The verse is quite cleverly written - if you know Sanskrit, you'll see it can also be read as being in praise of Shankara. However, as I have said earlier in this thread, it is not a Vedic text.Quote:
Originally Posted by SRS
The earliest source in which the "gopi bhagya" verse occurs is the book on Vedic Mathematics by Jagadguru Bharati Krishna Tirtha, the late Shankaracharya of Puri, published in the 1960s. The book cites it as a verse with spiritual and numeric content, but does not claim that it is an ancient verse. In point of fact, the verse is not found in any known Sanskrit text.
Nor is it even likely that the verse is an old one. To anyone possessing a passing familiarity with ancient Indian texts, it is painfully obvious that the system it uses is not an ancient one, and bears no resemblence to any of the systems for encoding numbers which were actually used in ancient India.
Let's look briefly at how numbers were encoded in ancient India. The Sulbasutras - which are the oldest extant mathematical texts - usually simply specify numbers by name, and provide formulae for calculating numbers which cannot be easily specified by name. The verse from the Baudhayana Sulbasutra which gives the formula for calculating the square root of two is a good example of the system actually used in that time: pramANam tRtIyEna vardhayEttacca caturthEnAtmacatustrim shonena savisheSHaH. There is not a single verse from the vedic or post-vedic periods which uses the system of the "gopi bhagya" verse.
A second system, called "bhuta samkhya", came into use in the classical period. This represented numbers by using words that were associated with those numbers in philosophy. So "zero" was represented by "ambara akasa" (the aether) or "shunya" (the void) or "randhra" (a hole). "One" was represented by "sashi" (the moon) or "bhumi" (the earth), or "go" (cow), and so on, with a variety of other options for each of these. This system was not purely place-value based, in the sense that each word did not just represent one numeral: for example, "bha" (star) represented 27. This system was being still used by authors as late as Madhava (who probably lived in the 14th century AD). For example, Madhava's famous verse which gives a value of pi accurate to 11 decimal places actually ran thus:
vibudanEtra gaja ahi hutasana
trigunavEdabha vArana bAhavaH
nava nikharvamitE vRtivistarE
paradhimanam idam jagadur budhah
Summarised, this says that the circumference of a circle is 2827433388233 when its diameter is 900000000000. One can then use these to calculate the value of pi (which works out to 3.141592653592222.... on this formula).
Note that this verse, too, gives a formula rather than the number itself, which was not uncommon in ancient Indian mathematics. Note also that one must read the number starting at the end and working to the beginning - if one were to decode the number in the verse starting from "vibudha" (gods, and thus 33) and ending with "bAhava" (arms, and thus 2), one would get 33, 2, 8, 8, 3, 3, 3, 4, 27, 8, 2, i.e., 3328833342782, not 2827433388233. This, too, is typical of the way numbers were encoded in older Indian mathematical texts. The order in the "gopi bhagya" verse is quite anachronistic, and strongly suggests a modern origin.
A third system used in older mathematical texts is the one presented by Aryabhatta in his Dasagitika. This system assigns the numerical values from 1 to 25 to the twenty-five varga letters of the Sanskrit alphabet. The seven avarga letters are given the respective values 30, 40, 50, 60, 70, 80, 90 and 100. Each of the vowels has a value as a multiplier: 1, 100, 100^2, 00^3, and so on. This system, too, bears no resemblance to the system used in this verse. It is far less flexible, much more difficult to use, and produces horribly complicated and usually meaningless and unpronouncable jumbles of letters to represent numbers. For example, in each yuga, the moon completes a number of revolutions. Aryabhatta encodes this number as "cayagiyiNGusuchRlR". Not only is this utterly devoid of meaning and impossible to pronounce, it is also more complicated to unravel than the "gopi bhagya" verse. To decode this, we have to calculate "ca" as 6, "ya" as 30, "gi" 300 (g=3, i=100), "yi" as 3,000 (y=30, i=100), "NGu" as 50,000 (NG is 5, u is 10000), "su" as 7,00,000 ("s" is 70, u is 10000), "chR" as 70,00,000 (ch=7, R=10,00,000), and lR as 5,00,00,000 (l=50, R=10,00,000), thus giving us 5,77,53,336. Clearly, this system is a lot less advanced than the one used by the "gopi bhagya" verse. In point of fact, there is not a single verse from the time of Aryabhatta or his immediate disciples which uses the system used in the "gopi bhagya" verse.
A system approaching that of the "gopi bhagya" verse finally appears in mediaeval India, in the writings of the Kerala school of astrologers. This is the so-called "katapayadi" system (literally, "ka, ta, pa, etc."). There are no texts older than the 9th or 10th century AD which use this system, and the fact that Aryabhatta felt compelled to present a much clumsier, less flexible system suggests very strongly that this system didn't exist then. The katapayadi system assigns the precise values to the letters of the Sanskrit alphabet that the "gopi bhagya" verse does, and it is therefore clearly influenced by katapayadi. But the two systems are not the same. Katapayadi, like bhuta samkhya and Aryabhatta's system, begins with the unit place and works its way upwards, thus requiring numbers to be read starting at the end in modern terms, not at the beginning like the "gopi bhagya" verse. A good example is the 16th century verse which presents an approximation of the calculation required to derive the sine:
vidvAm tunnabalaH kavIshanicayaH sarvArthashIlasthiroH nirviddhAnganarendraru
Unless you read the number encoded by each word from right to left, you get a meaningless sequence of numbers. This, again, is a universal rule in all katapayadi texts - there is not a single textual mnemonic prior to modern times which encodes numbers beginning with the highest place and ending with the lowest place as the "gopi bhagya" verse does.
The reason I have gone to these lengths to debunk the claims of antiquity for this one verse is because the verse is symptomatic of our uncritical acceptance of anything and everything as examples of ancient "Vedic" wisdom, even when every single piece of evidence screams to the contrary. This is no distortion of history - all I have said above can be very easily refuted by citing the "ancient Vedic text" in which the verse occurs, but the fact that no such text exists does not seem to make an iota of difference to people who desperately want to believe in it. I simply cannot understand why so many modern Indians are so ashamed of India that they cannot accept the society and culture that really existed in ancient times for what it was, a mix of good and bad as all cultures are, and instead feel the need to invent a false version of which they can then be proud.
The value of experimentation is that it tells us when our mathematical models are wrong. Without experimentation, we would not have realised that Newtonian physics is an incorrect model, which is only accurate in certain special cases. Or that the same is true of Euclidean geometry. On the other hand, with a more rigorous culture of experimentation, Aryabhatta would have realised that not all his formulae were correct.Quote:
Originally Posted by SRS
And thank you for these kind words:
Quote:
Originally Posted by SRS