An ancient grammatical riddle solved after 2,500 years

An ancient grammatical riddle solved after 2,500 years

A page from an 18th century copy of Pāṇini’s Dhātupāṭha (MS Add.2351) held by the University of Cambridge Library. Credit: Cambridge University Library

A grammatical problem that has overcome Sanskrit scholars since the 5th century BC has finally been solved by an Indian doctor. student at the University of Cambridge. Rishi Rajpopat made the breakthrough by decoding a rule taught by “the father of linguistics”, Pāṇini.

This discovery allows any Sanskrit word to be “derived” – to construct millions of grammatically correct words, including “mantra” and “guru” – using Pāṇini’s revered “language machine”, which is widely regarded as one of the great intellectual achievements in history.

Prominent Sanskrit experts have described Rajpopat’s discovery as “groundbreaking” and this could now mean that Pāṇini’s discovery grammar can be taught computers for the first time.

During his doctoral research. thesis, published today, Dr. Rajpopat has decoded a 2,500-year-old algorithm that allows, for the first time, to use Pāṇini’s “language machine” with precision.

Pāṇini’s system – 4,000 rules detailed in his greatest work, the Aṣṭādhyāyī, said to have been written around 500 BC – is supposed to work like a machine: introduce the base and suffix of a word and it should transform them into grammatically correct words and phrases through a step-by-step process.

Until now, however, there was one big problem. Often two or more Pāṇini’s rules are applicable simultaneously at the same step, leaving scholars to wonder which one to choose.

Solving the so-called “rule clashes”, which affect millions of Sanskrit words, including some forms of “mantra” and “guru”, requires an algorithm. Pāṇini taught a metarule to help us decide which rule should be applied in the event of a “rule conflict”, but over the past 2,500 years scholars have misinterpreted this metarule, meaning they have often misunderstood. found with a grammatically incorrect result.

In an attempt to solve this problem, many researchers have painstakingly developed hundreds of other meta-rules, but Dr. Rajpopat shows that they are not only incapable of solving the problem in question – they have all produced too many exceptions – but also completely useless. Rajpopat shows that Pāṇini’s “linguistic machine” is self-sufficient.

Rajpopat said: “Pāṇini had an extraordinary mind and he built a machine unequaled in The human story. He didn’t expect us to add new ideas to his rules. The more we fiddle with Pāṇini’s grammar, the more it escapes us.”

Traditionally, scholars have interpreted Pāṇini’s metarule to mean that in the event of a conflict between two equally strong rules, the rule that comes later in the serial order of the grammar wins.

Rajpopat rejects this, arguing instead that Pāṇini meant that between the rules applicable respectively to the left and right sides of a word, Pāṇini wanted us to choose the rule applicable to the right side. Using this interpretation, Rajpopat found that Pāṇini’s language machine produced grammatically correct words with almost no exceptions.

Take “mantra” and “guru” as examples. In the phrase “Devāḥ prasannāḥ mantraiḥ” (“The Gods [devāḥ] are satisfied [prasannāḥ] by the mantras [mantraiḥ]”) we encounter a “conflict of rules” when deriving the mantraiḥ “by the mantras.” The derivation begins with “mantra + bhis.” One rule is applicable to the left part, “mantra'”, and the other to the right part, “bhis”. ” We have to choose the rule for the right part, “bhis”, which gives us the correct form, “mantraiḥ”.

In the phrase “Jñānaṁ dīyate guruṇā” (“Knowledge [jñānaṁ] is given [dīyate] by the guru [guruṇā]”) we encounter a conflict of rules when deriving guruṇā “by the guru”. The derivation begins with “guru + ā.” One rule is applicable to the left part, “guru” and the other to the right part “ā”. We have to choose the rule for the right part, “ā”, which gives us the correct form, “guruṇā”.

Eureka Moment

Six months before Rajpopat made his discovery, his supervisor at Cambridge, Sanskrit professor Vincenzo Vergiani, gave him prescient advice: “If the solution is complicated, you are probably wrong.”

Rajpopat said: “I had a eureka moment at Cambridge. After 9 months trying to solve this problem I was almost ready to quit, I wasn’t going anywhere. So I closed the books for a month and I just enjoyed the summer, swimming, biking, cooking, praying, and meditating. Then, reluctantly, I returned to work, and within minutes, as I turned the pages, these patterns started to emerge, and everything started to make sense. There was still a lot of work to do, but I’ve found most of the puzzle.”

“Over the next few weeks, I was so excited that I couldn’t sleep and spent hours in the library, including the middle of the night, checking out what I had found and solving related issues. This work took another two and a half years.”


Professor Vincenzo Vergiani said: “My student Rishi has solved it – he has found an extraordinarily elegant solution to a problem that has perplexed researchers for centuries. This discovery will revolutionize the study of Sanskrit at a time when interest in the language is on the rise. .”

Sanskrit is an ancient and classical Indo-European language of South Asia. It is the sacred language of Hinduism, but also the medium through which much of India’s greatest science, philosophy, poetry and other secular literature has been communicated for centuries. Although only spoken in India by about 25,000 people today, Sanskrit has been of growing political importance in India and has influenced many other languages ​​and cultures around the world.

Rajpopat said: “Some of India’s oldest wisdom has been produced in Sanskrit and we still do not fully understand what our ancestors did. We have often been led to believe that we are not important, that we I hope this discovery will instill confidence, pride and hope in Indian students that they too can achieve great things.

A major implication of Dr. Rajpopat’s discovery is that now that we have the algorithm that runs Pāṇini’s grammar, we could potentially teach this grammar to computers.

Rajpopat said: “Computer scientists working on nature Language processing abandoned rule-based approaches over 50 years ago… So teaching computers how to combine speaker intent with Pāṇini’s rule-based grammar to produce human speech would be a milestone in the history of human interaction with machines, as well as in the intellectual history of India.”

The research is published in the journal Apollo – Cambridge University Repository.

More information:
Rishi Rajpopat, In Pāṇini We Trust: Discovering the Algorithm for Rule Conflict Resolution in the Aṣṭādhyāyī, Apollo – Cambridge University Repository (2022). DOI: 10.17863/cam.80099

Quote: Ancient grammatical puzzle solved after 2500 years (December 14, 2022) Retrieved December 15, 2022 from

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