Amita Sharma

Who knows for
certain?

Who shall here
declare it?

Whence was it
born, whence came creation?

The gods are later
than this world’s formation;

Who then can know
the origins of the world?

None knows whence
creation arose;

And whether he has
or has not made it;

He who surveys it
from the lofty skies,

Only he knows — or
perhaps he knows not.

The Rig Veda
(X:129)

The Hymn of
Creation is, perhaps, one of the profoundest critical gazes cast on the creator
in the history of metaphysical thought, putting under erasure an a priori
cognisant principle, manifesting a spirit free to doubt and question. This
defines ancient Indian knowledge systems, cohabiting different realms of
‘realities’ generating at one level, the language of sophisticated argument,
technical detail and codification, and at another, a language that is
tentative, suggestive, pushing the borders of the known.

The genesis of
ancient Indian knowledge systems is this coupling of intellectual enquiry with
a sense of sublime wonder at the great mysteries of life. Ancient Indian
knowledge forms were divided into two broad groups, namely para vidya and apara
vidya. Para vidya or higher knowledge is knowledge by which the imperishable is
known. Apara vidya encompassed worldly knowledge, like science, technology,
arts, commerce and management. To the modern mind, thinking in exclusive
categories, dichotomising knowledge forms, these two knowledge worlds are
dualistically wedged. But the uniqueness of ancient Indian knowledge systems is
the coexistence of the transcendental with the empirical, generating several
distinctive features. The sacred and the secular flowed into each other.

There was no
Inquisition to be feared, no imposed dogma. Savants built upon inherited
knowledge forms while equally questioning them. We find Kautilya disagreeing
with earlier thinkers of political science on issues of warfare, or Brahmagupta
virulently rejecting Aryabhata’s theory of a rotating earth. A huge literature
of commentaries, many of them sadly lost, is evidence of ceaseless and tireless
scholarly discussion, debate and dissent.

Technical
knowledge often arose to serve religious practices. Over time, organised
systems emerged dealing with language, philosophy, mathematics, astronomy,
medicine, the arts, governance and administration, ethics and yoga and a host
of lesser known knowledge systems related to agriculture, animal husbandry,
water management, town-planning that were documented in numerous texts rarely
studied now.

Today the
enmeshing of ideas, of poetry with physics, maths with mantra, science with
mysticism, might appear as pre-scientific and, therefore, mere objects of
curiosity. Yet when submitted to rigorous tests, they have almost always proved
their worth. A few examples illustrate how the complexity of Indian knowledge
systems argues for analytical rigour, not a reductionist reading and uncritical
rejection. It is not for nothing that 20th century physicists such as Erwin
Schrödinger or Werner Heisenberg drew inspiration from Vedantic concepts.

Ancient Indian
mathematics arose from the Vedangas — a reflection on the Vedas. The
Shulba-sutras, India’s first texts of geometry, composed around 800 - 600 BCE,
exemplify traditional epistemological forms and their contribution to modern
knowledge. These texts add-ressed the theological requirement of constructing
fire altars with different shapes such as a falcon in flight with curved wings
or a tortoise with extended head and legs, but with the same surface area. The
altars had to be constructed with five layers of burnt bricks, each layer
consisting of 200 bricks and no two adjacent layers having congruent
arrangements of bricks. One of the geometric constructions involved squaring
the circle (and vice-versa) viz., geometrically constructing a square having
the same area as a given circle.

The Baudhayana
Shulba-Sutra says, a rope stretched along the length of the diagonal produces
an area which the vertical and horizontal sides make together. This is a
precise geometric expression of the Pythagorean theorem, which states that the
sum of the squares of the two sides of a right-angle triangle equals the square
of its hypotenuse. Were we more aware of the contribution of Indian
geometricians, the Pythagorean theorem might today be equally known as the
Shulba theorem.

The Vedic mantras
are chanted till today after a ritual prayer. Have we ever noticed the
incantation involves large numbers? For example, the mantra at the end of the
annahoma (food-oblation rite) performed during the ashvamedha invokes powers of
10 from a hundred to a trillion.

Maths and verse
enmeshed not just in style, but in substance. Pingala (300 - 200 BCE), author
of the earliest known Sanskrit treatise on prosody, Chandaḥsāstra (the science
of metres), gave elaborate rules for listing out all possible combinations of
‘heavy’ (long) and ‘light’ (short) syllables in Vedic metres. In the process,
Pingala constructed prastāras or tables which noted the combinations in what
would be called today a binary system of notation (for instance,
‘long-long-short... long-short-short’). The science of metres led to the Indian
equivalent of the famous Fibonacci numbers (in which each number is the sum of
the preceding two: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...).

A Vedic hymn could
have more than one meaning, embedding philosophical speculation with
mathematical concepts. A famous shloka from Ishavasya Upanishad reads,
purnamadah purnamidam purnat purnamudachyate purnasya purnamadaya purnameva
vashishyate: “That is whole; this is whole. From the whole comes the whole;
take away the whole from the whole, what remains is the whole.” Mathematically,
this can be interpreted in terms of zero as well as infinity, both of which are
meanings of purna.

While the zero
(variously called shunya, purna, bindu ...) as an empty place-holder in the
place-value numeral system appears much earlier, algebraic definitions of the
zero and its relationship to mathematical functions appear in the mathematical
treatises of Brahmagupta in the 7th century whose Brahmasphutasiddhant had basic
operations (including cube roots, fractions, ratios and proportions) as well as
applied mathematics (including series, plane figures, stacking of bricks,
sawing of timber, and piling of grain). His concept “divided by zero =
infinity” is etymologically interesting: khachheda means divided by kha, where
kha (space) stands for zero.

Consider the way
decimal story unravels. The present system of decimal numbers needed two
fundamental discoveries: the concept of zero and the principle of place value.
Both were developed in India between the 1st and the 6th centuries CE. The
first inscription with a decimal place-value notation is from Sankheda in
Gujarat, dated 346 in the Chhedi Era, or 594 CE, where ‘3’ stands for hundreds,
‘4’ for 10s and ‘6’ for units. But five centuries earlier, the Buddhist
philosopher Vasumitra, discussing the counting pits of merchants, had remarked,
“When [the same] clay counting-piece is in the place of units, it is denoted as
one, when in hundreds, one hundred.”

Decimal
representation was also employed in a verse composition technique, later
labelled bhuta-sankhya (literally, object numbers) used in technical books.
Since those were composed in verse, numbers were often represented by objects.
The number 4, for example, could be represented by the word Veda (there are
four Vedas), the number 32 by the word teeth (a full set consists of 32), and
the number 1 by moon, sun or atman, all of which are unique. So,
“Veda-teeth-moon” would correspond to 4-32-1 or our decimal numeral 1324, as
the convention for numbers then was to enumerate their digits from right to
left.

This rich
tradition of mathematics flowered in some of the greatest mathematicians of
their times who contributed towards discovering and formalising mathematical
principles. Aryabhata I (born 476 CE) described fundamental principles of
mathematics and astronomy in 121 verses of Aryabhatiya which deal with
quadratic equations, trigonometry or the value of π, correct to 4 decimal
places. His calculation of the circumference of earth was within 12 per cent of
the actual value, his table of planetary positions and his lengths of the
sidereal and solar years remarkably precise. Brahmagupta (born 598 CE) studied
many geometrical figures, introduced negative numbers and defined mathematical
infinity as “that which is divided by zero”.

Bhaskara II (born
1114), author of Lilavati and Bijaganita, proposed solutions to cubic and
biquadratic equations, worked out an efficient algorithm for some types of
second-degree indeterminate equations and laid down some of the foundations of
calculus.

As in the case of
mathematics, early astronomical insights were embedded in sacred texts often
veiled in allegorical or poetical forms. The Rig Veda refers to a wheel
consisting of 360 spokes, clearly the days of the year; some of its verses have
been interpreted in terms of eclipses and meteor showers.

The Aitareya
Brahmana (3.44) declares, “The sun never really sets or rises. ... Having
reached the end of the day, he inverts himself; thus he makes evening below,
day above... Having reached the end of the night he inverts himself; thus he
makes day below, night above; He never sets; indeed he never sets.” This seems
to reflect an awareness of the sphericity of the earth.

The famous scholar
Sayana (c. 1315-1387) commented thus on a hymn to the sun from the Rig Veda
(1.50.4): “Thus it is remembered, O Surya, you who traverse 2,202 yojanas in
half a nimesha.” With a yojana of about 13.6 km and a nimesha of 16/75thof a
second, this amounts to 280,755 km/sec — just 6 per cent from the speed of
light (299,792 km/sec) — a coincidence worth noting.

The Puranas
describe time units from the infinitesimal truti, lasting (according to
Bhaskara II) one 2,916,000,000th of a day or about 30 microseconds, to a
mahamantavara of 311 trillion years. Time is seen as cyclical, an endless
procession of creation, preservation and dissolution. The end of each kalpa
brought about by Shiva’s dance is also the beginning of the next. Rebirth
follows destruction. Each Brahma day and each Brahma night lasted a kalpa or
4.32 billion years, adding up to 8.43 billion years which is not too far from
the current 13.7 billion years for the age of the universe (another
coincidence, which the US astronomer Carl Sagan noted).

In contrast, till
the 19th century, much of Europe was convinced that the universe was no more
than 6,000 years old. And while we are on coincidences, let us mention that
Jain texts state that there are 8.4 million species on earth, which compares
well with the figure of 8.7 million arrived at in a 2011 research paper.

Sacred geographies
enfolded astronomical observations. According to the German archaeologist
Holger Wanzke, the east-west alignment of the main streets of Mohenjodaro’s
citadel (or acropolis) was probably based on the Pleiades star cluster
(Krittika), which rose due east at the time; it no longer does because of the
precession of the equinoxes. Ujjain, associated with the legendary king
Vikramaditya, is located on the Tropic of Cancer; it was a centre of
astronomical observations. Chitra-koot is associated with Rama, who is often
represented symbolically as an arrow. Mapped with GPS, ashrams and other holy
sites there form arrows that point to the sunrise and sunset on the summer
solstice. Varanasi’s 14 Aditya shrines precisely track the sun’s path through
the year, embedding time in the ancient city’s map.

The purpose of
alluding to diverse forms of cultural codification of knowledge is that even
while ambiguity may enwrap them, they have a steady stream of scientific
insights that merit research. The significance of culturally embedded knowledge
is supported by our material inheritance.

For the growth of
a truly scientific spirit, it is necessary that we critically evaluate our
intellectual inheritance. Bhaskara II said, “It is necessary to speak out the
truth accurately before those who have implicit faith in tradition. It will be
impossible to believe in whatever is said earlier unless every erroneous statement
is criticised and condemned.”

In ignoring our
own knowledge legacy, or rejecting it as myth, are we guilty of creating an
uncritical modernism that stultifies its own growth?

Fields Medal
winner, Manjul Bhargava has said that he was inspired not only from ancient
Indian mathematicians, but also from his practice of tabla and his knowledge of
Sanskrit. The statue of Nataraja, a symbol of the dance of subatomic particles,
which adorns the CERN where the hunt for the ‘ultimate’ particles goes on, is a
reminder that India’s wisdom offers much to the world in its tireless research
into the mysteries of life in its infinite complexity.

(With inputs from
Michel Danino)

Amita Sharma is
former additional secretary in the ministry of human resources development. Michel
Danino is a French-born Indian author, currently guest professor at IIT
Gandhinagar

This article was published
in financial chronicle, Tuesday, April 14, 2015

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