Ancient grammatical puzzle solved after 2,500 years by PhD student

CAMBRIDGE, United Kingdom — An ancient grammatical puzzle that has baffled scientists for 2,500 years has been solved by a University of Cambridge student.

PhD scholar Rishi Rajpopat finally cracked the riddle which has defeated Sanskrit experts since the 5th Century BC. The 27-year-old accomplished the feat by decoding a rule taught by “the father of linguistics,” Pāṇini.

The discovery makes it possible to “derive” any Sanskrit word – constructing millions of grammatically correct words including “mantra” and “guru” – using Pāṇini’s famous “language machine.” Language experts consider it to be one of the great intellectual achievements in history.

Leading Sanskrit scholars are describing the discovery as “revolutionary.” It could mean that computers can learn Pāṇini’s grammar for the first time. While researching his PhD, Dr. Rajpopat decoded a 2,500-year-old algorithm which makes all this possible.

Why is Pāṇini’s system so complex?

Pāṇini’s system — which includes 4,000 rules detailed in his greatest work, the Aṣṭādhyāyī — was written around 500 BC. Linguists say it works 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 huge problem. Scientists say two or more of Pāṇini’s rules are often simultaneously applicable at the same step, leaving scholars to debate which one to choose. Solving the so-called “rule conflicts,” which affect millions of Sanskrit words, needs an algorithm.

Pāṇini, who historians believe lived in a region in what is now north-west Pakistan and south-east Afghanistan, taught a metarule to help decide which rule is applicable in the event of a rule conflict. For the last 2,500 years, however, scholars have misinterpreted the metarule — meaning they often end up with a grammatically incorrect result.

In an attempt to fix the issue, many researchers worked hard to develop hundreds of other metarules. Despite that, Dr. Rajpopat showed that these metarules are incapable of solving the problem and are also completely unnecessary. He explains that Pāṇini’s language machine is “self-sufficient.”

“Pāṇini had an extraordinary mind and he built a machine unrivalled in human history. He didn’t expect us to add new ideas to his rules. The more we fiddle with Pāṇini’s grammar, the more it eludes us,” says Dr. Rishi Rajpopat in a media release.

How did Rajpopat solve the puzzle?

Traditionally, scientists 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.”

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

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

“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, within 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 says.

“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.”

“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 revolutionize the study of Sanskrit at a time when interest in the language is on the rise,” says Professor Vincenzo Vergiani, Rajpopat’s supervisor at Cambridge.

What is Sanskrit?

Sanskrit is an ancient and classical Indo-European language from 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 have been communicated for centuries.

While only spoken in India by an estimated 25,000 people today, Sanskrit has growing political significance in India, and has influenced many other languages and cultures around the world.

“Some of the most ancient wisdom of India has been produced in Sanskrit and we still don’t fully understand what our ancestors achieved. We’ve often been led to believe that we’re not important, that we haven’t brought enough to the table. I hope this discovery will infuse students in India with confidence, pride, and hope that they too can achieve great things,” Dr. Rajpopat says.

The researcher says a major implication of this discovery is that scientists now have the algorithm that runs Pāṇini’s grammar, making it possible for advanced computers to learn this grammar.

“Computer scientists working on Natural language Processing gave up on rule-based approaches over 50 years ago,” the researcher continues.

“So teaching computers how to combine the speaker’s intention with Pāṇini’s rule-based grammar to produce human speech would be a major milestone in the history of human interaction with machines, as well as in India’s intellectual history.”

South West News Service writer Stephen Beech contributed to this report.

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  1. The most important finding in this study was that swimming, cycling, cooking, praying and meditating lead to scientific breakthroughs. I have chosen to put this discrete finding into immediate practice. Bye for now! See you at the Nobel Prize ceremony!

  2. Something seems amiss here. You mean in 2,500 years nobody ever once guessed, even accidentally, to apply a contentious rule to the right side of a word? It has to be more complicated than that.

  3. This is fascinating! Wish I had been able to look over your shoulder as you went through the process. Puzzles are one of life’s greatest adventures.

  4. The important findings that these articles teach us over and over again would be that the anglo have murdered natives invaded their land stole their artifacts, the most evil human in history

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