Indian Scholar At Cambridge Solves 2,500 Year Old Sanskrit Algorithm Problem In Panini’s Text

Ashtadhyayi, which consists of principles for deriving or forming new words from root words, frequently contains contradictory laws. An Indian scholar at Cambridge solved a 2,500-yr-old Sanskrit algorithm problem in Panini’s text.

A grammatical issue with the writings of the legendary Sanskrit scholar Paṇini has been resolved by Rishi Atul Rajpopat, a PhD scholar at the faculty of Asian and Middle Eastern Studies in St. John’s College, Cambridge, reports ThePrint.

Paini’s work Aṣṭādhyāyī, which consists of a collection of principles for deriving or forming new words from root words, frequently has conflicting rules for creating new words, leaving many scholars perplexed over which criteria to apply.

Many researchers were interested in resolving such contradictions in this linguistic algorithm of a book. Paṇini himself established a meta-rule to handle rule conflicts, which scholars have read as follows: In the event of a conflict between two rules of equal strength, the rule that comes later in the grammar’s serial order wins.

Rajpopat contends in his dissertation that this metarule was historically misinterpreted — instead, what Paṇini meant was that the reader should pick between rules pertaining to the left and right sides of a word.

Rajpopat discovers that Paṇini’s algorithms generate grammatically correct words and sentences with no errors using this rationale.

For instance, in the line jñānaṁ dīyate guruṇā — knowledge (jñānaṁ) is given (dīyate) by the guru (guruṇā) — there is a rule conflict when attempting to make the word guruṇā, which means ‘by the guru’ and is a known term.

The term is made up of the roots guru + ā. Going by Paṇini’s guidelines to generate the word that will signify “by the guru”, two laws become relevant — one to the word guru, and one to ā. This is handled by selecting the rule that is relevant to the word on the right, culminating in the appropriate new form guruṇā.

Rajpopat’s work is a response to scholars spanning two and a half millennia.

Jayaditya and Vamana attempted to address Paini’s rule disputes in their commentary treatise Kāśikāvṛttī, Patanjali in his Mahābhāṣya, and Katyayana in his Vārttikakāra. 

“After Pāṇini wrote his text, Kātyāyana expounded upon it, followed by Patanjali,” Rajpopat told ThePrint. “Several months after I started working on my thesis, I discovered that Kātyāyana had also deduced the same logic in a remote corner of his work. However, he too seemed to have decided to use alternate interpretations for rule conflict as well. Since in the Sanskrit tradition, scholars build up on the previous expert’s work more than the canonical text, this interpretation of the rule seems to have fallen through the cracks.”

Panini’s algorithmic texts

The authoritative and thorough treatise on Sanskrit grammar was written by Paini, the definitive linguist of his day.

He provides criteria for producing variations of a root word that are grammatically and syntactically correct according to Sanskrit norms in the Aṣṭādhyāyī, which has eight segments as the name suggests. Grammatical rules for the production of new words, such as sandhi, or combining two words to generate a third, are examples.

In total, over 4,000 rules are assembled as sutras in the text, and each book or segment defines a step-by-step technique — similar to an algorithm testing for requirements — for producing and constructing new words. However, the meaning of the sutras is not always evident. Since they are succinct and made up of restricted words, they can be baffling to modern readers.

Furthermore, each sutra is constructed on the preceding set of rules in a language device known as anuvr̥tti, or the continuation of one rule into the next. This indicates that sutras use recall and reference keywords that were used previously.

It is also occasionally unclear whether a sutra refers to any earlier rules, and whether a rule needs to be extended to the next. Even when the meaning of a regulation is apparent, it is frequently unclear where to apply it.

Perhaps most perplexingly, when a linguist determines where to apply one rule, another contradictory rule becomes relevant at the same time. This causes one rule to block the other, or both rules to block each other. This rule conflict is where Rajpopat’s thesis enters the equation.

As an example, Rajpopat mentions the words formed by the root vr̥kṣa. Combining the words vr̥kṣa and bhyām produces vr̥kṣābhyām, where the last ‘a’ sound of the first word is replaced by a longer ‘a’ sound. On the other hand, combining vr̥kṣa and su gives vr̥kṣeṣu where the same sound is replaced with ‘e’. Now, when the word vr̥kṣa has to be added to the plural bhyas, should the ‘a’ be replaced with a longer ‘a’ or ‘e’?

Various academics contended that different rules should be interpreted differently, but Rajpopat’s Occam’s Razor method yields the proper form, vr̥kṣebhyaḥ.

Rajpopat’s work resolves both basic and complicated disputes, as demonstrated by the guru example above.

Consider the word meaning “from god,” which is broken into its origins deva + bhis, to exemplify the more complex rule conflict that Rajpopat solved.

There are two rules that contradict when these two terms are combined:

The word “deva” is subject to Rule 7.3.103, which stipulates that when the words are put together, the “a” should become a “e” to create the word “devaiḥ“.

In such a case, prior scholars have understood the metarule to refer to the subsequent rule that came after it, 7.3.103. Devebhih, however, is not the proper word; devaiḥ is. Scholars historically regarded this conflict as an exception, meaning that the other rule must be used when the relevant rule yields an incorrect outcome.

Panini’s meta rule states vipratiṣedhe paraṁ kāryam, which traditional scholars have interpreted as ‘in the event of a conflict between two rules of equal strength, the rule that comes later in the serial order of the Aṣṭādhyāyī, wins.’

Rajpopat went back to the canon text and reinterpreted the meaning of the term “para” to ‘right hand side’. According to his understanding, rule 7.1.9 applies, resulting in the new and correct word, devaiḥ.

This technique eliminates a number of inventive and sophisticated linguistic workarounds provided by others in the past to handle similar rule conflicts.

 In a statement, Rajpopat’s supervisor Vincenzo Vergiani said, “My student Rishi has cracked it — he has found an extraordinarily elegant solution to a problem which has perplexed scholars for centuries. This discovery will revolutionise the study of Sanskrit at a time when interest in the language is on the rise.”

Rajpopat recalled how he managed to arrive at his conclusion. “I had a eureka moment in Cambridge. After 9 months trying to crack this problem, I was almost ready to quit, I was getting nowhere. So I closed the books for a month and just enjoyed the summer, swimming, cycling, cooking, praying and meditating. Then, begrudgingly, I went back to work and with,in minutes, as I turned the pages, these patterns starting emerging, and it all started to make sense. There was a lot more work to do but I’d found the biggest part of the puzzle,” Rajpopat said in the statement.

Before completing his thesis, he spent an additional two and a half years working on the subject.