Just a place to jot down my musings.

Thursday, May 31, 2012

“The Splendor of the Great Hero”: Śrī Raghuvīra Gadyam aka Śrī Mahāvīra Vaibhavam

Among the most remarkable compositions of Swami Śrīman Nigamānta Mahādeśikar is the Śrī Mahāvīra Vaibhavam, also known as the Raghuvīra Gadyam. In about 90 lines, it summarizes the entire story of the Rāmāyaṇa, paying special attention to the glory and heroism of Rāma. I have attempted to translate the work here while paying close attention to the poetic effects of the original.

|| Śrīḥ  ||

śrīmān veṅkaṭanāthâryaḥ kavi-tārkika-kesarī |
vedāntâcārya-varyo me sannidhattāṃ sadā hṛdi ||

The noble Veṅkaṭanātha,
endowed with śrī,
saffron-maned Lion among poets and philosophers,
supreme teacher of the Vedānta
—may he be established forever in my heart!

jayaty āśrita-saṃtrāsa-dhvānta-vidhvaṃsanôdayaḥ |
prabhāvān sītayā devyā parama-vyoma-bhāskaraḥ ||

He conquers all,
His dawn dispelling the darkness of His devotees’ dread;
Luminous,
Inseparable from the Goddess Sītā, 
The Sun of the Supreme Heaven!

jaya jaya mahāvīra! 
mahādhīra dhaureya! 

Victory, victory to the great hero! 
to the steadfast, resolute, bearer of all burdens!


Wednesday, May 30, 2012

Appayya Dīkṣita on rūpaka (“metaphor”)

Among the works of the great 16th century savant Appayya Dīkṣita is the Kuvalayānanda (“Joy of the Water-lily”), which became the standard introductory textbook on figures of speech throughout India, particularly in the South. The Kuvalayānanda focuses entirely on arthâlaṅkāras, “ornaments of meaning”. My non-existent knowledge of Western rhetoric prevents me from translating the term precisely, but I suspect it may correspond to trope.

Prof. Yigal Bronner has a series of articles on Appayya Dīkṣita’s prodigious œuvre in literary theory, of which “Back to the Future: Appayya Diksita's Kuvalayananda and the Rewriting of Sanskrit Poetics” describes the structure of the Kuvalayānanda. Specifically, the text is organized in three layers: (1) kārikās, around 170 easily memorizable verses in the anuṣṭubh meter that define and exemplify exactly 100 alaṅkāras; (2) examples of these alaṅkāradrawn from kāvya; and (3) an auto-commentary of sorts, in which Appayya Dīkṣita explains his motivation for defining the alaṅkāra in that fashion and sets it into its context of over a millennium of alaṅkāra-śāstra. I shall draw solely from layer (1), the kārikās, here.

For now, I want to focus on just one trope, rūpaka, usually translated “metaphor”. Its definition takes up one verse; examples of its subtypes each take up half a verse. I’m not going to translate the definition literally, because the compactness of Sanskrit technical writing does not render well in English. In what follows, [the stuff inside brackets] isn’t part of the Kuvalayānanda itself.

[rūpakam]

viṣayayy-abheda-tādrūpya-rañjanaṃ viṣayasya yat |
rūpakaṃ tat tridhâdhikya-nyūnatvânubhayôktibhiḥ ||


Sunday, May 27, 2012

Counting, uncounting, and dust, part seven

The word “dust” has appeared in the title of every post in this series, and we will finally begin to see why. Many counterintuitive marvels remain to be unmasked in the counterintuitive worlds of cardinality and measure theory. Georg Ferdinand Ludwig Philipp Cantor, the mathematician who laid the foundations for the modern understanding of infinity, was responsible for the discovery of some of these truly unbelievable marvels.

There seems to be a whole sub-genre of math blog posts that focus on defining or presenting the Cantor set at different levels of rigor! For our purposes, I will offer two descriptions (without proof). 
  • The Cantor set can be described quite “simply” as the set of all real numbers between 0 and 1 whose ternary representation contains only 0 and 2. (We use the decimal place value system in everyday life, while computers use the binary, using only 0 and 1.) The ternary place value system uses 0, 1, and 2 as the only digits. So the number 0.1 in ternary represents the fraction \( \frac{1}{3} \), and 0.22 the fraction \( \frac{8}{9} \), and so on. It is also worth noting that just as we take the decimal 0.999… to be equal to the number 1, we must also take the ternary number 0.0222… to be equal to the ternary number 0.1, and so on.
  • The Cantor set can also be seen as the limit of an infinite process of cutting up the closed interval \( [0, 1] \). The rule is simple: at every stage, delete the middle third (excluding the endpoints) of every remaining interval. Repeat ad infinitum. The first few stages of such a process are shown in this picture.
How does the Cantor set measure up (pun intended) using our four different definitions of size?



Counting, uncounting, and dust, part six


Let’s quickly recap of some of the interesting things we have seen so far.
  • The real numbers are uncountable, and in fact every interval of the real numbers is uncountable. In other words, there are more real numbers between 0 and 1 than there are integers from negative infinity to positive infinity. 
    • However, this alone does not really give us a sense of just how much bigger uncountable is than countable. For instance, we can see that the sequence of fractional numbers \( \{ 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots \} \) is also contained within the interval \( (0, 1) \). It is clear, though, that this sequence has the cardinality of \( \mathbb{N} \). It is thus not really clear how it is so remarkable that there are more real numbers in \( (0, 1) \) than there are natural numbers anywhere at all.
  • The Lebesgue measure of an isolated point is zero. Consequently, the Lebesgue measure of a countable number of isolated points is also zero. In particular, the Lebesgue measure of \( \mathbb{N} \), the natural numbers, is zero.
    • But what if we take an uncountable number of isolated points? Wait, is that even possible?
    • And what if we take “non-isolated” points, whatever that means?

Counting, uncounting, and dust, part five


Alright, so now we finally know that there isn’t one infinity any more. In fact, there is an infinite number of infinities, each infinitely larger than the one smaller than it, and so on upwards. Excelsior is a good motto for the infinitude of infinities (as it is for the Coat of Arms of the State of New York).



But we haven’t dealt with another problem: this way of measuring the size of a set just isn’t good enough for our purposes. We need something more refined, something that does distinguish between countable and uncountable while also capturing common-sense notions of the “length” of a line, the “area” of a sheet of paper, the “volume” of a hill, and so on. This is exactly what is studied in the branch of mathematics known as measure theory.


Saturday, May 26, 2012

The Arabic nominal system, the regular pattern

Let’s begin by looking at the case-endings for the regular (sālim, سالم) pattern. 


Singular


Dual
Definite Indefinite Construct Definite Indefinite Construct
marfū‘
-u
-un
-u
-āni
-āni
-ā
manṣūb
-a
-an
-a
-ayni
-ayni
-ay
majrūr
-i
-in
-i
-ayni
-ayni
-ay


This applies to all regular nouns and adjectives in the singular and the dual, whether they are masculine or feminine. Nouns like walad- and bint- and sayyāra(t)-; participles used participially, like kātib-; participles used nominally, like mubārā(t)-: all follow the same pattern.


What’s more, some kinds of masculine broken plurals also follow the sālim regular singular pattern of declension. Thus, the masculine word kuttāb (“(male) writers”), which is the broken plural of the word kātib- (a participle, but being used as a noun), follows the singular sālim declension. Just because a plural is formed in a broken manner does not automatically mean that its declension is also irregular.


There is also a sālim plural pattern, but this varies depending on gender. There is also a subtype of regular feminine nouns, which end in an ā, and which show slightly different endings. 


Plural—Animate Masculine
Definite
Indefinite
Construct



marfū‘
-ūna
-ūna



manṣūb
-īna
-īna



majrūr
-īna
na





This is the pattern that would be followed by the participle kātib- used participially (to describe a group of males that are currently engaged in a process of writing).


Plural—Feminine

Plural—Long ā Feminine
Definite
Indefinite
Construct
Definite
Indefinite
Construct
marfū‘
-ātu
-ātun
-ātu
-ayātu
-ayātun
-ayātu
manṣūb
-āti
-ātin
-āti
-ayāti
-ayātin
-ayātu
majrūr
-āti
-ātin
-āti
-ayāti
-ayātin
-ayāti


For example, the word sayyārat- in the singular declines as sayyār-āt- in the plural. The feminine ā word mubārā(t)- declines as mubār-ayāt-, etc.


More to follow on the “irregular” nominals.



The Arabic nominal system, intro

Arabic has a somewhat tricky system of case-inflections for its nouns. I’ve decided to note down some patterns I’ve seen in order to act as a دلالة الحائرين, a Guide for the Perplexed (in whose company I fall).

In general, Arabic nouns vary along four dimensions:
  • number: singular (mufrad, مفرد), dual (muthannā, مثنى), plural (jam‘, جمع)
  • gender: masculine (mudhakkar, مذكر) and feminine (mu’annath, مؤنث)
  • state: definite, indefinite, and construct (iḍāfa,  إضافة)
  • case: “nominative” (marfū‘, مرفوع), “accusative” (manṣūb, منصوب), and “genitive” (majrūr, مجرور)
The Latinate case terms are pretty horrendous when it comes to describing the possible meanings of the Arabic cases, and so I will use only the Arabic terms for them. For the rest, I shall use the English. All of the other terms should be fairly clear, except for the “construct state”, which is generally absent in Indo-European languages. (I’m not going to go into the semantics of the construct state here.)

A fifth dimension, animacy, is implicit and shows up in the formation of plurals. Briefly: when an animate object modified by an adjective takes the plural, then both noun and adjective must be in the plural. But when an inanimate object modified by an adjective takes the plural, then the adjective must be in the feminine singular—regardless of the gender of the object. Consider the four nouns: walad (p. awlād) “boy”, bint (p. bināt) “girl”, qalam (masc., p. aqlām) “pen”, sayyāra (fem., p. sayyārāt), “car”.  Modified by the (regular) participial adjective mukhtalif-  “writing”, we see (in the marfū‘ case):
  • awlād mukhtalifūn(a)
  • bināt mukhtalifāt(un)
  • aqlām mukhtalifa(tun)
  • sayyārāt mukhtalifa(tun)
A few random notes:

  • Why “regular” adjectives? It’s because Arabic has two different kinds of plurals: the regular or “sound” (sālim, سالم) plural, which is formed regularly for (almost) all feminine nouns and adjectives and for many masculine nouns and adjectives (including all participial adjectives), and the “broken” (maksūr, مكسور) plural, which is formed for some masculine nouns and some masculine adjectives. The most common adjectives and nouns are often the ones that form the craziest broken plurals. Precisely how different broken plurals are formed doesn’t concern us here; all we care about are the ways in which they inflect.
  • The regular feminine noun ends in a t, the so-called tā’ marbūṭa(t), but this is not pronounced in pausa. I’ve therefore written it in brackets (which has the added benefit of vaguely resembling the way it’s written in Arabic, as a ة). When case-endings are added, though, the tā’ marbūṭa(a) is pronounced, along with the endings.
  • Incidentally, the Arabic word for inflections, i‘rāb (إعراب), is the verbal noun of the verb a‘raba (أعرب) formed from the root ‘-r-b (ع ر ب), which is also the source of the words “Arab” and “Arabic”. In fact, that particular form of the verb literally means “to make something Arab(ic)” or “to Arab-ize”. [I have no basis for this hypothesis, but if the claims made by Bohas, Guillaume, and Kouloughli in The Arabic Linguistic Tradition about the motivation behind Sībawayhi’s nomenclature are correct—i.e., that Sībawayhi picked as grammatical terms action nouns (maṣdar, مصدر) that describe the speaker’s intention—then it would seem that pronouncing the case-endings would stem from the speaker’s desire to make his speech as Arab as possible.]

Actual patterns to follow.


Wednesday, May 23, 2012

Verbal knowledge (śābda-bodha) in early modern India

(This is unlikely to be of interest to anybody but me, but then again most things on this blog fall into that category!)

In all things associated with language—grammar, semantics, exegesis, hermeneutics, literary theory, you name it—the Sanskritic intellectual tradition developed perhaps the most sophisticated toolkit available to pre-modern humans. One of the most substantial advances on this front was made by the Navya Naiyāyikas (the “New Logicians”), who came up with a formal terminology designed to make communication unambiguous (or at least as unambiguous as can be possible in a natural language). Their terminology was adopted by intellectuals with wide-ranging commitments and projects, such as Mīmāṃsā (hermeneutics), Vyākaraṇa (grammar), and Vedānta (philosophical theology, for lack of a better description).

Jan Houben’s article “‘Semantics’ in the Sanskrit tradition ‘on the eve of colonialism’” shows how Vaiyākaraṇas (grammarians), Naiyāyikas (logicians), and Mīmāṃsakas (exegetes) all used terminology borrowed from the Navya Naiyāyikas to precisely and unambiguously describe the kind of “verbal knowledge” (śābda-bodha) produced in a speaker of Sanskrit upon hearing the sentence:

rāmo ’nnaṃ pacati 
“Rāma cooks rice”

The question for all three groups of intellectuals is the same: what is the main meaning-bearing element of a sentence, and how does it relate to all the other elements? All three agree on what the sentence conveys to a speaker of Sanskrit; where they differ is on the “keystone” of the sentence.


Tuesday, May 22, 2012

"In Defense of Naïve Reading"

http://opinionator.blogs.nytimes.com/2010/10/10/in-defense-of-naive-reading/
Literature and the arts have a dimension unique in the academy, not shared by the objects studied, or “researched” by our scientific brethren. They invite or invoke, at a kind of “first level,” an aesthetic experience that is by its nature resistant to restatement in more formalized, theoretical or generalizing language. This response can certainly be enriched by knowledge of context and history, but the objects express a first-person or subjective view of human concerns that is falsified if wholly transposed to a more “sideways on” or third person view. Indeed that is in a way the whole point of having the “arts.”

Likewise—and this is a much more controversial thesis—such works also can directly deliver a kind of practical knowledge and self-understanding not available from a third person or more general formulation of such knowledge. There is no reason to think that such knowledge … is any less knowledge because it cannot be so formalized or even taught as such. Call this a plea for a place for “naïve” reading, teaching and writing—an appreciation and discussion not mediated by a theoretical research question recognizable as such by the modern academy.
The “restatement of the aesthetic experience in formalized, theoretical or generalizing language” is precisely what Sanskrit literary theorists like Abhinavagupta and his rasa folk do. The nature of the aesthetic experience generated in the sensitive connoisseur (sahṛdaya) by a drama or literary piece is theorized at great length in these works and in scores of modern secondary literature on the topic.

What interests me, though, is the author’s second claim, that literature “can directly deliver a kind of practical knowledge and self-understanding”. Sheldon Pollock argues in his epic article “Sanskrit Literary Culture from the Inside Out” that the Sanskrit literary understanding tends not to attribute such epistemological powers to kāvya in general. Now, Sanskrit theorists do claim that kāvya can potentially teach us how to act. As Viśvanātha Kavirāja states in his Sāhitya-darpaṇa: rāmâdivat pravartitavyam na tu rāvaṇâdivat—“one must conduct oneself like Rāma and his like, and not like Rāvaṇa and his like”—and kāvya is of course a major source of such information.


Monday, May 7, 2012

The birth of poetry in Sanskrit

While translating the first verse of the Rāghavayādavīyam of Veṅkaṭādhvarin, I came across a word that I simply could not decipher on my own: mārāmorāḥ (मारामोराः in Devanāgarī). I had to look up the English commentary of Dr. Saroja Ramanujam to figure it out. She resegmented it as mā-ārāma-urāḥ, and glossed it as a bahuvrīhi (an “exocentric” compound functioning as an adjective) that means “one whose chest is a pleasure garden for Mā”. (There is no way I would have figured that out on my own!) 

But what, or who, is Mā? Dr. Ramanujam simply noted that it was a name for Lakṣmī, but I wanted to find out more and dug deeper. Now, digging too deep is fraught with difficulties. (Just ask the dear departed dwarves of Dwarrowdelf, who delved too deep, disturbing a denizen of the dark depths that then dealt the deathblow to their delightful dominion.) But in this case, what I found was pure mithril.

Prof. Ajay Rao has written a fascinating paper called “Theologising the Inaugural Verse: Śleṣa Reading in Rāmāyaṇa Commentary” for the Journal of Hindu Studies. The underlying argument of the paper (which Prof. Rao elaborates in his dissertation) is that the Rāmāyaṇa was not always perceived as a fully religious text, and that at least early in its history it was seen as a work of literature (kāvya) and not a received tradition (smṛti). Indeed, the Rāmāyaṇa is seen not just as any literary work, but as the first literary work (ādi-kāvya), and its composer, the poet-sage Vālmīki, is regarded as the First Poet (ādi-kavi). Prof. Rao further argues that the “theologization” of the Rāmāyaṇa was accomplished by a series of Śrīvaiṣṇava commentators who interpreted key episodes in the narrative as illustrative of the theological ideas underpinning their philosophical theology. Foremost among these commentators was the sixteenth-century Govindarāja, upon whose Rāmāyaṇa-bhūṣaṇa commentary Prof. Rao relies.

Definitions of negation

The Sanskrit grammatical tradition loves to name and define its terms, often in verses. For example, the privative prefix, which manifests itself as a- or an- (and is cognate with the Greek a- in words like atom), is called naÑ in the Pāṇinian tradition. A concise verse (from the voluminous Śabdakalpadruma) summarizes the various meanings that this prefix can express:


tat-sādṛśyaṃ virodhaś ca tad-anyatvaṃ tad-alpatā |
aprāśastyam abhāvaś ca nañarthāḥ ṣaṭ prakīrtitāḥ ||

The tradition enumerates six different meanings that can be expressed by naÑ:


“Extreme Poetry”: Sanskrit śleṣa

Prof. Yigal Bronner at the University of Chicago has written a remarkable book called Extreme Poetry: the South Asian Movement of Simultaneous Narration. This describes the staggering intellectual and literary phenomenon in Sanskrit of composing works that can be read in multiple ways to simultaneously produce different narratives. It is a brilliant work that casts light upon a phenomenon that is astonishingly difficult both to read and to ’rite. In perhaps no other language could something like this be realized on such a colossal scale.

Reading Prof. Bronner’s book has inspired me to turn to a 17th century Sanskrit text of the viloma genre called the Rāghavayādavīyam, composed by the Śrīvaiṣṇava litterateur Veṅkaṭādhvarin of Aracāṇippālai. Veṅkaṭādhvarin is also famous for his Viśvaguṇādarśacampū, a “travel” work that describes the condition of the Tamil lands of his time through the eyes of two celestial beings (gandharvas), one idealistic, the other sarcastic and cynical. His Śrī Lakṣmī Sahasram is, as the name suggests, a thousand verses glorifying the Divine Mother Lakṣmī, who is central to the Śrīvaiṣṇava religious tradition. Veṅkaṭādhvarin divided his work into twenty-five chapters, invoking the twenty-five-verse Śrī Stuti composed perhaps 300 years earlier by his revered predecessor, Śrī Vedānta Deśika. [It would be fascinating to look for systematic connections between the two works.]

<UPDATE>
It turns out that Veṅkaṭādhvarin also composed another work, the Ācārya-pañcāśat, fifty verses honoring the great teacher (ācārya) Śrī Vedānta Deśika. 
</UPDATE>

In comparison, the Rāghavayādavīyam is a much shorter work, consisting of thirty verses. It narrates the story of Rāma when read forwards. However, when each verse is read backwards (while the whole work is still read forwards), it narrates the story of Kṛṣṇa! Translating this level of Sanskrit is beyond my capacity, but I would eventually like to give it a shot. 

For now, just the opening benediction, with the help of the English commentary and translation of Dr. Saroja Ramanujam. I have chosen different interpretations for a couple of words where I thought my choices fit the context of the verse better; it is, of course, entirely possible that I am wrong.

May the same power that animated Veṅkaṭādhvarin to compose this work allow me to translate it as best as I can into English!

Verse 1 (anuloma)
vande ’haṃ devaṃ taṃ śrītaṃ rantāraṃ kālaṃ bhāsā yaḥ |
rāmo rāmādhīr āpyāgo līlām ārâ ’’yodhye vāse || 1a ||
I bow down to the Lord, 
the one sporting with Śrī
        splendidly for eternity,

Who, as Rāma, 
        His mind fixed on that beautiful woman (Sītā),
returned from the ocean

and fulfilled His divine play (līlā)
        dwelling in Ayodhyā.
Verse 1 (pratiloma)
sevâdhyeyo rāmā-lālī gopy-ārādhī mā-’’rāmôrāḥ |
yaḥ sâbhâlaṃkāraṃ tāraṃ taṃ śrītaṃ vande ’haṃ devam || 1p ||


Worshipable through loving service,

He charms beautiful women,
        delights, and is delighted by, the milkmaids;

His chest is a pleasure-garden for Mother Lakṣmī—

to Him, 
        splendid,
        His ornaments radiating light,

to the one sporting with Śrī,
I bow down to the Lord.

[Reading a text forward is called anuloma in Sanskrit, which literally means “with / following the hair”. Doing something anuloma means following the natural flow of things. Its opposite is pratiloma, which literally means “against the hair”. The two terms can be felicitously translated into English as “along the grain” and “against the grain”.]

Saturday, May 5, 2012

The wondrous chain of hope

āśā nāma manuṣyāṇāṃ kācid āścarya-śṛṅkhalā |
yayā baddhāḥ pradhāvanti muktās tiṣṭhanti paṅguvat ||


What a wondrous chain Hope is for mankind!
Those bound by it run free; 
Those free from it stand still, lamed.



Why pearls, and why strung at random?

In his translation of the famous "Turk of Shirazghazal of Hafez into florid English, Sir William Jones, the philologist and Sanskrit scholar and polyglot extraordinaire, transformed the following couplet:

غزل گفتی و در سفتی بیا و خوش بخوان حافظ

که بر نظم تو افشاند فلک عقد ثریا را


into:

Go boldly forth, my simple lay,
Whose accents flow with artless ease,
Like orient pearls at random strung.

The "translation" is terribly inaccurate, but worse, the phrase is a gross misrepresentation of the highly structured organization of Persian poetry. Regardless, I picked it as the name of my blog for a number of reasons: 
1) I don't expect the ordering of my posts to follow any rhyme or reason
2) Since "at random strung" is a rather meaningless phrase, I decided to go with the longer but more pompous "pearls at random strung". I rest assured that my readers are unlikely to deduce from this an effort on my part to arrogate some of Hafez's peerless brilliance!

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Cambridge, Massachusetts, United States
What is this life if, full of care,
We have no time to stand and stare.
—W.H. Davies, “Leisure”