India has been a cradle not only to refined civilizational best-practices but also to multitudinous scientific developments. Evidence and knowledge of voluminous literature produced in Indian scientific pursuits has been well established by serious researchers. In contrast, there is prevalent ignorance about facts and feats that we have inherited.
Awakening Indians to Indian Sciences is important to build a better perspective about this land and its people, to own up to what is truly ours and align our actions in coherence with the vision and momentum set forth by the great Jnanis of our civilization. As we protect, preserve and celebrate various temples, monuments, artefacts and places of historic eminence, so too, we must preserve and protect intellectual breakthroughs in our Indian traditions through awareness, assimilation and dissemination.
Through a series of short articles, may we enlighten ourselves in a few “must-know” aspects about our rich scientific heritage. We set forth to cover a few highlights in the development of Jyotiṣa (Astronomy) and Gaṇitā (Mathematics).
Understanding the Origin
The science of Astronomy — Jyotiṣa has fascinated humans from earliest times and regarded by many as the earliest of all sciences . It has been put to use in a variety of ways by people of all walks of life including farmers, travellers, traders, administrators, calendar-developers, historians, fortune-tellers, priests, artists, philosophers and many others. The motivation ranges from mundane purposes such as keeping time, to navigation, to understanding issues of human survival, to interpreting the universe and our place in it.
In India, one can find examples of astronomical ideas all the way from rock art and megalithic structures, to codified mantras in the Vedas describing certain astronomical phenomena, to computational astronomy described in the Siddhāntas, to one of the world’s largest pre-telescopic observatories. This sheer breadth of variations one can see, makes it nearly impossible to keep track of in its entirety. Many of these contributions were path breaking and often crucial to the development of astronomy the world over.
Three Key Eras
In the chronology of literature we find that Jyotiṣa precedes Gaṇitā and the latter’s development was happening in parallel until becoming a separate field of study itself. And in many cases, aspects of Gaṇitā were embedded within works of Jyotiṣa. Over time, exclusive literature of the various sub-topics of Gaṇitā were brought forth.
Since their development has been in parallel impacting each other mutually, we shall also look at them in parallel over the ages. The development of both these fields can broadly be put in three eras:
Vedic or Pre-Siddhantic Era (1400–500 BCE) [some studies date further back to 2500 BCE as the origin]
Siddhantic or Classical Era (400‑1200 CE)
Post-Siddhantic or Medieval Era (1200–1850 CE)
In this series too we shall traverse through this chronology to bring out various salient Indian advancements in these sciences.
Jyotiṣa in the Vedic Era
Astronomy found in the vedic saṃhitās, brāhmaṇas and allied literature reveal India’s roots in the long running pursuit of excellence in Jyotisha & Gaṇitā. For the performance of the vedic sacrifices at the times prescribed by the śāstras, it was necessary to have accurate knowledge of the science of time.
Astronomy in those times was essentially the science of time-determination. It centred round the Sun and Moon and its aim was to study the natural divisions of time caused by the motion of the Sun and Moon, such as days, months, seasons, and years, special attention being paid to the study of the times of occurrence of new moons, full moons, equinoxes, and solstices.
There are many fascinating aspects of Astronomy well-known during this foundational period of our civilization. The following is not an exhaustive list. But it is intended to bring out many interesting facts:
The Moon is called Sūrya-raśmi. It means “one which shines by sunlight” (Taittirīyasaṃhitā 3.4.7.1). This sheds light on the fact that in the Vedic era we knew that the moon was not a self-illumined body.
The dependence of Moon’s phases on its elongation from the Sun is implicit in a description in Śatapatha-brāhmaṇa. 1.5.4.18–20. The Moon’s path was divided into 27 or 28 equal parts, because the Moon took about 27&1/3 days in traversing it.
Taittirīyabrāhmaṇa (1. 5. 1; 3. 1. 1–2; 3. 1. 4–5) give the names of the 28 nakṣatras along with Abhijit (Lyra). The Śatapathabrāhmaṇa (10. 5. 4. 5) gives the names of the 27 nakṣatras as well as those of the 27 upa-nakṣatras.
Constellations other than nakṣatras well known in Ṛgveda(1.24.10; 10.14.11; 10.63.10) are Ṛkṣas(Great & Little Bear), 2 divine Dogs (Canis Major & Minor) & the heavenly Boat (Argo Navis). Great Bear is Saptarṣi in Śatapatha-brāhmaṇa(2.1.2.4) & Tāṇḍya-brāhmaṇa(1.5.5)
The Aitareya-brāhmaṇa(13. 9) mentions the constellation of Mṛga or Deer (Orion) and the star Mṛgavyādha (Sirius).
ulkā (meteors) and dhūmaketu (comets) have been mentioned in the Atharvaveda (19. 9. 8–9, 19. 9. 10).
Eclipses have been mentioned and described as caused by Svarbhānu or Rāhu. The Ṛgveda (5. 40. 5–9) describes an eclipse of the Sun as brought about by Svarbhānu.
The names of the lords of the week days stated in Atharva-jyautiṣa are: Āditya (Sun), Soma (Moon), Bhauma (the son of Earth), Bṛhaspati, Bhārgava (the son of Bhṛgu), and Śanaiścara (the slow-moving planet). Many scholars have ascertained the origin of naming the days of a week is of Indian origin.
The Vedāṅgajyotiṣa (~500 BCE), is the earliest Hindu work dealing exclusively with astronomy. The Vedāṅgajyotiṣa has come down to us in two recensions, viz. the Ṛgvedic recension (called Ārca-jyotiṣa) and the Yajurvedic recension (called Yājuṣa-jyotiṣa). Their verses clearly give India’s calendrical system and account of months, years, days and day-divisions, nakṣatras, new moons and full moons, solstices, and seasons occurring in the cycle of five solar years.
In the following edition, we will delve into the development of mathematics that had happened in parallel during the Vedic periods.
Aum Tat Sat!