There are three clocks of nature; the diurnal clock that measures the days, the lunar clock that measures the months and the solar clock that measures the seasons. The calendar is man’s frustrated attempt(s) to synchronize these three clocks. Different cultures have attempted, in different ways, to synchronize these clocks or formulate a stable calendar.
The calendar of the Vedic period has confounded historians of science for over hundred years. The foundational elements of a calendar (season, year, month and day) are noted in Rgveda Samhita, the oldest surviving text in Sanskrit. However, the nineteenth and twentieth-century scholars failed to identify in the Vedic texts, any accurate procedure to synchronize the three clocks of nature. The consensus has been that the Vedic ritualists had only the crudest of calendar and they had failed to adequately synchronize the three clocks of nature.
This book shows that this conclusion is false. The Vaidikas had developed unique and accurate schemes to synchronize these clocks and had formulated a stable calendar. Vedañga Jyotisa is a continuation of the development of calendar science of the Vedic texts. Vedanga Jyotisa expresses the calendar concepts of the Vedic texts in mathematical form and introduces algorithms to compute calendar parameters significant to the Vedic ritualists. It also describes a (partial) ecliptic coordinate system to define the position of the moon and the sun. This coordinate system is not irregular divisions of the naksatras, as has been assumed up to now. With this coordinate system the algorithms of Vedañga Jyotia can be interpreted unambiguously, without it they are meaningless.
Prabhakar Gondhalekar graduated in physics from imperial College, London and obtained a Ph.D from University of London. He is an astrophysicist with major research interest in the interstellar medium and active galactic nuclei. He was formerly head of the Space Astronomy Group at the Rutherford Apleton Laboratory. he studied Sanskrit at the oriental Institute, Oxford University. His interest is in the study and analysis of Vedic texts
An obsession with time is one of the distinguishing characteristic of human beings. This obsession may have emerged with the realization of human mortality all life starts at birth and ends with death, and the sensation of passage of time is ever present during this period. As early humans became aware of the regularity of the rising and setting of the sun, the regularity of the phases of the moon, and the regularity of the seasons, they probably realized that it was possible to think of passage of time as an ordered process. This realization may have sparked numeration, mathematics and astronomy. The recognition of this ordered passage of time may have led early humans to identify, classify, and correlate the naturally occurring units of time, namely the day, month and the season. The fundamental unit of time is the day the period of rotation of the earth about its axis, or as common sense and observations dictate, the time taken by the sun to complete its journey and return to the ‘same’ point in the sky. Except in the polar regions, the alternating periods of light (day) and dark (night) mark the passage of a (lay. The month is the regularity of the waxing and waning of the moon. Similarly, the year is a complete cycle of seasons, the time taken by the earth to revolve around the sun in its orbit (or for the sun to move in a full circle against the backdrop of stars). The starting point of a day is well-defined; it is either sunrise or sunset. Similarly, the starting point of a month is also well-defined; it is either the new moon or the full moon. In ancient times, the beginning of the year was not so well defined: a year can be measured from one season to the same season the following year, but seasons do rot start on the same day each year. The recurring starting point of the next step in the evolution was determined after careful observation of the apparent motion of the sun across the sky and the identification of the two solstices and the two equinoxes. A very long period of careful observation and record-keeping must have preceded the recognition of these four cardinal days in a year.
A calendar is a system of organizing units of time for social, religious, agricultural, commercial, and administrative purposes. To achieve this it is necessary to identify the ‘clocks of nature’, classify and label the units of time defined by these clocks and synchronize these clocks. Most (but not all) calendars replicate astronomical cycles according to some fixed rules. The smallest calendar unit is the day (the measurement of fractions of a day is time-keeping). All calendars are based on the succession of days and nights, the waxing and waning of the moon and the rhythm of the seasons. The cycle of seasons controls the availability of food (a primary requirement for survival) for hunter-gatherers, pastoralists, and agriculturists. It is highly likely that the earliest calendar was the recognition and measurement of the duration of the seasons. The ability to count (by the number of days) the length of a season would have given the early man the ability to predict the time of migration of game or migration to pastures and for sowing and planting. The beginning and end of a season is not well defined as it depends on the local weather pattern and that can change in a random manner. However, a delay of a day or two in the start of migration, sowing or planting will not adversely affect a tribe or a village. The early man could thus have counted the length of seasons in integer number of days. It is impossible to guess of the calendar. It seems most likely that the early man attempted to group the number of days in a season in a unit of time larger than a day. For this, he turned to the second natural clock, the regular waxing and waning of the moon or the month (Box 1). At this stage, our ancestors would have encountered their first problem with the calendar the number of days in a lunar (synodic) month can sometimes be 29 and sometimes 30. When our ancestors measured the length of a year from a well-defined starting-point like the solstice or equinox or the heliacal rising of a star, as was done by the Egyptians and the Babylonians, they would have recognized the myriad of problems that plague the calendar. The number of days in a year is sometimes 365 and sometimes 366; there can be 12 new moons in a year but sometimes there can be 13. Twelve synodic (lunar) months account for approximately 354 days of the year, leaving a disconcerting deficit of about II or 12 days. It would have been apparent that there was not an integer number of days in a month, nor an integer number of days or months in a year. The history of calendars is man’s frustrated attempts to reconcile these three naturally occurring units of time or to synchronize these three naturally occurring clocks.
The calendar has been an indispensable requirement of human life for an awful long time; it has a pivotal role in formulating and regulating the religious, civic, agricultural and economic life of a society. A well-constructed calendar can also be a record of the chronology of a culture. Since the construction of a calendar requires the use of mathematics and astronomy and its use involves a level of sophistication, the calendar and its history provides an insight into the development of a culture. In India, varieties of calendars are in use today. The Calendar Reform Committee, appointed in 1952, identified more than thirty well-developed calendars (Saha and Lahiri 1992). The situation in Afghanistan and Pakistan is somewhat simpler as the Islamic calendar is the principal calendar in these countries. Owing to the continuity of South Asian culture and the diversity of cultural influences in the region, the history of the calendar in South Asia is an exceptionally complex subject. Absolutely nothing is known about the calendar of the Indus Valley Civilization that flourished in this part of the world from about 3000 to about 1300 BCE. The calendar of the Vedic culture that dominated the northern parts of South Asia from about 1500 to about 500 BCE, forms the subject of this book. The calendar of this period culminated in the calendar of Vedanga Jyotisa, the earliest extant codified calendar of South Asia. From 300 BCE onwards, there were increasing incursions into South Asia by people and cultures from the west and north. These contacts profoundly modified South Asian arts, sciences, sculpture, state-craft, and of course, the calendar. The calendar of Vedanga Jyotisa was gradually modified and eventually replaced. By about CE 400 it had disappeared from all parts of South Asia, leaving only traces in the new calendars that came into use.
In South Asia, an awareness of the order and periodicity of celestial phenomena is found in the oldest available Sanskrit text, namely Rgveda Samhitã. This awareness of the cosmic order is carried over into later Samhits and their associated Brhmanas. In the Rgveda Samhita the notion of a cosmic order is encapsulated in the concept of one of the great conceptions of early South Asian culture. This word, derived from the root r — to go (and with the suffix means ‘the correct order of going’ or the settled order; it encompasses the concept of both moral and physical world-order. Implicit in this is the idea of a dominant world-order of what is and what must be. The rta is conceived as absolute and eternal, impersonal in itself and entirely objective and mechanistic. It cannot be influenced in any way and both humans and gods have mandatory duties and functions under it. Events in nature that occur regularly are obedient to Ira or their regular occurrence is the ria. For example, dawn (usas) does not violate the heavenly ordinance/order (daivyani vratani) for each day she returns to her appointed place. The Vedic ritualists saw the calendar as a pare or an aspect of rta and in their ceremonies and observances, they attempted to emulate the cosmic order they saw in the sky. For example, they made offerings to gods from left to right in emulation of the path of the sun (as seen from locations north of Tropic of Cancer); this practice is seen in a number of present-day Hindu rituals. In the post-Rgvedic texts, the year is synonymous with both Prajãpati (Creator God) and yajña (sacrifice). The Vedic people identified the Creator God with phenomenal time and considered the year to have come into existence with Prajapati or through his creative activity—a numerical congruence is often noted; there are four syllables in both Prajãpati and samvatsara (year). Outside the year, there is nothing; in the beginning there was nothing, before the first creative act there was no year. Without the year, there are no natural processes. Like Prajapati, the year implies totality and completeness. The cosmic or the divine order was reflected in the rituals and ceremonies of the Vedic people; offerings were made everyday at sunrise and sunset, at every full and new moon, at the beginning of (at least three) seasons and the commencement of the northern and southern course of the sun, i.e. the solstices. The Vedic texts indicate that the daily rituals were (at least in part) performed to maintain a calendar, for example, the sattra (ceremony) of gavam ayana was performed for 360 days, the length of the Vedic ritual year.
The calendar of the Vedic period came under the scrutiny of the Western Sanskrit scholars from the time they became acquainted with Sanskrit texts. These scholars considered Vedanga Jyotisa, the earliest extant codified calendar text in South Asia (believed to have been composed around the middle of the first millennium BCE), to be the starting point of the calendar of this period. However, the earlier Vedic texts describe and justify the performance of yajnas (the ritual sacrifices). In South Asia, astronomy, geometryandmathematics were, at least partly formulated and developed to cater for the requirements of these yajñas. These rituals were performed at prescribed times and their performances presuppose a calendar. Therefore, a Vedic calendar must have existed long before Vedanga Jyotisa. In a seminal study in late nineteenth century, Diksita (1896) identified all elements of the calendar of Vedanga Jyotisa in these earlier ritual and sacerdotal texts. He also identified following fundamental elements of a calendar in the Rgveda Sainhita.
In addition, there are tantalizing clues to a stellar frame of reference (naksatros) to define the position of the moon. The final redaction of Rreda Samhita has been preserved with exceptional fidelity. The calendric parameters identified in this Sarnhita are, therefore, original and authentic to this text. There is not enough information in Rgveda Sarnhitã to reconstruct a calendar. However, it is possible to deduce that this is a lunisolar calendar incorporating various approximations. It is not clear if these approximations reflect the available measuring technologies, were introduced for ease of computations, or mirror the beliefs of the Vedic people. However, it is abundantly clear that the three ‘clocks of nature’ were identified for this calendar and a scheme was developed to synchronize these clocks. It is not possible to trace the origins of this calendar from the available Vedic texts but the sophisticated calendar of Rgveda Sarnhita, requiring astronomical observations over long periods, record-keeping, and computations, is more likely to have been developed in an urban culture rather than in a pastoral or semi-nomadic society. This conclusion is supported by the identification in this text of the quasi-synodic or ‘ideal’ year of 360 days and the intercalation of five days to synchronize this year with the tropical/seasonal year. This scheme of synchronization has been identified in the calendars of a number of ancient cultures, separated widely in space and time (N.Ill.9), and these are Bronze Age urban cultures and not nomadic or pastoral cultures. Although the fundamental elements of a calendar can be identified in the Rgveda Sarnhitã, this Samhita does not explicitly refer to the use of a calendar. The days and times at which rituals or ceremonies were performed are not given. This ambiguity is removed in the later texts in which the chronological markers like the position of the sun (that is, a season or a month) and the position and the phase of the moon among the stars, for performance of rituals, are unambiguously identified. The calendar of these texts is a development of the calendar of the Rgvedic Samhitã with the addition of following refinements:
• A fiducial season and month are defined for start of the tropical! seasonal year and the ritual year.
• The ‘length’ of a season is defined and the ‘date’ of the performance of the three seasonal sacrifices is identified by the coincidence of the full moon and predefined asterisms or nakcatras.
• Months are labelled by their seasonal characteristics and by asterisms or naksatras that conjoin twelve full moons in a year.
• Algorithms are given for intercalation.
• A greater degree of precision is introduced in the timing of the rituals and ceremonies by identifying the stars with which a phase of the moon should coincide for the performance of the ceremonies.
• The heliacal rising (and probably setting) of prescribed stars is used to determine the appropriate time for the performance of some rites.
• Time-keeping is explicitly introduced by dividing a day (sunrise to sunrise) into smaller time units.
In the post-Rgvedic texts, astronomers (naksatra darsa, TB.3.4.4) and mathematicians (ganaka) are mentioned, and a sacrificer is advised that in order to determine the correct time of a ceremony ‘he should either study astronomy, or ascertain the correct time from those who know it’. These texts describe both an arithmetic calendar and an astronomical calendar. In an arithmetic calendar, the synodic (lunar) year is synchronized with the seasons by simple but rigid arithmetic rules. The astronomical calendar, on the other hand, synchronizes the synodic (lunar) year with seasons by astronomical observations of the solstice, the new moon, the heliacal rising of specific stars, etc. The calendar that can be formulated from these texts is substantially the calendar described in Vedãnga Jyotisa. Not surprisingly, this text also describes an arithmetic and an astronomical calendar but the astronomical calendar of this text is different from the astronomical calendar of the Samhitãs and the Brahmanas. Moreover, Vedanga Jvotisa introduces a number of new and in particular mathematical concepts. Significantly, in this text the naksatras are not stars and asterisms, but are redefined as sectors of the ecliptic. These sectors may have been identified by naksatras (stars and asterisms) of the Samhitas and the Brähmanas but the absolute position (on the ecliptic) and width of the sectors are independent of naksatras. For calendar purposes, Vedanga Jyotisa defines the position of the sun and the moon within these sectors. The position of the sun with respect to the nksatras is not mentioned in the Sarnhitas and the Brahmanas and s original to Vedanga .Jyotisa. This text also introduces mechanical reans (clocks) for time-keeping.
A number of publications have explored the Vedic texts to show link between the Vedic calendar and calendar of the Vedanga Jyotisa. Others have asserted that the calendar of Vedanga Jyotisa has been almost entirely imported from sources outside South Asia and is a totally new development with no links to the South Asian past. In this book it is shown that there is an unbroken thread of development of the Vedic calendar from the Rgveda Samhita through the later Samhitas and their associated Brãhmanas and Sitras, culminating in the calendar of Vedanga Jyotisa. The history of this calendar is punctuated with a number of novel features, original and unique to South Asia. All civilizations and cultures are influenced by their neighbours and this would be true of the Vedic culture as well, but the analysis presented in this book demonstrates that there is no a priori reason to believe that, in its totality, the Vedic calendar was not a product of the cultures that flourished in South Asia.
The chronology of the Vedic culture has been a matter of contention since the time when Western scholars became aware of Sanskrit and in particular the Vedic texts. It has also been recognized, since this time, that astronomical references in these texts hold the promise of independent corroboration of chronology based on philological analysis. In the last decade of the nineteenth century and the first of the twentieth century, the astronomical significance of various passages of the Vedic texts and the dates that could be inferred from these passages, were subjects of intense speculation and debate. It is not the intention of this book to reopen this debate, but the analysis of the Vedic texts and the calendar derived from this analysis does lead to independent conclusions regarding the chronology of this period. The following four independent considerations suggest a date of 1400±300 Bcu:
• The visi.bility throughout the year of all seven stars of sapta rsis (constellation Ursa Major or Big Bear) from (mid) South Asian locations.
• The time of performance of the seasonal sacrifices defined by the coincidence of the season, the full moon and the prescribed naksatras.
• The time of start of a ynga defined by the heliacal rising and setting of a prescribed naksatra at the winter solstice.
• Cross correlation of the naksatra-sectors and the yogatãrãs of naksatra.
It is highly likely that around this time the New Year’s Day or the start of a yuga was moved from spring to the winter solstice. This analysis challenges the assumption and belief of (mostly) Western scholars and commentators that the Vedic people had only a crude calendar; that they were passive recipients of stellar astronomy (naksatras) and mathematical astronomy from West Asian sources, which they did not understand and were incapable of refining for their location. This analysis also does not support the high antiquity of ‘Indian astronomy’ favoured by some Indian scholars and commentators.
The calendar of the Vedic people, described in this book, is based entirely on the religious, liturgical and sacerdotal texts left to us by the Vedic culture. To put the Vedic calendar in a historic context, the complexities of the early history of South Asia are briefly described in Chapter I. The contentious ‘Aryan question’ is very briefly touched upon in this chapter. In addition, an opportunity is taken to briefly describe the Vedic texts from which the Vedic calendar is derived. A brief description of the geography and the current thinking on the chronology of these texts are given in this chapter.
The identification of the seasons is the foundational element of all calendars, and in Chapter II, the references to seasons in the Vedic texts are analysed to show that the Vedic people had identified and labelled the weather-system of the lands they occupied before the composition of the rcas (verses) of Rgveda Samhita. They moulded their classification to the requirements of their belief-system. Discussions over the last 150 years, of the seasons in the Vedic texts, are based on the belief that the climate of South Asia has been static for last 4,000 years and that the climate during the Vedic period was not particularly different from the present climate. Not a great deal of paleoclimatic data from South Asia is available at present, but enough is known to show that the assumption of a static climate of South Asia is false, and paleoclimatic data should be included in any future studies of the climate of the Vedic period. Chapter 111 describes the Vedic view of the heavens and how the ‘clocks of nature’ were identified and codified to establish the fundamental parameters of a calendar. The vexed question of intercalation in the Vedic calendar is addressed. It is shown that far from ‘no systematic intercalation scheme can be attributed to this (Vedic) period’ (Pingree 1970-80), the Vedic people had ‘experimented’ with a number of intercalation schemes. Mathematical interpretation of some passages of the Vedic texts suggests that a ‘perfect’ intercalation scheme may have been formulated. The importance of a calendar to the Vedic people is demonstrated by the fidelity with which they mapped their calendar onto the altars on which the ritual fire, which was fundamental to their belief-system, was lit.
The stellar frame of reference to chart the path of the moon (and later the sun) in the firmament reaches its full maturity in the post Rgvedic Samhits and the Brahmanas. This frame of reference, called the naksatras, is the subject of Chapter TV. It has been known for some time that, in the Vedic texts, the nakyatras can mean both the stars and sectors of the ecliptic. Nevertheless, almost all discussion has been about naksatras as stars; naksatras as sectors of the ecliptic, independent of the stars, have received no attention. It is shown in this chapter that a passage in Vedanga Jyotisa enables absolute (and invariant) coordinates of naksatra-sectors to be determined without reference to the stars. The division, in Vedanga Jyotisa, of the ecliptic into twenty-seven equal sectors to define the position of the moon (and the sun), is unique to South Asia.
An invariant coordinate system is essential to interpret unambiguously the algorithms of Vedanga Jyotisa. The algorithms of Vedanga Jyotisa are presented and discussed in Chapter V. These algorithms are mathematical expressions of the calendric concepts developed in the Sarnhitãs and the Brahmanas.
The analysis presented in Chapters IT to V suggests that the calendar of the Vedic Age can be divided into three broad overlapping periods; these are the RV-period, the post-RV-period and the VJ-period. Each period builds on the developments of the previous period but there were also unique developments in every period. The developments in each period and links to the following period are presented in Chapter VI.
The discussions in this book are based on the Vedic texts. The distance (in time) from the Vedic culture, the complexities of this culture and Vedic Sanskrit and the lack of understanding of these complexities makes interpretation of passages of Vedic text both difficult and not wholly unambiguous. The interpretation of the passages of the post-Rgvedic texts is marginally simple as the purpose of these texts is well defined. This is not so of Rgveda Samhita; the true purpose of this text has not been identified, as its contents are a complex of liturgical formulae, mythological tales, magic spells, and philosophical speculations. The verses of Rgveda Samhita that reinforce the discussions in this book are given in the Appendix. The available English translations and interpretations are also given in the Appendix. To allow for evolution in the understanding of Vedic Sanskrit and the Vedic texts, only translations made in the twentieth century are given. A number of verses referred to in this book have no published translations and translations of these verses in the Appendix are my translations, Some passages from the post-Rgvedic texts that are also deemed to be significant, are given in the Appendix. The reference to a passage in the Appendix is identified by ‘A’ followed by the chapter number and a serial number. Topics of relevance but not essential to the subject of this book are presented in the Notes. The notes relevant to the topic of a chapter are given at the end of the chapter. A Note is identified by ‘N’ followed by the chapter number and a serial number. A brief description of ritual and technical terms is given in the Glossary.
The primary purpose of a calendar is to identify days of civil, agricultural, religious or social significance. Thus, a calendar by its very nature should have predictive capability. In the past, passages in Vedic texts that have calendric significance were analysed in isolation and their predictive potential was rarely explored. Similarly, the astronomical observations implied in the calcndric passages were not interpreted in terms of concepts with which the Vedic calendar- makers would have been familiar. These explorations are only possible mathematically and these are presented in this book. It is hoped that this will not deter the lay reader, as every effort has been made to make this book comprehensible to the general reader and the simple description and the supplementary notes should guide a reader through unfamiliar terrain.
The people whose calendar is described in this book called themselves Arya. The word arya has been much abused in the West and has racial connotations. In South Asia, Urya used as an adjective means ‘noble, honourable’ and ãrya can also mean ‘those who maintain the world order by means of sacrifice and gifts’ (to the gods). In South Asia, the word arya has never been used to describe or define a race, and this tradition is followed here. Arya is not meant to indicate a distinct ethnic group but a group of people with common religious practices and a common spoken language (archaic Sanskrit). The rather cumbersome phrase South Asia (n) is used throughout this book because the usual practice of identifying the Vedic culture with India is geographically restrictive and incorrect. In the long history of South Asia; Afghanistan, India and Pakistan are recent constructs. The Indus and Vedic Civilizations are as much part of the heritage of the people of Afghanistan and Pakistan as they are of the people of India.
Brahma Sutras (79)
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