{"id":196,"date":"2019-08-22T06:33:42","date_gmt":"2019-08-22T06:33:42","guid":{"rendered":"http:\/\/icp02.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=196"},"modified":"2019-08-22T06:33:49","modified_gmt":"2019-08-22T06:33:49","slug":"science-in-ancient-india-an-overview","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/icp02\/chapter\/science-in-ancient-india-an-overview\/","title":{"rendered":"Science in Ancient India- an overview"},"content":{"raw":"
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Introduction:<\/strong><\/p>\r\n \r\n

As in all ancient cultures, astronomy was born in India before mathematics, beginning with observations of the periodicity of the moon\u2019s phases, a few identifiable planets, the northward or southward journey of the sunrise on the eastern horizon through the year, or to trace imaginary lines between the stars.<\/p>\r\n \r\n

1. Harappan Beginnings<\/strong><\/p>\r\n \r\n

In India, those beginnings are not adequately documented. It has been suggested that patterns of rock art found in Kashmir, such as a double sun or concentric circles, may have been depictions of a supernova and meteor showers respectively, perhaps witnessed some 7,000 years ago. Ring-stones found at Mohenjo Daro, the largest city of the Indus civilization (2600-1900 BCE), have been interpreted as calendrical devices keeping track of the sunrise at different times of the year. The alignment of main streets along the cardinal directions has been attributed to the sighting of the star cluster Pleiades (Krittik\u0101<\/em><\/strong>), which rose due east at the time. These interpretations are sound but remain conjectural.<\/p>\r\n \r\n

Harappan town planning, including the use of simple ratios in the dimensions of major structures (see module on The Aryan Issue), implies some knowledge of basic geometric principles and an ability to measure angles, as evidenced by a few cylindrical compasses made of shell, with slits cut every 45\u00b0. Besides, for trading purposes the Harappans developed a standardized system of weights (see Module on The Aryan Issue), in which, initially, each weight was double the preceding one, then, 10, 100 or 1,000 times the value of a smaller weight. This shows that the Harappans could not only multiply a quantity by such factors, but also had an inclination for a decimal system of multiples. However, there is no agreement among scholars regarding the numeral system used by Harappans.<\/p>\r\n \r\n

2. Science from the Vedic to the Early Historical Era<\/strong><\/p>\r\n \r\n

A few thousand years ago, the <\/span>Rig-Veda,<\/em><\/strong> the oldest of the four Vedas, spoke of a year of 360 days divided into twelve equal parts. It clearly recorded a solar eclipse, although in metaphorical language. A few centuries later, the <\/span>Yajur-Veda<\/em><\/strong> considered a lunar year of 354 days and a solar year of 365 days, and divided the year into six <\/span>ritus<\/em><\/strong> or seasons of two months each; it also gave the first list of 27 <\/span>nakshatras<\/em><\/strong> or lunar mansions, that is, constellations along the path of the moon on the celestial sphere.<\/span><\/p>\r\n \r\n

The Vedas mention multiples of 10 up to a million millions in the <\/span>Yajur Veda<\/em><\/strong> \u2014 a number called <\/span>par\u0101rdha<\/em><\/strong>. (By comparison, much later, the Greeks named numbers only up to 10,000, which was a \u201cmyriad\u201d; and only in the 13th century CE was the concept of a \u201cmillion\u201d adopted in Europe.) The <\/span>Br\u0101hmanas<\/em><\/strong>, commentaries on the Vedas, knew the four arithmetical operations as well as basic fractions.<\/span><\/p>\r\n \r\n

Because of the need to keep time for the proper conduct of rituals, calendrical astronomy grew more sophisticated in the late Vedic period, with the <\/span>Ved\u0101nga Jyotisha<\/em><\/strong> of Lagadha as its representative text. On the basis of its own astronomical data, it has been dated between the 12th and the 14th centuries BCE by most scholars. The length of the sidereal day (i.e. the time taken by the earth to complete one revolution with respect to any given star) it uses is 23 h 56 min 4.6 s, while the correct value is 23 h 56 min 4.091 s; the tiny difference is an indication of the precision reached in that early age. The <\/span>Ved\u0101nga Jyotisha<\/em><\/strong> also discusses solstices (<\/span>ayan\u0101nta<\/em><\/strong>) and equinoxes (<\/span>vishuva<\/em><\/strong> ) and uses an intercalary lunar month (<\/span>adhikam\u0101sa<\/em><\/strong>) to catch up with the solar calendar over a five-year <\/span>yuga<\/em><\/strong> (era): the solar year is about 365.24 solar days, while the lunar year is, at most, 360 days; after a few years, the difference between the two will be such that a month (or two, depending on the system) needs to be added to the lunar year to catch up with the solar cycle.<\/span><\/p>\r\n \r\n

In that era, a simple water clock was used to measure time; the gnomon, a vertical stick whose shadow is measured, must have come into use a little later.<\/span><\/p>\r\n \r\n

The first Indian texts dealing explicitly with mathematics are the <\/span>Shulbas\u016btras<\/em><\/strong>, dated between the 8th and 6th centuries BCE. They were written in Sanskrit in the highly concise <\/span>s\u016btra<\/em><\/strong> style and were, in effect, manuals for the construction of fire altars (<\/span>citis<\/em><\/strong> or <\/span>vedis<\/em><\/strong> ) intended for specific rituals and constructed with bricks. The altars often had five layers of 200 bricks each, the lowest layer symbolizing the earth, and the highest, heaven; they were thus symbolic representations of the universe, to which the sacrifice was in effect offered. Because their total area needed to be carefully defined and constructed from bricks of specified shapes and size, complex geometrical calculations followed, some of which led to interesting corollaries, such as the so-called Pythagoras theorem, or a rational approximation \u221a2 (correct to the fifth decimal).<\/span><\/p>\r\n \r\n

The <\/span>Shulbas\u016btras<\/em><\/strong> also introduced a system of linear units based on dimensions of the human body; they were later slightly modified and became the traditional units used across India.<\/span><\/p>\r\n \r\n

A couple of centuries later, Jain astronomy also developed in this period, based on a peculiar model of two sets of 27 <\/span>nakshatras<\/em><\/strong>, two suns and two moons; it nevertheless resulted in precise calendrical calculations. Jaina texts indulged in cosmological speculations involving colossal numbers and dealt with geometry, combinations and permutations, fractions, square and cube powers; they were the first in India to come up with the algebraic notion of an unknown (y<\/span>\u0101vat-t\u0101vat<\/em><\/strong>), and introduced a value of \u03c0 equal to \u221a10, which remained popular in India for centuries.<\/span><\/p>\r\n \r\n

This is also the period when huge scales of time were conceived of such as a \u201cday of Brahm\u0101\u201d (or <\/span>kalpa<\/em><\/strong> ) of 4.32 billion years, which happens to be close to the age of the earth (4.5 billion years). There are much longer time scales to be found in Jain texts and in the <\/span>Pur\u0101nas<\/em><\/strong>, but also infinitesimal dimensions of time, space, weight or angle. Indian scholars were keen to explore the two extremities of the infinite.<\/span><\/p>\r\n \r\n

With the appearance of the Br\u0101hm\u012b script a few centuries BCE, India\u2019s first numerals come into use, on Ashoka\u2019s edicts in particular, but as yet without any decimal positional value. These numerals will evolve in shape; eventually borrowed by Arabs scholars, they will be transmitted, with further alterations, to Europe and become our modern \u201cArabic\u201d numerals.<\/span><\/p>\r\n \r\n

Babylonian and Greek influences are clear in the introduction of the 24-hour day, the seven-day week and of the solar zodiac of 12 signs (<\/span>r\u0101shi<\/em><\/strong>), first recorded in the <\/span>Yavanaj\u0101taka<\/em><\/strong> (c.<\/span>269 CE).<\/span><\/p>\r\n \r\n

3. The Siddh\u0101ntic or Classical Era<\/strong><\/p>\r\n \r\n

The full-fledged place-value system of numeral notation worked out in India in the first centuries CE was a crucial advance. While positional systems existed earlier (e.g., in Babylonia and China), they had failed to integrate zero with the nine numerals. The new system was gradually adopted across India, and later taken to Europe through the Arabs.<\/span><\/p>\r\n \r\n

The Siddh \u0101ntic era opened in the 5th century CE, when texts called <\/span>siddh\u0101ntas<\/em><\/strong> were composed \u2014 a Sanskrit word meaning \u2018principle\u2019 or \u2018conclusion\u2019, but which applies here to a collection of conclusions or a treatise. \u0100ryabhata I (born 476 CE), working near what is today Patna, ushered in this era with his <\/span>\u0100ryabhat\u012bya,<\/em><\/strong> which dealt concisely but systematically with developments in mathematics and astronomy. Brilliant scholars followed, such as Var\u0101hamihira, Bh\u0101skara I, Brahmagupta, Lalla, Sr\u012bdhara, Mah\u0101v\u012bra, \u0100ryabhata II and many more. This was the time of great advances in algebra, geometry and the first steps in calculus, and in astronomy effective algorithms to track the paths of celestial bodies and predict eclipses.<\/span><\/p>\r\n \r\n

Among those advances, let us mention solutions of indeterminate, quadratic and cubic equations, finite and infinite series, negative numbers, trigonometry, expansions of fractions, permutations and combinations, and in astronomy issues of coordinate systems, time measurement and division, mean and true positions of celestial bodies, epicyclic models for the computations of planetary positions, and calculations of solar and lunar eclipses. The contributions of Bh\u0101skara II (born 1114 CE), better known as Bh\u0101skar\u0101ch\u0101rya, were the culmination of the Siddh\u0101ntic era.<\/span><\/p>\r\n \r\n

During those centuries, astronomy\u2019s interface with the society was mostly through calendars and <\/span>pa\u00f1ch\u0101ngas<\/em><\/strong> (almanacs), and the prediction of eclipses, which had great religious and social significance. Indeed, an astronomer\u2019s fame was guaranteed if he could accurately predict the occurrence, nature and duration of eclipses, and many inscriptions record a king\u2019s reward to such an astronomer. Another interface was architecture, and many monuments, including temples, show clear astronomical alignments with events such as the sunrise at solstices and equinoxes.<\/span><\/p>\r\n \r\n

4. The Kerala School<\/strong><\/p>\r\n \r\n

The common belief that there was no progress in Indian astronomy and mathematics after Bh\u0101skara II ignores the developments that took place in the southern state of Kerala. The so-called Kerala School of Astronomy and Mathematics flourished there from the 14th to the 17th century, when networks of knowledge transmission in north India were severely disrupted in the wake of repeated invasions.<\/span><\/p>\r\n \r\n

M\u0101dhava (c. 1340\u20131425 CE) laid some of the foundations of calculus by working out power series expansions for the sine and cosine functions (the so-called Newton and Gregory\u2013 Leibniz series). Parameshvara (c. 1360-1455 CE) was extremely productive in astronomical works and observations. N\u012blakantha Somay\u0101j\u012b (1445-1545 CE) carried out a major revision of the older Indian planetary model, achieving a quasi-heliocentric model. Results and methods produced by the Kerala School, both in mathematics and astronomy, remained in use well into the 19th century.<\/span><\/p>\r\n \r\n

5.<\/strong>Cross-cultural Developments<\/strong><\/p>\r\n \r\n

About the same time, a complex interface with Islamic astronomy took place, which, among other benefits, brought instruments such as the astrolabe to India. The famous and massive <\/span>yantramantra <\/em><\/strong>or Jantar Mantar observatories built in the early 18th century by the Maharaja of Jaipur, Sawai Jai Singh (1688-1743 CE), represent a convergence between Indian, Arabic and European astronomy. Indian astronomy interacted not only with Islamic (or <\/span>Z\u012bj<\/em><\/strong>) and European astronomies, but also with Chinese astronomy, in complex interplays that invariably enriched both players.<\/span><\/p>\r\n \r\n

In a general way, Indian scientists were more interested in efficient methods of computation than in theoretical models. Nevertheless, they did often provide logically rigorous justifications for their results, especially in the longer texts. Bh\u0101 skar\u0101c\u0101rya states that presenting proofs (<\/span>upapattis<\/em><\/strong>) is part of the teaching tradition, while Jyeshthadeva devotes considerable space to them in his <\/span>Yukti Bh\u0101sh\u0101<\/em><\/strong>. Some of the algorithmic methods used to calculate planetary positions and eclipses yielded remarkably precise results and impressed by their speed European astronomers such as Le Gentil, a French savant who stayed in Puducherry for two years to observe a solar transit of Venus in June 1769.<\/span><\/p>\r\n \r\n

Whether those specificities of Indian science limited the further growth of Indian mathematics is open to debate. Other factors have been discussed by historians of science, such as historical disruptions of centres and networks of learning (especially in north India,), limited royal patronage, or the absence of a conquering impulse (which, in Europe, did fuel the growth of science and technology in the colonial age). Be that as it may, India\u2019s contribution in the field was enormous by any standard. Through the Arabs, many Indian inputs, from the decimal place-value system of numeral notation to some of the foundations of algebra and analysis, travelled on to Europe and provided important components to the development of modern mathematics and astronomy.<\/span><\/p>\r\n\r\n<\/div>\r\n\r\n\r\n\r\n
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