Mathomathis would like to present an article on: Yajnavalkya and the Origins of Puranic Cosmology By Author Subhash Kak Department of Electrical & Computer Engineering Louisiana State University Baton Rouge, LA 70803-5901, USA (May 30, 2018)

The prehistory of Puranic astronomy is not well understood. Although it is known that the Puranas contain very old material, some modern historians of astronomy have believed that the cosmology presented there has no Vedic antecedents. In this paper, we show that this belief is wrong, and a system similar to Puranic cosmology is described in the Vedic tradition. In the past few years a new understanding of the origins of Indian astronomy has emerged. In various publications, we have sketched a history of Indian astronomy from the earliest Vedic conceptions— as expressed in the astronomy of geometric altars to the classical Siddhantic astronomy. Meanwhile, the use of modern computer packages has made it possible to reexamine the astronomical references in the early texts. Although recent work showed that Puranic and Siddhantic astronomies have several common points, the origins of Puranic astronomy remained unclear. Here author presents Yajnavalkya’s cosmology from Brihadaranyaka Upanishad (BU) 3.3.2 which has hitherto escaped scholarly attention. We show that this cosmology has all the basic features of the later Puranic cosmology and so it may be viewed as the original source. The great Upanishadic sage Yajnavalkya is a major figure in the earliest Indian astronomy, that precedes Lagadha’s Vedanga Jyotisa. Elsewhere, we have noted that in the Satapatha Brahmana, Yajnavalkya speaks of a 95-year intercalary cycle to harmonize the lunar and solar years and he describes the non-uniform motion of the Sun. We showed that these were significant links in the early development of Vedic astronomy. The 19th century European Indologists tended to assign him to around 800 B.C., but a reexamination of the evidence suggests that he should be assigned to around 1800 B.C. However, the chronology of Yajnvalkya is not our concern here, so will not

Vedic and Puranic Cosmological Ideas: In brief, the Vedas take the universe to be infinite in size. The universe is visualized in the image of the cosmic egg, Brahmanda. Beyond our own universe lie other universes. The Pancavimsa Brahmana 16.8.6 states that the heavens are 1000 earth diameters away from the Earth. The Sun was taken to be halfway to the heavens, so this suggests a distance to the Sun to be about 500 earth diameters from the Earth. Yajurveda, in the mystic hymn 17, dealing with the nature of the universe, counts numbers in powers of ten upto 1012. It has been suggested that this is an estimate of the size of the universe in yojanas. The Puranas provide material which is believed to be close to the knowledge of the Vedic times. Here author specifically considers Vayu Purana (VaP), Vishnu Purana (ViP), and Matsya Purana (MP). VaP and ViP are generally believed to be amongst the earliest Puranas and at least 1,500 years old. The Puranas instruct through myth and this myth making can be seen in their approach to astronomy. For example, they speak of seven underground worlds below the orbital plane of the planets and of seven “continents” encircling the Earth. One has to take care to separate this imagery, that parallels the conception of the seven centers of the human’s psycho somatic body, from the underlying cosmology of the physical universe of the Puranas, that is their primary concern in their Jyotisha chapters. The idea of seven regions of the universe is present in the Rigveda 1.22.16-21 where the Sun’s stride is described as saptadhaman, or taking place in seven regions. The geography of concentric continents is a representation of the plane of the Earth’s rotation, with each new continent as the orbit of the next “planet”.

The different Puranas reproduce the same cosmological material. There are some minor differences in figures that may be a result of wrong copying by scribes who did not understand the material. In this paper, we mainly follow ViP. ViP 2.8 describes the Sun to be 9,000 yojanas in length and to be connected by an axle that is 15.7×106 yojanas long to the Manasa mountain and another axle 45,500 yojanas long connected to the pole star. The distance of 15.7 million yojanas between the Earth and the Sun is much greater than the distance of 0.46 million yojanas used by Aryabhatta in his Siddhanta. (But note that the yojana of the Puranas is different from the yojana of the Siddhantas) This greater distance is stated without a corresponding change in the diameter of the Sun. The size of the universe is described as 500 million yojanas. In VaP 50, it is stated that the Sun covers 3.15 million yojanas in a muhurta. This means that the distance covered in a day are 94.5 million yojanas. MP 124 gives the same figure. This is in agreement with the view that the Sun is 15.7 million yojanas away from the Earth. The specific speed given here, translates to 116.67 yojanas per half-nimes. Author have argued that the speed of 2,202 yojanas in half-nimes. a mentioned by Sayana, may have emerged from the theory that light should travel at a speed that is able to illuminate the entire universe in one day. The size of the universe is described in two different ways, through the “island-continents” and through heavenly bodies.

The planetary model in the Puranas is different from that in the Siddhantas. Here the Moon as well as the planets are in orbits higher than the Sun. Originally, this supposition for the Moon may have represented the fact that it goes higher than the Sun in its orbit. Given that the Moon’s inclination is 5◦ to the ecliptic, its declination can be 28.5◦ compared to the Sun’s maximum declination of ±23.5◦. This “higher” position must have been, at some stage, represented literally by a higher orbit. To make sense with the observational reality, it became necessary for the Moon is taken to be twice as large as the Sun. A point of note is that this model effectively assumes that all the heavenly bodies go around the Sun.

Table 1: Earth To Pole Star

Interval I Yojanas
Earth To Sun 15,700,000
Sun To Moon 100,000
Moon To Asterisms 100,000
Asterism To Mercury 200,000
Mercury To Venus 200,000
Venus To Mars 200,000
Mars To Jupiter 200,000
Jupiter To Saturn 200,000
Saturn To Ursa Major 100,000
Ursa Major To Pole Star 100,000
Sub Total 17,100,000

Further spheres are postulated beyond the pole-star. These are the Maharloka, the Janaloka, the Tapoloka, and the Satyaloka. Their distances are as follows:

Table 2:  Pole Star To Satya Loka

Interval II Yojanas
Pole Star To Mahar Loka 10,000,000
Mahar Loka To Jana Loka 20,000,000
Jana Loka To Tapa Loka 40,000,000
Tapa Loka To Satya Loka 120,000,000
Grand Total 207,100,000

Since the last figure is the distance from the Earth, the total diameter of the universe is 414.2 million yojanas, not including the dimensions of the various heavenly bodies and lokas. The inclusion of these may be expected to bring this calculation in line with the figure of roughly 500 million yojanas. Or, it is more likely, that the universe is taken to be egg-like in shape, as suggested by the name of Brahmanda, the world-egg. Beyond the universe lies the limitless Pradhana, that has within it countless other universes. These other universes were visualized to be independent world-eggs. The geography of the Puranas describes a central continent, Jambu, surrounded by alternating bands of ocean and land. The seven island-continents of Jambu, Plaksa, Salmala, Kusa, Kraunca, Saka, and Pushkara are encompassed, successively, by seven oceans; and each ocean and continent is, respectively, of twice the extent of that which precedes it.

It is important to realize that the continents are imaginary regions and they should not be confused with the continents on the Earth. Only certain part of the innermost continent, Jambu, that deal with India have parallels with real geography. Although, in earlier work author have provided the context on the non-orthodox interpretation that the doubling of the dimensions applied to the “oceans” as well as “continents”, author returns to the orthodox view here, where the increase in dimension by a factor of two is only across the seven “continents.” At the end of the seven island-continents is a region that is twice the preceding region. Further on, is the Lokaloka mountain, 10,000 yojanas in breadth, that marks the end of our universe. The Lokaloka mountain can be compared to the shell of the world-egg. Assume that the radius of Jambu is Jr yojana, then the radius of the universe is:

Ur = Jr(1+1+2+2+2^2+2^2+2^3+2^3+2^4+2^4+2^5+2^5+2^6+2^6)+10, 000 –> (1)
Ur = 254 Jr + 10, 000 yojanas –> (2)

If Ur is roughly 250 million yojanas, then Jr should be about 1,000,000 yojanas.

The Orbit of the Sun: Since the Sun’s axle is taken to have dimensions of 15.7 × 106 yojanas, let’s see where exactly it will fit into the island-continent scheme. This is clear when we see that: 15.7 × 106 ~= Jr(1 + 1 + 2 + 2 + 4 + 4) –> (3). In other words, the orbit of the Sun will be somewhat beyond the Salmala continent. Since the total radius of the Universe is roughly 254Jr, it means that beyond the roughly 14Jr orbit of the Sun, there is present an approximately 16-fold expansion.

Yajnvalkya in Brihadaranyaka Upanishad:

Given the background of the Puranic system, we are ready to examine the
statement by Yajnavalkya in Brihadaranyaka Upanishad (BU) 3.3.2. He says:

dvatrim satam vai devarathahnyanyayam lokastam samantam prthivi dvistavatparyeti tamsamantam prithivi dvistavatsamudrah paryeti

Thirty-two times the space traversed by the Sun’s chariot in a day makes this plane (loka); around it, covering twice the area is the world (prithivi); around the world, covering twice the area, is the ocean. (4); This describes a system where beyond the Sun’s orbit there is an expansion by a factor of 32; further beyond that there is doubling of the area in the dimensions of the “Earth” and a further doubling in the dimensions of the ocean beyond. In other words, there is a total expansion by a factor of 128 beyond the Sun’s circuit. Notice that it is essentially the Puranic system in a simplified form. Like the Puranic system, the land-mass and ocean alternate, increasing by a factor of 2 for each land-mass, although there is explicit mention in this passage of just one such region. A second region is the ocean just beyond the Earth and other similar regions are suggested by the Rigvedic reference. Yajnvalkya, collapses several steps by considering 32 times the space traversed by the Sun, multiplied by another factor of 4, to be the Earth’s plane. This system retains the idea of alternating land and water.

Expansion by Factor of 32: Assuming that the seven continent-ocean scheme is meant by the saptadhaman of the Rigveda, Yajnavalkya, must use it in defining the plane that is 32 times the space traversed by the Sun’s orbit. Since beyond this space lie just one continent with the corresponding ocean (of double the area), the last continent must be Pushkara. Since these two last regions have a combined size of 128Jr, this plane must be at a distance of 126Jr from the center of Jambu. Let the orbit of the Sun be at a distance of Sr from the center of Jambu. Since (4) does not make it absolutely clear whether the phrase “space traversed … in a day” simply defines the circuit of the Sun, or whether one should multiply this circuit by 2, we consider both these possibilities separately.

  • In the first case, 32Sr = 126Jr, which means that Sr ~= 4Jr. Or the circuit of the Sun is just beyond the second continent Plaksa.
  • In the second case, 2π × 32Sr = 126Jr. Or Sr ~= 0.627Jr.

In this latter case, only a part of the Jambu continent is the Earth, and most of it represents the atmosphere. If one were to assume that Yajnavalkya knew that Jr was approximately 1,000,000 yojanas, the radius of the Sun’s orbit will then be 4,000,000 yojanas or 626,000 yojanas, respectively. It is noteworthy, that the Siddhantas use a figure which is not too different from the latter one.

Conclusions: The model of the universe described by Yajnavalkya in Brihadaranyaka Upanishad (BU) 3.3.2 appears to be the prototype that led to the full-fledged Puranic system. The two systems share essential features of area doubling and alternating land and water masses. There are some difference of details, however. The Puranic system seems an expansion of the Sun’s circuit by a factor of 16. On the other hand, in Yajnavalkya’s system the expansion is by a combined ratio of 128. If it is assumed that Yajnavalkya knew the dimensions of the continent and ocean scheme, the size of the orbit, in one of the interpretations, comes out to be 626,000 yojanas, which is only slightly larger than the number used in the Siddhantas. This suggests that Yajnavalkya’s scheme was the model from which both the mature Siddhantic and Puranic systems emerged. Even if Yajnavalkya did not use the same dimensions as the later Puranic astronomy, the structural similarity of the two systems is striking. Author finds that Yajnavalkya’s scheme moved the Sun closer to the Earth, compared to the earliest Vedic scheme where the Sun was right at the center of the cosmos. It is interesting, nevertheless, that Yajnavalkya projects the Sun’s circuit, through his multiplication factor of 32, to this middle point. The mature Puranic system involves an increase in the size of the Sun’s orbit, compared to Yajnavalkya’s scheme. Yajnavalkya’s description of the nature of the cosmos solves a longstanding puzzle regarding the origin of the Puranic system.


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