Bharat ki Chhap - Episode 7: Mathematics & Temple Architecture
Director: Chandita Mukherjee; Cinematographer: Ranjan Palit
Duration: 00:50:26; Aspect Ratio: 1.366:1; Hue: 358.929; Saturation: 0.055; Lightness: 0.338; Volume: 0.212; Cuts per Minute: 4.976; Words per Minute: 69.803
Summary: In this episode we learn that techniques and sciences were limited to caste barriers. We understand the operations of 'zero' and its Indian origins. We briefly understand alchemy or Rasvidya that developed experimental chemistry, extraction methods for Zinc and the lost wax process for Chola bronzes. We also explore temple architecture from the towering gopuram to rock-cut caves of Ellora and an emerging architecture brought by the invading Arabs, Turks and Afghans.
Bharat Ki Chhap: EPISODE 7
Mathematics and Architecture (700- 1200 A.D.)
1. Chandita: Looking at this material after a long gap in time jogs one’s memory and brings up thoughts. So I can keep spilling out and what we would like to put in the Pad.ma archive and what is useful to other researchers, scholars, teachers who may like to use this material would be a little different.
We made some choices about what to show in the series, anticipating a charged-up, polarized communliased situation where identity politics would come to the forefront. These choices have to be made more obvious now and I feel that is one function my annotations can fulfill.
How does science grow? Evolving from what things?
And how do we absorb the new techniques it brings?
Let's look at society in those days
Let's look at the science of that time
See why the gains of a certain age
Were lost at a later stage
And a civilization that once led...
fell back, while others forged ahead
Why does this happen? Oh, why?
How does science grow? Evolving from what things?
This is the question that our own age brings
2. Ep7 begins with a song – how do scientific techniques evolve, how does society adopt those techniques? Why does it happen that some things come to the fore at a certain period and just a little later the entire civilization seems to forget it and throw it away and go into something else. Why does all this happen? This question can never be answered but we must underline this question and be aware of it so that science never grows still.
Nissim: Science never stands still. Obstacles might slow it down, it might appear to slide backwards or change direction or form but new routes emerge and science moves ahead.
Maitreyi: The obstacles in the path of science are things like caste. Take the potter - he knows different soils, and how they react with various substances at different temperatures. But such knowledge was confined to one caste - as with blacksmiths, carpenters etc. The skills and principles of different fields did not come together, there was no integration.
Nissim: Astronomy is an example. But if, rather than ritual and horoscopy, this science had grown through navigation? We too might have had a Galileo or a Kepler. Instead, astronomy, along with astrology, stayed with the
brahmans, and navigation, with the sailors. The barrier of caste always separated the two.
Nissim: But now we approach 700 AD. It used to be thought that 700 to 1200 was a bleak period for science. Yet this age saw an active exchange between different lands. This laid the foundations of modern science
Maitreyi: At that time, our lawbooks were banning sea voyages. Thus overseas trade declined, as did our interaction with other cultures.
The country was divided into isolated parts. Cities were few, villages largely self-sufficient.
Nissim: Even so, some ideas spread, and took root. Alchemy travelled from China to India. Our number system reached Europe - this was the basis of the modern number system - the digits 1 to 9, and the zero
3. There was a lot of prejudice about moving freely with people of other countries. As a result international overseas trade also declined, coupled with the fact that many embargos were placed on products from here. Conditions in Rome changed and they put in place a law that forbade paying for products from here with gold. Import declined because nobody paid with gold and trade came down.
Within the country we see great empires broken up into small principalities in different locations. The great cities and market places declined. Villages became self sufficient, and they would have weekly bazaars and haats and exchange locally.
In this isolation, some ideas still spread and its hard to say why these ideas and not others though these are questions worth pondering. For instance, alchemy reached India from China, probably via the Chinese trade boats that came here. In south India Siddha medicine became very important and even to this day a lot of people follow it, and Siddha medicine uses a lot of metals and alchemic processes.
Three little mice cried “choo choo”
One ran away and then there were two
Two little mice cried “choo choo”
One ran away and then there was one
One little mouse cried “choo choo”
He ran away and then there was zero!
A friend of mine teaches at this nursery school. I heard the children sing this song the other day. How easily, I thought we grasp the zero today! How did people manage for centuries without it? The zero was needed when numbers had to be
written. Depicting numbers is not the same as doing sums. Any sign, like x, y or z, can stand for a number. Or if I say this sofa is 'one' and the table 'four',
as long as we all agree, we can use these symbols. The problem arises when you want to add the two. How do you add a sofa and a table?
You count on your fingers - four, plus one, makes five. That's what the merchants of Alexandria did. A Roman merchant's cargo once came from India. He wrote down in Roman numbers the price of ivory – 2,322, and of silk - 6,739. How to add these up? With an abacus! First, the ivory. Two rings in the
I column, two in the
X, three in the
C and two in the
M. Then he added the price of the silk. Nine in the
I, three in the
X, seven in the
C and six in the
M column. If a stick had ten rings, he took one to the next stick, and removed the other nine.
The total was nine thousand, sixty sixty-one. Nine thousand and sixty-one.
This was simple. But merchants have to do complicated sums. Writing numbers this way makes things difficult. But the Arab sea captain who'd brought the cargo had another method. His symbols were of this type. We saw this added on the abacus. For the numbers of rings on each abacus stick the Arab had specific symbols. Now is this nine
hundred and sixty-one, or
thousand? Or
Ninety thousand and sixty-one? In the empty spot he drew a new Indian symbol. He'd have written ninety thousand, sixty-one thus. But this
must be nine thousand, sixty-one because each symbol has a definite place.
1 is in the unit place, 6 in the tens, 0 in the hundreds and 9 in the thousands! So with just the digits 1 to 9 the largest of numbers can easily be depicted.
4. Zero: The character Shahnaz takes us through an appreciation of zero and of the modern number system. Our number system went through the hands of Arab traders to Europe to the city of the Renaissance, and this became the basis for the modern number system. 1 to 9 and 0.
Shahnaz compares it to the old Roman system of using an abacus and counting and carrying over from 9 to 10 and moving to the next column. She shows how difficult it was and cumbersome it was to keep doing big calculations and doing fractions in such a manner. The zero made it all very easy and that is why it was eagerly adopted all over the world. In China, Central Asia, Western Asia and Europe. The idea is not to say that Indians are the greatest and cleverest, or anything crudely nationalistic.
Here the attempt is to say that a good idea travels and catches fire and people see the benefit and convenience of it. It’s something to feel proud about. We ought to remember that it started up here. China and Babylon had similar ideas – for instance the Babylonians used a dot as a symbol for that place value.
5. Rules of zero:
The invention was not of the figure of zero as depicted in different cultures, but what Brahmagupta framed as the rules
a+0 = a.
a-0=a
aX0= 0
a÷0 =∞
The most important is the last one. This is something that is adapted and picked up immediately all over the subcontinent because these visitors from abroad who took it away were calling upon ports in Kerala, Gujarat, Tamil Nadu, Orissa. They were coming to all places along the Malabar and Corommandel coastline, and they were picking it up.
It spread within India through the educated classes, or the Brahmins – the keepers of knowledge. In this instance India is used in a generalized sense, rather than specific place names.
The zero existed also in other civilizations like Babylon and China. But Indian mathematicians first used the digits 1 to 9 to depict numbers of
any size. And they made the zero an independent number. Brahmagupta, in the 7th century, framed rules for the operations of zero. The zero freed maths from the limits of the abacus, and went on to cross newer boundaries.
Banaras Hindu University, Varanasi
6. Give and take: We may have invented the zero but we also learnt and exchanged many ideas. The Chinese bring alchemy to India.
Alchemy at that time had a lot to do with amarta or immortality, which was an obsession of all ancient cultures. People didn’t want to grow old, they didn’t want to rot away and die. There is a legend in almost all cultures about some sort of magic potion that you drink and remain eternally youthful. All ancient texts, the Bible and others have this fantasy.
In China the popular notion grew out of observing how gold never rusted while other metals would decay because of exposure to the elements. Gold remained golden. The notion that grew was that if in some way we can figure out how to consume gold then our body will be rust and rot free. The twin search with this was to figure how to turn base metals and cheap metals like iron and lead into gold. These were the experiments that led to modern day chemistry in Europe and so many processes and drugs and metallurgy and chemistry comes out of that. Here that didn’t happen – our knowledge of metals and alchemy was restricted to Ayurvedic medicine and making of bhasmas, sublimation of metals and so on.
Definitely this lack of vigour has something to do with the fact that all experiments and knowledge of this kind was restricted to a very limited group of people. These people were not thinking of big furnaces where you can make huge amounts of steel. They were thinking of a medicine to give to the king, bring out how to turn gold into something which could be eaten without poisoning the person. And that was the limit of their quest.
Exchanges between the Arab world, China and India gave an impetus to science. From the 3rd to the 7th century trade with China grew.
And from China came a new science – alchemy. The wish to be immortal is as old as humankind. The
Rig Veda refers to
soma rasa which was believed to grant eternal youth.
Ayurveda, too, has recipes of this kind. Of the metals, gold most impressed the ancients, for it never lost its lustre. They felt that partaking of gold in some form would ensure an equally perfect body. And so alchemy strove to discover how base metal could be turned into gold and immortality attained. They experimented with many minerals and plants. Their finds could have led them modern chemistry, but did not go beyond the medicines of
ayurveda.
Ranjan: Mercury and sulphur - these elements became the basis of such medicines. Take the
kajjali being made here.
Ayurveda still uses these old alchemy methods.
Prof: The
Rasaratnasamuchchaya of Vagbhatt says 'If we learn to refine mercury we can rid the world of poverty, old age, disease'.
Ranjan: These impossible searches of alchemy led to experiments through which knowledge of chemical processes and of metals grew.
Cinnabar is a compound of sulphur and mercury. Here, mercury is being extracted from it. It is ground, lemon juice added, and pellets made. This
damru yantra is made from two earthen pots. Mercury is sublimated in this instrument.
Ranjan: Has the mercury formed?
-Yes, we'll take it out
The alchemy texts described many other instruments. How much is there?
- Let's see.
7. Alchemy And More: Alchemy was believed to hold the secret for eternal life, and whether it did or not, it did lead to a lot of play and experiment with chemicals. Along with this quest for eternal life and so on, they were playing around with a lot of chemicals particularly mercury and sulphur which they were obsessed with. There are so many medicines that are made out of combinations of mercury and sulphur and here we show a scene of mercury being taken out of cinnabar. Cinnabar is a natural chemical compound of mercury and sulphur.
Here the experiment is being done and without any mask against the fumes, just like it was done for centuries. This is perhaps a curiosity piece for people who would believe that such an experiment is dangerous to do today, now that we know many of the ill effects of direct exposure to metal.
So I kept worrying that guy and saying what about minamata disease and stuff like that. And he said its been done for centuries like this and no one has been killed yet. And we continued to do it. I don’t know if I agree with this but I didn’t say anything in the film. Like why aren’t at least the workers in your lab wearing gloves.
Minamata disease first spread widely in Japan, where lot of mercury was dumped, deformed babies are born. The story of the Mad Hatter also comes from mercury poisoning. Mercury was being used for making felt hats and so the workers developed all these twitches and they were babbling and talking nonsense, because their brains were getting effected. They didn’t realize that this was because of the fumes of sulphur.
Maitreyi: The alchemists discovered the properties of many substances, and invented various instruments. These may look like cooking pots to us but this was their laboratory equipment. While sciences like maths are abstract, ayurveda and alchemy depend on observation and experiment. These had little status in our culture. Such work was, despite its potential, done in secret.
Nissim: Thus alchemy led to modern chemistry elsewhere but remained confined to craft traditions here. Metallurgy gained from alchemy experiments. Alchemy texts reflect knowledge of metals. The 13th century
Rasaratnasamuchchaya refers to a process then unknown in the rest of the world - the extracting of pure zinc. John Marshall, after Takshashila excavations wrote this report. He says that analysis of the brass objects found reveals the use of pure zinc in their making. This implied that they had the know-how. But where was the zinc ore mined and refined?
Maitreyi: The answer was found in 1984, at Zawar, where the British Museum, Hindustan Zinc Ltd. and the MS University conducted excavations.
8. Caste plays an important role in the distribution and production of knowledge in India. The potter may know the quality of different soils. He may not have a theory about the chemistry of it. But he knows and will explain in a language that is different from modern chemistry, what he understands about soil and silica content, or what kind of earth will produce a red or white glaze. This kind of practical or experience based knowledge remains with the potter or the blacksmith or the carpenter or the textile weaver.
In this way the principles from practice and abstract or principle based knowledge do not come together and because of this there is no integration or cross-pollination between different streams of sciences or knowledge systems.
Astronomy is an example where there is all this wonderful work done by people like Aryabhatta, Varamihira and Brahmagupta and others. Even if some of them did give obeisance to sprits and ghosts, they also did some very complex math and astronomy thinking. But that knowledge of astronomy never turned into exploration and travel, and people going on sea voyages. This was largely because there were great restrictions on mingling with people of other countries and communities and eating their food and so on. And we never saw that native knowledge of astronomy being used for navigation and exploring the world.
To know more, Raghu went to Zawar in Rajasthan and to the University in Baroda where he met Prof KTM Hegde.
Dept of Archaeology and Ancient History, MS University, Baroda
Prof. Hegde: Brass was in great demand for it shone like gold.
9. Philosopher’s Wool: One such thing is zinc. Indians had discovered how to make zinc. The process is rather difficult and is shown in this sequence. It is because of the complicated process, if you don’t make it in just the right way, everything evaporates into the air and turns into philosopher’s wool.
European alchemists discovered how to do (this) only much later than it was done here. In India this technique was known, and we could make alloys, brasses and bronzes, but it was totally forgotten. In the Aini-Akbari there are references to zinc being made somewhere near Udaipur.
William Champion patented and is given credit for discovering the technique for mass production and industrialization of making brass. He was following a similar method to the one shown here. Our ancient texts refer to a baigan (brinjal) shaped crucible – something like a bulb with a narrow stem neck in which this process is done. This is then precipitated into a bowl of water so that it cools in the water and gets a solid metal shape instead of turning into a fiber cloud or philosopher’s wool that disappears into thin air. Ironically it is the technique that was lost to Indians like philosopher’s wool.
This is something we want the viewer to think about. The parallel questions in our own time would be why do the most beautiful fine handicrafts die and require all kinds of aid to be kept alive and for the craftspersons themselves to not give up that profession.
The zinc sequence actually consists of two sub sequences – one is the scene at Baroda, at a museum in the university and experiment with Professor Hegde. And the other is at Zaver itself where these objects have been found by archaeologists and local employee of Hindustan zinc take Raghu, one of the BKC characters, into the underground chambers and deep into the ground to see what’s happening there. This was fairly difficult to shoot, without electricity and with hand held battery operated lamps. Nice work by Ranjan Palat, the cameraperson.
Prof. Hegde: But to make brass shiny like that, they needed zinc. But there was no actual evidence as to where this zinc was found or extracted, until we found ancient zinc distillation sites at Zawar.
Zawar Mines, Udaipur Dist., Rajasthan
Raghu: Some 40 km from Udaipur, in the Aravali hills is Zawar, where Hindustan Zinc Ltd has its mines.
Raghu: This is the largest zinc producing unit in India. Here zinc is made by a modern electrolytic process.
A geologist, Lalit Gurjar, took me around old Zawar. He had worked with the excavating team.
Lalit: Evidence of mining here is more than 2,500 years old. Smelting finds take us only to the 10th century, but reveal a fairly sophisticated technology. This must have evolved over time.
Lalit: This furnace has two sections. The upper part, and the cooler chamber below are separated by a perforated plate.
Prof. Hegde: Zinc is not easy to make. To extract zinc from its oxide requires a temperature of 1,100º Celsius.
Prof. Hegde: But zinc vaporises at 908º and forms zinc oxide, so light that it escapes through the furnace flues. A special furnace, then, is needed.
This is a scale model of the Zawar furnace.
Prof. Hegde: It has two sections - the furnace chamber, and condensation chamber. In the furnace chamber were placed retorts packed with zinc oxide and carbonaceous matter.
Prof. Hegde: The temperature inside was raised to 1200º. The carbonaceous matter formed carbon monoxide and descended with great pressure into the condensation chamber, while zinc vapour collected in the condensation vessels.
Raghu: The zinc industry must have brought prosperity to Zawar?
Prof Hegde: Yes. Brass made with pure zinc was much in demand. The heaps of industrial debris around Zawar indicated a long-lived, prolific industry. And the ruin of temples and houses reflect how much wealth there was.
Zawar Mines, Udaipur Dist., Rajasthan
Lalit: Here lived the people who mined and smelted zinc.
Raghu: Shall we go down?
Lalit: Yes, why not.
10. It was thought that 700 to 1200 was a bleak period for science. But here today we know enough that there was also a great exchange going on between different countries and this laid the foundations for modern science. We cannot just call it the dark ages as it is called in European history.
11. Western V. Eastern Science: There could be some concern that in this series we are privileging the western model of science by even stating a slight regret that we didn’t exhibit a similar level of development of science or scientific principles as in the west. For instance, we say that here the knowledge of alchemy remained restricted to medicine and didn’t turn into modern chemistry.
Even in this highly relativistic picture, other factors are emerging. Aryabhatta would soon be able to tell the circumference of the globe and the equator, distance of sun from the earth.
So the question remains - how it is that in these other sciences like chemistry, where we have been dabbling for centuries with the properties of chemicals reacting on the human body – how is it that this ‘practical’ knowledge didn’t extrapolate to larger explanations of the phenomena of nature.
Perhaps the answer lies in that we can’t really compare two very different systems of living and governance and patronage. Like early capitalism and industrial revolution in England with life in the court of the Guptas where only certain privileged people had royal patronage and could carry own experiments.
12. Secret Science: Much of what was going on as experimentation in alchemy and Ayurveda was done in secret. The knowledge in relation to the body was not well regarded by the dominant Brahmins who were involved in ritual activity and so on. This bold and fearless way of thinking and experimentation and open minded thinking, generally associated with the Tantrics was considered dangerous and subversive.
A lot of the experiments with the body, chemicals and metals, medicine and related knowledge streams was done in secret and was written up in a language called Sandhyabhasha which was a coded and clouded language. Sandhya also means evening. A dark language.
Only the initiated ones would come to know about it and the initated ones had a very bad reputation – they were Tantrics. They were doing experiments with drugs on their bodies, or experiments with sex, or with diet and exercise. Their quest was to stretch the limits of the body and its inter-relation with the material world. These were all people with a bad reputation and respectable people stayed away from them and only came to them when desperate, probably when their loved ones were dying.
13. Tantric Knowledge: Tantrics were unruly people who were not adherents of the Manusmriti. They did not obey those laws of conduct that other Brahmins followed and they were very bold and experimental. They cut up dead bodies and were always doing all kinds of experiments with drugs and sex and so on, which were beyond prescribed limits. Even some of these cults had initiation rituals that were all about crossing the threshold of disgust.
The new initiates had to get over their choo-achuth repulsion that all Brahmins were trained in; it was ingrained into their awareness right from the time they were small. All these activities of theirs brought them a lot of disrepute but at the same time a lot of knowledge came from their experiments and exploring.
14. We now go to the south and we look at the Chola bronzes.
We explored ancient mines and ruins in the valley. He took me down a disused shaft -pitch dark, but for our helmet lamps.
Raghu: Was this used for transporting ore?
Lalit: This was a ladder, used by people to come down, or carry ore up. It's 2,000 years old.
Raghu: Can wood survive so long?
Lalit: In this sealed-off environment, yes - it's completely cut off from the outside world
Raghu: Was it carbon-dated?
Lalit: It was. You see these galleries? They lit fires in hollows to heat the rock, then sprinkled cold water, so the rock cracked. This made it easy to chisel out the ore - that's how these galleries were created
Lalit: Let's have a look.
Raghu: And the tools you found?
Lalit: Yes, I'll show you and we'll visit the old township. Look – there are thousands of used retorts all over. They removed the zinc, and used them like bricks.
Raghu: So they recycled used materials even then!
Alloys were rare till the 7th century but grew more common as metallurgy developed. The most striking examples are the figurines.
National Museum, New Delhi
By the 9th century, this art was flourishing in the South, under the Chola kings. The relative proportions of the figure were based on strict rules. The face was a basic measure, known as
taal. The other parts were multiples of this length.
Government College of Architecture & Sculpture, Mamballapuram
15. Lost-wax casting (cire perdue) is how a lot of statues are made in India. This is the process being shown now. Its always a moment of tension, when you don’t know the Dancing Shiva will come out with one leg or arm or something like that. It takes experience, watching colour of flames, there is no thermometer, so you have to look at the colour temperature of the fire to know what form it will take.
Chola bronzes are still made in South India. First, the figure is made in wax according to the medieval aesthetic rules. Then it is covered with clay and when dry, wrapped with wire. Then it is heated, so the wax flows out leaving a hollow mould. Special alloys, of five or eight metals, are used
Molten metal is poured into the mould.
It is a tense moment for the craftsman. Has the casting been successful? Every Chola bronze is unique despite the complex method and strict rules. Figurines of the
Bhakti saint-poets are also found. Their hymns, in the local tongues – not Sanskrit - helped regional language and literature to grow.
Government Museum, Chennai
Madurai Meenakshi Temple, Madurai
16. Importance Of Being A Temple:
It was the temple as an institution that was important in this age. Here patrons donated the statues and bronzes that they bought from craftsmen. These temples were huge market places with lots of business taking place, and over time became institutions in themselves that often overshadowed the present king. So kings had to declare loyalty to a temple and add further walls and gates to the gopurams of the temple.
These were the accumulations of wealth and influence that were created through south India, and perhaps were not quite like cities as in the rest of the world, but were similar. These temple complexes had schools, dancing girls, market places, huge number of cow sheds and production of ghee and milk taking place.
Temples became centres of social activity. Large halls were built for religious assemblies. Donations brought wealth. Temples performed banking functions. Thousands were employed - flower-sellers, milkmen, singers, musicians and dancing girls. The temples became small townships with markets, resthouses, treasuries, dairies, godowns etc. Education here emphasised the old texts. After universities like Nalanda declined, temple schools became the centres of learning. Thus the temple became an institution invested with power and social status. Rulers changed, but the temple remained. New kings looked to the old temples for sanction. So the temple became a symbol of political power. No wonder each had to be grand and immense.
Old temples could not really be made taller, nor could they be broken down and rebuilt. So began the convention of boundary walls and
massive gateways, known as
gopurams in the south. Each new ruler would build a taller
gopuram.
17. The Science Of Temple Architecture
Earlier there were sacred caves when some markings may be chiseled or painted on walls , like Ajanta and Ellora, the famous cave temples of western India and the Buddhist monasteries along the Western Ghats. As time went by, instead of making the temple where the rock occurs in nature and designating that as the holy spot where people trek to, the temple was brought down to the plains, to market places where people lived and markets were, where wood, stone, textile is available. These became the centers and the temples were shifted there and those Brahmins who controlled temples and kings who patronized them derived influence from the temple and the deity who belonged to it.
Through this trabeated architectural forms dominated which entailed stone put upon stone, and mortar was also used sometimes. New influences then came from the west such as the arch and dome, and that would revolutionize architectural forms.
18. Trabeated Architecture
Trabeated architecture is often disparaged as simple but in itself it requires a lot of forethought and calculation. Especially to make a building as tall as the Brihhadeeshwarar temple. But such an architectural form has limits and the temples were made taller and bigger, but over time it was the decoration and sculpture that marked a temple’s form rather than architectural innovation. These were sculptural forms and seen more as achievements of art rather than architecture.
19. Arch and Dome: The arch and the dome came from central Asia, not necessarily described only as Mughal as Mughal refers to a particular set of people, namely Babar and his descendants or the Tughlaqs, Ghoris and Ghaznis. Before the Mughals came to India, the architectural form of the arch and the dome could already be found in India. The dome is basically a series of arches put together in a circle.
The key idea of the arch is the keystone. That is what ensures that the stones on the side become a support and don’t let the structure fall down. One of the biggest domes in the world is the Golghumbas found in Gulbarga.
Soon the dome and arch were part of the architectural language in India. Initially when these forms were used, Indian masons still used supports and beams to support the arch that they believed would collapse in an earthquake or otherwise. For instance, in Ghiassudin’s tomb in Delhi. They also believed that if the keystone got loose then the whole building would tumble and people would die. They often added supporting beams as a decoration or emphasis.
The number of boundary walls and
gopurams grew. Temple construction became widespread after the 7th century. Earlier, places of worship were carved from rock. Take the Lomas Rishi caves in Bihar's Barabar hills. Carved around 250 BC by the Ajivika sect,
they replicate wood, mud and straw dwellings. Those houses do not survive but we can see them in sculpture, as at Sanchi. The carving of caves with chisel and hammer is more sculpture than architecture. No materials, or tests for strength, are needed. All you need is a rock face.
Lomasrishi Cave, Barabar Hill, Bihar
Kailashnath Temple, Ellora, Verul
For centuries, shrines were made in caves like those at Karla, Kanheri, Ajanta, Ellora. The Ellora caves date from the 6th to the 13th century. Like house roofs that need beams for support these caves have carved stone beams and pillars!
This 8th century temple of Kailashnath at Ellora represents the peak of rock-cut architecture, carved so that it stands free from the mother rock. A masterly achievement, but it is basically sculpture.
Gradually, temples became symbols of social prestige. And idol-worship grew importance. So temples now had to be built in the cities
rather than far away on a hill.
Sanchi Stupa, Raisen Dist., Madhya Pradesh
Putting stone on stone is a very old technique - an example being this Sanchi gateway of 150 BC. The weight of the stone ensures stability. Take these four pillars – if I place four beams and then a roof on top, this structure won't fall. No cement or other mortar is needed. This is known as trabeate construction. This is, vertical pillars to support horizontal beams. This Gupta period temple at Sanchi and, later, temples everywhere were built this way. One weakness of trabeate construction is obvious - this 12 ft sq roof needs four supporting pillars. Later, huge assembly halls had hundred of pillars. Yet, temples could now be built anywhere, and so played a more intimate role in people's lives.
20. Ritual And Architecture: Architecture was closely related to ritual. The temple was based on a ritualistic graph of 64 squares as is explained in this scene. What were initially mere mostly practical injunctions about where to place the temple, how to use wood and stone, were later translated into good and bad omens. Here knowledge is once again circumscribed because of the distance between those with practical knowledge of building, such as the mason, and aesthetic rules that were included by writers of higher castes in texts about temple architecture.
21.The quotes here are from the Vishnudharmottara Purana which is written in Gupta times when the king asks his guru and the author of this book, Markendeya to instruct him in architecture. So Markandeya says – O King, to master this art of architecture you must know painting, singing, dancing, music, lit, and all of them are bound by the same common aesthetic rules.
The temple was also the staging ground where all these other arts were in evidence.
I came upon this book recently - the
Vishnudharmottara Purana, of Gupta times. It has this dialogue - King Vajra asks his
guru Markandeya to instruct him in architecture. The
guru says, “O king, to master this art you must know painting, dancing, music, literature” By that time, all the arts had begun to be bound by common aesthetic rules.
Chidambaran Temple, Cuddalore, Tamil Nadu
The stage for all these arts was – the temple.
22. Developing writing skills: Tikka and tippani or writing commentaries and writing criticisms and critiques was a common preoccupation at these times. The earlier sutras were being relooked at and being combined, collated, compared etc.
This is also the time for Bhaskaracharya’s seminal work Leelavati where he has a dialogue with his daughter leelavati who is a mathematician in her own right. The text shows that Bhaskaracharya is assimilating what is known from other parts of the country and world and innovating on his own as well. He ventures into areas such as calculus and ideas that the Europeans would arrive at six or seven centuries later.
The
Purana gives rules for temple-building - the type of wood and stone to be used, how to select a site, water arrangements -
down to details of its day-to-day running. Many injuctions are, however, superstitions. Thus along with rules for soil analysis etc. there is much talk of good and bad omens, perhaps because the writer and mason were different. The masons' guild followed given plans and trained apprentices, while the
brahmans transformed the masons' know-how into theory. Over time, this became scripture - beyond change or question.
Other than Bhaskaracharya’s seminal work on mathematics there is also Madhavacharya’s work in Kerala. This is not mentioned in Bharat ki Chaap as it wasn’t known at the time and has been discovered later. All this work on mathematics and other fields took place in India but did not catch on and get propogated or known in other parts of the world. The pity here is that good ideas didn’t spread and not that India could have been the epicenter of knowledge.
Take the basic concept of the temple. A mountain-like exterior and a small, dark sanctum.
23. Geometry Of Temples: Temples also connect us to mathematics because the circle, square and rectangle is the basis of all the temple structures.
Bhaskara in India proved Pythogaras’ theorem using a different kind of proof for the Euclidean proof that is based on the triangle. Bhaskara’s proof uses squares and is algebraic rather than geometric and this is why it is interesting to modern mathematicians as well.
Trabeated architecture is often disparaged as simple but in itself it requires a lot of forethought and calculation. Especially to make a building as tall as the Brihhadeeshwarar temple. But such an architectural form has limits. Temples were made taller and bigger, but over time it was the decoration and sculpture that marked a temple’s form rather than architectural innovation. These were sculptural forms and seen more as achievements of art rather than architecture.
Arch and Dome: The arch and the dome came from central Asia, not necessarily described only as Mughal. 'As Mughal' refers to a particular set of people, namely Babar and his descendants or the Tughlaqs, Ghoris and Ghaznis. Before the Mughals came to India, the architectural form of the arch and the dome could already be found in India. The dome is basically a series of arches put together in a circle.
The key idea of the arch is the keystone. That is what ensures that the stones on the side become a support and don’t let the structure fall down. One of the biggest domes in the world is the Golghumbas found in Gulbarga.
Soon the dome and arch were part of the architectural language in India. Initially when these forms were used, Indian masons still used supports and beams to support the arch that they believed would collapse in an earthquake or otherwise. For instance, in Ghiassudin’s tomb in Delhi. They also believed that if the keystone got loose then the whole building would tumble and people would die. They often added supporting beams as a decoration or emphasis.
This inner shrine was always square. The square suits trabeate construction well.
Ground plans reveal the square's importance.
The square is a geometric shape that can be divided into equal units. They called this square a
mandala.
This basic square was divided into 64 squares. The four inner squares were the
sanctum sanctorum.
Then its walls and then the path for circumambulation. And then the outer walls.
This was the basic ground plan for all temples - known as the
vastupurusha mandala, for in this perfect square they saw the perfect man.
These 64 squares can be divided into thousands of smaller squares. This grid was used like graph paper.
By adding or subtracting squares temples of different designs could be built. Thus temples grew more and more decorative.
The texts describe several temple styles. By 1,000 AD, two styles had become common. One was the
vimana style as in the Brihadeshwara temple at Thanjavur.
Brihadeshwara Temple, Thanjavur
Lingaraja Temple, Bhubaneswar, Orissa
In the north, the
shikhara style dominated. The Lingaraja temple in Orissa is a famed example.
On the surface, these styles look different but both as based on the
vastupurusha mandala and on the putting of one stone on another.
Bound as they were by the scriptural limits the temples could only be built taller or be sculpted more richly.
Prasannakesava Temple, Somnathapura, Karnataka
Built in 1270 in the Hoysala tradition this is the Somnathpur's Prasannakeshava temple - more sculpture, really, than architecture.
True, there were some innovations - the top here is a blend of
vimana and
shikhara. But such constructions were usually weak.
This temple is unique in having three sanctums on a single, star-shaped platform.
But this is no advance in architecture - the stars are achieved by rotating the familiar square on itself.
Maitreyi: The plans of all these temples were based on the circle, square, rectangle. The
Shulbhasutra proved Pythagoras' theorem using the rectangle, instead of the triangle as in Euclid's proof, which we learned in school. The mathematician Bhaskara proved it with squares quite differently.
Amrita: And more simply. This right-angled triangle has sides
a and
b and the hypotenuse
c. We must prove that
a² + b² = c². If we make squares on each side, their areas will be a², b² and c². We've to prove that
a² + b² = c².
Let's add four
ab triangles on both sides to make two sqaures. The square on the left has side
(a + b) so its area is
(a + b)². The area of the other square is also
(a + b)². Remove the triangles of identical area and we have
a² + b² = c².
In his
Lilavati, Bhaskara gives this diagram and calls it the proof. How does it work?
The area of the outer square with the side
(a +b) can either be seen as
(a + b)² or the inner square with
c sides i.e.
c² plus the four triangles i.e.
4(½ab). We can expand this to
a² + 2ab + b² = c² + 2ab. Cancel
2ab on both sides, and there we are!
a² + b² = c².
Matrieyi: This proof interests us because it is an algebraic, not a geometric, proof. The algebra makes it simpler than Euclid's.
Nissim: In Indian mathematics the algebra tradition was strongest. It emerged with Aryabhata in the 7th century and by the 15th was the most advanced in the world. The use of symbols, indeterminate equations of the first and second order, equations with more than one unknown, higher order equations - attempts to solve these were special to this time. We were behind in geometry but trigonometry reached a peak by the 10th century or so, then stood still.
24. Not An Age For Science: This is seen as a period where not much development happened in the sciences, but there were many exchanges that took place during this period, including in alchemy and in maths.
This period which is the 8th to 12th century – the Arabs came, Al Beruni and Ibn-Battuta came from Magrid. They absorbed Indian numbers, algebra, astronomy and carried it to other parts of the world. The static, stagnant intellectual currents that start moving onwards from 11th century.
Amrita: Bhaskara, of this period, is an exception who may be compared to Aryabhata. Bhaskara assimilated the known mathematics and made his own contributions.
Maitreyi: His work contained new ideas - he even had glimmerings of differential calculus. A pity that later, only his early work was pursued, not the new aspects. Europe independently arrived at these ideas, six or sever centuries later. Yes, work in series
was done here.
Nissim: From the 8th to the 12th century, the Arabs absorbed Indian numbers, algebra and astronomy. Later, people came from the Gulf and Central Asia, bringing new technologies, religion, languages, ideas. These played a major role in ending the stagnationthat had set in here by the 11th century.
Ghiyasuddin Tughlaq's Tomb, Tughlaqabad, Delhi
25. New Architectural Forms: Ghiaassudin’s tomb is a fine example of the new architecture. It is built in 1325 and we see the arch and the dome. Early visitors from central Asia came to raid and pick up stuff and loot and carry back home, and later migrants came and assimilated into the life here because they came from small places.
Babar for instance comes from Fergana and is just overwhelmed by horticulture and agriculture. He gets rapidly into doing experiments himself with mangoes and flowers and so on.
There is, it’s a place that had become stagnant, but has a lot of knowledge and natural physical circumstances that excited the new seekers from the west. And they decided they stayed on. And because of their patronage crafts and architecture goes zooming up. New things and cities come up, around the new courts. And we see a period of great turbulence.
26. The Mixed Age: It took a long time to make a synthesis of the old ideas and new influences, especially as the learned intellectuals in Indian society thought their achievements were supreme and everyone else was ignorant. When people come from the west – the first people to respond to the impetus are the artisans, the masons and construction people, the boat builders, the bridge makers. In this period there are lot of decorative and luxuorious innovations, because of the wealth of the new patrons – like cloth with gold, silver and copper woven into, glass and gold fused together to make containers of various sorts.
Shehnaaz: Mahmud of Ghazni made many raids on India in the 11th century. This was a time of change. Many foreigners – Arabs, Turks, Afghans were to come here. Their influence was felt in many spheres, including architecture.
Raghu: Loot may have motivated some people at first, but later, many strayed to make India their home. And they tried to recreate their old environments through mosques, mausoleums, palaces.
Shehnaaz: And thus the arch and the dome came to India. These techniques were ancient, and by then were common in many places. But they came to India only with the new culture. These new forms blended with our old stone carving traditions.
Shehnaaz: A new style of Indian architecture was born.
Raghu: Ghiyas-ud-din Tughlaq's tomb, built in 1325, has one of our first true arches. The keystone is at the centre of a circular arrangement. In the trabeate style, a beam can crack under pressure, which is evenly distributed here. So the structure won't easily collapse. As the beam's length no longer matters, the arch may span any length.
Shehnaaz: It took time to adopt these innovations. For example, this beam below the arch is superfluous! Yet the masons put it there.
Raghu: But once the arch is understood, the dome may be seen as an arch rotated through space.
Shehnaaz: Arches and domes transformed our architecture making possible the most exquisite monuments in the period to come.
Arab ki Sarai, Nizamuddin, New Delhi
Itmad ud dualah's Tomb, Agra
Humayun's timb, Nizamuddin, New Delhi
Ibrahim Rauza, Bijapur, Karnataka
Taj Mahal, Agra
26. The Mixed Age: It took a long time to make a synthesis of the old ideas and new influences, especially as the learned intellectuals in Indian society thought their achievements were supreme and everyone else was ignorant. When people come from the west – the first people to respond to the impetus are the artisans, the masons and construction people, the boat builders, the bridge makers. In this period there are lot of decorative and luxuorious innovations, because of the wealth of the new patrons – like cloth with gold, silver and copper woven into, glass and gold fused together to make containers of various sorts.
Nissim: Craftsmanship was to scale new heights. Arches and domes helped transcend the limits of trabeate construction. Incomparably lovely buildings followed. Of course, it took time to make a synthesis of old and new.
Maitreyi: For this, people had to be open to new ideas. But the learned ones who thought they were supreme - could they adopt anything new? No wonder our
artisans were the first to absorb the new influences. The coming period tells the story of these changes.
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