A verse from Vairōcana’s “Rasikaprakāśana” (29)

I was reorganizing my notes for an unpublished anthology of Prakrit verse by one Vairōcana (a Buddhist) and I came across the following gīti verse (no. 29, of 448):

दुल्लहसुअणमिलावो उच्चलिउं अहव उच्चलावेउं ।
जाण मणे विप्फुरए को ताण समो हु णीरसो भुअणे ॥ २९ ॥

dullaha-suaṇa-milāvō uccaliuṁ ahava uccalāvēuṁ ~
jāṇa maṇē vipphuraē kō tāṇa samō hu ṇīrasō bhuaṇē ~~

When the company of good people, so hard to come by,
continues to illuminate the heart after one has left,
or been made to leave,
not even solitude lacks its pleasures.

Maybe “solitude” is not the most exact translation for sama-/śama-, but it’s close.

Syllables per line of a gāthā

The gāthā is not a syllable-counting meter. It can vary from 30 to 56 syllables. But scribes still counted (and presumably charged) by the syllable. So one would like to have a good way of converting between a the number of verses in a text and the number of syllables represented by those verses. If you have a program that can count syllables in a text (like the validator for Prakrit gāthās that I posted some time ago) then this is pretty easy. For the Pāiyalacchī of Dhanapāla, I counted 9983 syllables over 279 verses, thus averaging 35.8 syllables per verse. But let’s say we want to see the distribution of numbers of syllables for the first line and second line of each verse (the second line being shorter). We can easily collect this information (I’ve updated the validator to produce CSV output for each line) and here it is:

Note that the weighted average number of syllables for the first line is 18.95, and for the second line, 16.83. When we multiply these by the number of verses, we get 9983, the total number of syllables I counted.

These distributions might be of interest for trying to go between the number of syllables/granthas and number of verses in an unknown text. They might also be of stylistic relevance.

A. N. Upadhye’s teachers

What was the intellectual formation of such a great textual scholar as A. N. Upadhye? B. K. Khadabadi says in his short monograph on Upadhye:

From Dr. P. L. Vaidya he received a sense of the importance of, and an interest in, Prakrit literature and language, which had largely been created and developed by Jain teachers. From Dr. V. S. Sukthankar he got the foundational elements of sensitive editing: the ability to engage in the textual criticism of manuscripts of ancient Jain texts, and the art of principled selection of readings. From Dr. Belvalkar he learned the adage ‘One thing at a time, and that too to its completion,’ taking up only one research project, or one edition, at a time. From Muniśrī Jinavijaya he knew a principle of experience, namely, that being able to imagine the various formats of ancient manuscripts, and the complete knowledge of the tradition of the Jain dharma, were the basis for sensitive research and editing. From such serious scholars as Professor Schubring, who stood in the place of his own guru, he knew the currents of Western research in his own research and editing, and he adopted them in moderation. All of these components are visible in his research and editorial work.

I have not learned Belvalkar’s lesson.

From B. K. Khaḍabaḍi’s Ḍā. Ā. Nē. Upādhye Jīvana-sadhane, p. 35. (My translation.)

Parsing Tamil verse: some observations

As I am learning more about Tamil meter, I have been very interested in Kevin Ryan’s suggestion (Phonology 34.3 [2017]: 581–613) that the metrical units of Tamil verse consist of a strong position and a weak position which are subject to weight-mapping of different strictness. The Tamil metrical tradition doesn’t distinguish between a strong and a weak position within a cīr, as far as I know, but it might not need to: it may have been taken for granted that the first acai in a cīr was “strong,” and the second “weak,” in some sense.

I tried writing another Python script to automatically parse a Tamil text into metrical units (syllables, acaicīr, and lines). The script can be found in this GitHub gist. The data I used was the electronic text of the Kuṟuntokai posted on GRETIL by Project Madurai (evidently from 2001!).

Luckily, that version of the Kuṟuntokai is typed according to the “traditional” system of putting spaces between cīr rather than between words. (I don’t know how traditional it is, only that modern editions have started to favor putting spaces between words rather than between cīr.) Hence all I had to do was parse each cīr into syllables, and then try to match these syllables to patterns of acai (this second part was the hardest). The result is a JSON file that represents every cīr as an array of two acai, each of which is labelled according to the type (nēr, nirai, nērpu, and niraipu) and quantity (G or L for nēr, LG or LL for nirai, etc.). I wasn’t able to parse every syllable — either because of errors in the electronic text, or more likely, my own lack of understanding of the intricacies of Tamil meter — but I think I got 97% of them. Hence the following statistics should be more or less right, at least for the Kuṟuntokai.

One way to think about positional asymmetry (i.e., strong and weak positions being regulated by somewhat different rules or constraints) is in terms of conditional probability. What is the chance that a nēr-acai will occur in a strong position? What is the chance that this nēr-acai will be constituted by a heavy rather than a light syllable? What is the chance that it will be followed by another nēr-acai in the weak position? And what is the chance that this nēr-acai will itself be constituted by a heavy syllable? And so on. These questions will require much more research, and asking intelligent questions of the data, but here are a few initial observations:

  • Nēr-acai are almost never light in the strong position. I only counted 18 instances, in contrast to 5,322 instances of a heavy nēr-acai.
  • Whether a nēr-acai or a nirai-acai occurs in the strong position, there is still about a 65% chance that a nēr-acai will occur in the weak position.
  • When a nirai-acai occurs in the strong position, if a nēr-acai follows in the weak position, it is more likely that the nēr-acai will be heavy if the final syllable of the preceding syllable of the nirai-acai is light (71% as opposed to 58%). This might simply be due to the different frequencies of word shapes in the lexicon.
  • Among the possibilities for a nirai-acai, LL predominates over LG (60% to 39%) in the strong position, but they are more closely matched in the weak position (53% for LL following a nēr-acai, and 49% for LL following a nirai-acai).

A few caveats: I have basically ignored nērpu and niraipu in these numbers, since they usually don’t rise above a single percentage point. Also, I am taking the traditional system more or less at its word. It might be that alternative ways of parsing Tamil verse (based on foot structure, example) will reveal other patterns and generalizations. Finally, I only allowed cīr to have a maximum of 2 acai. I don’t know if this is correct for the meter of the Kuṟuntokai, and some of the errors look like they might involve cīr with three acai, but I’ll have to wait until I understand the system a bit better.

Automated checking for metrical errors: Prakrit gāhās

For a few of my projects it would be useful to ensure the metrical correctness (which often co-varies with grammatical correctness) of a text that I’ve typed up. I was inspired by Shreevatsa’s metrical analysis tool to come up with a very simple Python script for validating a text that has been composed in Prakrit gāhās. The code is below, pasted from this GitHub gist.

Unlike Shreevatsa’s tool, which is used primarily for identification, I use this script for proofreading. The input file follows a certain set of conventions:

  • It has to be in the ISO-15919 encoding. Hence for anusvāra.
  • The vowels e and o should be written like so when they are metrically short, and as ē and ō when they are metrically long.
  • Similarly, when a following anusvāra nasalizes a vowel without making the syllable metrically heavy, the vowel should be written with a tilde (ĩ, mostly in the endings –āĩ and ēhĩ) rather than with .
  • The labels for each verse are expected to be in Arabic numerals and placed, after a hyphen and a space, at the end of the second verse line.

Some of these requirements will seem a bit “fussy” to most readers and also from a technical point of view. The script, for example, should be able to parse a line without knowing in advance whether the signs for e and o represent long or short sounds in any given case. But I want to end up with a file where these distinctions are in fact marked, so I want the script to tell me when the letters as I have written them don’t produce a completely metrical text. This is because I’m shooting for a representation of the text in which the metrical structure (and hence the phonological structure) is perfectly represented by the writing. I’ll have more to say about the orthography of Prakrit later.

The output file will, for each line, print the parsed text if there are no errors. If there is an error, it will say where in the line the error occurs. Hence here is the input for the first verse of Dhanapāla’s Pāiyalacchī:

namiūṇa paramapurisaṁ purisuttamanābhisaṁbhavaṁ dēvaṁ
vucchaṁ pāiyalacchi tti nāmamālaṁ nisāmēha - 1

And here is the output:

Verse 1, line 1: namiūṇa paramapurisaṁ purisuttamanābhisaṁbhavaṁ dēvaṁ
Verse 1, line 2: vucchaṁ pāiyalacchi tti nāmamālaṁ nisāmēha

The script showed me an error for verse 223:

Verse 223, line 1: uya piccha dharaï jīvaï duccaṁ duattaṇaṁ disā āsā
Gaṇa number 5 in line 1 of verse 223 has the incorrect form LGL.

When I consulted Bühler’s edition again, I saw that I had to correct duattaṇaṁ to dūattaṇaṁ.

More interesting was the error that the script showed me for verse 175:

Verse 175, line 2: avarillam uttarijjaṁ uyaṭṭhī uccaō nīvī
Gaṇa number 4 in line 2 of verse 175 has the incorrect form LGG.

When I checked on this, it turned out that uyaṭṭhī was indeed the reading of Bühler’s edition, although he gave ujjattō (which would be metrically fine). Uyaṭṭhī is also given in the Pāiyasaddamahaṇṇavō for nīvī. I didn’t have the temerity to change the text, but something is clearly wrong here.

Note that I’ve written the script for Prakrit, and it won’t work for Sanskrit āryās, because of Sanskrit’s greater phonological complexity.

Here is the gist:


Metrics and Combinatorics: Number or Saṅkhyā

The fifth combinatorial technique that Hēmacandra describes is called saṅkhyā, which simply means “number”: it gives the number of possible combinations of light and heavy syllables for a verse of k positions. This is the simplest of all of the techniques. For samavr̥tta meters, which have an equivalent number of positions in each line, the solution is simply 2k. Hence, as we have already seen, for k = 4, the number of possible combinations is 24 = 16. For meters of the śakvarī class, with fourteen syllables per line, the number of possible combinations is 214 = 16,384.

In case you want to find the number of possibilities up to a certain value of k (e.g., k = 1, 2, 3, 4 … 14), you can multiply the highest value of k by 2 and subtract 2 from the product. Hence, the total number of possibilities for k = 1, 2, 3, 4 … 14 is 2(214) -2 = 32,766.

For ardhasamavr̥tta meters, we have to modify the procedure somewhat. There should be a greater number of such meters: in samavr̥tta meters, all of the lines must be identical, but in ardhasamavr̥tta meters, only the first and third, and second and fourth, lines are identical to each other. Hence we start by raising the number of possibilities to the power of 2. For k = 4, this gives us (24)2 = 256. But this number also includes patterns where all four lines are identical, i.e., the samavr̥tta forms. We subtract the total number of these samavr̥tta forms, which in this case is 24 = 16. There are thus 240 ardhasamavr̥tta forms for k = 4. Hence the general formula is (2k)2 – 2k.

For mātrā-based meters, we have to generalize the procedure a little. In sama- and ardhasamavr̥tta meters, there can only be 2 possibilities for any given position, namely, light or heavy. This is not the case in mātrā-based meters. We must therefore multiply the number of possibilities at each position (effectively: each group, or gaṇa, of mātrā). Ignoring for the moment the requirements of word-break, the gāthā has the following possibilities at each group:

First line: 1st gaṇa 2nd gaṇa 3rd gaṇa 4th gaṇa 5th gaṇa 6th gaṇa 7th gaṇa 8th gaṇa Product
Possibilities: 4 5 4 5 4 2 4 1 12,800
Second line: 1st gaṇa 2nd gaṇa 3rd gaṇa 4th gaṇa 5th gaṇa 6th gaṇa 7th gaṇa 8th gaṇa Product
Possibilities: 4 5 4 5 4 1 4 1 6,400

Hence the number of possibilities is 12,800 × 6,400 = 81,920,000.

Finally, one might be interested, in principle, in how many possible combinations of light and heavy syllables can be accommodated within a unit (gaṇa) that contains a specified number of mātrās. We know, for example, that four mātrās can be realized by the following five patterns: ऽऽ, ।।ऽ, ।ऽ।, ऽ।।, ।।।।. But Hēmacandra tells us that the number of possibilities is a Fibonacci number. (Hēmacandra wrote about 50 years before Fibonacci, and the principle was known to earlier authors who were concerned with Prakrit metrics.) Thus:

Number of mātrās: 1 2 3 4 5 6 7 8
Number of possible syllabic realizations: 0 + 1 = 1 1 + 1 = 2 2 + 1 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 8 + 13 = 21 13 + 21 = 34

Metrics and Combinatorics: The Mēruprastāraḥ

We’ve seen one example of “spreading out” metrical patterns according to a certain rule in order to determine the number of possible patterns that can be made with k syllablic positions. There is a different procedure for determining the number of patterns, among the total, that contain a given number of light or heavy syllables. This procedure was called sarvaikādigalakriyā “working out the light and heavy syllables by starting with the number one in all positions” by Hēmacandra and other Jain authors (and hence it is Hēmacandra’s version that I will discuss here, since I am relying on Ludwig Alsdorf’s 1933 article), but it was known to other authors by the much punchier name Mēruprastāraḥ, “spreading out Mount Meru.” This technique, by the way, is the same as Pascal’s triangle, although, as the Wikipedia page notes in detail, the name should not be taken to imply that Pascal was the first person to discover or use the technique.

The technique is this. If you are dealing with k syllables, write out “1” k+1 times in a line, horizontally and vertically. For example, if k = 6:

Then, going from left to right and from bottom to top, write the sum of each square and the square that is to its top-left in the square that is immediately above it. [Note that you could do this step also to generate the vertical column, since adding zero to the value written in the leftmost square in each line — that is, 1 — yields one.] For example:

You follow this procedure for each square in the line, except for the last. Then you move up a line. You should end up with the following picture:

This is Pascal’s triangle. It gives us a couple of interesting facts about the patterns of each class:

  • Since k = 6, we can add all of the numbers on the hypotenuse of the triangle, and we will get the number of different syllabic patterns of a six-syllabled meter: 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64.
  • But the same triangle will give us the solutions for any value of k. So if we are interested in the number of patterns for k = 4, we can add 1 + 4 + 6 + 4 + 1 = 16 (as already shown here).
  • The number of squares in the hypotenuse represents the number of combinations of different quantities of light and heavy syllables. This number will always be k + 1. Hence if k is 6, then there are 7 possibilities: 6 light syllables [and 0 heavy], 5 light [and 1 heavy], 4 light [and 2 heavy], 3 light [and 3 heavy], 2 light [and 4 heavy], 1 light [and 5 heavy], and 0 light [and 6 heavy].
  • The number in the square in the series along the hypotenuse represents the number of combinations of decreasing numbers of light syllables. Hence for k = 6, there is 1 combination of all light syllables, 6 combinations of 5 light syllables and 1 heavy syllable, and so on. You can confirm this by comparing the number of combinations of a decreasing number of light syllables for k = 4 with the prastāraḥ given here.

On Gāhāsattasaī W191

Verse 191 in the Gāhāsattasaī reads:

ciraḍiṁ pi aṇāantō lōā lōēhĩ gōravabbhahiā
sōṇāratulē vva ṇirakkharā vi khandhēhĩ ubbhanti

People who don’t even know the alphabet [?]
are popularly taken to be worthy of honor.
They’re like a goldsmith’s scales:
even though they are unlettered,
they’re carried on one’s shoulders.

The comparison in this verse depends on two things: a goldsmith’s scale should be (a) without letters, and (b) held on the shoulders. Regarding (a), Sreeramula Rajeswara Sarma discusses this verse in the most recent issue of the International Journal of Jaina Studies Online, where he surveys ancient balances, with a focus on the devices described in Pālitta’s Jōisakaraṇḍagaṁ or Jyōtiṣkaraṇḍakam. The form of the steelyard described in Pālitta’s text has no letters. The gradation marks on the scale of the beam are marked with lines representing weights (measured in karṣās and palas), and the marks for 5, 15, 30 and 50 palas should be decorated with a nandī, which in Sarma’s interpretation is a floral decoration. The other lines will be straight. The goldsmith’s balance in this text will be similarly marked. Regarding (b), none of the steelyards illustrated in Sarma’s article (from Gandhara, Mathura, and Nagarjunakonda) are actually carried on the shoulder: they are held, by the hand, from an adjustable loop on the beam.

The other interesting thing about this verse is the word ciraḍiṁ. Nobody knows what it means. The interpretatio ad sensum is “alphabet” (Gaṅgādhara says: siddhir astv ityādi varṇāvalīm). Bhuvanapāla glosses it as “moving the lips” (ōṣṭhasphuraṇa-), but gives it the same interpretation (“if they can’t even move their lips, then they are a long way from eloquence”). It seems likely that the word comes from a Dravidian source. The initial c- makes it likely that it was a Dravidian language with a palatalization rule (i.e., Tamil-Malayalam and Telugu), rather than, say Kannada. And why should a word putatively meaning “alphabet” have been borrowed into Prakrit? One possibility is that it doesn’t exactly mean “alphabet,” but some other aspect of literate culture that would motivate the simile in the following line. Could it come from Tamil cīr-aṭi, i.e., a metrical line (aṭi) made out of repeating metrical units (cīr)? The cīr of Tamil verse is, after all, very similar to the gaṇa- in Prakrit verse.

There are a few variants: ciraḍiṁ and ciriḍiṁ; abbhahiā (i.e., abhyadhika- or abhyarhita-) and agghaviā (i.e., *arghāpita- or *arghyāpita-).

Metrics and combinatorics: uddiṣṭaḥ or “indicated”

We have gone over the first two of six standard combinatorial techniques, prastāraḥ or “spreading out,” and naṣṭaḥ or “lost.” The third technique was developed to answer the following question. Suppose the sequence of light and heavy syllables in a given combination has been indicated (uddiṣṭaḥ). How can we find out the serial number of this particular combination in the prastāraḥ or “spreading out” of combinations?

The procedure is very simple:

  1. Start from the last light syllable in the pattern, and start with x = 1.
  2. For each syllable, going from right to left:
    1. If it is light, multiply x by two, and use this as the new value of x for the next syllable.
    2. If it is heavy, multiply x by two, then subtract one, and use this as the new value of x for the next syllable.
  3. The final value of x is the serial number of the pattern.

Actually, one can start from the last heavy syllable in the pattern, too. But since the value of x passed onto the next syllable will inevitably be (1×2)-1 = 1, you might as well skip it.

For the pattern ।ऽ।ऽ (light-heavy-light-heavy), we can work out the serial number in the prastāraḥ of four-syllable patterns as follows:

  • Fourth syllable: heavy, so skip it.
  • Third syllable: light, so we use 2x = 2×1 = 2.
  • Second syllable: heavy, so we use 2x-1 = 2×2-1 = 3.
  • First syllable: light, so we use 2x = 2×3 = 6.

Here it can be verified that ।ऽ।ऽ is the sixth pattern in the prastāraḥ of four-syllable patterns.

A more interesting problem would be to work out the serial number for well-known meters like the vasantatilakam. That is a 14-syllable meter, and hence there should be 214 = 16,384 combinations. What is the serial number of the pattern ऽऽ।ऽ।।।ऽ।।ऽ।ऽऽ, that of the vasantatilakam? You can try to work it out yourself. The answer I came up with is 2,933.

Dhanapāla on Chess (from the R̥ṣabhapañcāśikā)

The 10th-century poet Dhanapāla, whom I have written about a lot on this blog lately, includes an early reference to the game of chess (actually I don’t know how early it is, relative to other evidence — I am sure there has been some scholarship on this that I am not aware of) in one of his most well-known works, Fifty for R̥ṣabha (R̥ṣabhapañcāśikā). This is a hymn in fifty Prakrit verses to the first Tīrthaṅkara, R̥ṣabha. Verse 32 runs as follows:

सारि व्व बंधवहमरणभाइणो जिण न हुंति पइं दिट्ठे ।
अक्खेहिं वि हीरंता जीवा संसारफलयम्मि ॥
sāri vva bandhavahamaraṇabhāiṇō jiṇa na hunti païṃ diṭṭhē ~
akkhēhiṁ vi hīrantā jīvā saṁsāraphalayammi ~~

Living beings are like chess pieces
on the gameboard of worldly life:
although they would be captured by their senses,
    [although they would be taken
    from the board by throws of the dice,]
if they see you, they are not subject
to capture, killing, and death.

The word sārī- (Sanskrit śārī-) means a “chess piece,” and phalaa- (Sanskrit phalakam-) is a “board.” The interesting thing about this reference, though, is that it suggests that pieces can only be removed from the board subject to the outcome of a throw of dice (akkha- or akṣa-).