ORIGINS OF SECRET MANTRA (DAY 8): THE AGE OF PHILOSOPHY, ARRIVAL OF SUTRAS, DIVINE GEOMETRY AND DEVANAGARI SCRIPT by 17th Karmapa
— Rens Bod
“Sūtras are called so because they have the following qualities: few letters, i.e. aphoristic in nature; unambiguous; contain the essence of the śāstra; comprehensive and universal; without superfluous words; and free from error. (alpākṣaramasandigdhaṃ sāravadviśvatomukham astobhamanavadyañca sūtraṃ sūtravido viduḥ ||)”
This is the write-up of the eighth day of the 17th Karmapa’s teachings on the Origins of Secret Mantra (see video here). In the first part of the teaching, the Karmapa discussed the Age of Philosophy and the area of India, Magadha, in which it flourished. This was the third section of the Vedic Period of India, in which the branches of the Vedas, the six Indian non-Buddhist Philosophical schools and versified Sutras developed.
This was followed by an explanation of the four stages of a person’s life and the advanced development of various aspects of Indian knowledge such as poetics, grammar, astrology and mathematics and geometry. The Karmapa then went on to present the different styles of ancient writing script at that time, that developed into the Devanagari Sanskrit script, ‘language of the Gods’, still used today in India and Nepal.
It is clear that Indian culture and civilisation was not only extremely advanced but also unique and the mother, or root, of other systems of mathematics, grammar and language. It was within that culture that the Buddha arrived and was able to teach his profound experience and truth of Dharma.
Written, compiled and edited by Adele Tomlin, 9th September 2021.
“When we talk about this Age of Philosophy, the situation was that the Indo-Aryans had continued to expand from the Punjab to the Ganges River Valley and went outwards beyond that to cover a larger area. The traces left by the politics and literature of that time are said to be some of the greatest and stand out in the history of Indian civilisation.
As for politics (see the map above), from the beginning of the Brahmanical era, when it comes to the Age of Philosophy, the area of Magadha was one of the places where that was happening at an even more rapid pace. The Aryans eventually covered that entire area. This map shows the six great Kingdoms that appeared during that era.
One of these was Magadha which became very important. from the beginning to the end of the Brahmanical period, everyone knew of this kingdom. In Magadha, advances were occurring at a rapid pace during the Age of Philosophy. Eventually, all of Northern India came under the control of this kingdom, and it became a cultural and political hub.
Later, when the Buddhist teachings appeared, they mainly were established in Magadha. Similarly, the great emperor Chandragupta Maurya (reign: 321–297 BCE), renowned as a chakravarti (universal emperor), also came from this kingdom. So this central India area was a great Kingdom at that time.
Likewise, there were connections with the Dravidian civilisation from lands even further to the south. This had become a third great Kingdom, containing Dravidian people who had been exiled by the Aryans. So, at that time, there became three powerful kingdoms, out of these developed the six great Kingdoms, Gradually, this civilisation was able to spread throughout the whole geographical area of India.”
Magadha is the brown area on the map. It was the most important ancient Indian kingdom. It was important not only during the Age of Philosophy, but also later, during the time of Buddhism. Bhagavan Buddha spent over half of his life in Magadha and the early Buddhist councils were convened in Magadha at Shravasti and Pāṭaliputra. It is one of the most well-known Indian areas in terms of Buddhism.
The kingdom of Magadha was located on the lower reaches of the Ganges River Valley. Most of the areas of present-day eastern India were formerly regions in Magadha. The size of the area controlled fluctuated greatly during the different dynasties that ruled Magadha. So we cannot say it was one particular area. There were times it covered all of Northern India and some parts of Southern India came under its control. However, it was a vast kingdom and very significant in the history of India.
Yesterday, I mentioned the Indian Pūraṇa history texts; ‘tales of the past’, in English. This is the name for a genre of Indian literature that includes many different texts. Their content is quite extensive, which discusses many issues, but primarily they describe how the universe was formed, how the various types of gods appeared, the history of the kings, religious movements and so forth. The Pūraṇas include many myths and legends, philosophy, events related to religion and so on. There are many extant Pūraṇas, which probably appeared not that long after the Buddha passed away. Thus, they are a later genre of literature and important historical sources for the Age of Philosophy. When we speak about the Age of Philosophy we need to use the Pūraṇas as historical sources.
The Haryanka dynasty. The kingdom of Magahda probably predated this dynasty but the available historical sources do not clearly indicate that there was. This dynasty reigned in Magadha for over 200 years. There were ten kings. This period probably included the birth of Shakyamuni Buddha, and it was also the time of the 16 powerful kingdoms—the Mahajanapadas. The Shaiśhunāga dynasty reigned for 60 years, during which there were two Kings. However, this is disputed by scholars. This also was during the time of the 16 powerful kingdoms. The Nanda dynasty (Nanda means ‘joyful’) reigned for 100 years and had nine kings. The Chandragupta Maurya dynasty, which took over Magadha after the Nanda dynasty. Chandragupta Maurya’s grandson was probably the Emperor Ashoka.
“After the Upanishads appeared, the Brahmans continued to preserve their ancient forms and customs, and performing sacrificial offerings. This was like a symbol of being a Brahmin. Likewise, the common people had become habituated to performing rituals and regarded them as part of their way of life. They couldn’t give them up.
However, many different philosophies had developed and raised doubts which threw these rituals into question. The Brahmins wanted to preserve their own function and status and to give future generations and education in ancient traditions. Thus, the Brahmans codified the hierarchies, procedures, and rituals, and made rules detailing the different responsibilities of the four castes. These rules were compiled into textbooks or manuals that became like textbooks used in schools.
The way they were written was very concise. This produced a new genre of literature, mainly in verse and extremely concise, called sūtras. In Tibetan, the word is ‘do (mdo)’ and in Sanskrit they are called ‘sūtras’. The word sūtra means ‘thread’; its linguistic root is the word ‘siv’, to sew. A thread is like the string in a garland of flowers. Thus, the original meaning of the word is “condensing vast meanings into a few words”. The reason they were written so concisely, was that instead of having a lot of elaborations they wanted to teach the meaning in as few words as possible that could be memorised easily, so they were written in verse.
The earliest sūtras probably appeared in the 6th Century BCE, and the latest around the turn of the millennium, the beginning of the Common Era. The content of the sūtras are a repeat, or iteration, of the content of the Brāhmanas. Although there is some new content, most of it is a repetition. Thus, they are not all that different from earlier Vedic literature. However, unlike the Brāhmanas which are very long and complicated, the sutras are concise and simple, that is their special feature, and they use verse. They were intended for children (from age 8 or 9) to study with, so having them in short stanzas, made them easier to memorise. They were thinking about what was useful for practice and what could easily be joined with one’s mind.
At the time, there were many different sūtras. They were like textbooks for each school. There were many traditions, each of which had its own sūtras. Sadly, most of the sūtras have been lost. There are still a few remaining ones. We can differentiate them into three traditions, or genres, of these philosophical schools.”
I will talk about these in detail later.”
2. Yóga (Neljor-pa)
“The seeds of both the Jain and the Buddhist religions are found in the philosophical texts in the Upanishads. That is the basis for them, many scholars say. However, these are also different from the previous six philosophical schools. They are highly advanced with a high degree of freedom in their way of thinking. They both appeared after the complete development of the earlier traditions. Neither accepted the Vedic traditions or the Vedic texts. This is a feature of these two.
Both Jainism and Buddhism were taught in the form of Sutras and preserved in that fashion, but the teachings were not recorded in written form during the Vedic period. it was only later they were written down. The words of the Buddha, for example, were not written down during the Buddha’s lifetime. So the Sutras of these religions did not appear during the Vedic period.”
I will now give an introduction to the first of these, the six branches of Veda.”
This word ‘kalpa’ is translated as ‘ritual’ in Tibetan. There are three categories of text: Śrautasūtra, [[[Sutra]] of Listening], Dharmasūtra, [[[Sutra]] of Dharma], and Gṛhyasūtra [[[Sutra]] of Household Life]. The first category, the Śrautasūtra, are called the ‘listening’ sutras because they explain Vedic ritual very simply.
The second category, the Dharmasūtras are important and significant texts because they speak about the customs and laws of that time, thus they have become an important historical source. Later, many points in the Dharmasūtras became an integral part of the Manusmṛiti.
At that time in India, children would memorise these laws from a young age, so that when they grew older they knew what their responsibilities ere and could put them into practice. Nowadays, we have only fragments of the original dharmasūtras and not the entire texts.
As for the third category, generally, whether a son, husband, or father, all the men had to fulfil roles in the family, and these are explained clearly and in detail in the Gṛhyasūtra. For example, the responsibilities of the eldest son and of a father. It speaks about rituals related to marriage, having children, breastfeeding, education, and so forth, in great detail. It also describes rituals that must be practised in the household—it describes each of the religious rituals. When researching the Gṛhyasūtra, we can learn clearly how people led their lives at that time.
These three Sutras are what we call sutras of ritual, or kalpa. Originally there were separate sutras of different traditions and regions, but now only a few fragments remain. [More details of these genres are provided below.]”
“Sikṣā provide detailed instructions on correct pronunciation when reciting or reading the Vedas. The reason for this was because the Vedas had been memorised for generations and recited from memory, but if the pronunciation of even one word was mistaken, it was thought to be offensive to the gods. One needed to know the weight of the letters, which sounds are strong, which are soft, the nature of the vowels, the point of origin of the sounds, the position of the tongue, labials, gutturals, etc. without getting anything wrong. Thus several areas of knowledge developed around this.
There are many texts in Tibetan that are similar to these on how to recite the mantras, but no one studies them anymore and checks if we are reciting them correctly or not. Some scholars might be interested but usually most people do not. Yet, it is crucial to know how to pronounce them correctly so they do not decline. The source of the mantras was originally from the Buddhist texts and were taken out of it and became important for that reason.”
“These etymology texts give explanations of difficult words/etymology in the Vedas. In particular, round 400 BC there was a celebrated Indian grammarian called Yāska. As he was so great, earlier Sanskrit grammarians could not compare to him, so they lost all their influence and their texts were entirely lost. Yāska wrote a text called Nirukta, which gave new explanation of words found in ancient texts. We could understand it like a linguistic study of the origins of language.”
“The fifth branch is grammar. These Sanskrit texts on grammar are primarily an explanation of the grammar of the Vedas. At that time, there were many texts on grammar, but later, due to the work of the great scholar Pāṇini all the texts written by previous scholars were no longer used and were lost. He wrote the text called Pāṇini’s Grammar. He lived in the northwest of India. There are different assertions by different scholars about when he lived, but roughly it was between the 4th to 3rd centuries BCE.
In contemporary times, there was a modern German Indologist, Friedrich Max Müller (1823-1900) who said that in terms of people globally studying grammar, there are only two ancient traditions on grammar, one from India and one from Greece. However, he said that compared to the depth of knowledge shown in the work of Pāṇini, the Greek grammatical texts are worthless and don’t show any great knowledge. Pāṇini’s level is even higher than the ancient Greek grammatical texts. So this tradition om grammar and linguistics was founded that was both extraordinary and unique in the world.
Scholars and researchers have this the idea and hypothesis that all the languages in the world come from the same, single, common ‘mother’ language. Yet, Pāṇini suggested the same idea 2000 years ago in India. This shows that there was a high level of thinking on grammar and linguistics back then. There was a massive and rapid advance in grammar and linguistics, which is amazing. This is what various scholars say.”
“Astrology was necessary in order to determine the right time to perform sacrificial rituals and which dates would be auspicious or inauspicious. To know when the right time was they developed astrology. “
“That was the first branch of the Vedas called rituals, of which there are Sutras. First, I will talk about the Dharmasūtras. These primarily discuss the rules of the rituals and how to pay respects daily. It determines the standards for how Dharma practitioners should live their lives; describes the powers and responsibilities of different people in society; and explains how to handle conflicts between people and deal with criminals. In contemporary terms, they are like the rulebooks in Tibetan monasteries. As people considered the Vedas to be extremely important, taking them as the basis, all the traditions and customs of the Aryans were systematised in the Dharmasūtras. Also the caste divisions were codified into rules in the Dharmasūtras.
However, if we have to codify caste divisions, the classifications of the castes must be clearly known and defined. So they had to settle these classifications. At that time, this created great difficulties for the people who were writing the laws, because many castes did not fit within the classification of the four castes. They didn’t know what to do and where to put them.
It was not possible to create more castes because the texts stated that there could be no more and no fewer than four castes. As a result of this difficulty, they tried to explain this clearly, the authors of the law texts brainstormed and used their imagination to create their own reasons and did whatever they could. They didn’t have proper reasons. We know this because there were three very influential scholars compiling law texts at that time, and when we compare their texts, there is not a single area of agreement among them. The way they distinguish the castes don’t match.”
“For example, here is a table of lineages (above) from the Gautama Dharmasutra which provides the caste status for children born from mixed caste parents e.g. a Kshatriya father with a Brahman mother, where do they fit in the caste system? This is explained in the Gautama text but it not supported by the other law texts, which demonstrates how explanations of the four castes were arbitrary and without sources. There was no factual basis for their explanations.
During this period of clarification, the reason it happened at that time, was that the two most powerful kingdoms in the Ganges River Valley were Videha and Magadha. However, the people in these two kingdoms, were not 100 percent Aryans, they were mixed, and some doubted that they were Aryan. The logic was that all humans had to be included within the caste system and, as they were aware of the existence of the ancient Greeks, they wondered where they fit into the system. Even though there was no connection at that time between Indian and Greek society, they included the ancient Greeks within the four-caste system because they knew they existed. Thus they forced them into one of the four categories.
Although they talked of four castes, Brahmans, Kshatriyas, and so on, it was very difficult to say there were pure caste lineages since there had been so much inter-mixing between castes beforehand. So from beginning to end, the whole caste system was essentially made up and people worked hard to try and rationalise and determine the system.
Modern scholars say that during that time, the educational levels of the ordinary people were not that high, and the educated Brahmans invented things and used contradictory analogies. However, no-one seemed to doubt why whether there were reasons for it. Everyone believed that the caste system was the natural order decreed by the gods. It is incredible people believed it. If we were to say it was invented arbitrarily but people just accepted it, this is hard to understand. If they had no authoritative sources for creating the system, even later Buddhists did not query it. Even now in the 20th Century in India, people believe in these caste distinctions and that they are important.
The Dharmasutras cover other topics such as governance, taxation, administration, trade, farming, military strategy, criminal law and punishment, and civil law. People of that time would love to memorise things and memorise everything. There existed paper and pens, but few used them. So the judges and lawyers would recite the Dharmasutras from memory, and there were no legal texts, and cases would be decided based on this. Thus, if they forgot something or made a mistake, then one had to accept it. So it was based on their memory that judges took decisions. There was a danger that the judge would make mistakes because of that.
When people spoke about past events, it was like they read from a diary. People these days don’t have such stable memories because we use our phones and computers so much that we do not train our minds. In any case, at that time, people in India really liked memorising.”
“In this sutra it speaks about Indian people’s daily lives. As I mentioned before, there were four castes, yet the Brahman, Kshatriya, and Vaishya were considered to be “double born” and had specific religious responsibilities. They divided their lives into four stages [Skt. Ashrama]:
1. The stage of celibacy (stage of study)
2. The stage of household life (the stage of running a household)
4. The stage of going forth (wandering through the land)
The fourth phase of going forth (becoming a monastic) existed before the Buddha appeared, even though it is a Buddhist tradition. By discussing this, we can then understand why Buddhism has that tradition too.
“The stage of celibacy [Brahmacarin] was the time when young boys were students: from the age of 8 to 16 for Brahman boys, for Kshatriya one studies from 11 to 21, and 12 to 24 for Vaishya. So the phases are different for each caste.
They would wear the white ‘Brahman thread’, to show they are ‘double-birth’ castes and not the Shudra/outcastes. They would go to a guru and live as students. in their teacher or guru’s home. They could choose to study for the 12, 24, 36, 48 or however many years they wished. The main topic of study was memorisation of the Vedas.
While studying there was a strict code of conduct. There was a lot of smoke then and students could not inhale smoke or wear jewellery. They had to wear linen/hemp clothes, not high quality clothes and follow one’s desires. and wear their hair in a top knot. They had to be obedient and respectful towards the guru. Every morning they would go on alms rounds in the surrounding villages and begging for alms. After that, they had to give all they received to the guru. Only after the guru had finished his meal, the students were allowed to eat. They also had to gather firewood, fetch water, sweep in the morning, and tend the Brahma fire during the sacrifices. In the evening they had to wash the guru’s feat and prepare his bed and so on. They were only allowed to go to sleep after the guru had gone to sleep. The students had to study not like students do today. They would join the guru’s household and become his servant. They believed that if they worked hard, then through their efforts, they would receive some understanding of the ancient wisdom passed down from the ancestors. Students would study in this way with one or several gurus, and after completing the education they would make large offerings to the gurus. Then they would return home. That was the phase of celibacy/study.”
2. Household Life (Grhasta)
“The second stage is that of household life (grhasta). Once the student had completed studies then they returned home, and were expected to marry and begin the second stage of life as a householder. Once married, then the lifestyle was very different. This period of household life was considered the most important of the four stages because the majority of people lived as householders. There were innumerable rituals for them to perform, some daily, some monthly, and some annually.”
“Sometimes, we hear about Indian masters in secret mantra who would go off to perform conduct (chopa la sheg), this is probably talking about this or the 4th phase. This stage of forest life was when people would leave home and go to live in the forest, mainly eating food such as roots and bark of trees. They had meagre food to live on.
Even so, there were many religious practices to be done at dawn, in the morning, and in the evening. The Brahman fire had to be lit and there were also prostrations and particularly meditation practice on the profound meaning. The third stage was mainly the stage of practice.”
“The fourth stage, is called the period of ‘going forth’ [samyasin], some call it the ‘stage of the yogi’. This is giving up the household completely, and the practitioner shaved their head, abandoned everything, and went forth. One would give up all physical things, other than the body. This was a time of asceticism: giving up food, having only one robe, and one meal per day from alms that had been begged for. You had no fixed location and went to other places. You were not allowed to stay longer than one night in a town and wandered from place to place. It was not necessary to do many rituals, but you had always to recite the Vedas, and meditate on dhyana, and try to see the true nature of world and separate themselves from the samsara of birth and death. The aim was to become one in taste with Brahman. In brief, one had to attain the happiness of liberation.
“In any case, if we think about these in our Buddhist traditions, such as ‘going forth’ [Tib.rabjung] and Bikkshus, all existed prior to the Buddha in India. If we understand this history, then we can get an idea why these traditions existed in Buddhism too. Some scholars have suggested that the tradition of begging for alms arose in India at that time, the Aryans had come to live in the fertile region of the Ganges valley, so people had a good life and there was an excess of food. Thus, when people asked for alms, they had a lot to offer them. The living was good and so giving alms was easy to offer.
This order of the four stages was not an obligatory thing where it was necessary to go through all four stages sequentially. Those with a great desire to free themselves from samsara could go from the 1st stage of study directly to the final stage of going forth.
Usually, those who ‘went forth’ were older people, in their sixties or seventies, who had completed the life of a householder and given the responsibilities to their children and interested only in attaining liberation. Later, people who finished all four stages were seen as people who had completed all the stages of human life. there are many examples in history of people who did that. India had their own education, advice and methods and so these were unique to India. This was not pointless to do this and extremely meaningful and beneficial. This idea of the four stages of a human life also had a powerful impact on Indian civilization.”
“The main cause or condition for India’s distinctive development of areas of knowledge such as astrology, grammar, poetics, and philosophy, medicine, mathematics and geometry was connected to religion.
Indian medicine is another case in point. As they had to offer specific parts of animals, such as the liver or the heart or the legs, as sacrifices to the gods. Thus, they had to open up the carcass and look at it, and so they developed a knowledge of anatomy. So it is said that medicine came from the blessings of the Gods. However, Indian medicine had already developed to a certain degree when sutras appeared.
Likewise, there was the development of mathematics. It was also developed in India and has unique features. For example, the decimal system originated in India, after 1, 10, 100 and so on. . The Arabic numerals from 1-9, spread to Europe from Arab lands. However their original origins is India. It is said. Indian mathematicians invented zero; it originated from the Sanskrit word śūnya meaning “empty”.
Also, geometry (measuring shapes) developed independently in India. It was necessary to know geometry was to be able to make mandalas for rituals, their height, width and so on, accurately for sacrifices. All these areas of knowledge arose from the existence of religion.
“Now I will speak about ancient Indian writing systems. In the early Vedic era, the age of Rigveda, there was no writing in India. Later they developed a writing system , which led to the development of Sanskrit language. Due to Sanskrit, traditions of literature could be passed down.
There was a writing system of the Indus Valley Civilisation but we cannot read it. So Brāhmī is the earliest writing system in India; it probably appeared in the 6th century BCE. At the time of the emperor Ashoka, in the 3rd century BCE, there were many edicts inscribed on caves and rocks. There were two widespread scripts : Kharosthi, which read right to left, and Brāhmī, which read from left to right.”
Later, around 400 CE, the Gupta script appeared. They took the Brāhmī script as the basis and changed it a little. That script disappeared in the 7th century but the reason for that is not known. In the 8th century, the Gupta scripts spread.”
“Then, around the 13th century, the Nagari script was reformed and improved and the prefix deva, meaning ‘god’ or ‘divine’ was added to make it the Devanagari script. This prefix was added in order to praise the Sanskrit language, as ‘the language of the Gods’ This is the script used to write Sanskrit and other Indian languages even now.
In terms of languages, as the Aryans in the North gradually spread throughout India into the Ganges Valley, they encountered various colloquial languages and mixed with them, as a result, many different colloquial languages developed. These were known as Prakrit or “natural languages”. Later, as it mixed each language has different pronunciations and dialects. This is like the existence of many dialects and colloquial languages across Tibet, such as Amdo and Kham ke and so on. Later, as a method to make a single language, the Brahmins used the grammar points in the Vedas, Brāhmanas, and Upanishads and created a new, standardised grammar. This was probably during the time of Yaksa in the 5th century BCE, and Panini in the 4th century BCE, So the grammar of the Sanskrit language was settled and it was accepted throughout India and it became the commonly accepted Sanskrit language. Compared to colloquial languages, it was a language that scholars had created, and so Its name derives from the adjective sáṃskṛta which means “well-formed” or “perfected”.
“Finally, I will compare these three types of texts. Each has its own unique style. When the Vedas appeared in the Punjab, the Aryans worshipped aspects of the natural environment as gods, and they were principally written in verse. Yet the Vedas were said to have come from the blessings of the gods.
The Brāhmanas were written after the Aryans had migrated to the Ganges Valley, and their written style is in prose form. Their main topic is about the rituals in order to come to a better understanding of them. They too are also said to have come from the blessings of the gods.
Later, the Aryans gradually migrated further along the Ganges River Valley, the Brāhmanas became common but they were very long, complex, and difficult. So in order to make them more concise and easier to understand, the sutras were created and these were basically textbooks. Their style was in verse.
There is so much to speak about and it is difficult to speak about it all. I am not going to rush through it though. In particular, the teachings of Buddha will not be rushed and I want to give a good introduction to it, even if I cannot say much about Secret Mantra.”
Bronkhorst, Johannes (2019), A Śabda Reader: Language in Classical Indian Thought, Columbia University Press,
Kulkarni, R. P. Geometry according to Śulba Sūtra. Pune: Vadika Saṁśodhana Manḍala, 1983.
Patrick Olivelle (2005). Manu’s Code of Law. Oxford University Press.
Staal, Frits (1972). A Reader on the Sanskrit Grammarians. MIT Press.
 Quote taken from : https://www.prekshaa.in/eight-atma-gunas-gautama-dharma-sutras-part1
 Friedrich Max Müller (1823 –1900) was a German-born philologist and Orientalist, who lived and studied in Britain for most of his life. He was one of the founders of the western academic disciplines of Indian studies and religious studies (‘science of religion’, German: Religionswissenschaft). Müller wrote both scholarly and popular works on the subject of Indology. The Sacred Books of the East, a 50-volume set of English translations, was prepared under his direction. He also promoted the idea of a Turanian family of languages.
Interestingly for myself as someone who has studied Kant and the German philosophers, Muller connects the work of Kant with the ancient Indian Vedas: “In 1881, Muller published a translation of the first edition of Kant’s Critique of Pure Reason. He agreed with Schopenhauer that this edition was the most direct and honest expression of Kant’s thought. His translation corrected several errors that were committed by previous translators. In his Translator’s Preface, Müller wrote:
The bridge of thoughts and sighs that spans the whole history of the Aryan world has its first arch in the Veda, its last in Kant’s Critique. … While in the Veda we may study the childhood, we may study in Kant’s Critique of Pure Reason the perfect manhood of the Aryan mind. … The materials are now accessible, and the English-speaking race, the race of the future, will have in Kant’s Critique another Aryan heirloom, as precious as the Veda—a work that may be criticised, but can never be ignored.”
 “An examination of the earliest known geometry in India, Vedic geometry, involves a study of the Śulbasūtras, conservatively dated as recorded between 800 and 500 BCE, though they contain knowledge from earlier times. Before what is conventionally known as the Vedic period (ca. 1500–500 BCE), there was the Harappan civilization dating back to the beginning of the third millennium BCE. Even a superficial study of the Harappan cities show its builders as extremely capable town planners and engineers requiring fairly sophisticated knowledge of practical geometry. An interesting conjecture has been suggested by a drawing on a seal found from Harappa (ca. 2500 BCE): was there an awareness then that the area of a polygon inscribed in a circle approaches the area of the circle as the number of sides of the polygon keeps increasing? This is the basic idea behind techniques that were developed for the mensuration of the circle in a number of mathematical traditions including Indian.”