## The Language of Mathematics (1)

In Computer Science, Literature, Mathematics on June 18, 2012 at 7:37 pm

I’m working on a software project (more soon) that involves a notation that is interpreted by computers.  As a way of specifying the language formally, I’m trying out parsing expression grammars, a relatively new alternative to the methods that have been traditionally used to define the syntax of programming languages, like context-free grammars.  I’ve been reading the original paper in which Bryan Ford introduces PEGs, and something struck me about the way in which it builds up to the mathematical definition of the idea.  The paper begins with an “informal” explanation that starts with an example of a PEG written in ASCII text, like you would use as the input to a program:

```# Hierarchical syntax
Grammar <- Spacing Definition+ EndOfFile
Definition <- Identifier LEFTARROW Expression
Expression <- Sequence (SLASH Sequence)*
Sequence <- Prefix*
Prefix <- (AND / NOT)? Suffix
Suffix <- Primary (QUESTION / STAR / PLUS)?
Primary <- Identifier !LEFTARROW
/ OPEN Expression CLOSE
/ Literal / Class / DOT```

[…]

Although the paper explains what it means in a very prosaic way, placing it in historical context and comparing PEG’s practical implications with those of other types of grammar, this bit of ASCII text seems intuitively like the most formal thing in the paper.  The mathematical definition of the construct is set off much less from the text of the article than the ASCII example, which is in a fixed-width font and embedded as “Figure 1.”  The definition begins:

Definition: A parsing expression grammar (PEG) is a 4-tuple G=(VN, VT, R, eS), where VN is a finite set of nonterminal symbols, VT is a finite set of terminal symbols, R is a finite set of rules, eS is a parsing expression termed the start expression, and VN ∩ VT = ∅. Each rule r ∈ R is a pair (A, e), which we write A ← e, where A ∈ VN and e is a parsing expression. For any nonterminal A, there is exactly one e such that A ← e ∈ R. R is therefore a function from nonterminals to expressions, and we write R(A) to denote the unique expression e such that A ← e ∈ R.

One reason why the informal explanation is informal in comparison with this is that it describes the syntax of PEGs using a PEG, making it a circular definition.  But two things jump out at me.

1. The mathematical notations in the formal definition are interpolated into a paragraph of written English, while the informal definition describes the syntax of the system in a way that a computer could understand.
2. It would be much harder to see what the formal definition is doing without reading the informal one first.  If the paper had started talking about 4-tuples right off the bat, it would be unclear in what sense the objects it defines could be considered “rules” and “parsing expressions.”  There is something, a sort of mathematical anamnesis, that the reader takes away from the circular definition at the beginning of the paper that makes it possible to see the meaning of the more rigorous math that follows, in a sense of the word “meaning” that is not yet clear to me.

## Positivity

In Art, Literature, Philosophy on September 28, 2011 at 5:52 pm

I used to claim that there was no such thing as self-expression in art. That’s not something I’d say any more, but not because I’ve changed my mind. Quite the opposite; I’ve gotten even more dead set against the dualism underlying the popular conception of self-expression than I was a couple years ago. I think it’s a worldview that makes an ideal of an empirical falsehood, causing a great deal of misery. But I’ve realized that a true materialism, one that really frees itself from that falsehood, can’t work entirely by negative definition. If the concept of the “true self” that was the fixation of the Modernists is incoherent, and I think that it is, then so is the statement that “there is no true self” with “true self” meant in that way. Reveling in superficiality as a response to Modernism’s failure is, to torture an expression, throwing out the baby and then taking a big drink of bathwater. What we need to do us come up with a new definition of self that isn’t at odds with materialism. As we do so, popular ideas like self-expression will be things we need to account for, not things we need to deny.

One reason I think that negativity has become so popular among literary scholars is that it’s associated, in no small part due to Hegel, with historicism, a philosophical approach that lends itself particularly well to supporting the importance of literature as an object of study. But I don’t want to discount the ethical case against the positive. One can find ample evidence in any history book that positive definitions of what it is to be human or American or a member of society can oppress. There is an ethical onus on the head of anyone who speaks positively about the human, to be sure. But ethics can be a problem for negative approaches as well, and I suspect that it is partially due to institutional constraints in the field of literary scholarship that the ethical arguments made in English departments have been skewed against the positive. A good epistemic standard is not all it takes to be responsible, but sticking to one generally is a prerequisite, and this is quite simply more difficult to do when speaking positively. Oftentimes to really back up a positive claim about the world takes experimental study, and for the most part the institutional support for serious experimental studies is not there in English departments.

This is something that I hope will change as technology makes empirical humanities more practical. Positive statements about culture and the “human” are not going to disappear, and denying them legitimacy in the intellectual world only insulates them from scrutiny. The U.S. is wanting for an institution that could serve as a legitimate place for such claims, where standards of responsibility can be entrenched as, if not explicit points of policy, at least norms of professionalism. If the right is trying to tear down the academy, that means it’s time to start building.

## Quine as literary theory

In Literature, Philosophy on September 22, 2011 at 11:27 pm

W.V.O. Quine’s project in Word and Object is the derivation of a formal language suitable for scientific hypothesis in a way that does not rely, like logical positivism, on protocol sentences that are taken to communicate observations in impartial and objective terms, or the existence of “meaning” independently from language.  Instead of building his system from the ground up out of logical primitives, Quine derives something quite similar to the language of propositional logic from empirically-testable regularities in our natural ways of speaking.

What’s crucial to Quine’s project is the idea of paraphrase.  In Quine’s terms, we accept a sentence as a paraphrase of what we’ve said not because the two sentences express the same underlying meaning, but because we judge that the second would have served whatever our purpose was just as well.  Quine sets out in detail a procedure for transforming arbitrary sentences into clear logical form using only operations that normally, at least when we are trying to speak objectively, produce acceptable paraphrases.  The operations he chooses to use are not meant to apply with certainty in every single case, but their applicability is supposed to be empirically testable in a reasonable range of circumstances.  As I’ve noted before, Quine emphasizes that it’s the original speaker who must finally judge whether a paraphrase is acceptable.  Any supposition we might make about what the other person is getting at can ultimately be no more than an educated guess unless we ask them and have reason to trust in the truthfulness of their answer.

Since Quine’s primary interest is science, he proceeds in his regimentation of language by using operations that he thinks would normally produce acceptable paraphrases in scientific discourse.  What happens if we apply a similar approach to literature?  A canonical form that arises out of, say, poetry, might look quite different from what Quine comes up with for science.  I don’t have the space to try this out in this post, but I will sketch out how the process might go.

First off, arguments about authorial intent would have to be off-limits in a Quinean approach to literature.  The theory that Quine sets out puts the focus on the speaker, but he expects that, if we are in doubt of what someone’s getting at, we can actually ask them to confirm our paraphrase.  To apply his approach to literature, we would have to set the standard for paraphrase in reader-centric terms based on the effect that the work has on us, so that we have a reasonable epistemic standard.  An acceptable paraphrase of a poem, then, would be one that produces approximately the same response in us as the original.  With this definition in mind, we would proceed by examining what changes we could make that produce acceptable paraphrases, looking for regularities in the sorts of operations that tend to leave a poem’s effect intact and perhaps learning something, thereby, about how a poem does what it does.

Those who’ve made a fair effort at understanding both analytic and continental philosophy won’t be surprised that, by applying Quine’s approach to literature, we’ve gotten quite close to deconstruction.  Both approaches avoid having to talk about meaning by focusing on the relationships between different pieces of language.  There is a difference in valence, though, and I think the Quinean approach has an advantage – it would, I think, be able to avoid making everything look like a “surface.”  The question that a deconstructionist asks is what difference it would make if another word were used in a particular spot – she aims to get everything she can out of the little textual details, with the assumption that every word has an equal chance at significance.  Instead, we would be looking for changes that wouldn’t make much of a difference, with the aim of stripping out all but a skeleton.  In the process we would be building a logic of poetry in terms of connectives and quantifiers like the structuralists tried to do, but we wouldn’t be building them from the ground up.  We would be enmeshing our theory with a living body of poetry.

This approach has an obvious affinity for the Imagists, and in particular the eliminative editing style of Ezra Pound, but I don’t think it would take us back to the Modernist distinction between surface and essence that has been rightly criticized from so many quarters.  Instead, it provides an explanation of what Pound was doing if he wasn’t finding poetry’s essence.  It would also provide, if it were to succeed, a class of literary universals that consists not of supposed “objective correlatives” between image and emotion, but, instead, of invariancies under transformation.

## Lot 49

In Literature, Music on July 16, 2011 at 1:24 pm

I guess I should be glad that my favorite author is being forced upon tens of thousands of undergraduates, but I’m worried that a lot of them are getting the wrong impression of Thomas Pynchon from The Crying of Lot 49. I can’t help but feel a fondness for the book, but I’m fond of it mainly insofar as it represents an interesting dead end from which Pynchon had the good sense to retreat.

If he is a postmodernist writer, Pynchon generally stays closer to the early form of postmodernism that emphasized the “ethical turn” against systematization in response to the Holocaust than to their followers who blathered on endlessly about “surfaces.” The Crying of Lot 49 is unique among his novels in that its critique of systems of meaning takes on an air of inevitability. Crying depicts a world in which it is actually impossible to believe in anything without falling into insanity. Absent are fearsome figures like Weissman (from V. and Gravity’s Rainbow), who are threatening beyond anything in Crying because of the extent to which they’ve successfully actualized their murderous belief systems. Instead we are presented with an Umwelt so overloaded with evidence of underlying meanings that the protagonist must be in constant doubt of whether or not her beliefs are the right ones. The only way to believe something without being driven mad by this evidence is to withdraw from the world altogether and live in fantasy; Oedipa ends up alienated not because she’s afraid of the violence that has been committed in the name of grand purposes, but because she can’t get over the idea that there might be a grand purpose for her to be alienated from.

Armchair sociologists have mused that young people can no longer understand the appeal of Crying because the paranoid alienation of Oedipa Maas has become their normal way of looking at the world. To the extent that the present-day person does look at the world in an alienated way, it is only because of the constant repetition of statements like this. For all its supposed rejection of Modernism, postmodernism continues to define alienation in terms of a Modernist concept of the self based on authenticity. Because the epistemic standards of “authenticity” have always been unclear, asking someone whether or not their experience of life is authentic is more likely to start them worrying about whether or not it “really” is than to get you a truthful answer.

The fact is that modern life never was characterized by alienation for more than a small class of highly-educated Westerners who thought themselves into it. The problem with Crying is that it inhabits the alienated state too fully, and with too little counterweight, to be meaningful to someone who hasn’t already bought into that line of thought. As such, it implicates readers in the paranoia that it seems intended to criticize.

One positive thing Crying does do for me, though, is give me the chance to get a thrill of inclusion whenever I see scrawled on a bathroom wall or cut into a park bench a loop, triangle and trapezoid, thus:

The critical consensus is surely right that if we look for meaning in Pynchon’s works by trying to interpret them, all we get is: looking for meaning in texts is madness. But that’s not all there is to the novels. The purpose of art is not to say something about our world; it’s to become part of our world, and for at least the small group of people who constitute Pynchon’s core audience his work serves much the same goal that Bob Dylan sets out for himself in “Tombstone Blues”:

Now I wish I could write you a melody so plain
That could hold you, dear lady, from going insane
That could ease you and cool you and cease the pain
Of your useless and pointless knowledge

Rather than looking for meaning in the “text” of Pynchon’s novels, then, why not think about what they do for their fans? It is, I think, quite a lot.

## Joyce nerds

In Literature on June 16, 2011 at 9:00 am

It’s Bloomsday and I just realized that my crumbling copy of Ulysses is packed away with the rest of my Joyce shelf in bed bug bags.

My first encounter with James Joyce’s work was not ideal.  As a very young one I came across a thread about Bloomsday on a discussion forum, knowing next to nothing about Joyce, and I read post after post about what nonsense this “high” literature was.  I didn’t have my own opinion, but I followed along until someone posted the first page or so of Portrait as an example of how nonsensical Joyce’s writing was.  I read it ready for a laugh, but once I was done I closed the browser window and resolved to get a copy of the book as soon as I could.

The anti-Joyce sentiment that I saw bubbling up there is a part of a common strain of anti-elitism in the United States that rests on a gross misconception of what the elite that matters actually is.  Although Joyce does demand quite a lot of the reader in terms of cultural knowledge (or, at least, willingness to look things up), the material involved – Romantic poetry, Greek mythology, the writing of centuries-old Catholic heretics – hardly correlates with status nowadays.  The people with what it takes to read and enjoy Ulysses are not the social or economic upper crust.  They’re middle-class nerds.

A few years ago I attended the Joyce Summer School, and I was surprised at how many non-academics were attending just for fun.  There’s a significant body of such people out there with enough of a taste for Joyce to spend a week in Dublin immersed, and they’re not all just in it for the museums and tours.  People with no stake in literature beyond liking it came to the seminars and even gave some of the lectures at the conference.  There are undoubtedly those who read Ulysses just so that they can brag to their friends, but for a lot of people who really love it it’s a culturally-marginal interest, and it’s not necessarily easy to find someone to talk about it with.  The culture that arises has much the same nerdy earnestness as sci-fi and fantasy fandoms.

Though I suggested that there’s something more to be valued in seminars than in pub crawls, I’m not opposed to the “fetishistic” character of Bloomsday or the “Joyce Industry” in general.  One of the great purposes of literature is to add to the common store of ideas by which we can connect to others, even if only within a group of enthusiasts.  It is a peculiarly Modern conception of the world that draws a clear line between myth and reality, and not one that jibes well with a novelist as deeply concerned with the realistic depiction of place as Joyce.  To be sure, Joyce’s works follow the model that Deleuze & Guattari would call the radicle, maintaining the work as an artistic unity despite the fragmentation of the vision of reality in which it is rooted.  But the roots are real, and Joyce gives us no reason to construct a distinction between, say, the St. Stephen’s Green of his novels and the one in Dublin.  Actual Joyce fans see them as the same.  And why not?  Leopold Bloom may never have lived in 7 Eccles St, but the character is as much a part of our world as the house was, in its way.