India and the West

A German manuscript page teaching use of (indo...
A German manuscript page teaching use of (indo-)Arabic numerals (Talhoffer Thott, 1459). (Photo credit: Wikipedia)

The Flow of Science and Mathematics

From India to Arabia and Europe

Dr Kenneth Chandler

Origins Of Vedic Civilisation

A Lighthouse for Scientific and Mathematical Discovery

India remained a lighthouse for the advance of civilisation long after the classical Vedic period. Our modern zero-based number system (the place-value number system) was first developed in India. Called ‘Arabic numerals’ in the West, they actually originated in India and were passed into Europe through Arabia, whence they derived their name in the West.

In Arabia, mathematics was called the “Indian Art,” and the numerals used in Arabia were called “Indian numerals.” Arabic scholars knew that mathematics had come into Arabia from India and not vise versa. It was also in India that the counting numbers were first invented. This inspired Albert Einstein to say, “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.”

The following chart shows the evolution of the numerals from the early Indus-Saraswati valley script to Devanagri to the Arabic to the present :

  • Evolution of the “numerals” which are mistakenly called “Arabic numerals” in the West. In fact they came into Arabia from India. In ancient Arabic, these numerals were called “Indian numerals” and mathematics was called the “Indian art.”

  • The value of “pi” was first calculated in India by Baudhayana (conservative scholars put him at least in the sixth century BC) long before it was known in Europe.

  • Baudhayana was also first to introduce a mathematical way to calculate the hypotenuse of a right triangle. The Shulba Sutra (the Baudhayana) written prior to the eighth century BC in India, used the theorem about two centuries before it was introduced by Pythagoras into Greece in the sixth century BC.

The wording of the theorem in the Shulba Sutras is exact :

“The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately.”

  • The Shulba Sutra are among the most ancient of mathematical texts known to man. In the valley of the Indus River of India, the world’s oldest civilisation had developed its own system of mathematics. The Vedic Shulba Sutras (fifth to eighth century BC), meaning “codes of the rope,” show that the earliest geometrical and mathematical investigations among the Indians arose from certain requirements of their religious rituals. When the poetic vision of the Vedic seers was externalized in symbols, rituals requiring altars and precise measurement became manifest, providing a means to the attainment of the unmanifest world of consciousness. “Shulba Sutras” is the name given to those portions or supplements of the Kalpa sutras, which deal with the measurement and construction of the different altars for religious rites.

The word shulba refers to the ropes used to make these measurements. Although Vedic mathematicians are known primarily for their computational genius in arithmetic and algebra, the basis and inspiration for the whole of Indian mathematics is geometry. Evidence of geometrical drawing instruments from as early as 2,500 BC. has been found in the Indus Valley. The beginnings of algebra can be traced to the constructional geometry of the Vedic priests, which are preserved in the Shulba Sutras. Exact measurements, orientations, and different geometrical shapes for the altars and arenas used for the religious functions (yagyas), which occupy and important part of the Vedic religious culture, are described the Shulba Sutras. Many of these calculations employ the geometrical formula known as the Pythagorean theorem. This theorem (c. 540 BC.), equating the square of the hypotenuse of a right angle triangle with the sum of the squares of the other two sides, was utilized in the earliest Shulba Sutra (the Baudhayana) prior to the eighth century BC. Thus, widespread use of this famous mathematical theorem in India several centuries before it being popularised by Pythagoras has been documented.

The proof of this fundamentally important theorem is well known from Euclid’s time until the present for its excessively tedious and cumbersome nature; yet the Vedas present five different extremely simple proofs for this theorem. One historian, Needham, has stated, “Future research on the history of science and technology in Asia will in fact reveal that the achievements of these peoples contribute far more in all pre-Renaissance periods to the development of world science than has yet been realised.”

  • The Shulba Sutras have preserved only that part of Vedic mathematics which was used for constructing the altars and for computing the calendar to regulate the performance of religious rituals. After the Shulba Sutra period, the main developments in Vedic mathematics arose from needs in the field of astronomy.

  • Jyotisha, the science of the planets, utilizes all branches of mathematics. The need to determine the right time for their religious rituals gave the first impetus for astronomical observations. With this desire in mind, the priests would spend night after night watching the advance of the moon through the circle of the nakshatras (lunar mansions), and day after day the alternate progress of the sun towards the north and the south. However, the priests were interested in mathematical rules only as far as they were of practical use. These truths were therefore expressed in the simplest and most practical manner. Elaborate proofs were not presented, nor were they desired.

  • Major centers of learning operated in ancient India. The World’s first major university and trade school was in Taxila (Takshila) then in northwestern India, around 700 BC (some scholars estimate). It boasted a thousand students from all over the known world who studied 60 disciplines taught there. The University of Nalanda, established in the forth century BC, was also a major center of learning in the ancient world.

  • The Indian astronomer and mathematician Bhaskaracharya in the 5th century BC (this is an estimated date that may be too recent), calculated the time taken by the earth to orbit the sun to nine decimal places. Algebra, trigonometry, and calculus were first set forth in ancient India.

Aryabhata the Elder (476-550 AD) gave a summary of Indian mathematics that covers astronomy, spherical trigonometry, arithmetic, algebra and plane trigonometry. Aryabhata also gives a formula for finding the areas of a triangle and a circle. His main work, the Aryabhatiya, contains continued fractions, quadratic equations, sums of power series and a table of sines. Aryabhata gave an accurate approximation for “pi” of up to 3.1416 and was one of the first to use algebra. His most important achievement was the invention of the “0,” which enabled the development of the place number system. Aryabhata also wrote a text on astronomy, the Siddhanta, which taught that the apparent rotation of the heavens was due to the rotation of the Earth on it axis.

Aryabhata gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun. He believed that the Moon and planets shine by reflected sunlight, and he taught, incredible though it may seem, that the orbits of the planets around the sun are ellipses. This was over a thousand years before Copernicus and Kepler came up with the same discovery in Europe. He also correctly explained the causes of the eclipses of the Sun and the Moon and calculated the value for the length of the year at 365 days 6 hours 12 minutes 30 seconds. This is a slight overestimate since the true value is less than 365 days 6 hours. His work, written in 121 stanzas, gives a remarkably accurate view of the structure of the solar system.

  • Brahmagupta (598-670 AD, again an estimated date that may off), head of the astronomical observatory at Ujjain, the foremost mathematical center of ancient India, developed algebraic notation and gave remarkable formulas for finding the area of a cyclic quadrilateral and for the lengths of the diagonals in terms of the sides.

  • According to Bhaskaracharya’s calculations, which were made in the 5th century BC, the time taken by earth to orbit the sun is 365.258756484 days (slightly larger than the correct time).

  • Aryabhata also introduced the versine (versin = 1-cos) into trigonometry.

  • Brahmagupta also studied arithmetic progressions, quadratic equations, theorems on right-angled triangles, surfaces and volumes, and calculated the length of the year at 365 days 6 hours 12 minutes 36 seconds.

  • Quadratic equations were first discovered by Sridharacharya in the 11th century. Then Bhaskara (1114-1185 AD) reached an understanding of the number systems that solved equations which were not solved in Europe until several centuries later. Like Brahmagupta before him, Bhaskara was head of the astronomical observatory at Ujjain, where he developed a sophisticated understanding of 0 and the negative numbers.

  • The art of navigation was invented 6,000 years ago by navigators of the Indus river. The English word navigation is derived from the Sanskrit word ‘Navgatih’ and the word navy from the Sanskrit ‘Nou.’ The first known reservoirs and dams for irrigation were also built in India.

  • Ayur-Veda, the earliest known system of medicine and surgery, was developed in the Vedic period in India. Sushrut, the father of surgery, developed surgical procedures including cesareans, cataract removals, setting fractures, removing urinary stones and even plastic and brain surgery. Over 125 surgical tools are named in the ancient Sushrut medical texts. Anesthesia was also well known. Detailed texts on anatomy, physiology, etiology, embryology, digestion, metabolism, genetics, and immunity date from Vedic times.

  • Sometime around 444 BC, Empedocles introduced a medical system into Greece modeled on the then ancient Ayurvedic system of India. Empedocles’ book on Purification gives, as we saw, the same definition of health as the Charaka Samhita. It bears repeating: health is the balance of the fundamental elements (earth, air, fire and water) in all parts of the body, each part having the proper proportion of each that is right for it. Empedocles adopts this definition from the Vedic tradition. Plato’s Timaeus defines health in the same way.

India’s most substantial gift to world civilization was, however, the discovery of pure consciousness and the mapping out of the architectonic structure of pure knowledge. All other achievements derive from this great awakening of knowledge that took place in ancient Vedic India.

To be concluded …

Astronomical detail, Jantar Mantar.
Astronomical detail, Jantar Mantar. (Photo credit: Wikipedia)

2 thoughts on “India and the West

  1. Reblogged this on Truth Within, Shines Without and commented:

    Indian astronomer and mathematician Bhaskaracharya in the 5th century BC (this is an estimated date that may be too recent), calculated the time taken by the earth to orbit the sun to nine decimal places. Algebra, trigonometry, and calculus were first set forth in ancient India….

  2. Vedic maths is based on sixteen sutra’s or principles . These principles are general in nature and can be applied in many ways . In practice, the vedic system is used to solve difficult problems or huge sums in more effective and easy way.These method are just a part of a complete system of mathematics which is far more systematic than the modern system taught now. The simplicity of vedic mathematics helps us to solve the calculations mentally with sifficient practice.
    Vedic maths is highly helpful in cracking competitive exams .There are many vedic math online course one of them is So if anybody is intrusted to learn vedic math online can visit the link.

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