Dr. Alok Kumar's Project to Design a Curriculum on Ancient Indian Science

The Educational Council on Indic Traditions (ECIT) seeks to improve the ways in which India and her cultural, scientific and religious traditions are portrayed in the educational system. To facilitate this ECIT and the Infinity Foundation will provide funding to Dr. Alok Kumar to develop a class on Indic contributions to science. Since Dr. Kumar will eventually disseminate the course outline and resources, it is hoped that his contribution will assist in bringing these contributions to a wider audience in the United States and abroad.

Sciences of the Ancient Hindus: Its History and Implications on World Cultures

Dr. Alok Kumar, Department of Physics, State University of New York, Oswego, NY 13126.

Project Outline
I'll write the modules and articles mentioned in the Products section during the summer of 2001. These modules will later be tested during the Fall 2001 or Spring 2002 semester. Based on my experiences in the course, they will be revised during the summer of 2002. Depending on the schedule and location, I plan to attend one/two national meetings to present my findings in this project. At this point, I am aiming at the meetings organized by the American Physical Society, the National Science Teacher's Association, or the History of Science and Technology Society. With $500 I mostly want to buy books that are essential to my project.

At the State University of New York at Oswego, a new upper-division general education, The Beginnings of Science: A World View (PHY 303), will be offered for the first time during the academic year of 2001-2002. The course was approved by the General Education Board in 1998-1999 academic year and will fulfill the Natural Science requirement for the juniors and seniors at the university under the Intellectual Issue category. The course explores the origins and diffusion of the early scientific ideas and practices that served as the necessary foundations of what came to be known as "science." Through case studies of several ancient civilizations, the nature of science, the contexts in which science flourished, the cultural exchanges by which science was diffused, the reasons of its occasional decline, and impact of science on society will be explored.

The course covers several ancient civilizations, including the Indian civilization. The present proposal is to seek funds to prepare several modules that will be used to teach the Indian civilization component of the course. A proposed copy of the syllabus is attached in Appendix A.

Rationale of the Course
Today, the North American continent is witnessing a new demographic reality that may pose major problems if enclaves of various cultures remain isolated from each other's viewpoints, roots, and contributions. The idea of "tolerance of diversity" when interpreted as "enduring differences" is thin and fragile. It has never worked in the past. A much more solid foundation for a diverse society is respect and appreciation for the achievements of various cultures.

Respect and appreciation come only from experience and knowledge. This is often the raison d'être of the recent emphasis for the establishment of university courses that have "a multicultural component." Most reforms so far have taken place primarily in the liberal arts, with little or no apparent effect in sciences.

Most cultures have derived material benefits and intellectual satisfaction from their attempts to understand physical and biological phenomena. As a result, in the growth of science, influences came from all parts of the world like a thousand capillary venules joining to form the venae cavae magna. Modern society certainly did not spring into existence full grown with the Renaissance in Europe. It is the product of a natural evolution that involves many cultures.

The present course is organized around three inter?related themes: (a) the diverse cultural contexts of scientific discovery and invention in ancient and medieval world history; (b) the conditions that led to cultural exchange and the spread of scientific advances, and, on the other hand, to cultural and scientific isolation; and (c) revision of the conventional Eurocentric view of science and its origins.

Maximum class size will be 100 students. The course will be offered once or twice a year, depending on the staff availability.

A Brief Discussion on the Contributions of India
"The first nation (to have cultivated science) is India. This is a powerful nation having a large population, and a rich kingdom (possession). India is known for the wisdom of its people. Over many centuries, all the kings of the past have recognized the ability of the Indians in all branches of knowledge," wrote Sa`id al?Andalusi, a leading natural philosopher of the eleventh century Muslim Spain (Salem and Kumar, 1991, p. 11). The emphasis in the above quotation is not on India being "the first nation to cultivate science." It is on the fact that the European scholars, as late as the eleventh-century, thought India as a leader in science and technology. This is in contrast with the modern common perception about India in the Western minds or with the colonial period.

Poetry in Science: As early as 2600 B.C., the Egyptian monarch Khufu erected a great "house of writings," thus inaugurating a tradition that, by the time of Rameses II (ca. 1300 B.C.), yielded a collection numbering at least 20,000 papyrus scrolls, each protected in a cloth or leather cover. During the 300 year period, between the sack of Thebes by the Assyrians and the invasion of Alexander the Great's armies in 332 B.C., practically all of Egypt's libraries were turned to ash and dust. We know, of course, that this great loss was soon compensated-and afterward repeated-by the great library at Alexandria. This was not typical of only Egypt. Similar decimation of the written words occurred elsewhere in China, Europe, and the Middle East. The Qin dynasty in China, the Reformation in Europe, and Kublai Khan invasion of the Middle East remind us clearly and concretely: the written words are fragile.

While the textual riches of Alexandria, China, and Rome were being put to the flame, a wholly different tradition of scientific expression was brought to a peak in India, in a manner that would prove enormously more resilient to the vicissitudes of time and adversity. This was the oral, poetic tradition of Indian thought, whose greatest purveyor in astronomy and mathematics was Aryabhata I (b. 476 A.D.). }Aryabhata I, by almost any account, was the equal in Indian astronomy to what Cladius Ptolemy became to the tradition of Greek science in Islam and late medieval Europe.

Aryabhata I composed a most remarkable work in Sanskrit known as the Aryabhatiya. Its text consists of a mere 121 stanzas, each with several lines in varying metre and rhyme scheme. The whole is divided into a brief introduction (ten verses), followed by three major parts, one on mathematics (Ganita, 33 verses), one on time reckoning and planetary models (Kalakriya, 25 verses), and one on the mathematics of the sphere and its applicability to astronomical calculation (Gola, 50 verses).

There are no numbers anywhere in the composition. Nor are there figures, drawings, or equations. The Aryabhatiya expresses the highly sophisticated mathematics of sine functions, volumetric determinations, calculation of celestial latitudes and motions, and much more, in the form of a poetic code. This code, invented by Aryabhata I (though others like it had existed earlier on) and delineated in the introductory section, uses an alphabetical system of numerical notation. Specific values are assigned to specific letters and letter combinations, such that any value can be expressed in words and recited through the given metric scheme.

Use of a poetic code did mean, however, that transmission of this most valuable text could be achieved orally. This means through memorization and spoken transfer, or more accurately, by this particular text becoming a part of living memory among succeeding generations of scholars. This occurred during much of the medieval era, when many famous libraries and teaching centers were destroyed in India, as elsewhere, by foreign conquest and civil strife. However, many books were reproduced later on from the oral tradition

The image brought to us by the history of Aryabhata I's seminal work is indeed striking: at the very moment when Ptolemy's, Hipparchus', Eudoxus' and Euclid's books darkened the Alexandrian sky with textual ash, the Aryabhatiya was being passed and preserved through the most transient yet durable medium, the spoken and memorized word in the hearts of the Indians.

Mathematics: The present place?value notation system (base 10), used to represent numbers, is Indian in origin. The Mayas (base 20) and the Babylonians (base 60) used place?value systems as well, although their systems were different from that of the Indians. The role of place-value notation is quite important in mathematics and computers. For example, the extreme difficulty of performing mathematical operations in the absence of a place?value notation system caused Greek mathematics and astronomy to suffer. Nicholas Copernicus (A.D. 1473?1543) was forced to use the Hindu numerals for their ingenuity (Rosen, 1978, p. 27): "This [Hindu] numeral notation certainly surpasses every other, whether Greek or Latin, in lending itself to computations with exceptional speed. For this reason I have accepted [it]." Copernicus, in his book, On the Revolutions, used Hindu?numerals for his computations while advocating the heliocentric model of the solar system.

Trigonometry deals with specific functions of angles and their applications to calculations in geometry. It unites the disciplines of arithmetic, algebra, geometry, and astronomy. The Alexandrian Hipparchus (ca. 150 B.C.) and Ptolemy (ca. A.D. 100--170) helped to lay the foundations of trigonometry. With the work of Aryabhata I (ca. A.D. 500) in India, trigonometry began to assume its modern form. For example, consider a circle of unit radius, so that the length of an arc of the circle is a measure of the angle it subtends at the center of the circle. In order to facilitate calculations in geometry, the Greeks tabulated values of the chords of different arcs of a circle. This method was replaced by Indian mathematicians with another system that used the half chord of an arc, known today as the "sine" of an angle.

The origin of the word "sine" in trigonometry can be traced to the Sanskrit language. The Sanskrit word for the chord of an arc comes from an analogy with a "bow string," which is called "samasta?jya." The half?chord of the arc was called "jya?ardha," later shortened to "jya." The Arabs borrowed the concept from India and chose a similarly word "jaib" for the mathematical operation, which linguistically means a "lace fold or pocket" used in clothes.

This Arabic word was literally translated into Latin and called "sinus," meaning curved surface or fold. This Latin word was later metamorphosed into "sine" or "sin" in the English language. (Joseph, 1991; Kumar, 1994) Such etymological knowledge can be found in some dictionaries and encyclopedias but, ironically, only rarely in trigonometry books.

When the Arabs borrowed a concept from the Indians, they usually attributed the source correctly, especially in their early medieval literature. They often kept the same or similar pronunciation for many words, as shown by the previous example. In other instances, they translated the Sanskrit word into Arabic.

For example, the Sanskrit word for zero (a Hindu concept) is sunya, which translates literally into the Arabic word sifr. When the Europeans learned of it, they called it cipher or zephirum in Latin. This was transformed eventually as zero in English.

Natural Sciences: Regarding the earth's motion in his heliocentric model, Aryabhata I, some thousand years before Copernicus, suggested that the earth might be in axial rotation, with the heavens at rest, so that the apparent motion of the stars would be an illusion. In order to explain the apparent motion of the sun, Aryabhata I used the elegant analogy of a boat in a river: "As a man in a boat going forward sees a stationary object moving backward, just so at Lanka (Sri?Lanka) a man sees the stationary asterisms (stars) moving backward in a straight line." (Clark, 1930, Gola 9) The interpretation is that a person standing on the equator of the earth (Sri?Lanka) that rotates toward the east would see the stars (asterisms) moving in a westward direction. Aryabhata I's hypothesis of the earth's rotational motion is clearly explained by the analogy of the boatman as given above. He incorporated the concept of relative motion, many centuries before its more formal discussion by the noted Parisian scholar Nicholas Oresme in the fourteenth century. (Toulmin and Goodfield, 1961).

The ancient Indians realized the common connections between plants, animals and humans. They also realized the role of plants in medicine and the role of animals in the preservation of nature. In view of the importance of trees for humans, unnecessary cutting of a tree was against social and religious codes in India. Asoka (2nd century B.C.), a king in India known for his Maurya?empire and propagation of Buddhism, defined a strict law against the demolition of trees. Similarly, protection of animals led to the movement of vegetarianism. The Hindus went to the extent of worshiping both life forms; Animals and plants are revered along with gods. It is a curious fact that the Hindu concept of transmigration of souls was a common belief among the Greek philosophers and not the Greek society. Some connections between the Greek philosophers and Indian philosophy and the possibility of such interactions will also be explored.

Kanada wrote a book, Vaisesika?Sutra, in which he proposed that matter is made up of small particles, called parmanu (atoms). Kanada's description is based on the impossibility of infinite division of matter: "parmanu is not visible; the non?perception of atoms disappears when they mass together to form a combination of three double?atoms, a combination which does assume visibility." Cyril Bailey compared the Indian description of atoms with the Greek description, and wrote: "It is interesting to realize that an early date Indian philosophers had arrived at an atomic explanation of the universe. The doctrines of this school were expounded by Vaicesika Sutra [VaiÑesika?Sãtra] and interpreted by the aphorisms of Kanada . . . .Kanada works out the idea of their combinations in a detailed system, which reminds us at once of the Pythagoreans and in some respect of modern science, holding that two atoms combined in a binary compound and three of these binaries in a triad which would be a size to be perceptible to the sense." (Bailey 1928, p. 64)

As this section amply demonstrates that India made substantial contributions to science and technology in the ancient and medieval period. However, such contributions are not in the mainstream knowledge in the absence of its inclusion in the academic curricula. This project is a modest effort to bridge such gaps.

Salient Features
Most writings related to Indian scientific contributions are written in specialized or obscure journals on Indology. Most articles are written in isolation with little or no connection/comparison with the western science or with other contemporary cultures. In the absence of a cross-cultural study, it is unlikely that such knowledge will ever be assimilated into the mainstream knowledge of science. For this reason, I plan to write my articles/modules with a cross-cultural emphasis. Such a study will not be in conflict with the mainstream science; it will fill the gaps in our understanding of science. I also plan to publish my articles in the mainstream journals/magazines (examples: Science as Culture, The Physics Teacher, Journal of College Science Teaching, or American Educational Research Journal)

Most of the modules prepared will aim to cover the 55 minutes lecture period. Several modules will cover more than one lecture, as shown in the Products section.

Most of the needed information is already available in scholarly articles and books. The main emphasis in this project is to adapt the available scholarly information for the PHY 303 course. To accomplish the task, several modules of teaching will be prepared in a simple language that should be accessible to science as well as non-science majors.

Several modules related to Indian science will be written under the grant. These modules will be disseminated to general public through teaching of the mentioned course, publications in magazines or journals, or presentations in workshops/conferences.
Module 1: A Brief History of India, 1 lecture
Module 2: The Role of Language in the Preservation of Culture and Science: Poetry in Science, one lecture
Module 3: A History of Numerals and the Place Value Notation, 1 lecture
Module 4: A History of Trigonometry, 1 lecture
Module 5: A History of Astronomy (This modules will consist the work of Aryabhata I in comparison with Ptolemy, Copernicus, and Brahe.), 2 lectures
Module 6: A History of Biology (This module will consist topics on ayurveda, yoga, and vegetarianism, along with the above-mentioned topics), 3 lectures
Module 7: A History of the Physical Sciences (This modules will consist the concept of atom, gravitational force, medicinal chemistry from Caraka and Susruta, and metallurgy.), 2 lectures

I'll also write one or two articles that will be based on the project. Also, I'll attend two conferences related to my project.

Within six months of the award, I'll submit three articles for posting on the website of the Infinity Foundation. These articles will either be original publications, previously peer-reviewed publications, or modifications of my previously peer-reviewed publications.

Bailey, Cyril, The Greek atomists and Epicurus, Claredon Press, 1928.

Clark, W. E., The Aryabhatiya of Aryabhata, The University of Chicago Press, Illinois, 1930.

Joseph, George Gheverghese, The Crest of Peacock, Penguin Books, London, 1991.

Kumar, A., Improving Science Education by utilizing historical ethnic contributions, Physics Education, 11(2), 154-63 (1994)

Rosen, E., On the Revolution by Nicholas Copernicus, The Johns Hopkins University Press, Maryland, 1978.

Salem, S.I. and A. Kumar, Science in the Medieval World, University of Texas Press, Austin, 1991.

Toulmin, S. and J. Goodfield, The Fabric of the Heavens: the Development of Astronomy and Dynamics, Harper Torchbooks, New York, 1961.