Pāṇinian Grammar: Part 2 - Pāṇini’s Problem

Pāṇini was facing the same problem as a fruit vendor. There is a phenomenon called Sandhi in Saṃskṛta wherein final sounds of a word change so as to accommodate well with the beginning sound of the word that follows it. For example, no language in this world tolerates two vowels coming together at word boundaries - they avoid it by some or the other means.

Example: a book (OK in English) but a egg (not OK in English). Why? Because there is a succession of two vowels “a-e” in the phrase a egg! English avoids this vowel-vowel hiatus by inserting a consonant in between - it chooses N - and hence we have an egg! So, the addition of “N” to change “a” to “an” is actually a sandhi in English. Both “a” and “an” are exactly the same as far as meaning is concerned - indefinite articles. Just that “an” is a Sandhi adjusted form to avoid a vowel-vowel hiatus when the word following the article also begins with a vowel. Saṃskṛta speakers were very conscious of these sound changes happening at boundaries since their language flourished in a purely oral culture and hence minutely noted these changes. Saṃskṛta however follows a different strategy to avoid a vowel-vowel hiatus. When the vowel that ends the first word is इ/उ/ ऋ/ऌ (i/u/ṛ/ḷ), then instead of inserting a consonant, the initial vowel itself converts into its appropriate semi-vowel consonant य्/व्/र्/ल् (y/v/r/l). These transformations are:

• इ => य् (i=>y)
• उ => व् (u=>v)
• ऋ => र् (ṛ=>r)
• ऌ => ल् (ḷ=>l)

Examples:

• प्रति + उषा = प्रत्युषा
• सु + आगतम् = स्वागतम्
• मातृ + अंशः = मात्रंशः
• prati + uṣā = pratyuṣā
• su + āgatam = svāgatam
• mātṛ + aṃśaḥ = mātraṃśaḥ

So Pāṇini wanted to actually say that

If an (इ/उ/ ऋ/ऌ i/u/ṛ/ḷ) is followed by any other vowel, then replace (इ/उ/ ऋ/ऌ i/u/ṛ/ḷ) by (य्/व्/र्/ल् y/v/r/l)” respectively.

Pāṇini could not afford to say this in so many words - he was not writing a book but rather composing orally transmittable texts. He had 4000 sutras (lines of code) and he wanted each line to be as compressed and brief as possible. So to compress them, Pāṇini uses two strategies:

1. Creating an efficiently arranged list of sounds to call upon easily (reminds you of the fruit basket problem?!)
2. Hijacking the normal meaning of small endings in his language and using them to convey algorithmic transformations of sounds (sounds like the auxiliary verb problem?!!)

Note that Pāṇini not only had to call the group of sounds like (i,u,ṛ,ḷ) and (y,v,r,l) but also dozens of other groups of sounds for other sandhis and other purposes as well. So this is exactly the fruit vendor problem and what he did was exactly what we had said there also - create a well ordered list so that the required groups of sounds to be called, fall consecutively and hence can be summoned by just saying the initial and final sound (with the implicit understanding that sounds in between are also included).

Pāṇini did arrange the sounds of Saṃskṛta in such a list, and it is called the Śivasūtras because he believed that these sounds originated from the drum of Lord Shiva. The list is:

• अ इ उ ण् | a i u ṇ
• ऋ ऌ क् | ṛ ḷ k
• ए ओ ङ् | e o ṅ
• ऐ औ च् | ai au c
• ह य व र ट् | ha ya va ra ṭ
• ल ण् | la ṇ
• ञ म ङ ण न म् | ña ma ṅa ṇa na m
• झ भ ञ् | jha bha ñ
• घ ढ ध ष् | gha ḍha dha ṣ
• ज ब ग ड द श् | ja ba ga ḍa da ś
• ख फ छ ठ थ च ट त व् | kha pha cha ṭha tha ca ṭa ta v
• क प य् | ka pa y
• श ष स र् | śa ṣa sa r
• ह ल् | ha l

This is the list that Pāṇini created and credited to Lord Śiva. There is only one difference between this and the fruit list. The last sound in each line which are pure consonant sounds (with no inherent vowel attached) together are called “mute letters” and are not a part of the list and hence excluded in any enumeration. Only letters with the inherent vowel “a” are part of the list (black letters). Why would Pāṇini add these mute bolded letters anyway? Wait till the next article in the series: Pāṇini is a genius. Everything he does has amazing foresight and reason behind it.

How efficient is this ordering of letters in the Śivasūtras for the groups of sounds that Pāṇini wants to refer to? For the collection of letters he wants to refer to, this ordering is the most optimal, as per the analysis done by the mathematician Wiebke Petersen in his paper here.

Now, seeing this list, for the Sandhi rule we saw earlier, recalling it: “If an (इ/उ/ ऋ/ऌ i/u/ṛ/ḷ) is followed by any other vowel, then replace (इ/उ/ ऋ/ऌ i/u/ṛ/ḷ) by (य्/व्/र्/ल् y/v/r/l)” respectively”.

Now, hence we need to call three sets of sounds for this Sandhi rule:

1. First set - the four vowels (इ/उ/ ऋ/ऌ i/u/ṛ/ḷ) that precede
2. Second set - the set of all vowels that can follow
3. Third set - the four consonants (इ/उ/ ऋ/ऌ i/u/ṛ/ḷ) that are going to replace the vowels in 1.

Seeing the list above, the three sets can be called as:

1. इक् ik (set of all sounds in the list from इ to क् excluding the red letters)
2. अच् ac (set of all sounds in the list from अ to च् excluding the red letters)
3. यण् yaṇ (set of all sounds in the list from य to ण् excluding the red letters)

If you collect the sounds as directed above from the list (Śivasūtras), you will end up with the exact set of sounds that you want for the rule in the same order! So, the rule can now be compressed somewhat as: “When an इक् ik letter is followed by an अच् ac letter, replace the इक् ik letter by its corresponding यण् yaṇ letter”

But Pāṇini is not happy with this level of compression - he wants to further compress the conditional statements and the replacement rule also. For that, we need to take a slightly congruent detour of Saṃskṛta case endings. For words ending in consonants, we have the following meanings associated with endings. Eg. The words जागत् jagat and मरुत् marut mean “world” and “wind” respectively. In the normal Saṃskṛta language, the following endings change the meaning as follows:

• जागत् | jagat = the world
• जगतः | jagataḥ = of the world
• जगति | jagati = in/on/at the world?
• मरुत् | marut = the wind
• मरुतः | marutaḥ = of the wind
• मरुति | maruti = in/on/at the wind

So, we see that in normal language, for words ending in consonant, the ending aḥ conveys the meaning of of and the ending i conveys a sense of location as conveyed by a preposition like in/on/at. But these prepositions are the meanings of the ending in the unhiijacked Saṃskṛta language in normal usage! Oh my god - what Pāṇini does now would be unbelievable! He will now hijack these case endings and use it for his special operations in the sūtras!

What Pāṇini does here is this. He indirectly declares something like: “Grammarians, forget what the endings aḥ, i mean in our normal Saṃskṛta language. As far as my sūtras are concerned, they will stand for these operations:

1. aḥ => this will stand for the group of sounds that precede and need to be replaced.
2. i => this will stand for the group of sounds that follow.
3. no ending => this will stand for the group of sounds that replace the first set of sounds.

Pāṇini hijacks the normal Saṃskṛta language (at least some part of it - the case endings) for his coding purposes - in computer jargon - this is called metalanguage! Pāṇini is essentially creating a metalanguage out of a natural language (Saṃskṛta) for his coding purpose!!!! Isn’t this genius!

In case of auxiliary verbs, a word gets hijacked within the natural language itself to convey certain other abstract grammatical purposes - Pāṇini now hijacks some case endings of the language - strips them of their normal meaning - and encodes them with a new instructional meaning as far as the context of his sutras are concerned!!

So, in this elegant meta-language and the well-ordered list of sounds in the Śivasūtras, this rule can be summarized elegantly as: इकः यण् अचि | ikaḥ yaṇ aci

• Literal meaning of the Sutra: Of IK, in AC, yan (does not make any sense)
• Actual meaning in the meta-language of the sutra: Whenever an IK sound is followed by an AC sound, replace the IK sound by its corresponding YAṆ sound

(Actually the sutra reads इको यण् अचि iko yaṇ aci due to Sandhi of the visarga sound : ḥ but let’s not bother with such minutiae now). So we see how an elaborate set of Sandhi rules has been so efficiently compressed to a very small statement “ik aḥ yaṇ ac i” using efficient lists and meta-language. This meta-language will be useful throughout the language because Saṃskṛta is a left-changing language predominantly - that is when two sounds meet, mostly it is the first sound that gets replaced while the second sound stays put. So, this meta language of aḥ denoting both the first sound and the sound that needs to be replaced is useful across all operations concerning the Saṃskṛta language.

Thus far, we have seen two important concepts in advanced mathematics and computer science used in Pāṇinian grammar. In the next sections, we will see what those bolded/underlined letters are doing in the Śivasūtras and also more sophisticated metalanguage. Gradually, we will see other concepts.

Authored by Rama Seshan Chandra Sekaran. Published by Brhat.