A RECENT ARTICLE IN Nice Newscaught my eye for several reasons: First, the grammatical puzzle arose in the linguistics of Sanskrit. I’ve been tantalized by this language after learning that Lithuanian has been called the nearest modern language to this Indo-European base. (Not that I speak Lithuanian, mind; but my ancestors did.)
Also, I am highly impressed that a Ph.D. student came up with something so monumental. (My Ph.D. in mathematics, by contrast, leans toward the grad school parable that some are “bits of academic research done by thesis advisors under extremely trying circumstances.”)
Last, this article served as a springboard in encouraging me to research lots of things related to this topic. Here are tidbits gleaned from them all.
Sanskrit Linguistics. According to Britannica, Sanskrit is an inflected language, with changes in a word “to mark such distinctions as tense, person, number, gender, mood, voice and case.”
“For instance,” Britannica notes, “the Sanskrit nominal system—including nouns, pronouns, and adjectives—has three genders (masculine, feminine, and neuter), three numbers (singular, dual, and plural), and seven syntactic cases (nominative, accusative, instrumental, dative, ablative, genitive, and locative), in addition to a vocative.”
I’m told that Lithuanian displays similar linguistic complications. By contrast, English is easy-peasy in this regard.
Pāṇini’s Aṣṭādhyāyī. Pāṇini was a revered scholar in ancient India, variously dated between the 7th and 4th century B.C. (See MacTutor for historians trying to pin down ancient dates.)
According to Wikipedia, “Since the discovery and publication of his work by European scholars in the nineteenth century, Pāṇini has been considered the ‘first descriptive linguist‘ and even labelled as ‘the father of linguistics.’ ”
In his treatise called Aṣṭādhyāyī, Pāṇini assembled 3996 verses in eight chapters of Sanskrit grammatical rules. (And you thought McGuffey Readers were a pain.) Pāṇini’s “language machine” was considered to be one of the great intellectual achievements in history. And, for some 2500 years, its use has been something of a puzzle for linguist scholars.
A Significant Ph.D. Rishi Rajpopat learned Sanskrit in high school and was introduced to Pāṇini’s grammar while pursuing his Bachelors in Economics. He continued to a Master’s at Oxford, then a Ph.D. at St John’s College, Cambridge in 2017.
Pāṇini’s Rule Conflicts. As described in a University of Cambridge news release, Rajpopat focused his studies on conflicts in Pāṇini’s grammar: “Pāṇini taught a metarule … 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.”
More often than not, not only were these misinterpretations wrong, they also added complexity to what was already a complex grammar.
Also see the news release for a discussion of “mantra” and “guru” and its examples of the existing complexities. And note too Rajpopat’s thesis advisor Vincenzo Vergiana’s sage advice: “If the solution is complicated, you are probably wrong.”
Resolution. Briefly, when confronted with two grammatical rules of equal importance, scholars traditionally interpreted Pāṇini’s metarule to mean “apply the rule that comes later in the grammar’s serial order.”
Instead, Rajpopat tried a simpler but more elegant interpretation: “choose the rule applicable to the right side of the word, not the left.” In doing so, the news release notes, “Rajpopat found that Pāṇini’s language machine produced grammatically correct words with almost no exceptions.”
How to say Q.E.D., Quod Erat Demonstrandum, “Which Was to be Proven,” in Sanskrit? ds