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Solving grammar’s greatest puzzle

How a determined student made Sanskrit’s ‘language machine’ work for the first time in 2,500 years

A grammatical problem which has defeated Sanskrit scholars since the 5th Century BC has finally been solved by an Indian PhD student at the University of Cambridge.

Rishi Rajpopat (St John’s College) made the breakthrough by decoding a rule taught by “the father of linguistics” Pāṇini.

The discovery makes it possible to ‘derive’ any Sanskrit word – to construct millions of grammatically correct words including ‘mantra’ and ‘guru’ – using Pāṇini’s revered ‘language machine’ which is widely considered to be one of the greatest intellectual achievements in history.

Leading Sanskrit experts have described Rajpopat’s discovery as ‘revolutionary’ and it could now mean that Pāṇini’s grammar can be taught to computers for the first time.

While researching for his PhD thesis, published on 15th December 2022, Dr Rajpopat decoded a 2,500 year old algorithm which makes it possible, for the first time, to accurately use Pāṇini’s ‘language machine’.

Pāṇini’s system – 4,000 rules detailed in his renowned work, the Aṣṭādhyāyī, which is thought to have been written around 500BC – is meant to work like a machine. Feed in the base and suffix of a word and it should turn them into grammatically correct words and sentences through a step-by-step process.

Until now, however, there has been a big problem. Often, two or more of Pāṇini’s rules are simultaneously applicable at the same step leaving scholars to agonise over which one to choose.

Solving so-called ‘rule conflicts’, which affect millions of Sanskrit words including certain forms of ‘mantra’ and ‘guru’, requires an algorithm.

Pāṇini taught a metarule – termed by Rajpopat ‘1.4.2 vipratiṣedhe paraṁ kāryam’ – to help us decide which rule should be applied in the event of ‘rule conflict’ but for the last 2,500 years, scholars have misinterpreted this metarule meaning that they often ended up with a grammatically incorrect result.

In an attempt to fix this issue, many scholars laboriously developed hundreds of other metarules but Dr Rajpopat shows that these are not just incapable of solving the problem at hand – they all produced too many exceptions – but also completely unnecessary. Rajpopat shows that Pāṇini’s ‘language machine’ is ‘self-sufficient’.

Traditionally, scholars have interpreted Pāṇini’s metarule as meaning:

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 rejects this, arguing instead that Pāṇini meant that between rules applicable to the left and right sides of a word respectively, Pāṇini wanted us to choose the rule applicable to the right side.

Employing this interpretation, Rajpopat found Pāṇini’s language machine produced grammatically correct words with almost no exceptions.

Take ‘mantra’ and ‘guru’ as examples.

In the sentence ‘devāḥ prasannāḥ mantraiḥ’ (‘The Gods [devāḥ] are pleased [prasannāḥ] by the mantras [mantraiḥ]’) we encounter ‘rule conflict’ when deriving mantraiḥ ‘by the mantras’.

The derivation starts with ‘mantra + bhis’. One rule is applicable to left part ‘mantra’ and the other to right part ‘bhis’. We must pick the rule applicable to the right part ‘bhis’, which gives us the correct form ‘mantraiḥ’.

And in the the sentence ‘jñānaṁ dīyate guruṇā’ (‘Knowledge [jñānaṁ] is given [dīyate] by the guru [guruṇā]’) we encounter rule conflict when deriving guruṇā ‘by the guru’.

The derivation starts with ‘guru + ā’. One rule is applicable to left part ‘guru’ and the other to right part ‘ā’.

We must pick the rule applicable to the right part ‘ā’, which gives us the correct form ‘guruṇā’.

Eureka moment

As Rajpopat struggled to make progress, his supervisor at Cambridge, Professor Vincenzo Vergiani, Professor of Sanskrit, gave him some prescient advice: “If the solution is complicated, you are probably wrong.”

“Six months later, I had a eureka moment,” Rajpopat says. “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, within minutes, as I turned the pages, these patterns starting emerging, and it all started to make sense.

“At that moment, I thought to myself, in utter astonishment: For over two millennia, the key to Pāṇini’s grammar was right before everyone’s eyes but hidden from everyone’s minds!”

“There was a lot more work to do but I’d found the biggest part of the puzzle. Over the next few weeks I was so excited, I couldn’t sleep and would spend hours in the library including in the middle of the night to check what I’d found and solve related problems. That work took another two and half years.””

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