On crafting poems

A chance conversation on an email thread reminded me of some lines about poetry by W.B. Yeats:

We sat together at one summer’s end,

That beautiful mild woman, your close friend,

And you and I, and talked of poetry.

I said, “A line will take us hours maybe; 

Yet if it does not seem a moment’s thought,

Our stitching and unstitching has been naught.

Better go down upon your marrow-bones

And scrub a kitchen pavement, or break stones

Like an old pauper, in all kinds of weather;

For to articulate sweet sounds together

Is to work harder than all these, and yet

Be thought an idler by the noisy set

Of bankers, schoolmasters, and clergymen

The martyrs call the world.”

These lines on the difficulty of crafting poetry—not just rhyming, rhythmic utterances but real poetry—reminded me in turn of two Sanskrit verses on the same topic. The Sanskrit literary tradition is acutely self-aware of its linguistic nature (one of the words for literature or literariness / литературность, is vāṅ-maya, literally “speech-stuff”), as befits an intellectual and cultural universe that has perhaps paid more systematic attention to the Word and the World than any other from its very inception. The two verses, and my attempts at translating them, follow:

Auxiliary Verbs, in German

After our long detour through the French auxiliary verbal system, it’s time to tackle something a little closer to home. German is often sold to native English speakers as a “harder” language to learn than French, and this is certainly true insofar as learning German requires us to learn lots of unfamiliar vocabulary. English has absorbed so much Latinate vocabulary that even without knowing no French or German, it’s far easier to understand les langages sont compliqués than Sprachen sind schwierig. But given German’s deep familial relationship with English, I would argue that in some ways German is actually easier to learn than French, because English speakers already possess a(n admittedly incomplete) knowledge of German structure.


This structural similarity is not very visible in the case of nouns, for modern English has almost completely abandoned the complex nominal declension system that Old English had and modern German and Icelandic still possess. Its remnants can be seen in the pronouns, where English him and her are clearly related to the German dative pronouns ihm and ihr, and your is similar to euer. To identify clear structural similarities between English and German, one must turn to their verbal systems.


An Overview of the German verbal system
German verbs fall into two broad categories: “strong” and “weak”. This terminology was developed by the Grimm brothers (yes, of fairytale fame!) based on the logic that weak verbs, being regular and predictable, were too weak to break free of the system of rules, whereas strong verbs were strong enough to behave unpredictably and break the rules. English verbs can also be classified into these categories; furthermore, if a verb is strong in one of the two languages, it will likely be strong in the other as well. Thus, knowing that “to sing” and “to swim” are “irregular” in English (see “I sang” and “I have sung”, and “I swam” and “I’ve swum”), we can guess that the German cognates singen and schwimmen are also strong (in the same order, ich sang and ich habe gesungen, and ich schwamme and ich bin geschwommen). This isn’t a hard-and-fast rule, though, since English verbs have tended to weaken over time, becoming more regular. Witness that the English cognate of the German strong verb backen is the regular verb “to bake”.


But German verbs, whether strong or weak, are not so strong as to entirely eschew the use of auxiliaries. (The Germanic tribes served as a source of auxiliaries to the Roman legions, but I don’t know if that had anything to do with this!) Indeed, one of the most obvious differences between the English and German verbal systems on the one hand and the French verbal system on the other is precisely the fact that both English and German use auxiliaries much more extensively. 


In fact, given a German infinitive, only two purely synthetic verbal forms exist in the indicative mood: the present (das Präsens) and the preterite (das Präteritum or das Imperfekt). All other verbal forms are generated using auxiliaries. And like English (and unlike French), the auxiliary verbs are of two types, modal and non-modal.

• The non-modal auxiliaries, which also do double-duty as full-fledged verbs:
• haben (“to have”), used for the perfect construction
• sein (“to be”), also used for the perfect construction (like the French use of être)
• werden (“to become”), used in two roles:
• to form the passive voice of all TAMs
• to form the future aspect
• The modal auxiliaries, which (as in English) convey a whole host of modal nuance, and which are cognate with the English modal auxiliaries but often carry different meanings:
• können, cognate with “can” and meaning “to be able to”
• mögen, cognate with “may” and meaning “to like”
• dürfen, meaning “to be permitted [to do something]”
• sollen, cognate with “shall” and meaning “to be obliged / required [to do something]”
• wollen, cognate with “will” but meaning “to want”
• müssen, cognate with “must” and meaning “to have to”

Two pairs need a bit of clarification: wollen expresses a stronger desire than mögen; and müssen expresses a stronger need or compulsion than sollen (compare “I must eat” to “I should eat”). Wollen is also worth noting carefully, because its English cognate “will” has come to be used as the future aspect auxiliary in the third person. Its use in German shows how this makes sense: “he will go” must have meant at some point “he intensely desires to go”. The German usage also shows why “I will go” is seen in ‘propah’ English as less polite than “I shall go”, and why it may seem rude to some to say “he shall go” in place of “he will go”. In the first situation, the use of “will” comes across as rather insistent; in the second situation, the use of “shall” eliminates the third person’s personal agency.


More to come, as always.

Religion and narrative

This post on The Daily Dish, on religion as theater, has got me thinking: All the talk these days of faith versus reason, of religion versus science, seem to me to be misplaced. A lot of this stems from what I think is a misplaced emphasis on religion as “blind faith”. Perhaps we would do better to think of religion as “shared stories” (or better yet, “shared experiences”), for every religious community has a particular narrative about the human condition.

To the “non-believers”, the “outsiders”, it is the “story” that matters—whether the content is “true” or “false”, “historical” or “mythological”, “revealed” or “constructed”. Hence arguments about whether Genesis can literally be true or whether Rāma actually had a bridge built to Laṅkā.

To the “believers”, the “faithful”, the “insiders”, it is the “shared” part that matters—the fact that these stories resonate not just with one person but with an entire community; the fact that this resonance has held true for this community over time (even if, and possible especially if, it has resonated with different concerns at different times); and the fact that these stories will continue to be shared with the community to come, if the current generation does its job right. In fact, I think that this “shared” aspect is so important that the “stories” themselves gradually change over time, emphasizing certain things and downplaying others—but always in a way that allows them to be shared and accepted by the majority of the community.

To the “Truthseeker”, both aspects matter equally—if it is false, then it is not worth pursuing; if it cannot be shared, in at least some dilute form, then it cannot be a goal towards which one can guide others, around which a community can be built.

“God-obsessed”

A fascinating essay by Tony Woodlief, called “Dreaming God”:

We are god-obsessed and god-seeking and at least the intellectuals of earlier ages—even if they couldn’t bring themselves to belief—recognized this. So many of today’s intellectuals are so far removed from religion that they don’t know the half of how deeply it’s intertwined in the lives and hearts of the rest of us.

And even more provocative:

We are god-obsessed because we have lost God or we are running from God or we are hopelessly seeking Him, and maybe all of these at once.

An extremely interesting analogy:

We are god-obsessed the way a child snatched from his mother will always have his heart and flesh tuned to her, even after he forgets her face. Cover the earth with orphans and you will find grown men fashioning images of mothers and worshipping strong women and crafting myths about mothers who have left or were taken or whose spirits dwell in the trees.
And at the edges of their tribal fires will stand the anthropologist and the philosopher, reasoning that all this mother-talk is simply proof that men are prone to invent stories about mothers, which is itself proof that no single story about a mother could be true, which is proof that the brain just evolved to work that way.

I’ll comment on this one of these days when I get more time.

LaTeX on Blogspot

Blogspot is pretty bad at displaying math; \( \LaTeX \) is pretty awesome at displaying math. So how do we get Blogspot and \( \LaTeX \) working with each other? Using MathJax!

All it takes is the addition of one line to the HTML code for each blog, and presto! we can include \( \TeX \) and \( \LaTeX \) commands into our blog. And not only can we do inline math, like \( \int_{0}^{2 \pi} \mathrm{d}x = 2 \pi \), but also display math, like:

\[
\begin{eqnarray}
(a + b)^2 & = & (a + b) \cdot (a + b) \\
& = & a(a+ b) + b(a + b) \\
& = & a^2 + ab + ba + b^2 \\
& = & a^2 + 2ab + b^2
\end{eqnarray}
\]

Truly remarkable! Now all I need to do is update all my old math posts using MathJax and good ol’ \( \LaTeX \).

Counting, uncounting, and dust, part four

I’d been completely side-tracked from this set of posts, and I only just realized I had forgotten to finish it. Last time we checked, we had finally figured out that there are different levels of infinity. We had, however, ended up with a rather strange idea: the idea that the set of all real numbers between 0 and 1 is somehow as big as the set of all real numbers in its entirely. In effect, we have shown that there is no difference between a mountain and a molehill!


We thus have two different lines of inquiry to pursue:

1. Are there levels of infinity beyond the infinity of the real numbers?
2. Are there ways to measure the size of a set that can distinguish mountains from molehills?

Levels of infinity
We begin with the idea of a power set: the power set of a set is defined as the set of all subsets of the set. Huh? An example should make things clearer: if \( A = \{ a, b, c \} \), then the power set of \( A \), sometimes written as \( \mathcal{P}(A) \) and sometimes \( 2^{A} \) (we’ll see why), is the set \( \mathcal{P}(A) = \{ \{ a \}, \{ b \}, \{ c \}, \{ a, b \}, \{ b, c \}, \{ a, c \}, \{ a, b, c \}, \{ \}  \} \). All those braces are necessary, because every element of \( \mathcal{P}(A) \) is a subset (and not an element) of \( A \) itself. We note that \( A \) itself is an element of \( \mathcal{P}(A) \), as is the empty set \( \{ \} \).

Indulge me, por favor

I don’t normally soar away in flights of fantasy; I enjoy feeling grass underneath my feet and sand between my toes far too much. But just this once, I request you, gentle reader, to forgive my rhapsodizing. If it doesn’t make sense, well, it wasn’t necessarily meant to!


So here goes: Each of us is a link in an infinite chain of being that spans space and time. Each of these links is, of course, comprised of smaller links, ad infinitum; each of this links, of course, participates in a greater link, ad infinitum. Do I exaggerate when I speak of twin infinities? Maybe, and maybe not.


What I’m really trying to say is that everything is doubly emergent.


Now materialist reductionism is the idea that things can be understood entirely by parsing them into their constituent material parts. It is a remarkably powerful, persuasive idea, and the basis of much modern theoretical and practical advancement, but according to at least some thinkers, it cannot explain the phenomenon of emergence. For them, an anthill is more than the sum of its parts; similarly, each of us human beings is more than the sum of our parts. There is something about our complexity that is irreducible to the parts that constitute us. (Note that emergence does not automatically reject materialism; it does, however, reject reductionism.)


But at the same time, we ourselves are also parts of a bigger, emergent reality—society, we call it. We take it for granted and thus forget how much of who we are (of our emergent selves!) is both affected and effected by this layer of abstraction that lies atop organized collections of interacting human beings. 


We are different from computers because our operating systems are able to rewire the physical hardware on which they run.


And paradoxically, the more “concrete” and “elementary” our constituents get, the more conceptual and abstract they become! We smash atoms into electrons and protons and neutrons, only to find that these “elementary” particles are probability distributions; we take them apart even further, and are ultimately left with vibrating 26-dimensional strings. And yet somehow causality travels up this chain in powerful, largely well-understood ways!


We have become accustomed to thinking of causality purely in instrumental terms. In that sense, it is of course true that it is the parts that alter the whole. But we forget that the word “cause” used to have a much wider sense. What we think of as the “cause” these days is only the Aristotelian “effective cause”. We have forgotten that other “causes” exist and have real effects. The “formal cause”, for instance, can be seen as the way in which higher layers of abstraction limit and direct lower layers. Again, this does not necessitate a belief in a Platonic realm of Forms. When a carpenter builds a chair, it is obviously true that his tools operating on the wood are the “effective causes” of what is produced. But is it not true that a “formal cause”—an understanding of what it means to be a chair, which is necessarily influenced by his social position—also has a part to play in this? We no longer think of this as causality, but as a result we are unable to fully grasp what’s going on here. Causality goes both upwards and downwards (and maybe sidewards as well!) over the web of existence.


Levels of description matter. “Romeo loved Juliet” is as true as “a certain well-structured collection of organic compounds produced certain levels of serotonin and oxytocin in the presence of a similarly well-structured collection of organic compounds”, but they don’t mean the same thing. Even if you ignore the fact that Romeo and Juliet are literary figures! Levels of description matter, and although the same truth can be expressed at different levels, it is significant in different ways at those levels. This is very similar to Karl Popper’s “Three Worlds”, but I think “Three” is too much and too little: too much, because there is only one world; too little, because that one world exists and interacts at many, many different levels. This is not the same as saying there are “Two Truths”; there aren’t, and there cannot be. But the same truth can be expressed at different levels.


Some who face this tower of concrete-yet-abstract layers dismiss it all as illusion or as emptiness. I think the exact opposite is the case. This is reality: a unified whole, an infinitely diverse, infinitely layered, fractal, organic tower that grows, breathes, becomes self-conscious, tries to comprehend all of itself, and shrinks.