Solving a 2,500-Year-Old Puzzle: How a Cambridge Student Cracked an Ancient Sanskrit Code

If you find your­self grap­pling with an intel­lec­tu­al prob­lem that’s gone unsolved for mil­len­nia, try tak­ing a few months off and spend­ing them on activ­i­ties like swim­ming and med­i­tat­ing. That very strat­e­gy worked for a Cam­bridge PhD stu­dent named Rishi Rajpopat, who, after a sum­mer of non-research-relat­ed activ­i­ties, returned to a text by the ancient gram­mar­i­an, logi­cian, and “father of lin­guis­tics” Pāṇi­ni and found it new­ly com­pre­hen­si­ble. The rules of its com­po­si­tion had stumped schol­ars for 2,500 years, but, as Rajpopat tells it in an arti­cle by Tom Almeroth-Williams at Cam­bridge’s web­site, “With­in min­utes, as I turned the pages, these pat­terns start­ed emerg­ing, and it all start­ed to make sense.”

Pāṇi­ni com­posed his texts using a kind of algo­rithm: “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,” writes Almeroth-Williams. But “often, two or more of Pāṇini’s rules are simul­ta­ne­ous­ly applic­a­ble at the same step, leav­ing schol­ars to ago­nize over which one to choose.” Or such was the case, at least, before Rajpopat’s dis­cov­ery that the dif­fi­cult-to-inter­pret “metarule” meant to apply to such cas­es dic­tates 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.”

That may not be imme­di­ate­ly under­stand­able to those unfa­mil­iar with the struc­ture of San­skrit. Almeroth-Williams’ piece clar­i­fies with an exam­ple using  mantra, one word from the lan­guage that every­body knows. “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,’ ” he writes. ” The deriva­tion starts with ‘mantra + bhis.’ One rule is applic­a­ble to the 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 ‘mantraih.’ ”

Apply­ing this rule ren­ders inter­pre­ta­tions of Pāṇini’s work almost com­plete­ly unam­bigu­ous and gram­mat­i­cal. It could even be employed, Rajpopat has not­ed, to teach San­skrit gram­mar to com­put­ers being pro­grammed for nat­ur­al lan­guage pro­cess­ing. It no doubt took him a great deal of inten­sive study to reach the point where he was able to dis­cov­er the true mean­ing of Pāṇini’s clar­i­fy­ing metarule, but it did­n’t tru­ly present itself until he let his uncon­scious mind take a crack at it. As we’ve said here on Open Cul­ture before, there are good rea­sons we do our best think­ing while doing things like walk­ing or tak­ing a show­er, a phe­nom­e­non that philoso­phers have broad­ly rec­og­nized through the ages — and, like as not, was under­stood by the great Pāṇi­ni him­self.

Relat­ed con­tent:

Learn Latin, Old Eng­lish, San­skrit, Clas­si­cal Greek & Oth­er Ancient Lan­guages in 10 Lessons

Intro­duc­tion to Indi­an Phi­los­o­phy: A Free Online Course

Can Arti­fi­cial Intel­li­gence Deci­pher Lost Lan­guages? Researchers Attempt to Decode 3500-Year-Old Ancient Lan­guages

Why Algo­rithms Are Called Algo­rithms, and How It All Goes Back to the Medieval Per­sian Math­e­mati­cian Muham­mad al-Khwariz­mi

How Schol­ars Final­ly Deci­phered Lin­ear B, the Old­est Pre­served Form of Ancient Greek Writ­ing

Has the Voyn­ich Man­u­script Final­ly Been Decod­ed?: Researchers Claim That the Mys­te­ri­ous Text Was Writ­ten in Pho­net­ic Old Turk­ish

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on Twit­ter at @colinmarshall or on Face­book.