So, while all this was happening in Europe, what was happening in India?
As we have said earlier, the Indus Valley Civilization, Valley Civilization
was approximately 3500 BC to about 1700 BC and then the Vedic age was around 1500 BC
to about 600 BC. And then after that we call the post-Vedic
age, which is around, say, 600 BC to ... I will not define exactly when it was.
But let us discuss this period. I will not talk about the Indus Valley Civilization
because, apart from technology used there, we do not really know much of the thought
process or the science that was there. But in the Vedic age, whatever science was
there, we can get some glimpse of it from the Vedic literature.
And we know that during that time, well initially in the Vedic age writing was not there.
So, things were propagated in Shruti and Smriti, but after around 1000 BC, writing developed
and things started being written up. And at that time, we get some glimpse of the
number system they used. In the number system they used, it was a 10
best number system. But there was no zero, there was no place
value system. So, in their number system it was basically
1, 2, 3, 4, 5, 6, 7, 8, 9 and then, since there was no 0, one cannot write one-zero
as 10. So, there was a separate symbol for 10 and
that symbol followed by 1 would be 11 and so one and so forth.
Again at 20, you will need a separate symbol and this method of writing continued for a
long time. In fact, the Kharoshti stone inscriptions
at the time of Ashoka also has the same writing, number writing system.
One important development that happened in the Vedic age was the Shulvasutras.
Shulvasutra was, the word, means the rule of the thread, shulva means thread.
So, essentially these were instruction manuals for constructing alters for yagnas and in
that, they had to tackle some some theoretical problems.
For example, how to identify the exact East-West line?
They could figure that out. How to construct a circle of the same area
as a square or how to construct a square of the same area as a circle?
So, these are problems that were tackled in the Shulvasutras and we see in the Shulvasutra
the the first statement of what is today known as the Pythagoras theorem.
As we we have seen that the Vedic age, essentially we say that the the onset of the post Vedic
age with the onset of the Jainism and Buddhism, because after about 100 years of Buddha's
life practically the whole sub continent become became Buddhist.
And so after that time we say that the Vedic age had ended and the post Vedic age has started.
And in this transition period we see a lot of developments.
And in the early post Vedic periods we see a lot of developments.
Most notably, there was a development of medical science.
Towards the end of the Vedic age we see the Atharva Vedas being written up and in the
early post-Vedic period, in continuation of that Atharva Veda tradition, the AyurVeda
was written up. And we see great medical practitioners like
Charaka, Sushruta in that early period of the post Vedic age.
Sushruta, in fact, introduced surgery and that is unprecedented anywhere in the world.
Surgery per se was not practiced anywhere in the world at that time.
So, it was a great development for that matter. In the Vedic age, Sanskrit was developed as
a language, but it was... it did not have a uniform form.
And Panini the greatest grammarian of antiquity Panini; I was so, far talking about the the
Atharva Veda and Ayur Veda and we talked about Sushruta, Charaka and there were other important
medical practitioners. For example, Athreya, Jivaka.
Jivaka was the court physician of Bimbisar. And I was I am talking about now of Panini,
the greatest grammarian of antiquity, around 5th Century BC.
So, Panini actually formalized Sanskrit grammar and gave it a very structured form so that
it could become the link language of the whole Indian subcontinent.
Link language. Not only link language, but also the language of the of education educated
class. And the way we write our alphabets, that's
also a contribution of Panini. So, Panini was one of the greatest grammarian
of antiquity. And after that, we find that the Jains, the
Jain lineage, create a created a group of mathematicians called the Jain mathematicians.
So far, in the Vedic age—the mathematics that I just mentioned, in the Shulvasutras—these
were mathematics for the service of religion, religious practices, while the Jain mathematicians
took it out of the religious practice and made mathematics stand on its own feet.
They conceived large numbers, even infinity and things like that.
The greatest development in the Veid... in the post-Vedic age in mathematics was the
introduction of zero. The absence of anything is also a number—conceiving
that was not easy. That happened in the Indian subcontinent,
though I must admit that at that time there were trade between India, China, Indo-China
and all those regions and it is somewhat uncertain as to where zero originated first.
Because it could have... The idea could have originated in any of these
places and through trade routes, that might have you know come to the other places, because
the oldest inscription of the symbol 0 is found in a temple in today’s Cambodia.
So, it is not in the Indian land per se, but nevertheless it is normally believed that,
early on, Indians took up this zero and the place value system.
And when you introduce a new kind of writing numbers the whole mathematics has to be redone.
So, the ways of addition, subtraction, multiplication, division, square, square root and all that
had to be invented afresh, was done in Indian subcontinent.
And then we see a a plethora of great mathematicians and astronomers.
We see Aryabhata (5th century), we see Varahamihira, we see Brahmagupta, after Brahmagupta there
were say Sridhara was there. And there were many such mathematicians.
But crowning all that was Bhaskara. I would say Bhaskara II, because there was
another Bhaskara I. He was in the 12th century.
Aryabhata was in the 5th century and they were in between: 6th century, 7th century,
then he was in 9th century and so on and so forth.
So, in this period we see a lot of developments. What did they do?
Aryabhata, for for example, found the value of Π much more accurately than anybody contemporary
to him. He expressed it as a fraction, but when you
evaluate that you find that 3.1416 is correct. At that time astronomy and mathematics was
developing hand in hand. The primary incentive for doing mathematics
came from astronomy because things in the sky always aroused curiosity.
People had been looking at the the things in the sky primarily initially for the purpose
of making a calendar because calendar is necessary in any agricultural society.
So, in order to make a calendar you have to find some repetitive events, cyclic events,
and the motion of the sun, the motion of the moon are such cyclic events.
So, the ancients of India of that time minutely observed the motion of the sun and the moon.
They observed that the sun does not rise in the same place every morning.
So, it goes toward South and then again goes towards North.
So, uttarayana and dakshinayana, those things were identified and when it reaches the last
point in the North, when it is the last point in the South—these were identified.
Not only that, people realized that the sun and the moon go in a particular strip and
all the planets go in the same strip. Today we know that as the zodiacal strip,
and in order to identify the position of the sun and the moon, the ancients in India named
27 stars along that zodiacal strip. They named the the rashis that we know today—the
constellations. The Leo, the Libra and all that. Those constellations
were named. Aryabhata, for the first time realized that,
we see this the sun going from one side to the other, from the East to the West, we see
the moon going from the East to the West, we see the all these stars the whole sky going
from the East to the West, and he realized that the easiest solution of all that is to
assume that Earth itself is spinning on its own axis.
This was the first in the world when somebody could make the comment that the Earth itself
is not static; it is in fact, a spinning globe. The people contemporary to Aryabhata even
a century, couple of centuries later like Varahamihira, Brahmagupta—they did not accept
Aryabhata's idea that the earth is a spinning globe.
But but they also had their own contributions in Mathematics and Astronomy.
Well Brahmagupta for example... Aryabhata was not the first to introduce the
sine tables and cosine tables because, as I said earlier, the Greek Greek Astronomers
Aristarchus and Hipparchus—they introduced the sine and cosine in order to make their
observations correctly. And Aryabhata make made a sine table of one
degree difference. So, sine 1 degree, sine 2 degree, sine 3 degree,
cosine 1 degree, cosine 2 degree—he made tables like that.
And when we really look at the tables we find that it satisfies the "sin square plus cos
square equal to one" rule. So, that rule was also definitely known to
them. And whatever trigonometric relationships we
learn in school, the simple ones, all these were invented in by Aryabhata, Varahamihira,
Brahmagupta. In fact, in Brahmagupta’s book Brahmasphuta
Siddhanta, you see practically most of the simple trigonometric relationships that one
learns in school today. So, those things were introduced in the Indian
soil. Algebra! Algebra was done using Sanskrit alphabets:
ya was to represent today’s x. And if there was x and y, that means, two
unknowns, then that was represented by the first letters of the color names.
So, red and blue: the first letter, Sanskrit letters of the color names were used and people
wrote equations with that. Not only that, one of the peculiar mathematical
developments in India was the solution of indeterminate equations.
Something like ax+by=c, an equation like that, one equation like that cannot be solved because
there are two unknowns. But some Indian mathematicians noticed that
if a, b, c are whole numbers and x and y are also whole numbers, then there are solutions.
And they found such solutions. And through that you can see Sridhara Brahmagupta
introduced what is known as the quadratic equation and its solution, and it was formalized
by Sridhara. So, sometimes it is called Shridhara’s equation.
And the last of that that sequence of mathematicians was Bhaskara.
He was a great mathematician. In all fields of mathematics he had contributions
and I will not elaborate on each of them. All that I want to point out was that after
Bhaskara there was practically nothing, at least in the main part of India.
There was one lamp still lit in the corner of the Indian subcontinent, in Kerala, which
is called called the Kerala School of Mathematics and Astronomy.
They were followers of Aryabhata and continued that that tradition and developed mathematics
at a later time. But after the 11th century practically science
was dead in India. Bhaskara was, you can say an outlier.
He was actually not in Northern India, he was in today’s Karnataka.
His place was in today's Karnataka. And after that center of learning moved further
South, in Kerala. Well, so, you see that in India also a lot
of developments happened. And in the last class I pointed out that in
India also, both the material school as well as the ideal school existed, were fighting
for intellectual space, were were influencing people.
For example, the the names that I mentioned, Sushruta, Charaka, Aryabhata—most of them
subscribed to this or that school of materialist philosophy, but the idealist philosophy was
also very much there. And in the 7th century, idealist philosophy
started on an ascent with the work of Shankara. He forcefully made the point that the world
is illusion. The material world, as you see it, is illusion,
is Maya. And following him, his time, slowly the the
ideal school become stronger and stronger, and the as a result, the material school became
weaker and weaker. And Acharya P.C. Ray identifies the decline
and fall of science after the 11th century to three factors.
In his book ‘The History of Hindu Chemistry’, he writes that the first reason for the decline,
decline happened around started around 9th century and after the 11th century, it was
practically not there. Science was not there in India any further.
So, he identified that as the assent of the caste system.
Caste system was there earlier, but it was not entrenched in the society in a very strong
manner and after that time it became a very strongly entrenched caste system.
Prafulla Chandra makes the point that, in order for science to flourish, the doers and
the thinkers either have to be the same people, or have to be in close touch with each other.
But after the caste system was introduced, the doers and the thinkers were separate castes
with no contact between them. The second point he he made was that specifically
in the context of these medical practitioners because, as I said, surgery was the important
thing that did, they introduced surgery. Prafulla Chandra made the point that, in order
for a teacher to teach surgery to a student, you cannot do it without dissecting dead bodies.
By dissecting dead bodies, you can show what is inside and in which position, so that when
you actually perform surgery on a living body, the person must know what he is cutting and
where to find what. When the Manu the strictures of Manu, the
Manu-samhita was introduced, then it became impossible for a Brahmin or somebody of the
upper caste to touch a dead body because that was only to be done by a shudra.
So, the the learned people no longer could could touch the dead body.
So, dissecting the dead body became impossible and naturally the whole cult of surgery fell
into disuse. The third point that Prafulla Chandra makes
is that the the ascent of the the philosophy of Shankara, which saw... the idealist philosophy
of Shankara which saw the material wordld as illusion.
He says that, in order for to do science you have to believe that the material world exists.
You have to ask questions about the material world and have to seek answers.
If you believe that the material world is an illusion, you can do no science.
So, when this philosophy captured the intellectual space, then science slowly died out.
So, as you can see that there was an eclipse period of science in Europe during the Middle
Ages. There was an eclipse period in science during
the, in India also that lasted from about started as I said in the 19th century and
after the 11th century it was practically eclipsed.
There was no science in India for that matter, except the few work that we find in the Kerala
School of Mathematics. And again India started doing science proper
in what what is known as the Indian Renaissance. when Raja Ram Mohan Roy and Vidyasagar in
the 19th century they were enlightened by the ideas of European Renaissance.
They brought that idea of European Renaissance and tried to enlighten the Indian populace.
Vidyasagar tried to change the the Indian education system and through that, a new cult
started—the cult of doing science. And in the next stage we see a great number
of mathematicians and scientists. We see Jagadish Chandra Bose, we see Prafulla
Chandra Ray, we see Raman, we see Ramanujan, we see Meghnad Saha, Satyendra Nath Bose and
many others: great scientists doing great science in a very difficult situation.
So, India also had its very rich history of doing science.
India also had its history of science being eclipsed by idealism and again the ascent
of science at a much later period. In the next class we will continue our journey
with European science, because then a lot of things were happening in Europe.
But before leaving the history of science in India, let me tell you that in India, a
lot of fantastic developments happened in science which influenced the the science of
the rest of the world. The science of Aryabhata, Varahamihira, Brahmagupta
and people like that, where, the books by them were, translated by the Arabic scholars
and when there was a golden age, as it is called the ‘Islamic Golden Age’, where
the center of learning was practically in Baghdad and places like that.
There the Khalifas employed people to get literature from different places and to translate
them into Arabic and they translated these books by them.
Not only that, an Indian scholar was invited by the Khalifa in Baghdad and he he stayed
therefore some time and conveyed our number system to them.
And then the Arabic world accepted our number system, the zero, the place value system,
the decimal system and the from them the Europeans got it.
And that is why these numbers are still called the Arabic number systems.
But actually these were originated in the Indian subcontinent.
And through the exchanges that happened through trade routes especially after Alexander’s
invasion into India. The Greeks had their colonies, not colonies
their their empires in different places in the Middle East and Indias in various Indian
states had trade relationship with them. So, the Greek ideas reached India.
The Indian ideas reached various other places in Europe.
So, the developments that happened in India did not really remained in India.
It it spread in other places and influenced. Arabic astronomy was influenced by Indian
astronomy, but the Arabs developed it further and their specific focus was on on making
star charts and they call it ‘Zij’. They they produced various star charts.
And again, when Indian science was eclipsed, those star charts came back to India from
the Arabs. And their their mechanism of producing the
star charts was by using great observatories, masonry based observatories, and those things
were actually perfected in the Arab world and came back to India.
So, there was exchange of ideas between the Arab world, between India and the European
lands, but very little during the Dark Age of Europe.
Only after the Renaissance started, they translated the work of the Arab scholars, and Arab scholars
in turn had inherited some of the knowledge from the Indian scholars.
So, there was exchange of ideas; many of these had actually originated in India.
We have to be proud of that. But, I must also say that we should not...
We should understand what really happened in India, rather than harbouring fanciful
ideas regarding things that actually did not happen.
There was no aircraft in India, there was no plastic surgery that could plant elephant
head on human torso, there was no stem cell research in India at that time, there was
no biotechnology that could give birth to 100 sons of one lady.
So, these are actually mythological stories. We should not put any science behind them.
But these are hard science that was done in Indian soil and we have to be proud of it.