2,000 year old Sanskrit puzzle solved?

A PhD student may have found a way to simplify the analysis of Sanskrit grammar, overturning a time-honoured way of reading a classic grammatical description. In his PhD thesis, Dr Rishi Rajpopat (of St John’s College, Cambridge) analysed the oldest surviving descriptive grammar of any language. This is Pāṇini’s Aṣṭādhyāyī, a comprehensive grammar of Sanskrit, composed around 350 BCE.  

The Aṣṭādhyāyī is a collection of 8 (aṣṭa)’ books (adhyāyas), hence the name Aṣṭa-adhyāy(a)-ī. It contains 4,000, ‘rules’ (sūtras) describing how to construct words and sentences.

Sanskrit is an ancient and classical Indo-European language from South Asia. It is the sacred language of Hinduism, and the medium communicating much of India’s science, philosophy, poetry and other secular literature. Although spoken in India by only an estimated 25,000 people today, Sanskrit has growing political significance in India, and has influenced many other languages and cultures around the world. [description taken from Cambridge University announcement below]
Sanskrit is one of 6 languages designated officially as classical in India. Odia, a classical language in India – Language Miscellany

A rule for resolving conflicts between other rules

In many cases, 2 rules in the Aṣṭādhyāyī become applicable at the same step in deriving a construction but one rule blocks the other. The sūtra numbered 1.4.2 determines which rule prevails when one blocks the other. But that procedure sometimes produces a form that is grammatically incorrect.

Rajpopat quotes the following English translation of rule 1.4.2, saying that it accords with the traditional interpretation of the rule:
‘when rules of equal force prohibit each other, then the last in the order herein given is to take effect’.

Said differently: if two rules conflict and are of equal strength, the rule that comes later in the grammar’s serial order wins.

In many cases, applying that interpretation of rule 1.4.2 would lead to the wrong answer. To avoid those wrong answers, grammarians have:

  • added numerous further rules, often addressing very specific cases; or
  • found often tortuous ways to place some parts of the Aṣṭādhyāyī outside the scope of rule 1.4.2.

Rajpopat’s new reading

Rajpopat argues that the traditional approach has to led to elaborate systems of rules that are ad hoc, do not cover every case, generate some wrong answers, make it difficult to see underlying general principles and do not suit implementation by computer.

He proposes that rule 1.4.2 should be read as meaning the following:

if rule A would apply to the left-hand component of a word and rule B would apply to the word’s right-hand component, rule B is selected.
[I have paraphrased his explanation to make the wording less dense.]

Rajpopat has since clarified that by ‘right-hand part’, he really meant the part that is pronounced later. The reference to ‘right’ was because of diagrams present on the printed page, and presented in left-to-right writing. https://www.mail-archive.com/indology@list.indology.info/msg02202.html

It is not known whether the Aṣṭādhyāyī was produced originally in written form, or only orally.

Example of the traditional and proposed readings

As an example, consider the derivation of the instrument plural form of the masculine noun deva (God). The suffix for the instrumental plural is -bhis:

  • Sūtra 7.3.103 would change the final vowel of deva from -a to -e before a suffix beginning with various consonants, including bh.  
  • Sūtra 7.1.9 would change consonant-initial -bhis into vowel-initial -ais after a base ending in -a.
  • Sūtras 7.3.103 and 7.1.9 would block each other. If sūtra 7.3.103 applies first, the base would no longer end in -a and so sūtra 7.1.9 cannot apply. And if sūtra 7.1.9 applies first, the suffix no longer starts with a consonant and so sūtra 7.3.103 cannot apply.
  • The traditional understanding of sūtra 1.4.2 would apply sūtra  7.3.103 because that appears later than sūtra 7.1.9. But that would give the wrong answer (*devebhis). To avoid such wrong answers, scholars of Pāṇini’s work have made many attempts to create detailed and complex rules explaining why, for example, rule 7.1.9 should apply first in some cases.

Using Rajpopat’s proposal:

  • sūtra 1.4.2 means that the first rule applied is the rule covering the right hand component (the suffix -bhis). That rule (7.1.9) would change deva-bhis to deva-ais.
  • after some further rules, deva-ais becomes devais (by sūtra 6.1.88), then devair (by sūtra 8.266) and finally surfaces as devaiḥ (by sūtra 8.3.15).

Rules applying to a single component

The traditional reading of rule 1.4.2 views it as discussing cases where two different rules conflict. Rajpopat’s proposal views the rule as only covering cases where one rule would apply to the left-hand component of a word and a different rule B would apply to the right-hand component.

Under Rajpopat’s proposal, rule 1.4.2 would not cover cases where 2 different rules apply to the same component: both to the left-hand component, or both to the right-hand component. Such conflicts would be governed by a general principle that a more specific rule prevails over a more general rule. Rajpopat says that although Pāṇini did not state this principle explicitly, it is a traditional notion and is also an inherent feature style of sūtra style.    

The name Pāṇini is not to be confused with name of the Italian sandwiches known as panini. Pāṇini and Panini – Language Miscellany


Scholars of Sanskrit seem sceptical of Rajpopat’s ideas:

It may be too early too judge whether his approach will gain wide support.


In Pāṇini We Trust: Discovering the Algorithm for Rule Conflict Resolution in the Aṣṭādhyāyī, R A Rajpopat (PhD thesis, University of Cambridge, 2022). DOI: 10.17863/CAM.80099 https://www.cam.ac.uk/system/files/rajpopat_phd_thesis_15_dec_2022.pdf

Cambridge University announcement https://www.cam.ac.uk/stories/solving-grammars-greatest-puzzle?

PhD student solves 2,500-year-old Sanskrit problem https://www.bbc.co.uk/news/articles/cg3gw9v7jnvo  

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