Cambridge student solves 2,500-year-old grammar puzzle

As a purposeful student, for the first time in 2500 years, he put the “language machine” of Sanskrit to work. (CREDIT: University of Cambridge)

A grammatical problem that has baffled 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 a breakthrough by deciphering a rule taught by the “father of linguistics” Panini.

The discovery makes it possible to “extract” any Sanskrit word – to construct millions of grammatically correct words, including “mantra” and “guru” – using Panini’s revered “language machine”, widely regarded as one of the greatest intellectual achievements in history. .

Leading Sanskrit experts have described Rajpopat’s discovery as “revolutionary”, and this could now mean that Panini’s grammar can be taught to computers for the first time.

While working on his doctoral thesis, Dr. Rajpopat deciphered a 2,500-year-old algorithm that for the first time allows accurate use of Panini’s “language machine”.

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Panini’s system of 4,000 rules detailed in his famous work Ashtadhyayi, which is believed to have been written around 500 BC. e., is designed to work like a machine. Feed in a word stem and suffix, and it should turn them into grammatically correct words and sentences with a step-by-step process.

However, there is still a big problem. Often two or more of Panini’s rules are applied at the same time at the same step, leaving scientists agonizing over which one to choose.

An algorithm is required to resolve the so-called “rule conflicts” that affect millions of Sanskrit words, including certain forms of “mantra” and “guru”.

Panini taught a meta-rule called “1.4.2 vipratishedhe param karyam” by Rajpopat to help us decide which rule to apply in the event of a “rule conflict”, but over the past 2500 years, scholars have misinterpreted this rule, meaning that they often got grammatically incorrect result.

In an attempt to solve this problem, many scientists have painstakingly developed hundreds of other meta-rules, but Dr. Rajpopat shows that not only are they incapable of solving the problem at hand – they all generated too many exceptions – but they are completely unnecessary. Rajpopat shows that Panini’s “language machine” is “self-sufficient”.

“Panini had an extraordinary mind, and he built a machine that has no equal in the history of mankind. He didn’t expect us to add new ideas to his rules. The more we fiddle with Panini’s grammar, the more it eludes us.” – Rishi Rajpopat

Traditionally, scholars have interpreted Panini’s meta-rule to mean:

In the event of a conflict between two rules of equal strength, the rule that follows later in the sequential order of the grammar wins.

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

Using this interpretation, Rajpopat found that Panini’s language machine produced grammatically correct words with almost no exceptions.

Let’s take “mantra” and “guru” as examples.

In the sentence “deveh prasannah mantraih” (“Gods [devāḥ] satisfied [prasannāḥ] by mantras [mantraiḥ]’) we encounter a “rule conflict” when we receive mantraih “through mantras”.

The conclusion begins with “mantra + bhi”. One rule applies to the left side of the “mantra” and another to the right side of the “bhi”. We must choose the rule that applies to the right side of “bhis”, which gives us the correct form of “mantraiḥ”.

And in the sentence “jnanam diyate guruna” (“Knowledge [jñānaṁ] given [dīyate] guru [guruṇā]’) we run into a conflict of rules when we receive guruṇā “from the guru”.

The origin begins with “guru + ā”. One rule applies to the left side of ‘guru’ and another applies to the right side of ‘a’.

We must choose the rule that applies to the right side of “a”, which gives us the correct form of “guruna”.

eureka moment

As Rajpopat struggled to make progress, his research advisor at Cambridge, Professor Vincenzo Vergiani, professor of Sanskrit, gave him forward-thinking advice: “If the solution is hard, you’re probably wrong.”

A stamp issued by India in 2004 in memory of Panini. (CREDIT: University of Cambridge)

“Six months later, I had a moment of insight,” says Rajpopat. “I was almost ready to leave, I didn’t achieve anything. So I closed my books for a month and just enjoyed the summer swimming, biking, cooking, praying and meditating.

“Then I reluctantly returned to work, and after a few minutes as I flipped through the pages, these patterns began to emerge and it all began to make sense.

“At that moment, I thought to myself in complete amazement: for more than two millennia, the key to Panini’s grammar was right in front of everyone’s eyes, but was hidden from all minds!”

Page from an 18th-century copy of Dhatupatha Panini (MS Add.2351) held by the Cambridge University Library. (CREDIT: University of Cambridge)

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

Significance

Sanskrit is an ancient and classical Indo-European language from South Asia. It is the sacred language of Hinduism and also the medium by which much of India’s greatest science, philosophy, poetry and other secular literature has been transmitted for centuries.

Vakyapadiya Bhartrihari (5th century CE), a treatise on the philosophy of language belonging to the Panin school of grammar. Cambridge University Library (MS Add.876). Click here for more information on the Library’s Sanskrit collections. (CREDIT: University of Cambridge)

Although only about 25,000 people speak Sanskrit in India today, Sanskrit has a growing political importance in India and has influenced many other languages ​​and cultures around the world.

“Some of the most ancient wisdom of India was created in Sanskrit, and we still do not fully understand what our ancestors achieved.” — Rishi Rajpopat

“We were often made to think that we were not important, that we didn’t bring enough to the table. I hope this discovery will instill confidence, pride and hope in students in India that they, too, can achieve great things.”

Vincenzo Vergiani, professor of Sanskrit at the University of Cambridge, says:

“My student Rishi figured it out – he found an extraordinarily elegant solution to a problem that has baffled scientists for centuries. This discovery will revolutionize the study of Sanskrit at a time when interest in the language is growing.”

The main takeaway from Dr. Rajpopat’s discovery is that we now have an algorithm that runs Panini’s grammar, and we can potentially teach this grammar to computers.

Pages from the Bhagavad Gita, written in Sanskrit, which presents in poetic form some of the fundamental spiritual concepts of Hinduism (India, 1824). (CREDIT: University of Cambridge)

“Computers working on natural language processing abandoned rule-based approaches more than 50 years ago,” says Rajpopat.

“Therefore, teaching computers how to combine the speaker’s intent with Panini’s rule-based grammar to reproduce human speech will be an important milestone in the history of human-machine interaction as well as in the intellectual history of India.”

Panini is believed to have lived in a region in what is now northwestern Pakistan and southeastern Afghanistan.

Rishi Rajpopat was born in a suburb of Mumbai in 1995. Rajpopat learned Sanskrit in high school and Panini’s Sanskrit grammar informally from a retired Indian professor for free while pursuing a bachelor’s degree in economics in Mumbai.

After earning a master’s degree from Oxford, for which he raised money by writing to hundreds of potential donors, Rajpopat began his PhD at St John’s College and the Faculty of Asian and Middle Eastern Studies, Cambridge in 2017 on a full scholarship funded by the Cambridge Foundation and the Rajiv Foundation. Gandhi Foundation. In January 2022, he was awarded his Ph.D. He recently entered the Divinity School at the University of St. Andrews.

Cambridge has a long history of Sanskrit study, and the University of Cambridge Library has a significant collection of Sanskrit manuscripts.

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Note: Materials provided above by the University of Cambridge. Content can be edited for style and length.

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