Varuna,

varuna2 wrote:Dieter,

I found the passage that Martin taught me, but someone else will have to state where this is found in Ptolemy's works.

"of the twelve signs the most northern, which are closer than the others to our zenith and therefore most productive of heat and of warmth are Cancer and Leo"

I guess it states the zenith rather than solstice, but I think this means the same, so it is merely semantics.

Yes, it means the same. This is the passage I meant and I do not know of another one.

I believe Ptolemy just made a thinking error. Tropical Cancer and Leo are the hottest time of the year, and that may have been the actual reason (according to some ancient theory that Ptolemy refers to) why these signs were assigned the Sun and the Moon as rulers. (Tetrabiblos 1.17)

Dieter

dieterkoch wrote:After looking into Shukla and the Sanskrit text, I feel that Shukla is partly right and Pingree in error. In the crucial verses 79.6 and 7, Pingree refers te??m to days where grammatically it should refer to tithi (in 6) and to tithi where it should refer to days (dinar?tram, in 7). The numbers are also a problem. But Sukla?s solutions do not convince me either...

Correction: Pingree is aware of the problem and recommends that the halves of verse 6 and 7 be exchanged. This may solve the problem.

Dieter

With regards the nakshatras, I was under the impression that the nakshatras were inherently sidereal, but that texts such as the Surya Siddhanta offered ways of using an ayanamsha to position them tropically. Surely this means they are sidereal considerations which are put into a tropical context for a given reason, perhaps interpretive? Or perhaps the necessity of putting it tropically is for some reason in reference to the sign rising, which is, as I understand it, a tropical consideration rather than a sidereal one. In other words you cannot calculate the ascendant sidereally.

I do not know, I only go by the arguments others have made and thoughts which occur to me as a result of them.

On a separate issue, one question which forever troubles me with regards the sidereal zodiac, which may not be related to this but which I may as well raise in case someone wants to knock it on the head, is that the ideas of the modalities don't make much sense to me from a sidereal perspective. It makes sense that the cardinal signs are as they are tropically for example, but what is being 'hinged' or what is turning in the sidereal system?

With regards the translation issues, I have nothing to add as I do not know anything of sanskrit.
But I'm curious more about the context in which things appear.

Consider 14:9
"From the sun's entrance into Capricorn, six months are his northern progress; so likewise, from the beginning of Cancer, six months are his southern progress"

The previous pargraph describes what the equinoxes and solstices are, then the following paragraph mentions its effect upon seasons. This is all tropical right?

Paul

Paul wrote:With regards the nakshatras, I was under the impression that the nakshatras were inherently sidereal, but that texts such as the Surya Siddhanta offered ways of using an ayanamsha to position them tropically.

I don't think so. The planetary theory of the Suryasiddhanta is basically sidereal. Precession is mentioned in Suryasiddhanta 3.9-12. But apparently it is only used to calculate "declination, shadow, ascensional difference, etc.", (verse 10). There is no mention of calculating tropical nakshatras. Besides, modern scholars think these verses are not part of the original SS, but interpolated later, among other reasons because precession is not used or mentioned in other places of the work. More details are given by Burgess in the commentary to his translation of the work. Please forgive me if for reasons of time I cannot go into more details about the usage of precession in ancient and medieval India.

Consider 14:9
"From the sun's entrance into Capricorn, six months are his northern progress; so likewise, from the beginning of Cancer, six months are his southern progress"

The previous pargraph describes what the equinoxes and solstices are, then the following paragraph mentions its effect upon seasons. This is all tropical right?

I think the situation is more complicated. As I said, the solar year and planetary theory of the SS are sidereal, and the old SS most probably did not know the concept of ayanamsha, therefore was not able to calculate tropical positions of the Sun and the planets. For such reasosn, some people (among which Martin, if I am right) consider the above-quoted statement is not to be considered as a "definition" of the zodiac, but rather "accidental" in the sense that, at the time the work was written, the equinoxes and solstices were roughly at the beginning of the mentioned signs, but this should not be considered as a "definition" of the zodiac. However, as I do believe that the author of the SS had no clear understanding of the precession problem, I am of the opinion that he actually *wants* to have the winter solstice *exactly* at the ingress point of Capricorn. This is also what the text says: that the winter solstice is exactly at the solar ingress into Capricorn. I can only understand this as a definition of the zodiac. I cannot understand it differently. Therefore I say, the Suryasiddhantic theory is not purely sidereal, but it is a chimaera. Being sidereal in practice, it wants to be sidereal and tropical at the same time and is not aware that this is impossible. But the case is similar with the systems of other ancient authors like Aryabhata, Brahmagupta, and even Sphujidhvaja (the author of the Yavanajataka). As to the latter, although imho his solar and planetary theory was tropical (see my other posts) he does not mention the sidereal-tropical problem or precession, so most probably had no clear understanding of it. Or he did not know how to treat the problem.

Dieter

delete

I, too, have precious little time to spare; but in response to Paul's question about the modalities, I see two possibilities. One is that the Greek word tropikos really should be understood as relating to the 'turning' of the seasons, as Ptolemy thinks. Even if that is the case, however, we should remember that that designation predates the astrological use of the equinox as 0 Aries, and general knowledge of precession. Valens, for instance, calls Aries tropikos (if memory serves); but he also makes it clear that the equinox falls some distance into Aries. In most astrologers' minds, the zodiac was probably fixed in relation both to the stars and to the seasons, and there is no telling which was most important to them.

The other possibility, suggested by Robert Schmidt in an online discussion, is that tropikos does not originally relate to the turning of the seasons at all, but to the turning of the Thema Mundi on its 'pivots' or angles (Cancer rising, Aries culminating). If so, Ptolemy's explanation would be a projection of his own naturalistic views onto a pre-existing term. Note that the third modality is often referred to as 'double-bodied' signs, a designation that obviously has nothing to do with the seasons, but which well describes the constellations of Gemini, Sagittarius and Pisces.

Good morning,

Objection, dear Professor Gansten!

In Professor Robbin's English translation of Klaudios Ptolomaios' Tetrabiblos, Book I, Section 11, Of Solstitial, Equinoctial, Solid, and Bicorporeal Signs, one reads:

"The bicorporeal signs, Gemini, Virgo, Sagittarius, and Pisces, are those which follow the solid signs, and are so called because they are between the solid and the solstitial and equinoctial signs and share, as it were, at end and beginning, the natural properties of the two states of weather."

Obviously, no references to the appearances of constellations.

Best regards,

lihin

lihin wrote:Objection, dear Professor Gansted!

That's Gansten.

Obviously, no references to the appearances of constellations.

Obviously not, in Ptolemy. But does 'double-bodied' (or 'bicorporeal' if you prefer) seem to you a natural choice of term for the meaning 'in-between'? Or is it more likely that this is another bit of revisionism on Ptolemy's part?

Mark wrote:I have been looking at the text of the The Yavanajataka of Sphujidhvaja myself. Its a fascinating text for many reasons.

One section that intrigues me is in Chapter 1 68-69 discussing the rising times of signs.

68. The measure of the rising-times of the first and last signs is
demonstrated with certainty to be two muhiirtas each; know that the
measure of the rising-times (of the rest of the signs) in the two halves of
the zodiac, taken (respectively) in direct and reverse order, is (two
muhurtas) with a fifth (of that measure) added (successively to each).

69. Knowing that the signs are thus measured as being short, medium, or
long, they consider the lengths of journeys as being similar to the
divisions of the zodiac (and the limbs of the zodiacal man)

I am afraid maths is not my strong suit. However, might this give us any clues to what zodiac is involved? Obviously, in the tropical zodiac we have signs of short, intermediate and long rising periods. I am genuinely unclear what is involved in calculating the rising times of sidereal equal sized signs. Would the same terminology make sense there too?

Incidentally, I have only managed to download a version without David Pingree's commentary. Has anyone read his commentary? What view did Pingree take on the text and the type of zodiac involved?

Mark

In part, here is Pingree's commentary on this section of text:

"This list of rising-times is precisely that of System A for Babylon as found on cuneiform tables and in several Greek astrological texts (see O. Neugebauer, "On Some Astronomical Papyri and Related Problems of Ancient Geography." (....additional references...) It is only accurate for the extreme northwestern part of India; yet it is repeated by Satya..., Varahamihira...and Vaidyanatha..." (Volume 2, p.228)

Therese wrote:
In part, here is Pingree's commentary on this section of text:

"This list of rising-times is precisely that of System A for Babylon as found on cuneiform tables and in several Greek astrological texts (see O. Neugebauer, "On Some Astronomical Papyri and Related Problems of Ancient Geography." (....additional references...) It is only accurate for the extreme northwestern part of India; yet it is repeated by Satya..., Varahamihira...and Vaidyanatha..." (Volume 2, p.228)

Thank you Therese. Whatever one makes of his conclusions Pingree's notes must be very useful. This seems to put the text more in the mainstream of tables hellenistic astrologers were using in this period. In another thread Kenneth has mentioned that he believes the text arrived through the city of Ujain in central India. However, if the tables are accurate it points to the source of the text (or another source text entirely) being NW India around the territory of the Kushan Empire or possibly into Indo-Parthian territory.

Mark

Hello,

I looked into Shukla?s criticism of Pingrees edition and translation of Yavanajataka 79. And after I had vehemently contended that this text uses the tropical reference frame, I now feel obliged to concede that the facts may be a bit more complicated than I had thought.
I apologise if my following explanations may go beyond the interest of most readers, but I think I need to do justice to the presence of Martin in this discussion. Martin, in case you find errors in what I say, your feedback is welcome.

To begin with, the text is very badly preserved and in many places the original reading cannot be reconstructed anymore. Pingree does his best to make some sense out of it, however Shukla makes a few valid points against Pingree?s proposals.
What I don't like with Shukla is that he tries at any price (using conjectures, speculative translation) to make the text agree with his preconceived ideas. And then he dogmatically presents his readings with words like ?the correct reading of the text is ...?, with an obvious resentment against Pingree between the lines. There is not one word of recognition of the precious work of Pingree.

The first verse that seems to indicate a tropical year in Pingree?s translation is 79.6:
krame?a candra? k?ayav?ddhilak?yas / tithi?caturm?navidh?nab?ja?
?a?pa?cak?gre dvi?ate sahasra? / te??? yuge binduyut?ni ?a?ca
Shukla (partly from apparatus):
?a?pa?cak?gr? dvi?at? sahasra? / te??m yuge viddhyayut?ni ?a?ca.
Pingree translates: ?The Moon is to be characterized by waning and waxing in order. The tithi possesses the seed of the principles of the four (systems of time-)measurement. There are 60265 (days) in a yuga (of 165 years; D. K.)?.
Shukla: ?... there are 61230 of them (tithis; D. K.) in a yuga.?

Now, Pingree?s solution results in a year length of 365.2424 days, which is very, very close to the tropical year. However, I have to admit, unfortunately, that Shukla?s translation seems to make better sense:
? te??m refers to tithi, not days.
? verse 7, which is parallel in construction to verse 6, has ayut?ni in the last quarter. It is most probable, that verse 6 also has ayut?ni, not -yut?ni.
? Shukla?s translation with ?a?pa?caka- = 5 x 6 = 30 is more likely. In verse 12, even Pingree reads the same expression as meaning "30". BTW, the resulting number 61230 is exactly the number that Pingree wants to have in verse 7 as the number of tithis in a yuga.
So, I am quite sure that Pingree is wrong in vs. 6 and Shukla is right. There is no direct information about the year length in this verse. The verse does not support a tropical year length in Yavanajataka.

Vs. 7:
Pingree believes this verse to state that a 165-year yuga contains 61230 tithis. However, the verse is about nychthemera (dinar?tra-), not tithis, and most probably it contained information about the number of days in a yuga and therefore the year length. Unfortunately, the text is corrupt again. The Sanskrit text reads as follows:
Pingree: te??m ?ate dve tri?adekak?gre / ?a? kh?yut?nyarkayuga? vadanti
(var. trik?da??ak?gre; ?a?c?yutany-)
Shukla: te??m ?ate dve trik?da??ak?gre / ?a?k?yut?nyarkayuga? vadanti
Pingree translates: ?They say that a yuga of the Sun consists of 61230 (tithis).?
Shukla translates: ?... 60000 plus 200 plus 3^2 x 8 (i. e. 60272) of them (civil days).?

I do not believe in Shukla?s theory that trik?t mean "3x3", but I consider it most likely that the number originally intended by the text is 602?3, i. e. either 60263 or 60273 days in a yuga of 165 years.
Number of days in a yuga and length of solar year:
60263: 365.2303
60273: 365.2909
The first solution results in a better value for the year length (365.2303), which would be about 17 minutes less than the tropical year.
The second solution has the advantage that 60273 is exactly 61230 tithis x 63/64 (according to vs. 5) and seems to be consistent with the preceding verses. However, the resulting year is 50 min longer than the sidereal year. (Imagine an ayanamsha that is more than twice as fast as precession and in opposite direction.) As the text says that his theory comes from the Greeks (Yavanas), this year length would be very strange, because the Greeks knew quite well that the year was about 365.25 days long, not 365.29. Or does the text give an Indian or Babylonian value here? I don?t know.

Now, verse 34 about the solar year length at the beginning of the "theory of the planets":
sapa?ca?a??i? tri?ata? din?n?? / dy?na? dvibhinna? tu din???ak?n?m
try?na? ?at?rdha? dinak?tsam? sy?t / yay? bhavarga? savit? bhunakti
var. (b) yug?dibhinna?
Shukla: yug?dvibhinna?
Pingree translates:
?A year of the Sun consists of 365 days and 14;47 sixtieths (a??as) of a day, in which the Sun traverses the signs.?
The translation, which results in a *tropical year of 365.2464 days*, looks ok. However, Shukla dogmatically states that this is not the year ?according to Sphujidhvaja?, which he considers to be 365.284848 (6,5;17,5,27,16) days long. But in my opinion, this remains a speculative value.
To make the text agree with his theory, he arbitrarily conjectures yug?dvibhinna? as ?correct reading of the text? and translates as follows:
?A yuga of the Sun consists of 365 days and a fraction of a day equal to 50 minus three divided by (the number of years in) a yuga, in which the Sun traverses the signs.?
Or in formula: 365 + (50-3)/165.
I am afraid this is not exactly the way how numbers are usually expressed in this text. Shukla?s solution is rather a helpless guess than a conclusive result of text analysis. I clearly prefer Pingree?s straight-forward solution.
Or could the same verse be interpreted in different way that would support a sidereal year? (Is dy?nam correct?)

So what remains of tropical ideas in Yavanajataka? Not much.
Apparently only verse 79.34 about the solar year length (if the text is correct and correctly interpreted) and verse 30 about the solstices in the zodiac (which does not count in Martin?s opinion).
The tropical rising times of the zodiac signs I do not count either, because they were also used in sidereal systems. (Even a lot later by Manjula in the 10th century AD. He used the tropical Sun and tropical rising times of the signs in order to calculate a tropical ascendant and after that subtracted the ayanamsha to find the sidereal ascendant. Tropical rising times are very handy because they are constant over thousands of years, whereas sidereal ones depend on precession.)

Dieter

Mark wrote:Thank you Therese. Whatever one makes of his conclusions Pingree's notes must be very useful...

Mark, I'm glad that I could provide Pingree's commentary. I have the good fortune to own a copy of the two volume hardback of Yavanajataka (Harvard University Press, 1978), so in the future if anyone is curious about Pingree's notes on a section of text, I can provide that information.

Therese