Monday, July 27, 2015

Botanical and zoology in ancient science

Reproduction, Sex and Heredity of plants

Ancient Indian literature also deals with sex, genetics, and reproduction of plants by fruits, seeds, roots, cuttings, graftings, plant apices and leaves. Buddha Ghosa, in his Sumangala-vilasini, a commentary on the Digha Nikaya, describes some of these methods under such terms as mula-vija (root seed), khandabija (cuttings), phaluvija (joints), agravija (budding) and bija-bija (seed).

 Atharvaveda and Arthasastra describe the propagation by seed (bija-bija or vijaruha) and bulbous roots (kandavija), respectively. The method of cutting (skandhavija) is described in the Arthasastra, Brhatsamhita and Sumangala-vilasini in the case of sugar cane, jackfruit, blackberry, pomegranate, vine, lemon tree, asvattha (Ficus religiosa), nyagrodha (Ficus bengalensis), udumbara (Ficus glomerata) and several others. 

Some ideas related to sexuality in plants are noticeable in the Harita and Charak Samhitas. Charak recognized male and female individuals in the plant called Kutaja (Hollerhina antidysenterica), and the male categories of plants bearing white flowers, large fruit and tender leaves and the female categories characterized by yellow flowers, small fruits, short stalk, etc. 

The Rajanighantu mentions the existence of male and female plants in the plant Ketaki (Pandanus odoratissimus). The male plant is called sitaketaki, and the female is called svarna ketaki. Regarding heredity, Charaka and Susruta mention that the fertilized ovum contains in miniature all the organs of the plants, for example the bamboo seed containing in miniature the entire structure of the bamboo tree, and further that the male sperm cell have minute elements derived form each of its organs and tissues. 

http://www.infinityfoundation.com/mandala/t_es/t_es_tiwar_botany_frameset.htm

Reproduction, Sex and Heredity of plants Ancient Indian literature also deals with sex, genetics, and reproduction of plants by fruits, seeds, roots, cuttings, graftings, plant apices and leaves. Buddha Ghosa, in his Sumangala-vilasini, a commentary on the Digha Nikaya, describes some of these methods under such terms as mula-vija (root seed), khandabija (cuttings), phaluvija (joints), agravija (budding) and bija-bija (seed). Atharvaveda and Arthasastra describe the propagation by seed (bija-bija or vijaruha) and bulbous roots (kandavija), respectively. The method of cutting (skandhavija) is described in the Arthasastra, Brhatsamhita and Sumangala-vilasini in the case of sugar cane, jackfruit, blackberry, pomegranate, vine, lemon tree, asvattha (Ficus religiosa), nyagrodha (Ficus bengalensis), udumbara (Ficus glomerata) and several others. Some ideas related to sexuality in plants are noticeable in the Harita and Charak Samhitas. Charak recognized male and female individuals in the plant called Kutaja (Hollerhina antidysenterica), and the male categories of plants bearing white flowers, large fruit and tender leaves and the female categories characterized by yellow flowers, small fruits, short stalk, etc. The Rajanighantu mentions the existence of male and female plants in the plant Ketaki (Pandanus odoratissimus). The male plant is called sitaketaki, and the female is called svarna ketaki. Regarding heredity, Charaka and Susruta mention that the fertilized ovum contains in miniature all the organs of the plants, for example the bamboo seed containing in miniature the entire structure of the bamboo tree, and further that the male sperm cell have minute elements derived form each of its organs and tissues. http://www.infinityfoundation.com/mandala/t_es/t_es_tiwar_botany_frameset.htm

Iran's Hindu past

Baku Ateshgah or “Fire Temple” is an ancient Hindu religious temple dedicated to Jwala Ji in Surakhani, a suburb of greater Baku, Azerbaijan.

It was initially thought to be a Zoroastrian fire worship place as “Atash” is the Persian word for fire.Four holy elements of local people belief were: ateshi (fire), badi (air), abi (water), and heki (earth).

A pentagonal complex, which has a courtyard surrounded by cells for monks and a tetrapillar-altar in the middle, was built during the 17th and 18th centuries but temple ceased to be worshiped after 1883 with the installation of petroleum plants (industry) at Surakhany. The complex was turned into a museum in 1975.

Fire is considered sacred in both Indo-Iranian branches of Hinduism and Zoroastrianism (as Agni and Atar respectively),and there has been debate on whether the Atashgah was originally a Hindu structure or a Zoroastrian one. The trident mounted atop the structure is usually a distinctly Hindu sacred symbol (as the Trishul, which is commonly mounted on temples) and has been cited by Zoroastrian scholars as a specific reason for considering the Atashgah as a Hindu site.

There are several inscriptions on the Ateshgah. They are all in either Sanskrit or Punjabi, with the exception of one Persian inscription that occurs below an accompanying Sanskrit invocation to Lord Ganesha and Jwala Ji. Although the Persian inscription contains grammatical errors, both the inscriptions contain the same year date of 1745 Common Era (Samvat/संवत 1802/१८०२ and Hijri 1158/١١٥٨).

Taken as a set, the dates on the inscriptions range from Samvat 1725 to Samvat 1873, which corresponds to the period from 1668 CE to 1816 CE.

One press report asserts that local records exist that state that the structure was built by the Baku Hindu traders community around the time of the fall of the Shirvanshah dynasty and annexation by the Russian Empire following the Russo-Persian War (1722–1723).

The inscriptions in the temple in Sanskrit (in Nagari Devanagari script) and Punjabi (in Gurmukhi script) identify the site as a place of Hindu and Sikh worship,and state it was built and consecrated for Jwala Ji, the modern Hindu fire deity. Jwala (जवाला/ज्वाला) means flame in Sanskrit .

In his Travels Outside Bombay, Modi observed that “not just me but any Parsee who is a little familiar with our Hindu brethren’s religion, their temples and their customs, after examining this building with its inscriptions, architecture, etc., would conclude that this is not a [Zoroastrian] Atash Kadeh but is a Hindu Temple, whose Brahmins (priests) used to worship fire (Sanskrit: Agni).”

There is a famed shrine to Jwala Ji in the Himalayas, in the settlement of Jawalamukhi, in the Kangra district of Himachal Pradesh, India to which the Atashgah bears strong resemblance and few scholars have stated that some Jwala Ji devotees used to refer to the Kangra shrine as the ‘smaller Jwala Ji‘ and the Baku shrine as the ‘greater Jwala Ji‘.

In 1876, James Bryce visited the region and found that “the most remarkable mineral product is naphtha, which bursts forth in many places, but most profusely near Baku, on the coast of the Caspian, in strong springs, some of which are said to always be burning.”
Without referencing the Atashgah by name, he mentioned of the Zoroastrians that “after they were extirpated from Persia by the Mohammedans, who hate them bitterly, some few occasionally slunk here on pilgrimage” and that “under the more tolerant sway of the Czar, a solitary priest of fire is maintained by the Parsee community of Bombay, who inhabits a small temple built over one of the springs“.

The fire was once fed by a vent from a subterranean natural gas field located directly beneath the complex, but heavy exploitation of the natural gas reserves in the area during Soviet rule resulted in the flame going out in 1969. Today, the museum’s fire is fed by mains gas piped in from Baku city.


Baku Ateshgah or “Fire Temple” is an ancient Hindu religious temple dedicated to Jwala Ji in Surakhani, a suburb of greater Baku, Azerbaijan. It was initially thought to be a Zoroastrian fire worship place as “Atash” is the Persian word for fire.Four holy elements of local people belief were: ateshi (fire), badi (air), abi (water), and heki (earth). A pentagonal complex, which has a courtyard surrounded by cells for monks and a tetrapillar-altar in the middle, was built during the 17th and 18th centuries but temple ceased to be worshiped after 1883 with the installation of petroleum plants (industry) at Surakhany. The complex was turned into a museum in 1975. Fire is considered sacred in both Indo-Iranian branches of Hinduism and Zoroastrianism (as Agni and Atar respectively),and there has been debate on whether the Atashgah was originally a Hindu structure or a Zoroastrian one. The trident mounted atop the structure is usually a distinctly Hindu sacred symbol (as the Trishul, which is commonly mounted on temples) and has been cited by Zoroastrian scholars as a specific reason for considering the Atashgah as a Hindu site. There are several inscriptions on the Ateshgah. They are all in either Sanskrit or Punjabi, with the exception of one Persian inscription that occurs below an accompanying Sanskrit invocation to Lord Ganesha and Jwala Ji. Although the Persian inscription contains grammatical errors, both the inscriptions contain the same year date of 1745 Common Era (Samvat/संवत 1802/१८०२ and Hijri 1158/١١٥٨). Taken as a set, the dates on the inscriptions range from Samvat 1725 to Samvat 1873, which corresponds to the period from 1668 CE to 1816 CE. One press report asserts that local records exist that state that the structure was built by the Baku Hindu traders community around the time of the fall of the Shirvanshah dynasty and annexation by the Russian Empire following the Russo-Persian War (1722–1723). The inscriptions in the temple in Sanskrit (in Nagari Devanagari script) and Punjabi (in Gurmukhi script) identify the site as a place of Hindu and Sikh worship,and state it was built and consecrated for Jwala Ji, the modern Hindu fire deity. Jwala (जवाला/ज्वाला) means flame in Sanskrit . In his Travels Outside Bombay, Modi observed that “not just me but any Parsee who is a little familiar with our Hindu brethren’s religion, their temples and their customs, after examining this building with its inscriptions, architecture, etc., would conclude that this is not a [Zoroastrian] Atash Kadeh but is a Hindu Temple, whose Brahmins (priests) used to worship fire (Sanskrit: Agni).” There is a famed shrine to Jwala Ji in the Himalayas, in the settlement of Jawalamukhi, in the Kangra district of Himachal Pradesh, India to which the Atashgah bears strong resemblance and few scholars have stated that some Jwala Ji devotees used to refer to the Kangra shrine as the ‘smaller Jwala Ji‘ and the Baku shrine as the ‘greater Jwala Ji‘. In 1876, James Bryce visited the region and found that “the most remarkable mineral product is naphtha, which bursts forth in many places, but most profusely near Baku, on the coast of the Caspian, in strong springs, some of which are said to always be burning.” Without referencing the Atashgah by name, he mentioned of the Zoroastrians that “after they were extirpated from Persia by the Mohammedans, who hate them bitterly, some few occasionally slunk here on pilgrimage” and that “under the more tolerant sway of the Czar, a solitary priest of fire is maintained by the Parsee community of Bombay, who inhabits a small temple built over one of the springs“. The fire was once fed by a vent from a subterranean natural gas field located directly beneath the complex, but heavy exploitation of the natural gas reserves in the area during Soviet rule resulted in the flame going out in 1969. Today, the museum’s fire is fed by mains gas piped in from Baku city.

Untouchability was not in Vedas

Veda Vyasa & the question of untouchability
**********************************************************
Veda Vyasa is a legendary Hindu sage, whose very name is synonymous to Hindus with knowledge. According to traditional Hindu accounts, he lived at the end of the Dwapara Yuga and early Kali Yuga (the date for the beginning of the Kali Yuga is 3102BC).

Veda Vyasa is accredited with compiling the Vedas and writing the Brahma Sutras, which are one of the three great authoritative Hindu philosophical texts. He was also the recorder/writer of the earliest form of the Mahabharata (which was originally called the ‘Jaya’). The followers of Veda Vyasa (the Vyasas or ‘compilers’) carried out the compilation of the Puranas.

His birthday is celebrated as ‘Guru Purnima’ – one of the most sacred days in the Hindu calendar, which is the day when teachers are honored. A popular saying about Veda Vyasa goes: ‘Vyasocchishtasam jagat sarvam’ meaning that so great was the learning of Rishi Veda Vyasa, that even his voluminous writings represent only the periphery of his knowledge. Virtually every Hindu sampradaya (order) traces their lineage to him, and wherever knowledge is propagated and respected is called a Vyaspeeth – Vyasa’s throne.

Yet had Veda Vyasa, the compiler of the Vedas, lived in the later degenerate and perverted age of Hindu society, he may well have been considered an untouchable and not even allowed to touch the Vedas!

His mother (Satyavati) used to sell fish to make a living, and in many parts of Hindu society in its later period of caste insanity this would have made him an untouchable. Yet Vyasa is considered by all Hindus to be the very epitome of wisdom!

This is just one of many examples (another being Valmiki – author of the Ramayana) that shows that the terrible caste rigidity of Hindu society that we have seen at some points in our past, and which still persists today in some parts, was definitely not originally the state of things, and certainly does not represent the true spirit of Hinduism.

Veda Vyasa & the question of untouchability *********************************************Veda Vyasa is a legendary Hindu sage, whose very name is synonymous to Hindus with knowledge. According to traditional Hindu accounts, he lived at the end of the Dwapara Yuga and early Kali Yuga (the date for the beginning of the Kali Yuga is 3102BC). Veda Vyasa is accredited with compiling the Vedas and writing the Brahma Sutras, which are one of the three great authoritative Hindu philosophical texts. He was also the recorder/writer of the earliest form of the Mahabharata (which was originally called the ‘Jaya’). The followers of Veda Vyasa (the Vyasas or ‘compilers’) carried out the compilation of the Puranas. His birthday is celebrated as ‘Guru Purnima’ – one of the most sacred days in the Hindu calendar, which is the day when teachers are honored. A popular saying about Veda Vyasa goes: ‘Vyasocchishtasam jagat sarvam’ meaning that so great was the learning of Rishi Veda Vyasa, that even his voluminous writings represent only the periphery of his knowledge. Virtually every Hindu sampradaya (order) traces their lineage to him, and wherever knowledge is propagated and respected is called a Vyaspeeth – Vyasa’s throne. Yet had Veda Vyasa, the compiler of the Vedas, lived in the later degenerate and perverted age of Hindu society, he may well have been considered an untouchable and not even allowed to touch the Vedas! His mother (Satyavati) used to sell fish to make a living, and in many parts of Hindu society in its later period of caste insanity this would have made him an untouchable. Yet Vyasa is considered by all Hindus to be the very epitome of wisdom! This is just one of many examples (another being Valmiki – author of the Ramayana) that shows that the terrible caste rigidity of Hindu society that we have seen at some points in our past, and which still persists today in some parts, was definitely not originally the state of things, and certainly does not represent the true spirit of Hinduism.

Shiva is demchog of Buddhism

In Theravada Buddhism, Vishnu = Upalvan
In Mahyana Buddhism, Shiva = Demchog(Chakrasamvara Tantra)

Upulvan is also known Guardian God of Buddhism or Protector of Buddhism.
Demchog is same as Shiva because According to Mahayana Buddhism, Mt.Kailash is residence of Demchog.

-Kunal Modi

In Theravada Buddhism, Vishnu = Upalvan In Mahyana Buddhism, Shiva = Demchog(Chakrasamvara Tantra) Upulvan is also known Guardian God of Buddhism or Protector of Buddhism. Demchog is same as Shiva because According to Mahayana Buddhism, Mt.Kailash is residence of Demchog. -Kunal Modi

33 crore gods , deva- explanation

Hindus have 33 crore gods -explanation
**************************************************33 divinities are mentioned in the Yajur-veda, Atharva-veda, occurs in the Parsi scriptures of Avesta as well.The expression trayastrimsa deva is found in the list of classes of gods in Sanskrit Buddhist texts like the Divyavadana and Suvarnaprabhasa-sutra.The word koti in ‘trayastrimsati koti’ does not mean the number '33 crore’ or '330 million’. Here koti means 'supreme’, pre-eminent, excellent, that is, the 33 'supreme’ divinities. It has been documented in Brihadaranyaka Upanishad Śākalya : “How many gods are there?” Yājñavalkya : “Three hundred and three.” Then he says, “Three thousand and three.” Śākalya : “Is this the answer that you give me to my question, how many gods are there? Three thousand and three; three hundred and three! Have you no other answer to this question?” Yājñavalkya : There are thirty-three gods. Śākalya : “All right!” (not satisfied with answer) …Tell me again properly; how many gods are there?“ Yājñavalkya : "Six are there.” Śākalya : “How many gods are there. Tell me again. Think properly.” Yājñavalkya : “Only three gods are there.” Śākalya : “How many gods are there? Tell again. Yājñavalkya : "Two gods are there.” Śākalya : “Tell again; how many gods are there?” Yājñavalkya : “One and a half gods” (Then he was very much upset) Śākalya : “What is this you say, one and a half gods. Tell again properly; how many gods are there?” Yājñavalkya : “One god is there,” Śākalya : “All these numbers that you have mentioned – three thousand and three, three hundred and three – what are these gods? Give the names of these gods, the deities.” Yājñavalkya : “All these three thousand and all that I mentioned – they are not really gods. They are only manifestations of the thirty-three. The thirty-three are the principal manifestations, and others are only their glories, radiances, manifestations, magnificences or forces, energies, powers.” Śākalya : “But what are these thirty-three?” Yājñavalkya : “The thirty-three gods are eight Vasus, eleven Rudras, twelve Ādityas, then Indra and Prajāpati – these make thirty-three gods.” Śākalya : “What are these Vasus which are eight in number?” Yājñavalkya : “Fire is one deity; earth is one deity; air is another; the atmosphere is one deity; the sun is one deity; the heaven is one deity; moon is one deity; the stars are one deity. These constitute eight groups” Śākalya : “Why do you call them Vasus?” Yājñavalkya : “Everything is deposited as it were in these constituent principles. Therefore, they are called Vasus.” Śākalya : “Who are the Rudras?” Yājñavalkya : “The ten senses and the mind make eleven. These are the Rudras.” Śākalya : “What are the twelve Ādityas, the suns?” Yājñavalkya : “They are twelve forces of the sun, takes away the vitality of people.” Śākalya : “Who is Indra? Who is Prajāpati?” Yājñavalkya : “The rain cloud can be called Indra. Sacrifice can be called Prajāpati.” Śākalya : “What do you mean by rain cloud?” Yājñavalkya : “By rain cloud I do not actually mean the cloud, but the lightning which is the embodiment of energy.”

Durba or darbha grass

Darbha (Desmotachya bipinnata) is a tropical grass considered a sacred material in Vedic scriptures and is said to purify the offerings during such rituals.

Traditional tropical grass, Darbha, has been identified as an eco-friendly food preservative.

This finding was evolved in a research study undertaken jointly by the Centre for Nanotechnology and Advanced Biomaterials (CeNTAB) and the Centre for Advanced Research in Indian System of Medicine (CARISM) of the SASTRA University, Thanjavur, under the supervision of Dr. P. Meera and Dr. P. Brindha respectively.

At the time of eclipse, people place that grass in food items that could ferment and once the eclipse ends the grass is removed.

A systematic research was conducted by the SASTRA University researchers, in which cow’s curd was chosen as a food item that could ferment easily.

Five other tropical grass species, including lemon grass, Bermuda grass, and bamboo were chosen for comparison based on different levels of antibiotic properties and hydro phobicity.

Electron microscopy of different grasses revealed stunning nano-patterns and hierarchical nano or micro structures in darbha grass while they were absent in other grasses.

On studying the effect of various grasses on the microbial community of the curd, darbha grass alone was found to attract enormous number of bacteria into the hierarchical surface features.

These are the bacteria responsible for fermentation of cow’s curd.

During eclipse, the wavelength and intensity of light radiations available on the earth’s surface is altered. Especially, the blue and ultraviolet radiations, which are known for their natural disinfecting property, are not available in sufficient quantities during eclipse.

This leads to uncontrolled growth of micro-organisms in food products during eclipse and the food products are not suitable for consumption. Darbha was thus used as a natural disinfectant on specific occasions, say researchers at SASTRA University.

Further, the scientists say that darbha could be used as a natural food preservative in place of harmful chemical preservatives and the artificial surfaces mimicking the hierarchical nano patterns on the surface of darbha grass could find applications in health care where sterile conditions were required.

This entire research was funded by the SASTRA University’s Research Fund.

http://m.thehindu.com/news/cities/Tiruchirapalli/darbha-grass-a-natural-preservative/article7000098.ece/

Darbha (Desmotachya bipinnata) is a tropical grass considered a sacred material in Vedic scriptures and is said to purify the offerings during such rituals. Traditional tropical grass, Darbha, has been identified as an eco-friendly food preservative. This finding was evolved in a research study undertaken jointly by the Centre for Nanotechnology and Advanced Biomaterials (CeNTAB) and the Centre for Advanced Research in Indian System of Medicine (CARISM) of the SASTRA University, Thanjavur, under the supervision of Dr. P. Meera and Dr. P. Brindha respectively. At the time of eclipse, people place that grass in food items that could ferment and once the eclipse ends the grass is removed. A systematic research was conducted by the SASTRA University researchers, in which cow’s curd was chosen as a food item that could ferment easily. Five other tropical grass species, including lemon grass, Bermuda grass, and bamboo were chosen for comparison based on different levels of antibiotic properties and hydro phobicity. Electron microscopy of different grasses revealed stunning nano-patterns and hierarchical nano or micro structures in darbha grass while they were absent in other grasses. On studying the effect of various grasses on the microbial community of the curd, darbha grass alone was found to attract enormous number of bacteria into the hierarchical surface features. These are the bacteria responsible for fermentation of cow’s curd. During eclipse, the wavelength and intensity of light radiations available on the earth’s surface is altered. Especially, the blue and ultraviolet radiations, which are known for their natural disinfecting property, are not available in sufficient quantities during eclipse. This leads to uncontrolled growth of micro-organisms in food products during eclipse and the food products are not suitable for consumption. Darbha was thus used as a natural disinfectant on specific occasions, say researchers at SASTRA University. Further, the scientists say that darbha could be used as a natural food preservative in place of harmful chemical preservatives and the artificial surfaces mimicking the hierarchical nano patterns on the surface of darbha grass could find applications in health care where sterile conditions were required. This entire research was funded by the SASTRA University’s Research Fund.http://m.thehindu.com/news/cities/Tiruchirapalli/darbha-grass-a-natural-preservative/article7000098.ece/

Ancient Indian mathematics

ANCIENT INDIAN MATHEMATICS ********************************************* Despite developing quite independently of Chinese (and probably also of Babylonian mathematics), some very advanced mathematical discoveries were made at a very early time in India. Mantras from the early Vedic period invoke powers of ten from a hundred all the way up to a trillion, and provide evidence of the use of arithmetic operations such as addition, subtraction, multiplication, fractions, squares, cubes and roots. A 4th Century AD Sanskrit text reports Buddha enumerating numbers up to 1053, as well as describing six more numbering systems over and above these, leading to a number equivalent to 10421. Given that there are an estimated 1080 atoms in the whole universe, this is as close to infinity as any in the ancient world came. It also describes a series of iterations in decreasing size, in order to demonstrate the size of an atom, which comes remarkably close to the actual size of a carbon atom (about 70 trillionths of a meter). As early as the 8th Century BC, long before Pythagoras, a text known as the “Sulba Sutras” (or “Sulva Sutras”) listed several simple Pythagorean triples, as well as a statement of the simplified Pythagorean theorem for the sides of a square and for a rectangle (indeed, it seems quite likely that Pythagoras learned his basic geometry from the “Sulba Sutras”). The Sutras also contain geometric solutions of linear and quadratic equations in a single unknown, and give a remarkably accurate figure for the square root of 2, obtained by adding 1 + 1⁄3 + 1⁄(3 x 4) + 1⁄(3 x 4 x 34), which yields a value of 1.4142156, correct to 5 decimal places. As early as the 3rd or 2nd Century BC, Jain mathematicians recognized five different types of infinities: infinite in one direction, in two directions, in area, infinite everywhere and perpetually infinite. Ancient Buddhist literature also demonstrates a prescient awareness of indeterminate and infinite numbers, with numbers deemed to be of three types: countable, uncountable and infinite. Like the Chinese, the Indians early discovered the benefits of a decimal place value number system, and were certainly using it before about the 3rd Century AD. They refined and perfected the system, particularly the written representation of the numerals, creating the ancestors of the nine numerals that (thanks to its dissemination by medieval Arabic mathematicans) we use across the world today, sometimes considered one of the greatest intellectual innovations of all time. The Indians were also responsible for another hugely important development in mathematics. The earliest recorded usage of a circle character for the number zero is usually attributed to a 9th Century engraving in a temple in Gwalior in central India. But the brilliant conceptual leap to include zero as a number in its own right (rather than merely as a placeholder, a blank or empty space within a number, as it had been treated until that time) is usually credited to the 7th Century Indian mathematicians Brahmagupta - or possibly another Indian, Bhaskara I - even though it may well have been in practical use for centuries before that. The use of zero as a number which could be used in calculations and mathematical investigations, would revolutionize mathematics. Brahmagupta established the basic mathematical rules for dealing with zero: 1 + 0 = 1; 1 - 0 = 1; and 1 x 0 = 0 (the breakthrough which would make sense of the apparently non-sensical operation 1 ÷ 0 would also fall to an Indian, the 12th Century mathematician Bhaskara II). Brahmagupta also established rules for dealing with negative numbers, and pointed out that quadratic equations could in theory have two possible solutions, one of which could be negative. He even attempted to write down these rather abstract concepts, using the initials of the names of colours to represent unknowns in his equations, one of the earliest intimations of what we now know as algebra. The so-called Golden Age of Indian mathematics can be said to extend from the 5th to 12th Centuries, and many of its mathematical discoveries predated similar discoveries in the West by several centuries, which has led to some claims of plagiarism by later European mathematicians, at least some of whom were probably aware of the earlier Indian work. Certainly, it seems that Indian contributions to mathematics have not been given due acknowledgement until very recently in modern history. Golden Age Indian mathematicians made fundamental advances in the theory of trigonometry, a method of linking geometry and numbers first developed by the Greeks. They used ideas like the sine, cosine and tangent functions (which relate the angles of a triangle to the relative lengths of its sides) to survey the land around them, navigate the seas and even chart the heavens. For instance, Indian astronomers used trigonometry to calculated the relative distances between the Earth and the Moon and the Earth and the Sun. They realized that, when the Moon is half full and directly opposite the Sun, then the Sun, Moon and Earth form a right angled triangle, and were able to accurately measure the angle as 1⁄7°. Their sine tables gave a ratio for the sides of such a triangle as 400:1, indicating that the Sun is 400 times further away from the Earth than the Moon. Although the Greeks had been able to calculate the sine function of some angles, the Indian astronomers wanted to be able to calculate the sine function of any given angle. A text called the “Surya Siddhanta”, by unknown authors and dating from around 400 AD, contains the roots of modern trigonometry, including the first real use of sines, cosines, inverse sines, tangents and secants. As early as the 6th Century AD, the great Indian mathematician and astronomer Aryabhata produced categorical definitions of sine, cosine, versine and inverse sine, and specified complete sine and versine tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places. Aryabhata also demonstrated solutions to simultaneous quadratic equations, and produced an approximation for the value of π equivalent to 3.1416, correct to four decimal places. He used this to estimate the circumference of the Earth, arriving at a figure of 24,835 miles, only 70 miles off its true value. But, perhaps even more astonishing, he seems to have been aware that π is an irrational number, and that any calculation can only ever be an approximation, something not proved in Europe until 1761. Bhaskara II, who lived in the 12th Century, was one of the most accomplished of all India’s great mathematicians. He is credited with explaining the previously misunderstood operation of division by zero. He noticed that dividing one into two pieces yields a half, so 1 ÷ 1⁄2 = 2. Similarly, 1 ÷ 1⁄3 = 3. So, dividing 1 by smaller and smaller factions yields a larger and larger number of pieces. Ultimately, therefore, dividing one into pieces of zero size would yield infinitely many pieces, indicating that 1 ÷ 0 = ∞ (the symbol for infinity). However, Bhaskara II also made important contributions to many different areas of mathematics from solutions of quadratic, cubic and quartic equations (including negative and irrational solutions) to solutions of Diophantine equations of the second order to preliminary concepts of infinitesimal calculus and mathematical analysis to spherical trigonometry and other aspects of trigonometry. Some of his findings predate similar discoveries in Europe by several centuries, and he made important contributions in terms of the systemization of (then) current knowledge and improved methods for known solutions. The Kerala School of Astronomy and Mathematics was founded in the late 14th Century by Madhava of Sangamagrama, sometimes called the greatest mathematician-astronomer of medieval India. He developed infinite series approximations for a range of trigonometric functions, including π, sine, etc. Some of his contributions to geometry and algebra and his early forms of differentiation and integration for simple functions may have been transmitted to Europe via Jesuit missionaries, and it is possible that the later European development of calculus was influenced by his work to some extent.

Thursday, July 23, 2015

Ancient Indian Math and Science

THE INDIAN TRADITION IN SCIENCE AND TECHNOLOGY:     
Any study of the Indian tradition of science has to start with linguistics. This is so notonly because Linguistics is the earliest of Indian sciences to have been rigorously systematised, but also because this systematisation became the paradigm example for all other sciences of India.

Like all sciences and arts of the Indian tradition, Linguistics finds its first expression in the Vedas. For most of the Indian sciences, already by the Vedic period, the basic elements of study and the basic categories through which these are to be studied had been established, preliminary data for the operation of these sciences had been collected and rough systematisation had been achieved. Thus, for the science of Linguistics, in the siksha and pratiakhya texts associated with the various Vedas, we find a settled complete list of phonemes appropriately classified into vowels, semivowels, sibilants and the five groups of five consonants, all beautifully arranged according to the place of articulation which moves systematically from the throat to the lips. In fact phonetics and phonology are taken for granted by all authorities on etymology (nirukta) and grammar (vyakarana) including Yaska and Panini. In the pratisakhya literature one also find the morpho-phonemic (sandhi) rules and much of the methodology basic to the later grammatical literature.




The Indian science of Linguistics finds its rigorous systematisation in Panini’s Ashtadhyayi. The date of this text, like that of much f the early Indian literature, is
yet to settled with any certainty. But surely the Ashtadiyayi is not of a date later than 500 BC*. In the Ashtadhyayi, Panini achieves a complete characterisation of the Sanskrit language as spoken at his time, and also manages to specify the way it
deviated from the Sanskrit of the Vedas. Given a lit of the root words of the Sanskrit language (dhatupatha) and using the sutras of Panini it is possible to generate all possible correct utterances in Sanskrit. This is of course the main thrust of the generative grammars of today that seek to achieve a purely grammatical description of language through a formalized set of derivational strings. It is understandable that till such attempts were made in the West in the recent past, the Paninian sutras to the Western scholars looked like nothing but some artificial and abstruse formulations with little content.

Patanjali (c 1st C BC) in his major commentary on the Ashtadhyayi, the Mahabhashya gives an elaborate rationale for the Paninian exercise. According to the Mahabhashya the purpose of grammar is to give an exposition of all correct utterances in the language. An obvious way to do this is to enumerate all correct utterances individually. This is how the celestial teacher Brihaspati would have taught the science of language to the celestial student, Indra. However for ordinary mortals, not having access to celestial time scales this method can apparently not be of much use.

Therefore according to the Mahabhashya it is necessary to lay down general rules
(utsarga sutras) with a wide application so that with a comparatively small effort men can learn larger and larger collections of valid utterances. What falls to fit in this set of general rules should than be encompassed in exceptional rules (apavada sutras), and so on.

In providing this characterisation of the science of grammar Patanjali laid his finger on perhaps the most essential feature of the Indian scientific effort. Science in India seems to start with the assumption that truth resides in the real world with all its diversity and complexity. Thus for the Linguist what is ultimately true is the language as spoken by the people in all their diverse expressions. As Patanjali emphasises, valid utterances are not manufactured by the Linguist, but are already established by the practice in the world. Nobody goes to a linguist asking for valid utterances, the way one goes to a potter asking for pots. Linguist do make generalisations about the language as spoken in the world. But these generalisations are not the truth behind or above the reality. These are not the idealisation according to which reality is to be tailored. On the other hand what is ideal is the real, and some part of the real always escapes our idealisation of it.

There are always exceptions. It is the business of the scientist to formulate these generalisations, but also at the same time to be always attuned to the reality, to always to conscious of the exceptional nature of each specific instance. This attitude, as we shall have occasion to see, seems to permeate all Indian science and makes it an exercise quite different from the scientific enterprise of the West.

In the tradition of Linguistics after the period of Mahabhashya the major attempt of the grammarians seems to be to provide refinements and simplifications of Panini. In this period a number of Sanskrit grammars are written. One of them, Siddhanta Kaumudi 9c.1600) became eminently successful, perhaps because of its simplicity.

These attempts continue till the 19th century. Another form of study that became
popular amongst the grammarians is what may be called the philosophical semantics, wherein one starts with an utterance and by analysing it into its basic grammatical components tries to fix and characterise its meaning. This of course, is the major application for which grammar is intended in the first place.

Other Indian language grammars were written using Paninian framework as the basis. In fact these grammars are not fully formalised grammars in the sense of Panini. Instead what is attempted is to start with the Paninian apparatus and specify the transfer rules from Sanskrit as also the specific morpho-phonemic rules (sandhi), for the language under consideration. Such grammars for various Prakrit languages of the North and also the South Indian languages continued to be written till the 18th century, so much so that in the 16th century Krishnadas wrote a grammar for the Persian language. Parasi Prakash styled on the grammars of the Prakrit languages.

II

Among the sciences of the Indian tradition Astronomy and Mathematics also occupy an important place. Indian mathematics finds its early beginnings in the famous Shulva Sutras of the Vedic times. Purportedly written to facilitate the accurate construction of various types of sacrificial altars of the Vedic ritual, these sutras lay down the basic geometrical properties of plane figures like the triangle, the rectangle, the rhombus, and the circle. Basic categories of the Indian astronomical tradition wee also already established in the various Vedanga Jyotisha texts.

Rigorous systematisation of Indian astronomy however begins with Aryabhata (b.470
AD). His Aryabhatiya is a concise text of 121 aphoristic verses containing separate
sections on the basic astronomical definitions and parameters, basic mathematical
procedures in arithmetic, geometry, algebra and trigonometry, methods of determining
mean and true positions of the planets at any given time, and description of the
motions of sun, moon and the planets along with computation of the solar and lunar
eclipses. After Aryabhata, one comes across a long series of illustrious astronomers
with their equally illustrious texts, many of which gave rise to a host of commentaries
and refinements by later astronomers and became the corner stones of flourishing
schools of astronomy and of Varahamihira (d.578 AD). Brahmagupta (b.598 AD), Bhaskara 1(b.629 AD). Lalla (C.8th C AD), Munjala (932 AD, Sripati (1039 AD), Bhaskara II
(b.1114 AD), Madhava (c.14th C Ad), Parameshwara (c.16th C AD), Nilakantha (c.16th C
AD), Jyeshthadeva (c.16thC AD), Ganesha Dalvajna (c.16th C.AD) and a host of others.
The tradition continued and thrived right upto the late eighteenth century, and in
regions like Kerala, original work in the Indian tradition continued to appear till much
later.

The most striking feature of this long tradition of Indian mathematics and astronomy is
the efficacy with which the Indians seem to be handling and solving rather complicated
problems. Thus in Mathematics the Indians already in Shulva sutras know all the basic
theorems of plane geometry. Around this time they also develop a sophisticated theory
of numbers including the concepts of zero, and negative numbers. They also seem to
have arrived t simple algorithms for all basic arithmetical operations by using the place
value notation.

Thus by the time of Aryabhatiya the Indians have all basic mathematical concepts and
procedures that are today taught at the high school level. By the 10th or 11th century
they are able to solve sophisticated problems in algebra such as second order
Diophantine equations. By the 14th century infinite series for sine and cosine functions
are written down in trigonometry. High levels of approximations of and recognition
of its irrational character are also achieved by the same time.

The reason for this success of the Indian mathematicians lies perhaps in the explicitly
algorithmic and computational nature of Indian mathematics. The objective of the
Indian mathematician was not to find ultimate axiomatic truths in mathematics but to
find methods of solving specific problems that may arise in the astronomical or other
contexts. For the purpose the Indian mathematicians were prepared to set up simple
algorithms that may give only approximate solutions to the problem at hand, and to
evolve theories of error and recursive procedures so that the approximations may be
kept in check. This algorithmic methodology persisted in the Indian mathematical
consciousness till recently so that Ramanujan in the twentieth century seems to be
chalking up his impressive mathematical discoveries perhaps through the use of this
traditional Indian methodology.

The same pragmatic concern to be able to calculate the positions of the various planets
and eclipses of the sun and the moon reasonably accurately, informs the efforts of the
Indian astronomers. And in this they turned out to be eminently successful. In their
calculations Indians often take the beginning of the Kaliyuga in the year 3102 before
Christ as their starting point, and the so-called Siddhanta texts deal with a much larger
period consisting of 43,20,000 years called a Mahayuga or sometimes even a period
1000 times the above, which is called a Kalpa. In spite of dealing with such long time
periods the Indian astronomers were able to keep their techniques fairly simple and
their parameters fairly well refined so that even towards the end of the eighteenth
century and early parts of nineteenth, when the active astronomical tradition had
become dormant in large parts of India, European astronomers are able to locate
Brahmins in South India, who could calculate for them the details of the current
eclipses to an accuracy comparable to, and often better than the best calculations of
Europe of the time.

The reasons for the simplicity and accuracy of the Indian astronomical techniques are
again to be found in the pragmatic attitude of the Indians towards the sciences. The
Indian astronomers wee in the business to calculate and to compute; but not to form
pictures of the heavens, as they ought to be in reality. Indian astronomers do use some
geometrical models but these are supposed to be nothing more than artefacts
necessary to perform their calculations (see Appendix). It is obvious that the
astronomical parameters obtained using such artefacts will get out of tune with reality
sooner or later and the calculations made with such parameters will start deviating
from actual positions of the planets. Indian astronomers are aware of this and were
quite willing to take up the onerous task of continuously observing the skies,
continuously checking their computations against observations and repeatedly readjusting
their parameters so as to make their calculations accord with reality. Thus
the sixteenth century astronomer Nilakantha Somasutvan, finding a contemporary
commentator lamenting about the different times given in different Siddhantas and the
computed times differing from the actual ones, exhorts.

O faint hearted, there is nothing to be despaired of…one has to realise that
five Siddhantas had been correct at a particular time. Therefore one has
to search for a Siddhanta that does not show discord with the actual
observation at the present time. Such accordance has to be ascertained by
observations during time of eclipses, etc. When Siddhantas show discord
observations should be made with the use of Instruments and correct
number of revolutions etc, found, and a new Siddhanta enunciated.’
A little later Jyesthadeva in the Drikkarana tells how from aryabhata to the present
day the astronomers have adjusted the parameters to accord with observations and
how he too is doing the same job for his times and he ends with the statement that
‘henceforth too the deviations that occur should be carefully observed and revisions
effected.

III

The third major science” of the classical tradition is Ayurveda, the science of Life. Like
Linguistics and Astronomy this too finds its early expression in the Vedas, especially the
Atharvaveda in which a large amount of early; medicinal lore is collected.
Systematisation of Ayurveda takes place during the period 5th century BC and 5th
century AD in the Charaka Samhita Sushruta Samhit and the Ashtanga Sangraha, the so
called Brihat –trayee texts, which are still popular today. This is followed by a long
period of intense activity during which attempts are made to refine the theory and
practice of medicine, and to bring more and more information into the stream of
systematic medicine. This process of accretion of information and refinement of
practice continued right upto the beginning of the nineteenth century.

Like in Linguistics and Astronomy, the remarkable feature of Indian tradition of
medicine is its pragmatic attitude towards scientific theorization. The Ayurvedic texts
while providing a theoretical framework through which the problem of finding an
appropriate cure for a particular patent must be approached, never tire of reminding
the practitioner that he must be constantly observant of all the specific features that a
particular case presents in fact for Charaka Samhita the most desirable intellectual
accomplishment of a doctor is that of possessing Yukti, the Yukti is the capacity of the
trained intellect that manages to see the course of action through the complexity of
phenomena with their multiple causes.

The attitude of Ayurveda towards theoretical generalisations is very clearly brought out
in a revealing verse of Sushruta Samhita. While describing the theoretical qualities of a
substance through which its medicinal properties are to be determined, the text comes up with the warning that the wise physician should never raise theoretical arguments
about the properties of a drug when they are already known and established in
tradition based on actual practice, because afterall ‘a thousand reasons will not make
the drugs of the ambastha group perform laxative functions’. Therefore the physician
must rely on what is established in tradition based on actual practice, rather then
acting exclusively on his theoretical reasoning. This attitude towards theory gives the
Ayurvedic texts, a refreshing openness and a surprising keenness of observation.
Nothing that may have any effect on the problem of health seems to escape the
observation of the physicians. One finds the physicians worrying about the differing
aspects of the seasons, the soils, the waters and so on. And in the therapeutic sections
they bring into use all their theoretical understanding and all the folk practices that
have been proved to be efficacious in tradition.

This pragmatic attitude towards scientific theoretization made the doing of science in
India a rather painstaking business. The Indian scientists not having the luxury of
reducing the reality of the world to that encompassed by their theories of the time,
had to be continuously aware of the world in its complete complexity, and had to
continuously refine and simplify their procedures in order to operate successfully in
this complex world. That they were able to do this systematically in a number of fields
over a long period of over 2000 years is measure of their ingenuity and industry. Thus
one can only marvel of the stupendousness of the task of encapsulating the whole of
Sanskrit language as it was spoken in 4000 aphoristic rules. Equally remarkable is the
effort of the astronomer- mathematicians to repeatedly refine their parameters to fit
the observations so that ever since Aryabhata the Indians always had access to
reasonably accurate information about the motions of the heavens. But the
astronomer –mathematicians also simplified their computations to an extent that
learned Brahmins in their innumerable locales could also compute all the astronomical
information that mattered to the residents. The effort of Indian physicians also falls in
the same class. They were not only able to painstakingly acquire and systematize
within their theoretical framework all the information about drugs and diseases that
was current amongst the people in diverse areas, but were also able to simplify their
theories sufficiently so that much of the Ayurvedic science became the folders of
health known in all families. The fact that the Indian scientists given their theoretical
attitude had to be necessarily open to the world around them perhaps ensured that the
folk and the science had to remain in a symbiotic relation with each other.

Besides Linguistic, Astronomy and Mathematics, and Medicine, Indians also developed
the sciences of matter (Padartha Sastra), metallurgy (Rasa Sastra), architecture (Vastu
Sastra), music (Sangitha Sastra) etc. To all of these sciences they brought their
peculiarly Indian mode of careful but tentative generalisations and continuous keen
observation.

IV

The pragmatic attitude of conceptual sophistication and operational simplicity that we
have noticed amongst the sciences of India seems also to have informed the Indian
technologies. A systematic history of the traditional Indian technologies is yet to be
written. Therefore one has to rely largely on the accounts of European travellers and
administrators who observed and wrote about the Indian practices during the early
phase of European conquest of India.

The major technological endeavour of India was of course in the field of agriculture.
Col.Alexander Walker writing in the early nineteenth century seems to have been
amazed at the keen interest that ordinary Indians showed in everything connected with
agriculture. He is also greatly impressed by the care with which the Indian cultivators
tended their fields, so that to him the fields of Malabar and Gujarat seem more like
carefully laid out gardens. This care is coupled with an intimate knowledge of the
soils, the seasons and seeds. The Indians seemed to have mastered techniques of
rotation of crops, irrigation, manuring, and selection of seeds etc. from very early
times. These techniques had been so well studied and so optimised to the peculiar
conditions of each area that John Voeicker, the Consulting Chemist to the “Royal
Agricultural Society”, sent to India towards the end of the nineteenth century to
suggest ways of improving Indian agriculture through the use of chemistry, could
recommend little by way of technological changes. He was of the opinion if only the
traditional facilities of water and manure could be ensured the farmers of India could
obtain the best possible yields. As for suggesting improvements he seemed to have felt
that I was much easier to propose improvements in English agriculture, than to make
really valuable suggestions for that of India. Another expert of early twentieth century
John Kenny, remarks in the same vein that he did not consider it wise ‘to suggest seed
selection in a land where 4000 different sorts of paddy are grown in one province alone
and carefully differentiated according to their qualities and land suitable for them’.
The implements of the Indian cultivator often seemed rough and primitive to the
occasional observer. However it was soon realised that these implements were fully
adapted to the particular conditions in which they operated and even in the late
nineteenth century nothing could be suggested by way of their improvement. In fact
an early experiment during the later half of the eighteenth century to introduce the
heavy English plough near Salsette on the west coast had proved a total disaster. In
1795 Cap. Thos Holcott reported on the sophistication of the Indian drill plough widely
used in the Andhra region. The drill plough till then was considered a ‘modern’
European Invention.

With their simple but sophisticated implements and their meticulous techniques of
agriculture, the Indian farmers were able to obtain impressive yields. It was reported
that in early nineteenth century in the Allahabad region the produce of an acre of land
amounted to over 55 Bushels per harvest while that in England around the same time
was only about 20 Bushels. Since the Indian farmer in this region usually produced two
crops a year, the annual yield of each acre may be taken as over 110 Bushels at his
time. The productivity of Indian agriculture, however, declined very rapidly during the
nineteenth century. But even in the 1890’s lands which had access to irrigation and
manure yielded harvests comparable to those in England, and larger than the harvests
obtained those days in Europe, USA and Australia.

V

The Indian technical ingenuity in evolving simple techniques that are sophisticated
enough to take advantage of the full complexity of the local situation, and then
meshing these local techniques into a large impressive system can be best seen in the
tank irrigation system of South India. It seems that the whole of South India was
dotted with these tanks. A British expert writing in the 1850 ‘s estimated the total
number of such tanks in the Madras Presidency to be over 50,000. Another estimate
indicates that in the eighteenth century there were more than 38,000 tanks in the
region, which later constituted the Mysore state. The state had an area of around
29,500 square miles. It is, therefore, fair estimate that there were over a lakh tanks in
whole of South India. From what is known of the political circumstances of the time it
is clear that these tanks were constructed and maintained by local effort. However,
together they formed a closely knit whole so that the outflow from the one at a higher
level supplied the one at a lower level, and so on. This chain of tanks was so complete
and inter related within itself that the British engineers of the nineteenth century felt
that it would have been impossible to add another tank to the chain.

The Indian genius for performing vast tasks through simple, small and dispersed
techniques is seen even better in the case of metallurgy. Early European observers
noticed the Indians using small furnaces for something and refining iron and making
steel. Scores of seventeenth, eighteenth and early nineteenth century accounts of
Indian manufacture of iron and steel are available, and these pertain to perhaps a
hundred districts spread all over India. The smelting furnaces described in these
accounts seem to be of quite rough construction from the outside. However, the
observers noticed that the internal proportions and various angles needed to be rather
exact, and there were cases where the furnace had to be demolished and
reconstructed to correct some minor error in the angle of blast, or in some internal
proportion. Yet these sophisticated furnaces were routinely constructed by the Indian
iron-smiths in a matter of hours without the help of any very complicated Instruments.
These furnaces worked quite efficiently by the standard of those times. Thus,
according to one detailed account, two units of charcoal were sufficient to produce
one unit of crude iron in these furnaces. Processes of refining iron and steel making
were also equally efficient. Steel was prepared by direct carbonisation of Iron in
closed crucibles in which green leaves, wood and charcoal were all put together. This
process seemed mysterious to the British observers, since a process of direct
conversion was discovered in Europe only in the 1920’s. Even then, observers were
often surprised at the quickness with which steel was made in the Indian furnaces, the
process taking a few hours compared to many days taken in the corresponding
European processes.

The simplicity of these Indian techniques should be seen in the context of the fact that
Indian iron and steel had been renowned for their qualities for centuries past. All over
India one can find scattered Iron pillars and girders of very high quality, especially as
regards corrosion resistance. Indian steel has an equally distinguished record of
maintaining excellent quality, and even in the late eighteenth century an expert in
Britain when presented with a sample of Indian steel noted that it was ‘excellently
adapted for the purpose of fine cutlery, and particularly for all edged instruments used
for surgical purposes’.

It is worth remarking that with their small and dispersed furnaces, which produced
perhaps half a ton of iron during a week’s operation, Indians were capable of producing
a rather large amount of iron and steel. According to some nineteenth century
enumerations there were hundreds of such furnaces operating in certain districts and
taluks. On the basis of this information it has been estimated that the total number of
furnaces throughout India in the later part of the eighteenth century could have been
over 10,000 and these furnaces together had the potential to produce some 2 lakh
tonnes of iron annually.

VI

A survey of Indian technologies cannot be complete without some discussion of textiles,
the great industrial enterprise of pre-British India. Upto 1800 India was the world’s
leading producer and exporter of textiles. Yet this production was almost entirely
based on techniques that could be operated at the level of he individual or the family.
Spinning of yarn was an activity in which perhaps whole of India participated.
According to an observer from Manchester, Amo Pearse, who in 1930 visited India to
study its cotton industry, there were probably 5 crors spinning wheels (Charkhas)
intermittently at work even then. And this simple small wheel was so efficient that till
the early decades of the nineteenth century a widowed mother could still maintain a
whole family in reasonable manner by spinning on the charkha for a few hours a day.
Weaving was a relatively more specialised activity. However, the number to those
belonging to the weaver castes was smaller in comparison only to those from the
cultivating castes. Early nineteenth century data for certain districts of South India
indicate that each district had around 20,000 looms. Amo Pearse in 1930 estimated the
number of handlooms operating in India to be in the vicinity of 20 lakhs.

There were vast regions of India, which specialised in specific types of fabrics. Each of
these areas developed techniques of weaving, bleaching, dyeing and painting etc., that
were indigenous to the region, and also had its own characteristic designs, motifs and
symbols. For example, in Western India alone, Sironj in Rajasthan and Burhanpur in
Khandesh were major centres of cotton painting cheap printed cottons came from
Ahmedabad; woollens including the extra-ordinary Cashmere Shawls were produced in
Kashmir, true silks wee worked as Patolas at Patan in Gujarat and so on.

These dispersed and diverse techniques were so optimised that textile produced in
Britain through the post industrial revolution British technology could hardly match the
Indian textiles in quality or price. Till the early nineteenth century, mill produced
fabric had to be protected from Indian competition by the imposition of duties of 70 to
80 percent on the cottons and silks imported from India or, by positive prohibition. As
the historian H.W.Wilson notes, without such prohibitory duties and decrees, ‘the mills
of Paisley and Manchester would have been stopped in their outset and could scarcely,
have been again set in motion even by the power of steam’.

The Indians had developed their locality specific techniques not only in agriculture,
irrigation, metallurgy and textiles, but also in diverse other areas like building and
construction, sculpture, pottery, making of glass, and even luxuries like making of Ice
etc. That is perhaps why most historians of pre-British India are agreed that India of
that time was not only an agricultural, but also an industrial society.

Appendix: Computations in Indian Astronomy

By M.D.Srinivas

To get a flavour of the Indian way of doing Astronomy and Mathematics, it may be
instructive to look at the way they make particular Astronomical calculations like for
example the calculation of the longitudes of the grahas (the sun, the moon and the
various planets) at any given time. The following are the essential steps.

1. The Indian Astronomers first compute the shargana or the total number of
mean solar days slapeed from the chosen epoch till the given date, specified as
such and such Sakabda (Saka year) masa (lunar month) and and tithi (lunar
day). For this, they first compute the number of adhikamasas (intercalary
lunar months) elapsed since the epoch till the beginning of the current Saka
year. From this the number of tithis elapsed since the epoch till the given date
is calculated. Then the number of kshayahas (omitted lunar days) from the
epoch are computed and this when subtracted from the number of tithis, gives
the shargana for the given data. The computation of the number of
ashikamasas and kshyahas is based on specified basic astronomical parameters,
such as the mean motions of the sun and the moon.

2. From the computed shargana, the mean longitudes (madhyama graha) of the
sun, the moon and planets are calculated using the specified values of mean
(daily) motions of these grahas.

3. To take care of the irregular motion of the grahas a series of corrections are
applied to the madhyama graha mean longitude to get sphuta graha the true
longitude. For the case of planets the basic corrections are the manda karma
and the sighra karma. For the (outer) planets-Mars, Jupitar and Saturn – the
manda karma is roughly the equation of centre which takes care of the noncircular
orbit, and the sighra karma converts the corrected heliocentric
longitudes into the corrected geocentric longitudes. The basic form of the
manda and sighra corrections are obtained from a geometric epicyclic (or
eccentric) model and involves the mean motions of the apsides (mandocche
and sighroccha) and the circumferences (manda paridhi and sighra paridhi) of
the epicycles, as the basic parameters. However, what every text of Indian
astronomy prescribes is a series of manda and sighra type of corrections
performed iteratively till the results show a convergence to desired accuracy.
The actual steps involved in this sequence of corrections depend on the
particular planet and also varies from one school of astronomy to another. This
procedure seems to enable the Indian astronomers achieve much better fit with
observations than those achieved in other ancient traditions of astronomy
which operative with ideal geometrical models of planetary motion involving
epicycles, equants, etc. This sequence of operations is what enables the Indian
astronomers to incorporate for instance some of the higher order corrections to
the equation of centre which in modern astronomy are calculated using the
Kepierian orbits, etc.

4. The above planetary position is as observed at the time of sunrise (or midnight
in some schools of Indian astronomy) at the Indian zero meridians passing
through Ujjain. The desantara correction is applied to calculate the planetary
position at sunrise of places on a different meridian.

5. Finally, the planetary position at any given time of the day or night is
calculated from that at sunrise (or midnight) by using the so called sphutagati
or the true daily motion of the planet. This calculation also involves the
knowledge of the latitude of the place. Further it is necessary to know
whether the planet is in retrograde motion by computing the so called
sighragati phala in computing these gatis or velocities, various formulae which
are obtained by procedures which tantamount to differentiation of the
expressions for the sighra and manda corrections, are used.
The basic astronomical parameters involved in the above calculation are the mean
motions of the sun, he moon and the various planets, their apsides, and the
circumferences of the manda and sighra epicycles, etc. These have to be
determined on the basis of careful observations made over long periods. Each text
of Indian astronomy gives the values for these parameters current at its time.


http://indiansrgr8.blogspot.in/2011/05/indian-tradition-in-science-and.html

Kalachakra

Kalachakra
The Vedas, Epics and Puranas of ancient India describe an interesting concept of time called Kaalachakra, the wheel of time. This wheel of time is conceived as having twelve spokes indicating twelve points of time measurement on the wheel of time. Close examination of the imagery reveals that this concept is related to the Yuga System and used for various kinds of time measurements in ancient India. The same wheel of time is used to measure hours in a day, months and seasons in a year and large units of time like Yugas, which appear like seasons lasting for thousands of years as part of the 25,776 years long "Great Year" resulting from the precession of Earth's Axis of Rotation.




The twelve spoked wheel of time (Kaalachakra). Twelve divisions are named with zodiac signs for easy comparison with Western Systems. The Pisces-Aquarius transition base-lined at 2012 CE

Motions of Sun

The twelve spoked wheel of time (Kaalachakra) is mentioned extensively in Rig Veda and other Vedas. Vedic seers used to make observations of the sky with this framework called the wheel of time in their mind. For this they closely observe the path of the sun through the sky and locate its position in the sky
Observations from the South and North of India

Close to Equator in Southern India, the Sun traverse a path close to celestial equator, rising in the east and setting in the west, reaching zenith at noon. Besides this daily motion, Sun also makes a pendulum like motion on an yearly basis moving northwards and southwards clearly observable in northern India, 35 degrees north of equator. Ancient Indian astronomers, which includes many Vedic seers in northern and southern India, knew very well the reasons for all these movements. They were aware that Earth is a sphere moving around sun in an year, with a tilted axis, where it rotates once a day and that the axis of rotation itself will make one turn in around 26,000 years.
Depth of Knowledge of Ancient Astronomers

They knew that daily motion of sun in the sky is due to the rotation of Earth on its axis. They knew that yearly pendulum like motion of Sun in the sky to north and south is due to the yearly revolution of Earth in its orbit around Sun with a tilted axis of rotation. All these motions are partially confined in a band of region in celestial sky around 20 degrees north and south of the celestial equator. This band is called zodiac. It resembles the wheel of time (Kalachakra) and is one of the many aspect of the wheel of time, the other one being the orbit of the celestial pole in the sky. The zodiac is the region where the sun, moon and the five visible planets apparently wander in the sky of Earth. This region was of tremendous important for the ancient astronomers. It was divided into 12 constellations or regions where easily recognizable configurations of well known stars were defined. The twelve constellations were thus defined as stellar formations in the shape of fish, ram, bull, crab, lion, scorpion etc. These 12 constellations are Pisces (the fish), Aries (the ram), Taurus (the bull), Gemini (the twins), Cancer (the crab), Leo (the lion), Virgo (the virgin), Libra (the scales), Scorpio (the scorpion), Sagittarius (the archer), Capricorn (the sea animal) and Aquarius (the pot bearer). Each of these regions span around 30 degrees of the Zodiac wheel. These 12 regions are also called the 12 zodiacal signs and is one of the basis of astrology besides being fundamental to ancient astronomy.

The ancient astronomers also knew that the axis of rotation itself is slowly rotating, something which require many thousands of years of careful observation. All of these developments are already discussed in the article named Yugas.
The Daily Motion and Temperature Variations

Sun moves from eastern horizon to western horizon reaching zenith at noon. During zenith position sun's rays reach us perpendicularly and we feel maximum heat. During morning and evening sun's rays reach us with an inclination so that it travel a longer distance through atmosphere which dissipate much heat before it reach us. This changes create a smaller version of seasonal changes that we observe through out the year.
Yearly Motion and Yearly Seasons

The various seasons are the result of yearly motion of Sun in the terrestrial sky.
Uttarayana and Dakshinayana

The movement of Sun in the sky to the north is called Uttarayana. The movement of Sun in the sky to the south is called Dakshinayana. These apparent movements are due to the combined effect of Earth's motion in its orbit around Sun and due to the 23.5 degree tilt of Earth's Axis of Rotation. These motions are linked to the four important days of the year viz. Winter Solstice, Vernal Equinox, Autumnal Equinox and Summer Solstice. Uttarayana (northward motion of sun) commence after Winter Solstice day when northern hemisphere observe longest night. During Uttarayana at one point day and night becomes equal and that is Vernal Equinox day. Uttarayana ends at Summer Solstice day when the duration of night becomes lowest. After this Dakshinayana (southward motion of sun) begins. During Dakshinayana at one point day and night becomes equal again and that day is Autumnal Equinox day.
The Four Corners of the Sky

The position of sun against the background of stars in the sky, during all these four days viz. Winter Solstice, Vernal Equinox, Autumnal Equinox and Summer Solstice is considered as four crucial points in the zodiac. These four points constitute "the four corners of the sky". They are figuratively praised in the scriptures as the four great supports of the sky and as the four pillars that uphold the sky, due to obvious reasons.
The Six Seasons

When Sun moves to south and reach the southern most point in the celestial sky, Sun's rays reach earth obliquely. This reduces the amount of heat reaching northern hemisphere, due to reflection and refraction of sun's rays in the atmosphere. This generate a cold climate in northern hemisphere and causing winter season. Similarly when the Sun moves to north and reach the northern most point in the celestial sky, sun's rays fall in northern hemisphere perpendicularly causing maximum heat in northern hemisphere and thus summer season. In this way all the seasons are resulted from the motion of Sun and due to the resultant change in the energy distribution and energy flow in Earth's atmosphere.

The seasons are six in numbers (Shad Rtu, six seasons):- Vasanta (Spring:- February & March), Greeshma (Summer:- April & May), Varsha (Rains:- June & July) Sarath (Autumn:- August & September), Hemanta (Pre-Winter:- October & November) and Sishira (Winter:- December & January). The English months given are approximations. Seasons change widely in northern and southern India. Besides these seasons shift their temporal location in course of several centuries.
The Precessional Motion and the Shift of Seasons

Ancient Indian Astronomers including Vedic seers and Valakhilyas were keen observers of the motion of sun and were keepers of centuries long tradition of watching the movement of sun across the background of fixed stars and stellar constellations in the sky of Earth. They observe the position of Sun during Winter Solstice, Vernal Equinox, Autumnal Equinox and Summer Solstice in the background of the constellations observed in the sky. In a period of one or two years no change is noticeable. But in the course of a century, changes are noticeable. Due to the precessional motion (rotation of Earth's axis) the position of sun at Winter Solstice shift with respect to the stellar background by 1 degree in 71.6 years (length of the life of an average healthy human being). It traverses 30 degree or one zodiac-sign in 2148 years. It completes 360 degrees of one full circle of the zodiac in 25,776 years. This 25,776 years is figuratively called the Great Year, the Divine Year and One Year of the Devas.

Similarly all other points (Vernal Equinox, Summer Solstice and Autumnal Equinox) that constitute the "four corners of the sky" too shift following the Winter Solstice. Along with the four crucial points of the sky, all the six seasons too are shifted.

The shift progress in the anti-clockwise direction, ie instead of moving from Aries to Taurus to Gemini, they move from Aries to Pisces to Aquarius.
Calenders

Calenders are systems of time framework that help us to know what day of month it is and what month of an year it is. Calenders also count years from the year of start of the calender system. Examples of Calender systems are Shaka Calender established in 78 CE, Kolla Varsham Calender established (or rather re-established) in 825 CE, the Julian Calender established in 45 BCE and many more.

A 1 degree shift of Winter Solstice does not cause any disturbance in the calender system. But in a period of 2148 years (ie in around two millennia) the shift will be around 30 degrees, which is equivalent to one constellation in the sky and one month of an year. This is substantial change which makes all existing calenders useless. For example if one do not make any change in the existing calenders in 2148 years we will see that seasons are shifted by a month. For example, 2148 years in the past, ie in 136 BCE, Vernal Equinox occurred in April 21st instead of March 21st. Then spring started in January rather than in February.

Often calenders are designed such that Vernal Equinox is close to the beginning of the first month / first zodiacal sign. After 2148 years this no longer will be true, causing the astronomers to redesign their calenders. Some calenders adjust themselves to shift of equinoxes and solstices by changing the first month of the year. Some other calenders are discontinued and new calenders are adopted. Often the new-year date of discarded or destroyed calender is still remembered as a celebration. In some cases the practices followed in old calender continues to be part of some traditions though not attached to the active calender system.
A Calender with Pisces as the first month / sign

As an example of self-adjusting calender we have the astrological calender followed in Kerala, the southern state of India. In this calender the astrological year starts with Pisces (Meena) rather than with Aries (Mesha / Meda). Currently the Vernal Equinox is at the beginning of Pisces, ready to enter Aquarius. So it make sense to consider Pisces as the first zodiac sign or the first month.
A Calender with Leo as the first month

The Kolla Varsham calender in Kerala consider Leo (Simha / Chingam) as the first month of the year. Vernal Equinox was at the beginning of Leo, ready to enter into Cancer in around 8728 BCE. Thus this calender in Kerala is a remnant of an old calender that started in 8728 BCE when this region was ruled by a king named Mahabali. The first day of Chingam is considered as a New Year and the day when Moon in this month comes close to the star Sravana is celebrated as Onam a great festival associated with king Mahabali's return from his exile in Patala (South America).
Calenders with Aries as the first month / sign
Vishu Calender

Another New Year in Kerala is celebrated based on another calender in the month of Aries (Mesha / Meda) named Vishu or Vaishakhi. The date of this New Year usually falls in April 14, 15 or 16. It is now celebrated as an ancient Vernal Equinox. A Vernal Equinox in April 15 means it occurred 25 days later than March 21st (current date of Vernal Equinox). Since 365.25 days of the year corresponds to 360 degrees of the zodiac, 25 days corresponds to 24.64 degrees. One degree shift requires 71.6 years, so 24.64 degrees shift requires 1764.27 years. So Vernal Equinox was at April 15th 1764.27 years ago, ie in 247 CE. During this time Vernal Equinox point was still in Pisces but very close to the beginning of Aries. Hence the builders of calender in those days chose Aries as the first month and first zodiac sign. Arrival of calender start dates based on Gregorian calendar is not absolutely accurate because of errors in Gregorian - Julian calender and because of the Luni-Solar nature of the Vishu Calender due to which New Year day (Vishu) varies as April 14, 15 and 16.

As per Julian calender one year is 365.25 days. Gregorian calender corrected it as 365.2425. But Ancient Indian calenders were based on more accurate calculations which consider an year to be 365.2421756 days (only 1.4 seconds shorter than the modern scientific value of 365.2421904 days. See:- maya-s-theory-of-sun).
Western Astrology Calender

In some cases, the practices followed in old calender continues to be part of some traditions though not attached to the active calender system. For example in Western Astrology, Aries is considered as the first sign. Vernal Equinox was at the beginning of Aries ready to enter Pisces in around 136 BCE. This period was also the beginning of modern western astrology. There is a huge debate going on if the predictions based on western astrology needs to be shifted by a month. In my opinion, this depend on whether western astrologers want to base their predictions on the fixed zodiac or on the equinoxes and solstices which keep on moving around 1 degree every 72 years.
Nakshatra System

Much like the division of sky into 12 zodiac signs, the Nakshatra system is a unique division of sky into 27 parts using 27 easily identifiable stars in the zodiac, ie in the path of Sun, Moon and the planets. Some astronomers identify 26 and some others 28 such stars and hence the division of zodiac based on Nakshatra-system may vary from 26 to 30. In case of 26 Nakshatras, crossing of one Nakshatra region by Vernal Equinox will require close to a millennium (991.3846 years). In case of 27 Nakshatras, one division will span 13.3333 degrees (ie exactly 13 degrees and 1/3 degrees more, a more manageable fraction). When 30 Nakshatras are used one division will span exactly 12 degrees. The most popular Nakshatra system uses 27 Nakshatas. The system which provide ease of observation and which deals with more manageable fractions is preferred.

Yuga System



Kaalachakra with Yuga Chakra Inside. A refined Markandeya Yuga Chakra with Ascending and Descending Chaturyugas each with a duration of 12888 years is depicted. Negative Numbers are BCE years and Positive numbers are CE Years.

The Yuga System existed side by side with Nakshatra System (with its 27 divisions of zodiac) and with the Kalachakra system (with its 12 divisions of zodiac). But it has more to do with historical or geological epochs and less with astronomical observations. However the historical events expressed as having occurred in a particular Yuga may be fixed in time axis using astronomical observations. There are some indirect correlations with Yuga System and with Kalachakra (12 spoked wheel of time or zodiac).
Ascending and Descending Chatur Yugas

It has mainly four divisions called Rta Yuga, Treta Yuga, Dwapara Yuga and Kali Yuga. The divisions can be of equal size (1:1:1:1) or follow a ratio (4:3:2:1). The four Yugas together is called a Chatur-Yuga. In some definitions there are both ascending and descending Chatur Yugas. An Ascending Chaturyuga is defined starting with Kali Yuga, then Dwapara, Treta and Rta Yugas. After this the Descending Chaturyuga proceeds as Rta, Treta, Dwapara and Kali Yugas.
Duration of a Chatur Yuga

The duration of a Chatur Yuga varies based on the definition as 10,000 years (Sanjaya's Definition), 12,000 years (Markandeya's Definition) or 4,320,000 years (Shanti Parva Definition). Of this the 12,000 years Yuga defined by Markandeya is the one that aligns closely with the 25,776 year long axial precession if ascending and descending Chaturygas are taken together (a total of 24,000 years). Markandeya system also has the concept of dawn and eve. These are periods with 1/12th of the size of Yuga duration at the beginning and end of each Yuga were the effects of the adjacent Yuga too is felt. For example, the dawn and eve of Kali Yuga having 1200 years duration is 100 years each and that of Dvapara Yuga of 2400 years duration is 200 years each.
Reason for the 4.32 million long Chatur Yuga

In 4,320,000 year long Chatur Yuga definition 12,000 year long Markandeya Yuga duration is multiplied by 360 saying 360 human years constitute one year of the Devas. Actually what is meant here is that 360 degree motion of Vernal Equinox (ie one revolution of Vernal Equinox or one complete turn of axis of rotation due to precession) in 25,776 years constitute one Great Year, which can be figuratively described as One Divine Year or One Year of the Devas. But this does not require any multiplication of 12,000 years with 360. This error in the Shanti Parva of Mahabharata is copied into all Puranas including Vishnu Purana and Bhaagavata Purana. Currently many Hindus believe in this 4,320,000 year long Chatur Yuga in which current Yuga viz. Kali Yuga is thus unnecessarily and erroneously long (432,000 years long).
Refined Markandeya Yuga System

Markandeya Yuga system itself seems to be an approximation of the actual Chatur Yuga definition which was half the size of axial precession period (ie 12,888 years) so that ascending and descending Chatur Yuga will constitute one complete precession in 25,776 years. Such approximations are rampant in ancient Indian scriptures to facilitate easy memorization. For example the number 71.6 (the number of years taken for the Vernal Equinox to traverse 1 degree in its circular motion) is often approximated as 72 and is found in Vedic hymns.



YugaChakraWithDawnEve.png
A refined Markandeya Yuga Chakra with Ascending and Descending Chaturyugas each with a duration of 12888 years is depicted. Dawn and Eve of each Yuga is marked. Negative Numbers are BCE years and Positive numbers are CE Years.
Historical and Geological events in Yugas

The beginning and end of each Yuga is marked by an event especially the death or birth of a historical figure. The Descending Treta Yuga is marked by the death of Rama and the Descending Dwapara Yuga is marked by the death of Krishna. Birth of a king named Avikshit is mentioned as the beginning of Descending Treta Yuga. At the beginning and end of Descending Rta Yuga there were floods. There were floods in the beginning of the Descending Treta Yuga. Sarayu river that flows through Rama's city Ayodhya, was flooded during the end of Descending Treta Yuga. Dvaraka, the island city of Krishna was submerged due to flooding of sea water at the end of Descending Dwapara Yuga.
Saptarshi, the Seven Sages

Saptarshi is the name of a constellation near celestial pole and also the collective name of the seven sages who carries forward the secret of Kalachakra. This constellation also plays a role in the movement of the wheel of time as some of the stars in it becomes the pole-star due to the precessional movement. It is known as Big Dipper and Ursa Major (Great Bear) in western astronomy. The names of the seven sages differ based on the source text. Popular list include Bhrigu, Atri, Angirasa, Marichi, Pulastya, Pulalaha and Kratu. Sometimes Marichi is replaced by Vasistha and either Atri or Kratu replaced by Agastya.

 http://ancientvoice.wikidot.com/article:kalachakra