“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!

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 alaṅkāras drawn 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 ||

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.

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	-ū
manṣūb	-īna	-īna	-ī
majrūr	-īna	-īna	-ī

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.