But why repeat the rule twice? The common interpretation is that this was simply one of emphatic repetition in a sealing of the formula. Not so.
The correct unfolding of the code goes: ‘It is not this!; It is not: ‘It is not this!”. Ad Infinitum. It is the original laying out of the ‘Backward Step’.
[As Nagarjuna of the tradition of Shūnyathā [which closely approaches but stops-short of Shūnyam] summarily put it: ‘I reject nothing; and furthermore, there is nothing to negate‘.]
The rule properly interpreted is a self-scuttling circular loop. ‘The Backward Step’ designed to scuttle the presumed Subject and not a forward sweep for locating a new Object [such as an imagined That].
But used as linear rule Yagnavalkya’s formula has no natural convergence and enters into an insidious permanent spin. [And the reel will spin for ever if you don’t at some point see that you are part of the movie.]
No amount of negating will lead to convergence unless the negating turns in on itself. The circle is rounded only when the aim, act and agent of negation are themselves negated in full self-scuttle.
By about 500 BCE, the understanding of That had sharply regressed. Unfinished monks and ambitious gurus had re-crafted it down to an unverifiable dogma, superstitious cant and petitionary prayer.
The scholar-monks of the Prajñā-pāramithā, the radical fringe of the emerging Buddhism, picked up the thread. They correctly reset the linear interpretation of the formula into a perfected circular algorithm and called it Shūnyam. And its articulation is the celebrated Diamond Sūtra.
The perfecting of Yagnavalkya’s Rule was the full self-scuttle, the complete rounding of the circle with no remainder. This was the defining Buddhist insight. The Buddha-Dharma begins here.
This corrected interpretation of Yagnavalkya’s Rule was the first Self-Eating Expression, the original Koan, and the earliest complete formulated definition of the symbol ‘0’.
The literature shows that Siddhartha Gautama’s formal schooling, that of a high-born Kshatriya Prince, was firmly in the classic Dharmic paradigm. The Chandogya and the Bṛhadāraṇyaka Upanishads would have been standard fare for every beleaguered student in his day. [Much of early Buddhist vocabulary is in fact sourced in matured Jain scripture, a fact not widely appreciated.]
Did Yagnavalkya intend his rule to be a circular loop? We’ll never know [and other than for historians, its not very important]. Yagnavalkya himself talked in terms of what would later be called Coincidentia Oppositorum. His Atman is: ‘an endless infinite reality’ and simultaneously ‘an inner controller’; a ‘mass of intelligence’ which is also ‘the unattached and the undecaying’.
He definitely posits a named terminus, which would not have gone down well with the Sūtric scribes. But then this was truly ancient language and we are reading it across time and translation. It’s not a good idea to extract too much from the words. You can cheerfully disagree with the derivation and it wouldn’t affect the discussion on Shūnyam.