Tag: Indian Mathematics

  • Ancient Indian Astronomy: Time Keeping in the Vedic Age

    Ancient Indian Astronomy: Time Keeping in the Vedic Age

    Introduction: The Sky as a Laboratory

    Astronomy has been an integral part of Indian culture since the Vedic period (~1500 BCE). The Vedic astronomers studied the skies and celestial patterns to calculate directions, distances, seasons, and even agricultural cycles.  Astronomy or Jyotiṣa is even considered one of the six Vedāṇgas, which are the essential subjects for understanding the Vedas, the other being phonetics, ritual, etymology, grammar, and metrics. The Vedas themselves have numerous mentions of heavenly bodies, making ancient Indian astronomy very crucial.

    Time was also a very important aspect for the Vedic people, so much so that it was considered that the time (prajāpati) itself created the Vedas.

    In this blog post, we are going to discuss the most important aspects of Vedic astronomy. We will also discuss how timekeeping was crucial at that time, which slowly gave birth to the Indian scientific thinking, leading to numerous mathematical and scientific discoveries in the later period.

    Codifying the Stars: Astronomical Texts

    The works of Vedāṇga Jyotiṣa are generally attributed to the Vedic astronomer, Lagadha. Two of its most important textual editions are Ārcajyotiṣa (associated with the Ṛk Veda) and the Yājuṣajyotiṣa (associated with the Yajur Veda). The former contains 36 verses, and the latter contains 43 verses describing timekeeping units like months, seasons, days and nights, equinoxes, solstices, etc. They also mention terms specific to ancient Indian astronomy and cosmology, like yuga, tithi, etc.

    A yuga is a five-year cycle, which acts as a reconciliation between the solar year (~365 days) and the lunar cycle (12 lunar cycles approximate to about 354 days). Thus, in Vedic systems, the passing of a yuga denoted that the sun and moon had returned to almost the same initial positions.

    A tithi is 1/30th of a lunar synodic month. A synodic cycle is the time taken by the moon to return to the same phase, which is around 29.5 days. 

    The texts also mention 6 Indian seasons or ṛtus: spring, summer, monsoon, autumn, pre-winter, and winter.

    Apart from the longer time scales, the Vedāṇga Jyotiṣa also mentions shorter units like muhūrttas and kālas. The former is 1/30th of a day (48 minutes) while the latter is 1/603rd of a day.

    The Vedic people used these scales not only for their daily needs but also for detailed ceremonial activities, which required geometric precision. Altars for sacrificial pyres were designed with their geometry aligned to the time scales and positions of celestial objects, as mentioned in the mathematical and ritualistic texts called the Śulbasūtras.

    In the 10th chapter of the 3rd book of the Taittirīya Brāhmaṇa, a text within the Yajur Veda, a ritual called Sāvitrāgnicayana is mentioned. In it, 185 bricks need to be piled in concentric circles to form an altar. Each brick is named after a particular unit of time, like the 12 months, 24 fortnights, days and nights separately in each fortnight, muhūrttas, and even muhūrtta-muhūrttas (~3.2 minutes).

    Mapping the Lunar Path: The Nakṣatra System

    Nakṣatras were very important in ancient Indian astronomy. They are fixed divisions or coordinates that track the Moon’s position against the background of fixed stars. The moon takes around 27.31 days to return to the same position against the fixed stars. Thus, the entire cycle was divided into 27 nakṣatras, each spanning 13°20’ of the sky.

    Texts like the Taittirīya Saṃhitā and Śatapatha Brāhmaṇa mention these 27 nakṣatras, while some texts, like the Atharva Veda, also mention a 28th one (named Abhijit).

    They were also mentioned in the Vedāṇga Jyotiṣa texts, as a yuga begins and ends when the sun and the moon are within a particular nakṣatra coordinate.

    Beyond the astronomical role, each nakṣatra was associated with a presiding deity and formed the basis for ritual timing, guiding decisions related to sacrifice, travel, and other activities.

    They also acted as a natural seasonal calendar, as the position of the sun in a particular nakṣatra denoted a particular season or other yearly events, like the transition of the sun’s path northward or southward, called uttarāyana and dakṣināyana, corresponding to the solstices.

    Nakṣatras later became the foundation for the establishment of Indian astrology. After integrating with Greek astronomy, they helped in developing the Rāśis (Indian Zodiacs).

    Conclusion: The Dawn of Indian Science

    Vedic astronomy was the first step toward the gigantic leap that was about to come in later Indian scientific history. In the later Vedic period, this knowledge helped scientists and philosophers of the time to argue and discuss various concepts like space (ākāśa), sound (śabda), and atoms (anu).

    During the golden age of India (300 to 700 CE), ancient indian astronomy was integrated with arithmetic and trigonometric functions by scientists such as Āryabhaṭa and Varāhamihira to take Indian science to a different level, which we will discuss in another blog in this history of Indian science series.

    That’s all from this blog. In the next blog, we will travel to the later Vedic age to see how physics in India was slowly being born, with the synthesis of philosophy, mathematics, and astronomy.

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  • History of Indian Science: Space, Matter, and Time

    History of Indian Science: Space, Matter, and Time

    Introduction

    The history of Indian civilization is about six millennia old. The civilization has a rich cultural, societal, and intellectual history. In this blog series, we are going to dive deep into the evolution and history of Indian science, particularly in physics and astronomy. We begin from the Vedic period and journey through the classical age, medieval period, and finally to the modern era.

    The Timeline of the Evolution

    The journey of Indian physics began with Vedic astronomy and timekeeping, which conceptualized the early astronomical patterns like Nakṣatras, necessary for ritual calendars. In the later Vedic age, natural philosophy emerged along with an understanding of concepts like space (ākāṣa) and sound (ṣabda).

    India also developed its own school of atomism, Vaiśeśika, and introduced the concept of the atom (anu). Astronomy, combined with new mathematical inventions like zero and the decimal system, gave rise to scientific texts called siddhāntas. Later, the intellectual exchanges with the Greeks led to parallel developments in science and philosophy in both cultures.

    The history of Indian science was at its peak during the Gupta period, when scientists like Āryabhaṭa and Varāhamihira introduced new theories like trigonometric functions, calculation of eclipses, and the rotation of the Earth, leading to a golden age. Polymaths like Brahmagupta and Bhāskara II contributed to mathematics and astronomy, leading to early ideas of motion and gravity centuries before Newton.

    The Kerala School of Mathematics and Astronomy in medieval India introduced various infinite series and proto-calculus ideas, which evolved through generations into the modern era. Science, particularly physics, in India today, is thus a beautiful amalgamation of thousands of years of traditional research with the discoveries and inventions of modern science and technology.

    Conclusion

    This was a small introduction to the history of Indian science, and the successive blog posts will cover its various important phases. I hope you will appreciate the series and reflect on the evolving nature of the Indian scientific spirit. 

    That is all. Please comment, share, and subscribe to my newsletter below if you find this project interesting and want to be notified in the future. Thank you.