sivasutrani

[P.K.Ramakrishnan]

There are 14 sivasutras or maheswara sutras given by Panini.   His grammatical

treatise called ashtaadhyaayii  makes use of these to give terse sutras on grammar.

I am reproducing these sutras below.

शिवसूत्राणि

१.   अ  इ   उ   ण्

२.   ॠ  ल्   क्

३.   ए  ओ  ङ्

४.   ऐ ओ  च्

५.   ह् य व र  ट्

६.   ल  ण्

७.   ञ म ङ ण न म्

८.   झ भ ञ्

९.   घ ढ ध ष्

१०.  ज ब ग ड द श्

११.  ख फ छ ठ थ च ट त व्

१२.  क प य्

१३.  श ष स र्

१४.  ह् ल्

Here the letter ha appears in sutra 5 as well as in sutra 14.

I have see some European commentators justifying the two ha.  But I could not

understand their argument.  

Can someone throw some light on this in simple language?

Thanks in advance.

 

-----------------------------------
P.K.Ramakrishnan
http://peekayar.blogspot.com

[hnbhat B.R.]

Here the letter ha appears in sutra 5 as well as in sutra 14.

I have see some European commentators justifying the two ha.  But I could not

understand their argument.  

Can someone throw some light on this in simple language?

I myself could not understand you question. It is Grammar Text of Panini and I have seen commentaries in Sanskrit which are too much technical to be explained in simple language unless one is ready to undertake a study of Paninian Grammar seriously.

Anyhow, I do not see, for practical purpose, the need of two "ह" in any way different in pronunciation in the language. There are defended only purely grammatical functional needs in the elaborate scheme of Panini's अष्टाध्यायी.

I have not seen any English Commentary on this portion and somebody would throw light on any commentary you are referring, if you give the precise reference to the commentary in English you are referring.  Only on seeing what they have said in this respect, one can simplify it in normal language, I hope who can follow their method of commentary. Please give the bibliographical details of the commentary/commentaries you have referred to so that some scholar would refer to them and explain it in plain English. 

SC Basu has translated सिद्धन्तकौमुदी also and probably you will find his interpretation following the traditional commentaries and not any European Scholar. It is purely on grammatical purpose, the letter is added twice in the Sutra.

Hope someone would through light in this respect.

 

--
Dr. Hari Narayana Bhat B.R. M.A., Ph.D.,
Research Scholar,

Ecole française d'Extrême-OrientCentre de Pondichéry

16 & 19, Rue Dumas

Pondichéry - 605 001

[P.K.Ramakrishnan]

I was going through a long article from the net.

 

A Mathematical Analysis of Panini’s Sivasutras.

 

By   WIEBKE  PETERSEN

 

Institute of Language and Information

Dusseldorf ,

Germany

 

19 pages

 

He has written this using the set theory

with which I am not familiar.

This is in response to Dr. Bhat's query.

-----------------------------------
P.K.Ramakrishnan
http://peekayar.blogspot.com

[hnbhat B.R.]

Thanks for the response. I am not learned in Mathematics to understand any theory based on mathematics. Some conversant with mathematical theories would explain the text accordingly.

[venetia ansell]

Namo namah

 

I have heard at least one scholar posit the theory that 'hakAra' is an old semi-vowel which corresponds to 'akAra' just as 'yakAra' corresponds to 'ikAra' and 'vakAra' to 'ukAra'.  If you look at the order of the two relevant sutras this becomes clearer:

 

a-i-u-N 

 

ha-ya-va-ra-T

 

What I was told is that this hakAra as a semi-vowel can be seen in other Indo-European languages, or at least its remnants can, and that on that basis and on the basis of the arrangement of the Maheshvarasutras, where hakARa is the only non-it letter that is repeated, we must assume that hakAra was originally a semi-vowel in Sanskrit too.  The maheshvara sutras precede Panini so perhaps by his time it was no longer so. 

 

I'd be interested to hear other views' on this theory (and please excuse any mistakes I may have made in stating it, I do not have my notes to hand). 

 

Best,

Venetia

 

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www.venetiaansell.wordpress.com

[hnbhat B.R.]

On Wed, Oct 12, 2011 at 10:25 AM, venetia ansell <venetia...@gmail.com> wrote:

Namo namah

 

I have heard at least one scholar posit the theory that 'hakAra' is an old semi-vowel which corresponds to 'akAra' just as 'yakAra' corresponds to 'ikAra' and 'vakAra' to 'ukAra'.  If you look at the order of the two relevant sutras this becomes clearer:

 

a-i-u-N 

 

ha-ya-va-ra-T

 

What I was told is that this hakAra as a semi-vowel can be seen in other Indo-European languages, or at least its remnants can, and that on that basis and on the basis of the arrangement of the Maheshvarasutras, where hakARa is the only non-it letter that is repeated, we must assume that hakAra was originally a semi-vowel in Sanskrit too.  The maheshvara sutras precede Panini so perhaps by his time it was no longer so. 

 

I'd be interested to hear other views' on this theory (and please excuse any mistakes I may have made in stating it, I do not have my notes to hand). 

 

Best,

Venetia

Please make it clear with references to the original source.

Anyhow, traditional Indian Grammarians do not deal with Indo-European theory of languages and hence they find much difficult in defending the duplication of the "consonant" or semivowel (absent in Sanskrit). Will have to be checked with all the प्रत्याहार-s containing both and try to find any difference in their treatment within the framework of Panini.

Some contain the first ह and some the second one through out the text.

 

-- 

[Gérard Huet]

The śivasūtra is not a mere list of phonemes of the language.
It is a special data structure that represents in a compact way the
sets of phonemes (nasals, vowels, etc) that are needed to express the
grammatical rules in Aṣṭādhyāyī.
Such a set is encoded by an abbreviation called pratyāhāra, consisting
of a pair of a starting phoneme, and a end marker. The pratyāhāra
abbreviates the set of phonemes comprised in this interval, markers
excluded. Thus 'hal' stands for all consonants, 'ac' for vowels, 'zar'
for sibilants, etc.

The śivasūtra is arranged in a very ingenious way, so that there is
maximum sharing of the needed subsets. Thus there is almost no
duplication, only the phoneme 'ha' is repeated.
The mathematical problem that arises is: "Is this duplication
necessary?". In other words, is there
some other listing of the phonemes interspersed with markers such that
all needed sets of phonemes could be obtained without such a
repetition? This is the problem that Wiebke Petersen solved, using
graph theory. She showed that Pāṇini's representation is optimal,
since at least one phoneme (like 'ha') must be repeated.
This is a measure of Pāṇini's genius. Pāṇini is not just the first
linguist recorded in history, he is also the first expert in
information theory, having coined such ingenious data structures.
Of course the historical problem remains of who is the actual author
of the śivasūtra, since Pāṇini may have taken it from a tradition of
previous grammarians.

Gérard Huet

On Oct 12, 4:17 am, "hnbhat B.R." <hnbha...@gmail.com> wrote:
> Thanks for the response. I am not learned in Mathematics to understand any
> theory based on mathematics. Some conversant with mathematical theories
> would explain the text accordingly.
>
> --

> *Dr. Hari Narayana Bhat B.R. M.A., Ph.D.,
> **Research Scholar,
> *

[murthy]

Ramakrishnanji,

Could you please let me have the web address where this paper by Petersen could be accessed or dowloaded?

Regards

Murthy

--

[P.K.Ramakrishnan]

You may google search for "a mathematical analysis of pananis sivasutras"

Please try.

 

-----------------------------------
P.K.Ramakrishnan
http://peekayar.blogspot.com

---

From: murthy <murt...@gmail.com>
To: sams...@googlegroups.com
Sent: Wednesday, 12 October 2011 4:07 PM
Subject: Re: [Samskrita] sivasutrani

[Ramakrishna Upadrasta]

praNAmams Shri Gérard mahodaya,

Welcome to see you in this list Very nice to see you here! My
namaskaarams to you.

For others: Shri Prof. Gerard mahodaya an accomplished widely known
computer scientist, an ex director of INRIA, and highly respected
worldwide for his achievements in theoretical computer science
subjects like Information theory, Functional programming, Higher Order
Logic, Proof Checking, CAML, COQ, etc. etc.

http://sanskrit.inria.fr/huet/
http://www.eatcs.org/index.php/eatcs-award/624

Shri Gerard mahodaya is also the author of the Sanskrit Heritage
website at INRIA and the Zen toolkit and automatic sanskrit tagger
over there:
http://sanskrit.inria.fr/

praNAms
Ramakrishna

2011/10/12 Gérard Huet <Gerar...@inria.fr>:

[hnbhat B.R.]

This is the problem that Wiebke Petersen solved, using
graph theory. She showed that Pāṇini's representation is optimal,
since at least one phoneme (like 'ha') must be repeated.

This means he could not have avoided the repetition in way and construed the sets including the second "ha"

like रल्, शल्, झल् etc. Commentators tried to show even if he had rephrased these sets, it would create obstacles in the operation of the other sets and would not yield the required forms applying them. 

Thanks for the explanation.

-- 

Dr. Hari Narayana Bhat B.R. M.A., Ph.D.,

Research Scholar,

[ajit Gargeshwari]

Dear Muthy

A Mathematical Analysis of Pānini’s Śivasūtras by Wiebke Petersen

http://www.springerlink.com/content/t678888th08x260j/

Please use this link to download the article
Here is the papers abstract

" In Pānini’s grammar of Sanskrit one finds the Śivasūtras, a table which defines the natural classes of phonological segments in Sanskrit by intervals. We present a formal argument which shows that, using his representation method, Pānini’s way of ordering the phonological segments to represent the natural classes is optimal. The argument is based on a strictly set-theoretical point of view depending only on the set of natural classes and does not explicitly take into account the phonological features of the segments, which are, however, implicitly given in the way a language clusters its phonological inventory. The key idea is to link the graph of the Hasse-diagram of the set of natural classes closed under intersection to Śivasūtra-style representations of the classes. Moreover, the argument is so general that it allows one to decide for each set of sets whether it can be represented with Pānini’s method. Actually, Pānini had to modify the set of natural classes to define it by the Śivasūtras (the segment h plays a special role). We show that this modification was necessary and, in fact, the best possible modification. We discuss how every set of classes can be modified in such a way that it can be defined in a Śivasūtra-style representation."

Regards
Ajit gargeshwari

[ajit Gargeshwari]

Dear Murthy,

I found the complete article at scribd.com. I have attached the same

[murthy]

Thank you very much Ajitji.

Regards

Murthy

[murthy]

Dear Ajitji,Ramakrishnanji

I have located another more recent paper of the author on the same subject which I am attaching.

Regards

Murthy

----- Original Message -----

From: ajit Gargeshwari

To: sams...@googlegroups.com

Sent: Wednesday, October 12, 2011 5:54 PM

Subject: Re: [Samskrita] Re: sivasutrani

[ajit Gargeshwari]

Dear Murthyji and Ramkrishnaji

Thank you Murthyji for the more recent paper. Please click on the below link.

http://en.wikipedia.org/wiki/Shiva_Sutra

The link explains several points raised in this thread.  at the end of the page there is another interesting paper titled The "Generative power of Feature Geometry " By Andras Kornai which gives another interesting mathematical perspective on Shiva Sutra

Regards
Ajit Gargeshwari

[Shreevatsa R]

I am late to this thread. Coincidentally, I read two related papers just about four weeks ago. (Further coincidence: I read them because a friend posted on Google+ a remark by Prof. Huet about Panini, similar to the remark he has posted here!)

The papers are (both linked from the Wikipedia article, actually):

1. Economy and the Construction of the Śivasūtras by Paul Kiparsky, Stanford University

http://www.stanford.edu/~kiparsky/Papers/siva-t.pdf

and

2. A Mathematical Analysis of Pāṇini’s Śiva sūtras, by Wiebke Petersen, University of Düsseldorf

http://user.phil-fak.uni-duesseldorf.de/~petersen/paper/petersen_jolli_proof.pdf

Both of them explain how the śivasūtras can be derived just from the list of pratyāhāras that are used in the grammar, and that the śivasūtras are optimal. Prof. Kiparsky's paper is very readable, and he uses a few additional assumptions that he justifies as he goes along. Petersen's paper does the same without any additional assumptions. Below is a very simplified outline; I hope it is helpful to someone.

The śivasūtras go like:

1. a i u Ṇ

2. ṛ ḷ K

3. e o Ṅ

4. ai au C

...

where in each sūtra, the last letter is merely a "marker", and the remaining letters are actually significant.

From these sūtras are constructed pratyāhāras, the convention being that a letter followed by a marker stands for the sequence of (actual) letters starting with that letter and up to the marker. Thus

* aṆ stands for the set {a, i, u},

* iK stands for the set {i, u, ṛ, ḷ},

* uṄ (not used the grammar anywhere as far as I know) stands for the set {u, ṛ, ḷ, e, o}, etc.

So in his grammar, whenever Panini needs to refer to a set of letters, it happens to have a convenient pratyāhāra like aṆ or iK or whatever.

Everything thus far is surely known to every member of the mailing list. 

But we can work backwards (as the Indian grammarians—Panini or earlier ones—probably did). Given the sets of letters we need in the grammar, what should the sūtras be like, so as to be as short as possible (as few markers as possible)?

For example, we need the set {a, i, u, ṛ, ḷ} in one place (6.1.101). This only implies that these letters must occur consecutively in the sūtras, in some order, like {u, ṛ, i, a, ḷ}, say.

But we also need the set {i, u, ṛ, ḷ} in another place (1.1.3). So we are forced to  put 'a' immediately before* the set {i, u, ṛ, ḷ} (which should correspondingly start with i), and a marker after the set. 

Further, we need the set {a, i, u} in another place (1.1.51), so we are forced to put u next in the set: the sūtras must look like:  

a, i, u, [marker], {ṛ, ḷ} [marker].

[*There is another possibility: we can put 'a' immediately after the set {ṛ, ḷ, u, i}, so that it looks like {ṛ, ḷ} [marker], u, i [marker] a [marker], but this already uses more markers than the other case.]

To summarise, even if we are given only the facts that we need to represent the following sets:

* {ṛ, i, a, ḷ, u}

* {u, ḷ, i, ṛ}

* {i, a, u} (I jumbled the letters to emphasize that these are just sets) 

we can derive (assuming that no letter is repeated, and that no markers are used unnecessarily) that two of the sūtras must look like:

1. a i u [marker]

2. ṛ, ḷ [marker]

   or

   ṛ, ḷ [marker].

Continuing in this vein, almost the entire set of śivasūtras can be derived (except the markers of course, which are arbitrary) just from the list of sets that need to be represented. Kiparsky does it with a case-by-case analysis and some additional (justified) assumptions, and Petersen does it automatically, using the machinery of graph theory.

Now for the question about the repeated "h".

Sometimes, the set of sets we need to represent may simply not be amenable to arranging in a line as the sūtras do. To take a contrived example, suppose that, in addition to the three sets above, we also needed the set {a, ḷ}. Then it is impossible to fit into the above sūtras, and the only way around is to repeat a letter:

1. a i u [marker1]

2. ṛ ḷ [marker2]

3. a [marker3]

so that the pratyāhāra "ḷ [marker3]" would stand for the set {ḷ, a} that we want. 

Something similar happens with the "h", which forces it to be repeated.

On the one hand, we need the sets {i, u, ṛ, ḷ, e, o, ai, au, h, y, v, r, l} (in 1.1.69) and {a, i, u, ṛ, ḷ, e, o, ai, au, h, y, v, r} (in 8.3.3), so 'h' must occur near the vowels, somewhere between 'a' and 'l'.

On the other hand, we also need the set {ś, ṣ, s, h}, so 'h' must occur adjacent to {ś, ṣ, s} also. The only way to arrange this is to repeat 'h'. 

Rather amazingly, it turns out (as we know) that that is the only repetition needed to represent all the sets of letters that are needed in the grammar and are represented as pratyāhāras.

Here we have proved directly that 'h' needs to be repeated, but Petersen uses graph theory (non-planarity of the corresponding Hasse diagram). The linked papers also prove that the shiva sutras use the least number of markers (and therefore are shortest overall). Petersen also considers the general question (how to optimally represent an arbitrary set of sets).

Hope this helps rather than confuses,

Shreevatsa

[murthy]

While making an attempt to wade through Prof Petersen's paper I found that what is generally called "इत्" [उपदेशे अन्त्यरूपा हल्वर्णाः इत्संज्ञकाः स्युः] is consistently referred to as "अनुबन्ध". As per my knowledge "अनुबन्ध" is a flag attached to a धातु to indicate to which list it belongs.Is  "इत्" an "अनुबन्ध"?

Regards

Murthy

 

----- Original Message -----

From: Shreevatsa R

To: sams...@googlegroups.com

Sent: Wednesday, October 12, 2011 9:51 PM

Subject: Re: [Samskrita] Re: sivasutrani

[hnbhat B.R.]

On Thu, Oct 13, 2011 at 4:07 PM, murthy <murt...@gmail.com> wrote:

While making an attempt to wade through Prof Petersen's paper I found that what is generally called "इत्" [उपदेशे अन्त्यरूपा हल्वर्णाः इत्संज्ञकाः स्युः] is consistently referred to as "अनुबन्ध". As per my knowledge "अनुबन्ध" is a flag attached to a धातु to indicate to which list it belongs.Is  "इत्" an "अनुबन्ध"?

Regards

Murthy

 

All those augmentations to any Sutra or Dhatu are generally  referred as अनुबन्ध-s and only those assigned the designation as इत् are elided with some specific purpose. Others are for the convenience of pronunciation. "नानुबन्धकृतमनेकाल्त्वम्" "अनेकान्ता अनुबन्धाः" as these and other refer to the augmentations to Sutra-s as well as  the words in the गणपाठ and धातुपाठ and not restricted to धातु-s. In धातु-s the serve multiple purposes, like आत्मनेपद, परस्मैपद and many more functions.

 

-- 

Dr. Hari Narayana Bhat B.R. M.A., Ph.D.,

Research Scholar,

[hnbhat B.R.]

As per my knowledge "अनुबन्ध" is a flag attached to a धातु to indicate to which list it belongs.Is  "इत्" an "अनुबन्ध"?

I am afraid your understanding is wrong. The class is identified by those suffixes called विकरण like, १. कर्तरि शप्, २. अदिप्रभृतिभ्यः शपः (लुक्), ३. जुहोत्यादिभ्यः श्लु, ४.  दिवादिभ्यः श्यन्, ५. स्वादिभ्यः श्नुः, ६. तुदादिभ्यः शः, ७.  रुधादिभ्यः श्नम्,  ८ तनादिकृञ्भ्यः उः, ९.  क्र्यादिभ्यः श्ना, १०. सत्यापाश....चुरादिभ्यो णिच्

 

These are the markers of 10 गण-s of verbs classified by their विकरण- प्रत्यय-s.

--

Dr. Hari Narayana Bhat B.R. M.A., Ph.D.,

Research Scholar,

[vishvAs vAsuki]

2011/10/13 hnbhat B.R. <hnbh...@gmail.com>

१. कर्तरि शप्, २. अदिप्रभृतिभ्यः शपः (लुक्), ३. जुहोत्यादिभ्यः श्लु, ४.  दिवादिभ्यः श्यन्, ५. स्वादिभ्यः श्नुः, ६. तुदादिभ्यः शः, ७.  रुधादिभ्यः श्नम्,  ८ तनादिकृञ्भ्यः उः, ९.  क्र्यादिभ्यः श्ना, १०. सत्यापाश....चुरादिभ्यो णिच्

विकरण-प्रत्यय नाम-सूच्यै कृतज्ञः अस्मि।

[murthy]

I used "list" in a general way. I did not mean the 10 groups.

Regards

Murthy

----- Original Message -----

From: hnbhat B.R.

To: sams...@googlegroups.com

Sent: Thursday, October 13, 2011 4:48 PM

Subject: Re: [Samskrita] Re: sivasutrani

[murthy]

Thanks for the clarification,

Regards

Murthy

----- Original Message -----

From: hnbhat B.R.

To: sams...@googlegroups.com

Sent: Thursday, October 13, 2011 4:37 PM

Subject: Re: [Samskrita] Re: sivasutrani

[Nityanand Misra]

A bit late on the thread, but anyway, this was a great thread indeed. Excellent responses by Prof Huet and Shreevatsa. I had the chance to see Prof Huet speak in person at Hyderabad in 2009 at the Third International Symposium on Sanskrit Computational Linguistics, where Dr. Wiebke Pieterson had presented her research.

Indeed, Panini's (or Maheshvara's) entropy encoding in the Shivasutras is optimal. This is perhaps the first known instance of data compression and Paul Kiparsky has even termed the "Panini's Razor" as a stricter form of Occam's Razor in his talk which can be found here. The results of Pieterson and Kiparsky are not entirely new though (this is nothing to take away from their brilliant research and novel approach), for the traditional definition of the सूत्र is

स्वल्पाक्षरमसन्दिग्धं सारवद्विश्वतोमुखम्
अस्तोभमनवद्यं च सूत्रं सूत्रविदो विदुः

If we take the two qualities together, स्वल्पाक्षर = having very few letters (in other words as few as possible), असन्दिग्ध=unambiguous or precise, we get the Occam's Razor (or a stricter from of it). So since the शिवसूत्र are after all सूत्र, it is no surprise that the information encoding in the sutras is optimal.

Now the next possible question is - does the entire Ashtadhyayi have optimal information encoding? A related question was raised by Prof Amba Kulkarni during the talk of Dr Pieterson - is there a way to get the order of entire Ashtadhyayi just like order (or one of the possible orders) of the letters for the Shiva Sutras can be derived mathematically? These are more challenging questions, one has to prove that the anuvrittis (अनुवृत्ति)s are maximized with the current order of sutras, and that the number of nouns (संज्ञाs) used are optimal, and a host of other things - I don't know if anybody has done any research on this or not.

Another interesting thing to ponder over. A question I asked Dr Pieterson was if we consider the "a" sound in the laN (लण्) sutra to be another anubandha, would the analysis and the conclusions change? The "a" in laN is to be considered anunaasika to get the pratyahara र (ra), which makes words like तवल्कारः (tavalkAraH) possible from उरण् रपरः. Though not agreed to be Nagesh Bhatta, the existence of words like तवल्कारः and opinions of several other scholars makes me believe that the र pratyahara does exist. I don't know what analysis of Kiparsky and Pieterson would yield, but I think no, because the extra anunaasika anubandha leads to a compression of the code at the cost of an extra marker, so overall entropy of the system is the same with one use of the code. In other words, र् and ल् can also be referred to by the code (प्रत्याहार) रण् which is longer than the code र which we get with the anunasika a in लण् as anubandha. With more than one usages of the code, the shorter code and one extra marker have less entropy than the longer code and one less marker.

Finally, assuming both Shiva Sutras and Ashtadhyayi Sutras are optimal, the design of the Paninian grammar appears to be nothing short of a miracle. Call it Panini's genius or Shiva's revelation, there are few things which compare to Panini's grammar as the crest-jewel of achievements of human (or divine) intelligence.

--
Nityānanda Miśra
http://nmisra.googlepages.com

|| आत्मा तत्त्वमसि श्वेतकेतो ||
(Thou art from/for/of/in That Ātman, O Śvetaketu)
     - Ṛṣi Uddālaka to his son, Chāndogyopaniṣad 6.8.7, The Sāma Veda

[Sadagopan V]

"........Now the next possible question is - does the entire Ashtadhyayi have optimal information encoding? A related question was raised by Prof Amba Kulkarni during the talk of Dr Pieterson - is there a way to get the order of entire Ashtadhyayi just like order (or one of the possible orders) of the letters for the Shiva Sutras can be derived mathematically?..."

On this, with childish haste I beg to add:

 

Before any such analysis one should know exactly what was the field like when Ashtadhyayi blossomed. What were the constraints on account of Sanjas, paribhashas, already recognised ganas, dhatupatha etc. existing at that time..? Were there extraneous matters that contribute to the shape of sutras, for example is there a particular way of arrangement of Sutras and words in the sutras that will make it easy for people (who knew Sanskrit of that time) to memorise and reproduce the sutras

 

-- Sadagopan V