**Presidential
address to the **

**Symposium
on Ancient Indian Scientific Knowledge.**

(Feb.25, 2003)

I am delighted to be here today in the midst
of so many luminaries and under the benign divine presence of the most
respected sage that ever walked on Earth in the twentieth century. The

The Ancientness of Indian knowledge goes back
not just to a few centuries or even a
few millenia, but it goes back to several yugas, where each yuga is itself
several hundreds of millenia. The words ‘Scientific Knowledge’ may prompt you
to think that we are talking of the Mathematics, Physics, Chemistry and Biology
that we now know of from our contacts with the western world. There is a
mistaken impression in some quarters that science and scientific knowledge are
the prerogatives of only the past few centuries of history. It is not so. From
time immemorial all knowledge in

*adhIhi
bhagavo brahmeti .... sa tapas taptvA.*

The disciple is enjoined to investigate the
cause of all causes by doing tapas that is, one-pointed self-negating
concentration, a spiritual travail for which ancient

*Punareva
--- pitaramupasasAra*>

The disciple proceeds from the obvious and the
outer to the deeper and inward principles one by one: from matter to life, from
life to mind, from mind to intelligence, and finally from intelligence to
bliss;

From *anna*
to *prANa*, from *prANa* to *manas*, from *manas* to *vijnAna* and from *vijnAna*
to *Ananda.*

This spirit of enquiry is the sum and
substance of all quest in ancient times. Whether the object of enquiry was
spiritual or not, the method always incorporated this spirit of relentless
enquiry and experiment. This is why I call all ancient Indian knowledge
scientific.

In the beginning no distinction was made
between the so-called spiritual pursuit
and the secular pursuit of material knowledge. But even in later times when
such a distinction was made, the spirit of scientific enquiry continued.
Whether it was the magnum opus of the 6^{th} century B.C.E., namely,
the *ashTAdhyAyI *of Panini the
Grammarian, or the Vaiseshika *sUtras*
of Kanada (of about the same time) about the atomic theory of matter or the
vast treasures of Jain literature (around the 2^{nd} century B.C.E.) on
Infinity and the law of indices, or
Pingala’s *Chandas-shAstra* of
the 1^{st} century B.C.E. talking about Vedic metres, or it was Vedanga
jyotisha, or the *Sulva-sutras* of
Bodhayana and Apastambha (7^{th} and 8^{th} centuries
B.C.E.), or the AryabhatIya of
Aryabhata, or the conceiving of the *Shriyantra*
that goes back to even the *atharvaveda*,
or the *Surya-siddhanta* of
Varahamihira of the 6^{th} century C.E., or the *Brahmasphuta-siddhanta*
of Brahmagupta of the 7^{th} century C.E., or the *Rasa-ratnAkara*
of Nagarjuna of the 10^{th} century, or the *Siddhanta Siromani* of Bhaskara of the 12^{th} century -- whatever it was, the scientific quest
continued.

In spite of the significant and voluminous
contributions of the Greeks to Number
Theory, Geometry and Mensuration, the credit of inventing a practically useful
notation for writing and communicating with numbers goes back to the Hindu
school of thinkers of the first century B.C.E. It is again an amazing fact that
long before these notations were used, probably even before the time of the
Mahabharata, Samskrit literature had already been using unique word names for
powers of 10. Listen to a passage from Krishna Yajur Veda (4^{th}
Khanda, 4^{th} Prashna): This is a prayer and a wish for the wealth of
cows to abound in large numbers, like millions and millions.

*sahasrAyatvemAme
agna ishTakA dhenavassantv ekA ca shatamca sahasramcAyutamca
niyutamcaprayutamcArbudamca nyarbudamca* *samudrashca
madhyamcAntashca parArdhashcemAme agna ishTakA dhenavassantu.*

The counting of cows here goes by hundreds, thousands, and thousands and
millions of hundreds. The actual sequence of powers of ten has a word for each
power of ten upto the seventeenth, though not all of this is used in that
passage just quoted. The actual sequence as defined in books of Mathematics
like Leelavati is:

*Eka,
shata, sahasra, ayuta, laksha, prayuta, koti, arbuda, abja, kharva, nikharva,
mahapadma, shankha, jaladhi, antya, madhya, parArdha.*

Here *parArdha*
is 10 to the power of 17. It is the number of human years in one half of Brahma’s life. The very fact that these words
are picked and used in the veda itself shows how ancient the concept is. These
names have been freely used both in literary and scientific writings from the mahAbhArata times onward.

I dare not invade into the topic of the first
speaker today, Prof. M.S. Rangachari. But having enjoyed all my life the charms
and beauties of Mathematics I cannot resist the temptation of quickly and briefly summarizing for you the greatness
of our ancients in the Mathematical field.
The number zero, one of the most
significant inventions, is the subtle
gift of the Hindus of antiquity to mankind.. To it must be credited the enormous usefulness of its counterpart,
the place value system of expressing all numbers with just ten symbols. And to
these two concepts we owe all the arithmetic and mathematics. The mathematical
climate among the Hindus, was congenial for the invention of zero and for its
use as the null-value in all facets of calculation. Then there is Vedic
Mathematics which has caught the rapt attention of the whole world as a
pedagogical short-cut to manipulatory mathematics. Among the Sulba sutras, the Bodhayana
Sutras (800 - 600 B.C.) contains among other things a general
statement of the Pythagorean theorem, an approximation procedure for obtaining square roots and a number of geometric
constructions that include an approximate squaring the circle, and
construction of rectilinear shapes whose area was equal to the sum or
difference of areas of other shapes. To the Jaina thinkers must be given the credit of being the first, in the chronology of scientific
thinking, to have recognised that all
infinities were not the same. They also
were aware of the Theory of indices. The Bakshali manuscript has the unique
distinction of having, for the first time, in the entire history of Ancient
Indian mathematics, the subject matter organised in the sequence: a rule; a
relevant example in word form; the same in notational form; the solution and
finally the demonstration or the proof.. It was from here the Rule of Three
was taken to

Not only in Mathematics but in other fields
also the ancients of *ghora-timira-ghana-nibiDa-nishithe
–pIDita-mUrcita-deshe ...*’. Why did this fall happen? Why this all-round
decline? I hope the speakers will give some of their time to this.

I congratulate every one of the experts who
are going to share with us today their findings on this interesting topic of
Ancient Indian Scientific Knowledge. I am glad I have this opportunity and responsibility to listen to all of them.
And I look forward to a
thought-provoking symposium. In the process I expect to learn a lot from them.
Thank you.

**Copyright
© V. Krishnamurthy 1 Jan. 2007
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