemology is that the roots of Indian mathematics lie in linguistics, whereas the roots of Western mathematics lie in philosophy. Both cultures developed remarkable formal systems, but whereas Western formal developments focused on axiomatic proof, Indian attention focused on the development of constructive approaches to grammar. These approaches are in many ways complementary. Ultimately, they converged at the foundations of mathematics and the birth of computer science and information theory, in the 20th century.
C. Comparative analysis of 20th century Western crises in logic, computer science
In addition to researching the historical facts pertaining to these developments, a
novel feature of the forum will be a critical analysis of several “crises” in 20th
century Western logic (Mancosu1998; Anglin1994), foundations of mathematics and computer science, and how Indian epistemology of mathematics and science sheds light upon the resolution of these “crises”. These include the notion of computability (Turing1936),the limits of mathematical proof as summarized in Godel’s incompleteness
theorem, and the theory of information (Chaitin1982).
The inseparable relationship between physics and information, uncovered by the birth of computer science, has called into question many of the “metaphysical” underpinnings of the classical Platonist approach to mathematics (Zalta2003), originating in the philosophy of ancient Greece. In contrast to Greek scholars, those in India were always concerned first and foremost with the generation of mathematical results themselves and the means of communicating them in the most concise form possible. Formal axiomatic developments focused on the generative properties and power of the grammar used to communicate these truths not exclusively on the proof of theorems on the basis of axioms which were to ultimately lose their foundational uniqueness. Indeed, Panini’s Astadhyayi (Bohtlingk1998) has been compared in importance to Euclid’s Elements inasmuch as they both lay the formal groundwork for theoretical developments in their respective cultures.
This approach has been criticized by Western historians of mathematics as being insufficient to constitute discovery of the underlying mathematical theories, leading to the labeling of the Eastern developments as “intuitive mathematics” (Boyer1991). However, the fact remains that although the means differed, the results produced were in many cases startlingly similar. Moreover, with the development of information theory and computer-based mathematical proof, generative grammars and the algorithms they enable are beginning to replace, or at least complement axiomatic mathematics as a stable foundation for a formal description of the physical world. Forum members will consider how contemporary developments in logic and computer science may help put the importance of Indian mathematical developments in clearer perspective[1], untainted by the biases of culturally dependent epistemology (Raju2001).
III. Structure of the forum
The discussion forum will be incarnated simultaneously in two forms: an online forum including the international participation of Indian historians of science in India as well as US scholars; b) A local forum in Princeton, NJ that could meet biweekly or monthly.
A) Online forum. Invited scholars include : CK Raju, mathematician and historian of Indian mathematics (Delhi); DK Sinha, applied mathematician, ethnomathematics history expert, former vice chancellor of Santiniketan, pro-vice chancellor of Calcutta university and Dean of Science at Jadhavpur university, Calcutta; and Subhash Kak, Professor of Electrical Engineering, Louisiana State Univ, and prolific writer on the history of Indian
linguistics. Dr. Raju experimented with an online forum of this sort several years ago, and could play a role in designing the web interface/acting as co-moderator.
B) Local forum. The local discussion group will draw members from Princeton University, research institutes in Princeton (such as NEC), the Infinity Foundation, Bell Labs, and New York City (Columbia University and the Harvard Club of NYC). Local experts who have published on the subjects will be invited to present brief summaries of their work.
IV. Milestones/deliverables
The discussion forum will aim to achieve several concrete milestones that will
gauge its progress and maintain its position as a burgeoning research effort in addition to a survey of existing literature. Given the forum’s association with the Infinity Foundation - the Princeton, NJ nonprofit that supports research on Indic contributions to science, philosophy, and culture - meeting these goals will allow assessment of progress towards publications in the area, as well as possible communication of results in larger regional conferences.
a. Establish consensus among experts on current status of Wikipedia entries
on Indian maths
The free online encyclopedia Wikipedia is rapidly becoming the most widely used encyclopedia in the world. Wikipedia currently has several pages dedicated to the history of Indian mathematics (Wiki2007a, 2007b). The first milestone will be a critical assessment of the current status of the Wikipedia pages on Indian contributions to calculus. Much of the information on these pages is now flagged as being “disputed”. Each of the existing claims on the website must be more thoroughly corroborated. Dialogue with current contributors to the website, under the auspices of this discussion group, could play an important role in stabilizing the content of these entries. Success here would lay the foundation for subsequent efforts with respect to print encyclopedias like Britannica.
Wikipedia information dedicated to the relationship between Sanksrit grammar and modern computer science is now fairly limited (Wiki2007c) An associated milestone would be the establishment of new Wikipedia pages on this subject, managed by forum members.
B. Draft publication: Modern implications of Indian scientific philosophy vis-à-vis Greek metaphysics
An ultimate goal of the discussion forum is to generate new publishable results pertaining to the modern-day relevance of Indic approaches to the theoretical sciences. Broadly speaking, we are interested in amassing concrete evidence for why Indian philosophy is at its core not metaphysical (Zimmer1969)– which is properly the domain of ancient Greek philosophy (Zalta2003) -- but rather physical, and empirical. In this regard, the connection to modern information theory and computer science concepts of algorithmic computational complexity (Chaitin1974,1977), with their emphasis on the information content of a mathematical theorem, must be mined.
Our goal is not to show that Indian scientists were the first to identify these concepts, but rather to outline the possible contributions of Indian scientific philosophy to 21st century global scientific philosophy, given 20th century crises stemming from the historical dependence of science on Platonist metaphysics. A consistent scientific philosophy of this type could quite easily be taught within history of science and philosophy of science departments in both the Western and Eastern universities (Sinha2000; Sinha2001).