Posted: Mon Nov 28, 2011 10:23 am
Here is another aspect of the Koch article, which should be rephrased, since the Indians do not consider the Mahabharata to be prehistory.
Koch: The situation is similar in later Vedic texts like the great Mah?bh?rata epic, which relates us the story of an apocalyptic war in Indian prehistory.
"These scholars have discounted the fact that two of the greatest epics of
the world, Ramayana and Mahabharata are traditionally regarded as itihasa s, i.e., historic texts and that there are in addition, a host of supporting texts in the form of Puranas. Ignoring the fact that Bharata has its own sense of history and the purpose of history, which differs
from their own concept of history, the scholars have systematically misrepresented the chronology of Bharata" - Astronomical dating of events from Indian history
Also, first the Western story:
Koch: "From about the second century AD on, astrologers and astronomers from Hellenistic Egypt brought their knowledge to India and triggered a development that took the Indian sciences of the sky to new heights."
Koch: "The oldest astrological work in Sanskrit that knows the zodiac is the Yavanaj?taka ("birth chart according to the Greeks") by Sphujidhvaja, a textbook of astrology in verse that, according to its own testimony, is based on a Sanskrit translation of a Greek original. David Pingree suggested that this text was written in the 2nd century BC in Alexandria and came to India around 150 AD."
Koch: "Other old works from the Greek-inspired era, the so-called Siddh?ntas..."
Koch: "As has been said already, the most ancient astrological text, the Yavanaj?takam, teaches that the zodiac is fixed at the cardinal points of the year and at the same time also at the lunar mansions. According to David Pingree, this text was written around the year 150 AD."
For those who are interested in the history of astronomy and astrology, should we also consider what 'hindu' scholars say?
Here are some excerpts from: Vedic Cosmography and Astronomy by Richard Thompson. I was not going to copy the entire chapter, but I took excerpts to illustrate the hindu viewpoint on this matter, in order to demonstrate that maybe we should reconsider history from the hindu perspective, before imposing the Western version onto them.
I don't know if this book is still in print, but for those who are interested in this history of astronomical science issue, it may be something worth finding and taking into consideration.
Now, the hindu story:
"Nonetheless, even though our knowledge of the history of ancient astronomy is extremely incomplete, there are scholars who believe that they can uncover important parts of this history by speculative reconstruction. One example of this is a paper entitled ' The Recovery of Early Greek Astronomy from India,' by David Pingree (PG). In order to indicate the complexities and pitfalls of the speculative process, we will examine the key argument of this paper in detail. This will involve the use of a number of technical astronomical terms, but we will explain these as we go along. Our method will be to first present Pingree's theory, and then give his reasons for accepting this theory as true. Then step by step we will show the fallacies in his reasoning and present an alternative theory that is in better agreement with the facts..." p. 182
"...Now, how does Pingree know that this is what Aryabhata did some 1,400 years ago? His key argument is that if we us Ptolemaic calculations to reproduce Aryabhata's supposed steps, then we obtain Aryabhata's parameters for mean planetary motion almost exactly. Aryabhata's parameters, listed under R in Table A2.1, are in the hundreds of thousands and millions. Column (1) of this table lists the differences between Aryabhata's parameters and these parameters as reconstructed by Pingree. For example, for Jupiter, Aryabhata's rate is 364,224 revolutions per yuga cycle, and Pingree's reconstruction is larger than this by 4. Since these differences are very small, it is hard to imagine how Aryabhata could have arrived at his parameters without following the scenario that Pingree proposes. This makes it seem that Pingree's conclusion concerning Aryabhata is indisputable, and equally so his contention that nearly every aspect of Indian astronomy was imported by Greek sources without acknowledgement (PG, pp. 114-5).
An argument such as Pingree's has a great impact on the academic world. It tends to be immediately convincing to scholars, and it becomes established as a foundation stone in an imposing school of thought that cannot be easily challenged by nonprofessionals. As a result, scholars in other fields (such as comparative religion and history) accept the conclusions of such a school as a matter of course, and modify their own views in accordance with it..." p. 184
"However, one can indeed find other ways by which Aryabhata could have arrived at his parameters. The Brahmapaksa parameters are expressed in revolutions per kalpa of 4,320,000,000 years, whereas Aryabhata wanted parameters in revolutions per yuga cycle of 4,320,000 years (See Table A2.3). What happens if we simply divide the Brahmapaksa parameters by 1,000 and then round them off to suitable integers of the form 4n or 4n + 2? Column (4) of Table A2.1 shows the differences between the parameters computed in this way and Aryabhata's original parameters..." p. 184
"...As we shall see, this fine tuning can be accounted for in ways other than the one advocated by Pingree. To do this, it is first necessary to examine Pingree's argument more closely..." p. 185
"After we have checked our Ptolemaic calculations at the Kali-yuga starting date, the next step is to perform these calculations for noon of March 21, A.D. 499, the date of Aryabhata's alleged calculations. There are 454,759 days from Ptolemy's epoch to this date. If we compute the Ptolemaic mean positions for this date, a number of interesting points emerge. First of all, the Ptolemaic mean longitudes do not at all agree with Pingree's figures, as given in his Table 2 (PG, p. 116). This can be seen by comparing the rightmost and leftmost columns of Table A2.2." p. 187
"We have also not been able to account for the discrepancies between the middle and rightmost columns of Table A2.2, for it would seem that calculations for 454,759 days after Ptolemy's epoch should be even more precise than calculations for 860,172.25 days before that epoch. (We note that Pingree's Ptolemaic calculations apparently have not been corrected for the time difference between Ptolemy's city of Alexandria and Aryabhata's city of Ujjain; this possible correction does not account for the discrepancy.)" p. 188-9
"For Venus and Mercury the errors in Pingree's reconstruction of Aryabhata's parameters turn out to be worse than those reported by Pingree in his paper. (Compare columns 1 and 2 of Table A2.1.) This indicates errors on Pingree's part, but it might be argued that it does not detract very badly from his hypothesis. We therefore ask, Is there some reasonable way of reconstructing Aryabhata's parameters that produce smaller errors for all of the planets than Pingree's method? The answer is yes. To explain this, we must turn to a discussion of the mean positions of the planets according to modern astronomy..." p. 189
"...Let us suppose that Aryabhata did this, and that he then computed his parameters using his observed longitudes rather than longitudes copied from a Greek table. This leads to a reconstruction of his parameters based on modern calculation of the differences between mean longitudes and the sun's mean longitude. The longitudes and resulting parameters for this reconstruction are listed in the last two columns of Table A2.3, and the errors in this reconstruction are listed in column (5) of Table A2.1. As we can see, these errors are zero, except for Mercury, where the error is equal to that in Pingree's reported reconstruction (see columns (1) and (2)). Thus, the hypothesis of observation yields better results than the hypothesis of copying from Greek tables..." p. 193
"...Persia is the natural link between India and the West, but of this country Neugebauer says:
'We know of Pahlavi translations of such first and second century astrological writings as Teucer and Vettius Valens and the presence of 'Indian books' as well as of the 'Roman megesti' around A.D. 250 under Shapur I. Under Khosro I,... was revised, around A.D. 550, the famous Zij ash-Shah, which has been shown to be greatly dependent on Hindu sources (NG, p.
.'" p. 194
"...In the remaining part of this appendix, we will give two more examples of the process of speculative reconstruction. These examples deal with the theoretical ideas and mathematical methods of Indian astronomy, which Western historians of science say were derived entirely from Greeks or Babylonians via Greek intermediaries." p. 194
"...These statements certainly convey the impression that the Indian sine-table was directly obtained from a related trigonometrical table used by the Greek astronomer Hipparchus. However, what do we find if we actually examine the paper by G.J. Toomer that these authorities are citing? Let us briefly consider this.
The first thing that we learn from this paper is that there are no surviving Greek documents containing Hipparchus' chord table, even in a fragmentary form. Indeed, 'there is no explicit evidence about the nature of Hipparchus' chord table,' and no real proof that such a table ever existed (TMI, p. 6). It is important to note that only one work of Hipparchus' has ever survived - a commentary on the stars - and this does not present his mathematical methods. As we have already noted, this is typical of the state of our knowledge of pre-Ptolemaic Greek astronomy..." p. 195
"...By this reasoning Toomer maintains that ' the nature of Hipparchus' chord table is conclusively established' (TMI, p.16). Since the table has the structure of an Indian sine table, it follows that Indian trigonometry must have been derived from the Greeks. The idea that Greeks may have been influenced by Indian developments is never even suggested by modern Western historians of science. But in this case, of course, we have no evidence for influence either way, since the connection between Hipparchus' two numbers and the Indian sine table is purely speculative..." p. 196
"...Since the chord table of Hipparchus has not survived (if it ever existed), it is remarkable that such slender evidence can be offered as the basis for 'inevitable' conclusions about it. Yet, as we have seen, such speculative reconstructions are not unusual in the field of the history of science. Here we will give one more example. This is provided by the mathematician B.L. van der Waerden, who traces back Hipparchus' trigonometry to the Greek mathematician Apollonius of Perge (VW, pp. 211-12). Van der Waerden's reasoning goes as follows:..." p. 197
"...We have discussed the arguments of Pingree, Toomer, and van der Waerden in detail to show the kind of foundations that underlie scholarly conclusions about the origins of Indian astronomy. The main characteristic of these foundations is that they are composed almost entirely of unsupported assumptions, biased interpretations, and imaginary reconstructions. It is unfortunate, however, that after many scholars have presented arguments of this type in learned treatises, the arguments accumulate to produce an imposing stratified deposit of apparently indisputable authority. In this way, supposedly solid facts are established by the fossilization of fanciful speculations whose original direction was determined by scholarly prejudice. Ultimately, these facts are presented in elementary texts and popular books, and accepted on faith by innocent people." p. 198
I am not trying to pick on Koch, but it just so happened I came across Pingree in three sources at the same time, and so I thought it should be mentioned that there is conflicting stories about Pingree and his research. And the story of Pingree's research is foundational to the current understanding of the history of astronomy.
Eddy referenced me to a paper by Pingree earlier in this thread:
http://adsabs.harvard.edu/full/1972JHA.....3...27P
Richard referenced me to Koch's article at astro.com and that article was partly based on Pingree.
Then, I started reading more of Vedic Cosmography and Astronomy, and there was this Pingree again. Pingree is one of the main scholars whom is referenced to by others and it appears that his research is questionable.
Fate it seems...
Koch: The situation is similar in later Vedic texts like the great Mah?bh?rata epic, which relates us the story of an apocalyptic war in Indian prehistory.
"These scholars have discounted the fact that two of the greatest epics of
the world, Ramayana and Mahabharata are traditionally regarded as itihasa s, i.e., historic texts and that there are in addition, a host of supporting texts in the form of Puranas. Ignoring the fact that Bharata has its own sense of history and the purpose of history, which differs
from their own concept of history, the scholars have systematically misrepresented the chronology of Bharata" - Astronomical dating of events from Indian history
Also, first the Western story:
Koch: "From about the second century AD on, astrologers and astronomers from Hellenistic Egypt brought their knowledge to India and triggered a development that took the Indian sciences of the sky to new heights."
Koch: "The oldest astrological work in Sanskrit that knows the zodiac is the Yavanaj?taka ("birth chart according to the Greeks") by Sphujidhvaja, a textbook of astrology in verse that, according to its own testimony, is based on a Sanskrit translation of a Greek original. David Pingree suggested that this text was written in the 2nd century BC in Alexandria and came to India around 150 AD."
Koch: "Other old works from the Greek-inspired era, the so-called Siddh?ntas..."
Koch: "As has been said already, the most ancient astrological text, the Yavanaj?takam, teaches that the zodiac is fixed at the cardinal points of the year and at the same time also at the lunar mansions. According to David Pingree, this text was written around the year 150 AD."
For those who are interested in the history of astronomy and astrology, should we also consider what 'hindu' scholars say?
Here are some excerpts from: Vedic Cosmography and Astronomy by Richard Thompson. I was not going to copy the entire chapter, but I took excerpts to illustrate the hindu viewpoint on this matter, in order to demonstrate that maybe we should reconsider history from the hindu perspective, before imposing the Western version onto them.
I don't know if this book is still in print, but for those who are interested in this history of astronomical science issue, it may be something worth finding and taking into consideration.
Now, the hindu story:
"Nonetheless, even though our knowledge of the history of ancient astronomy is extremely incomplete, there are scholars who believe that they can uncover important parts of this history by speculative reconstruction. One example of this is a paper entitled ' The Recovery of Early Greek Astronomy from India,' by David Pingree (PG). In order to indicate the complexities and pitfalls of the speculative process, we will examine the key argument of this paper in detail. This will involve the use of a number of technical astronomical terms, but we will explain these as we go along. Our method will be to first present Pingree's theory, and then give his reasons for accepting this theory as true. Then step by step we will show the fallacies in his reasoning and present an alternative theory that is in better agreement with the facts..." p. 182
"...Now, how does Pingree know that this is what Aryabhata did some 1,400 years ago? His key argument is that if we us Ptolemaic calculations to reproduce Aryabhata's supposed steps, then we obtain Aryabhata's parameters for mean planetary motion almost exactly. Aryabhata's parameters, listed under R in Table A2.1, are in the hundreds of thousands and millions. Column (1) of this table lists the differences between Aryabhata's parameters and these parameters as reconstructed by Pingree. For example, for Jupiter, Aryabhata's rate is 364,224 revolutions per yuga cycle, and Pingree's reconstruction is larger than this by 4. Since these differences are very small, it is hard to imagine how Aryabhata could have arrived at his parameters without following the scenario that Pingree proposes. This makes it seem that Pingree's conclusion concerning Aryabhata is indisputable, and equally so his contention that nearly every aspect of Indian astronomy was imported by Greek sources without acknowledgement (PG, pp. 114-5).
An argument such as Pingree's has a great impact on the academic world. It tends to be immediately convincing to scholars, and it becomes established as a foundation stone in an imposing school of thought that cannot be easily challenged by nonprofessionals. As a result, scholars in other fields (such as comparative religion and history) accept the conclusions of such a school as a matter of course, and modify their own views in accordance with it..." p. 184
"However, one can indeed find other ways by which Aryabhata could have arrived at his parameters. The Brahmapaksa parameters are expressed in revolutions per kalpa of 4,320,000,000 years, whereas Aryabhata wanted parameters in revolutions per yuga cycle of 4,320,000 years (See Table A2.3). What happens if we simply divide the Brahmapaksa parameters by 1,000 and then round them off to suitable integers of the form 4n or 4n + 2? Column (4) of Table A2.1 shows the differences between the parameters computed in this way and Aryabhata's original parameters..." p. 184
"...As we shall see, this fine tuning can be accounted for in ways other than the one advocated by Pingree. To do this, it is first necessary to examine Pingree's argument more closely..." p. 185
"After we have checked our Ptolemaic calculations at the Kali-yuga starting date, the next step is to perform these calculations for noon of March 21, A.D. 499, the date of Aryabhata's alleged calculations. There are 454,759 days from Ptolemy's epoch to this date. If we compute the Ptolemaic mean positions for this date, a number of interesting points emerge. First of all, the Ptolemaic mean longitudes do not at all agree with Pingree's figures, as given in his Table 2 (PG, p. 116). This can be seen by comparing the rightmost and leftmost columns of Table A2.2." p. 187
"We have also not been able to account for the discrepancies between the middle and rightmost columns of Table A2.2, for it would seem that calculations for 454,759 days after Ptolemy's epoch should be even more precise than calculations for 860,172.25 days before that epoch. (We note that Pingree's Ptolemaic calculations apparently have not been corrected for the time difference between Ptolemy's city of Alexandria and Aryabhata's city of Ujjain; this possible correction does not account for the discrepancy.)" p. 188-9
"For Venus and Mercury the errors in Pingree's reconstruction of Aryabhata's parameters turn out to be worse than those reported by Pingree in his paper. (Compare columns 1 and 2 of Table A2.1.) This indicates errors on Pingree's part, but it might be argued that it does not detract very badly from his hypothesis. We therefore ask, Is there some reasonable way of reconstructing Aryabhata's parameters that produce smaller errors for all of the planets than Pingree's method? The answer is yes. To explain this, we must turn to a discussion of the mean positions of the planets according to modern astronomy..." p. 189
"...Let us suppose that Aryabhata did this, and that he then computed his parameters using his observed longitudes rather than longitudes copied from a Greek table. This leads to a reconstruction of his parameters based on modern calculation of the differences between mean longitudes and the sun's mean longitude. The longitudes and resulting parameters for this reconstruction are listed in the last two columns of Table A2.3, and the errors in this reconstruction are listed in column (5) of Table A2.1. As we can see, these errors are zero, except for Mercury, where the error is equal to that in Pingree's reported reconstruction (see columns (1) and (2)). Thus, the hypothesis of observation yields better results than the hypothesis of copying from Greek tables..." p. 193
"...Persia is the natural link between India and the West, but of this country Neugebauer says:
'We know of Pahlavi translations of such first and second century astrological writings as Teucer and Vettius Valens and the presence of 'Indian books' as well as of the 'Roman megesti' around A.D. 250 under Shapur I. Under Khosro I,... was revised, around A.D. 550, the famous Zij ash-Shah, which has been shown to be greatly dependent on Hindu sources (NG, p.
"...In the remaining part of this appendix, we will give two more examples of the process of speculative reconstruction. These examples deal with the theoretical ideas and mathematical methods of Indian astronomy, which Western historians of science say were derived entirely from Greeks or Babylonians via Greek intermediaries." p. 194
"...These statements certainly convey the impression that the Indian sine-table was directly obtained from a related trigonometrical table used by the Greek astronomer Hipparchus. However, what do we find if we actually examine the paper by G.J. Toomer that these authorities are citing? Let us briefly consider this.
The first thing that we learn from this paper is that there are no surviving Greek documents containing Hipparchus' chord table, even in a fragmentary form. Indeed, 'there is no explicit evidence about the nature of Hipparchus' chord table,' and no real proof that such a table ever existed (TMI, p. 6). It is important to note that only one work of Hipparchus' has ever survived - a commentary on the stars - and this does not present his mathematical methods. As we have already noted, this is typical of the state of our knowledge of pre-Ptolemaic Greek astronomy..." p. 195
"...By this reasoning Toomer maintains that ' the nature of Hipparchus' chord table is conclusively established' (TMI, p.16). Since the table has the structure of an Indian sine table, it follows that Indian trigonometry must have been derived from the Greeks. The idea that Greeks may have been influenced by Indian developments is never even suggested by modern Western historians of science. But in this case, of course, we have no evidence for influence either way, since the connection between Hipparchus' two numbers and the Indian sine table is purely speculative..." p. 196
"...Since the chord table of Hipparchus has not survived (if it ever existed), it is remarkable that such slender evidence can be offered as the basis for 'inevitable' conclusions about it. Yet, as we have seen, such speculative reconstructions are not unusual in the field of the history of science. Here we will give one more example. This is provided by the mathematician B.L. van der Waerden, who traces back Hipparchus' trigonometry to the Greek mathematician Apollonius of Perge (VW, pp. 211-12). Van der Waerden's reasoning goes as follows:..." p. 197
"...We have discussed the arguments of Pingree, Toomer, and van der Waerden in detail to show the kind of foundations that underlie scholarly conclusions about the origins of Indian astronomy. The main characteristic of these foundations is that they are composed almost entirely of unsupported assumptions, biased interpretations, and imaginary reconstructions. It is unfortunate, however, that after many scholars have presented arguments of this type in learned treatises, the arguments accumulate to produce an imposing stratified deposit of apparently indisputable authority. In this way, supposedly solid facts are established by the fossilization of fanciful speculations whose original direction was determined by scholarly prejudice. Ultimately, these facts are presented in elementary texts and popular books, and accepted on faith by innocent people." p. 198
I am not trying to pick on Koch, but it just so happened I came across Pingree in three sources at the same time, and so I thought it should be mentioned that there is conflicting stories about Pingree and his research. And the story of Pingree's research is foundational to the current understanding of the history of astronomy.
Eddy referenced me to a paper by Pingree earlier in this thread:
http://adsabs.harvard.edu/full/1972JHA.....3...27P
Richard referenced me to Koch's article at astro.com and that article was partly based on Pingree.
Then, I started reading more of Vedic Cosmography and Astronomy, and there was this Pingree again. Pingree is one of the main scholars whom is referenced to by others and it appears that his research is questionable.
Fate it seems...