Part 2.2.5 - Peculiarities of Gaṇita (calculations)

[Full title: Classification of Jyotiḥśāstra (1): Gaṇita of the Veda and the Vedāṅga Period (4): Peculiarities]

Vedāṅga Jyotiṣa a text on Gaṇita exists as the first extant one of this period sought especially for sacrifices to be carried on the parvasandhis.^[1] The study of parvans advanced in the Veda and the Vedāṅga period to the extent that refined observations as eclipses occurred at the end part of the parvan was acknowledged in this period.

The Sūryaprajñapti a contemporary and later text which displays a similar astronomical pattern to Vedāṅga Jyotiṣa furnishes the concept of Mount Meru, placed at the centre of the Earth which obstructs the light of the heavenly bodies moving parallel to the surface of the Earth. It offers that centre’s of the orbits of heavenly bodies are at the Meru and that Sun revolves round mount Meru at the same height (from the plane of Earth) but at different distances from Meru. These and such calculations based on a centralized Meru reveals that Gaṇita (calculations) of the Veda and the Vedāṅga period rests on an ideological quarter rather than an actual one.

This notion of Meru appears in a generalized form in the Purāṇa literature which make Meru as a dwelling place of the gods.^[2] Even Bṛhat Saṃhitā XXIV.2. mentions the grove of Mount Meru, as the abode of the Devas for which were displayed the laws of the Rohiṇi Yoga by Nārada to Bṛhaspati and later by the astrological teachers to their disciples.

Post-Greek Astronomers like Āryabhaṭṭa and Brahmagupta also comment on mount Meru. Āryabhaṭṭa mentions that Meru had no absolute height. Such reference retained the character of Jyotiṣagaṇita even after the advent of the Greek additions as pursuing the conventional idea of calculations of a region or a cosmic point which was perhaps without an astronomical base and which followed or was secondary to answer or implement an idea rooted in another quarter of the culture.

After the Veda and the Vedāṅga period there is a dark age in the development of Jyotiḥśāstra inclusive of the Gaṇita branch in which lie works like Arthaśāstra (2.20) and Śārdūlakarṇāvadāna (Divyāvadāna 33) which display Gaṇita similar to the Vedāṅga Jyotiṣa but these are not exclusively based on Gaṇita.

A striking feature of the Gaṇita up to this period is that it, calculate the mean longitudes of the Sun and Moon with reference to the Nakṣatras and there is an absence of mention of planets and the zodiacal signs. Also if Vedāṅga Jyotiṣa is a text on Gaṇita it is chiefly a text on Jyotiṣa in both senses as a representation on the earlier form of Jyotiṣa as well as of its purpose. It can be termed as a pioneer of the later Siddhāntas and can be termed as the first of Siddhāntas being the only one on Gaṇita in the known history of the Veda and the Vedāṅga period. Yet it starkly differs from the Siddhāntas as they neither carry the form nor the purpose of Jyotiṣa in its complete and true sense.

The phase between the two main astronomical periods, the Veda and the Vedāṅga period and the Siddhānta period can be perhaps in this sense termed as a dark age in which there is no clear evidence which reveals the collapse of the facade of Jyotiṣa Gaṇita of the prior period and the emergence of the latter one.

Footnotes and references:

[1]:

Vedāṅga Jyotiṣa (Ṛgveda-saṃhitā) verse 3.

[2]:

Matsya Purāṇa 11.37-38; Padma Purāṇa V. 8.72-73.