Methodology of Vedanta -
Standing Example from the Upanishads:

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kazyapa - continued
Then comes the passage narrating the claims of great sages about their experience of the seven Suns and the eighth Sun. Two sages by name
panca-karNa, son of vatsa; and sapta-karna, son of plakSa
claim to have seen the seven Suns; but, say the two, they have not been able to go to the mahaa-meru and see the eighth Sun. But everybody strongly recommends, says the text, that man should strive to go to the mahaa-meru and see that One-ness of Divinity, called kazyapa. It becomes clear that they are referring to the Supreme Reality here which is the substratum of all the seven Suns. 'tasya bhaasaa sarvam idam vibhati, say the scriptures in another place, referring thereby to the Transcendental Absolute. So these seven Suns themselves derive their strength and dalliance from the eighth Sun, namely kazyapa. The seven Suns originated from kazyapa, says the text:
kazyapaad-uditaas-sUryaah
The very name kazyapa is extolled and its meaning derived by going into its etymology.
kazyapah pazyako bhavati
is a statement occurring in the eighth section of the same chapter. It means kazyapa is the One that Sees -- meaning, He sees rightly. The next sentence in the text explains this:
yat sarvam pari-pazyati-iti saukSmyaat
meaning, 'because it sees everything in all its subtlety'. The root word for seeing is driz . When conjugated, this becomes pazyati . There is another esoteric significance here. The word kazyapa has three syllables:
ka , zya , and pa - in that order.
Reverse the order of these three syllables. We get
pa , zya , and ka .
They make up, in that order, the word pazyaka - which means, One Who Sees. That is why, kazyapah pazyako bhavati ! bhavati means ' becomes' . kazyapa happens to be pazyaka .
The existence of this eighth Sun in the form of the Ultimate Supreme (Who sees, as things are to be seen) is given only in the scriptures and one wonders whether this could have implications for the understanding of what Solar Energy really is.

# Note on mahaa-meru:
This is a mountain-peak which is supposed to be situated at the very centre of jambu-dvipa -- the island which has the jambu tree as its characteristic, the earthly portion according to the scriptures, which includes certainly our visible earth, but it includes also many unknown lands, rivers and mountains such that the geography that they together portray seem to be in total contradiction with what we know to be true.
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Back to Question on Vedas and Science

On the statement that the methodology of Vedanta is also the same as science - experiment, observation, conjecture, further experiment, observation and inference and so on.
(Back to the Reference for this statement)
A standing example of this is the third chapter of Taittiriya-Upanishad, known as Bhrigu-valli. The disciple is enjoined to investigate the Cause of all causes by doing tapas - one-pointed, self-negating concentration, a spiritual travail for which India was legitimately famous for probably more than three millenia. The disciple goes through the process step by step. At every stage of his 'finding' he comes back and reports to the Guru. The latter is not satisfied with the finding and exhorts the disciple to investigate again. The disciple proceeds from the obvious and the outer to the deeper and inward principles one by one: from matter to life, from life to mind, from mind to intelligence, and finally, from intelligence to bliss.

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Jan.28, 1999
Copyright Ó V. Krishnamurthy