Talk:Aryabhatiya

I'm doing a biographical research paper on Aryabhata right now, and one of the books I have in front of me says that there are 121 verses in Aryabhatiya. I'll just make the change.

Heliocentrism

I have flagged the following passage with {{Fact}}:

The treatise presents astronomical and mathematical theories which advocate Heliocentrism, where Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun (in other words, it was heliocentric).

There are two different questions raised here:

• Whether the Aryabhatiya describes the Earth's rotation on its axis.
  • If so, a simple quotation of the appropriate text, and appropriate modern scholarly commentary, is all that is needed.
  • This, of course, does not imply heliocentrism, which is another issue.
• What is the relationship between heliocentric planetary periods and the claim for physical heliocentricity.
  • How does this relate to the Aryabhatiya's use of a traditional Indian double epicycle model -- which pretty well rules out heliocentrism. (Pingree, "Astronomy in India," in Christopher Walker, ed., Astronomy before the telescope, 1996, pp. 133-5)
  • In this context, quotations of appropriate texts supplemented by modern scholarly commentary on them would be essential to justify this extraordinary claim.

Could someone who has the sources at hand deal with these issues? Thanks. --SteveMcCluskey 22:16, 27 May 2007 (UTC)

I've answered my own question by tracing down a source for this theory to a 1970 publication by B. L. van der Waerden. This book was given a lengthy critical review in Isis by the historian of astronomy, Noel Swerdlow and briefly dismissed by the late David Pingree in his "The Greek Influence on Early Islamic Mathematical Astronomy," Journal of the American Oriental Society, 93 (1973: 32-43 (at p. 32, n. 1).

Given the rejection of this view by two leading western experts on the history of Indian astronomy in two leading journals, the concept of Indian heliocentrism should be treated as a minority fringe opinion and does not deserve an important place (if any) in this and other articles on Indian astronomy. --SteveMcCluskey 15:20, 29 May 2007 (UTC)

Continuation

The text on heliocentrism is still problematic. Van der Waerden does not suggest that the Āryabhaṭīya "advocates" heliocentrism, neither does Thurston. Neither source says that "According to this view, it was heliocentric". What those sources do say is that certain aspects of Aryabhata's geocentric model were (maybe) influenced by an unknown heliocentric model. Swerdlow, who is one of the sources for this text, specifically rubbishes Van der Waerden's speculation (which I imagine is the source for Thurston's comment about glimmerings of heliocentricism). The cherry picked quote, inserted to bolster(?) heliocentrism, is also worthless, why not insert other quotes like, "Beneath the asterisms are Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon, and beneath these is the Earth situated in the center of space like a hitching-post." --92.4.166.21 (talk) 04:18, 17 July 2012 (UTC)

Paragraph on Yaqub ibn Tariq

There was a paragraph on Yaqub ibn Tariq in which it was stated that he produced a Zij based on Aryabhata's work, and that he gave estimates for planetary distances based on Aryabhata's system of elliptic orbits. I removed this as (1) Aryabhata's orbits were not elliptical (he used circular orbits together with two circular epicyclic corrections; see e.g. Hugh Thurston's book Early Astronomy, ISBN 038794107X, pp. 178-189 for an overview of his systems), (2) ibn Tariq's source for his Zij was not the Aryabhatiya but later works, while the source for his planetary distance estimates is not known (see e.g. [1], "The Fragments of the Works of Yaʿqūb Ibn Ṭāriq", David Pingree, JNES 27, 97–125, at 97, 105-109) and so this seems not relevant here. Spacepotato (talk) 23:45, 3 May 2010 (UTC)

Image of text

I believe that this article would be much improved by including a section on the provenance of the text (i.e., what physical copies do we have of the Aryabhatiya and where did they come from) and an image of the oldest know copy. —Preceding unsigned comment added by Jfgrcar (talk • contribs) 18:20, 9 October 2010 (UTC)

Earth's circumference

One question. Here's the translation of the original text, and I can't find in it where Aryabhata explains the circumference of Earth. Where is it? BigSteve (talk) 09:54, 6 May 2014 (UTC)

Right, Ive found it - it's not in the chapter relating to Earth, where all the mathematical formulae are located, but it's just a throwaway claim in the preliminary section, verse 5, with no supporting mathematical workings. The actual quote is "a yojana is 8000 times the height of a man, and Earth's diameter is 1,050 yojanas." Now, how we got from there to the article's claim that "Aryabhata accurately calculated the Earth's circumference as 24,835 miles, which was only 0.2% smaller than the actual value", I have no idea. (What, "the height of a man" is an SI unit of measurement all of a sudden, is it? Even current estimates of a yojana apparently vary from between 8 km and 14 km! Which is perfect if you want to fit your workings to a pre-conceived conclusion.) And then you research it and you see that this false claim is getting repeated all over the internet. I'm a fan of non-Euro-centrism and all, but this is just wrong. BigSteve (talk) 11:06, 6 May 2014 (UTC)

Ugh. I've removed it. It's quite a struggle to make sure these articles are accurate. The closest I could find is some book saying that "if a yojana is taken as 5 miles, this is [...] 24835 miles", which isn't true either (we need about 7.5 miles AFAICT). By the way, you don't have to be taken aback by "the height of a man" being used as a unit; there's loss in translation, and consider the still-used units like "feet". Shreevatsa (talk) 15:04, 6 May 2014 (UTC)

You're right, I assume back in his day it had a specific standardized size (which works out to about 1.51 metres if we're to fit it to current calculations for the circumference of Earth). What I meant was we have no reference to how it translates to any modern measurement systems. It's a shame he didn't include the workings for this in the later chapter on cosmology, I guess he must have had them somewhere in another work but they've got lost over time? BigSteve (talk) 15:22, 6 May 2014 (UTC)

Yes, perhaps there was more detail in another work of his that got lost, or perhaps no such work was composed at all, and these details were only orally transmitted to students. Many important works of the Indian tradition were composed in the sutra style, which means that the work as such is not expository by itself, but rather a sort of crisp, easy-to-memorize mnemonic aid (this is why, for instance, the Aryabhatiya is entirely in verse), for a teacher in the tradition to teach along to (a "course outline" of sorts). Often other authors (or even sometimes the same author) would compose a "commentary" on the sūtra work with more detail. In the case of the Aryabhatiya, just the commentary by his student (or student of student) Bhaskara I amounts to about 400+ pages for the 33 verses in the chapter!

So I guess, unless some commentary goes into that detail (because I'm not aware of any "autocommentary" by Aryabhata himself), we don't have a translation into modern measurement units. But the average height of men in India seems to be about 1.65 m today, and perhaps a bit lower back in his day, so if his unit was anywhere close to that value, his estimate of the earth's diameter is probably within about 10% of the true value, and I'm not sure it's possible to be more precise than that — the 0.2% claim is surely an exaggeration. Shreevatsa (talk) 16:16, 6 May 2014 (UTC)

That's interesting, hadn't thought of that, that it was mainly in verse for memorization purposes. I know Sanskrit was being written by that time, but the tradition of verse was probably still quite entrenched. Nice one! BigSteve (talk) 10:01, 7 May 2014 (UTC)