Thursday, November 28, 2013

Semantics, local and global

[The distinction between the local and the global view, with increasing enrichment of the latter, has brilliantly characterized geometry (and cosmology) for the past half-century or so.  Addressing a different problematics, we proceed in that spirit  here.]

In math, the familiar notion of a function  normally (and only-ever in one’s earlier education) assigns some value to each of a set of points.  Later, one studies function-like entities, or functions sensu lato, whose mandibular gape is more capacious, taking in as argument, not merely a point, but a variable region, or even another function:  thus we come to study things called functionals, densities, and distributions.

In the simplest popular literature, such as the Hardy Boys on which my generation of masculine rascals was raised, semantic interpretation is local, even punctual.   The interpretation may well be more than literal, and require certain background conventions for proper appreciation, but the meaning may nevertheless be derived directly from the sentence in question -- it does not require any sort of “contour integral” through surrounding text, mapping its textual neighborhood into a richly layered semantic space.

Thus, consider:

            Joe’s jaw dropped.

This, our legent lad is to understand, denotes, primo, that Joe’s mouth widened somewhat, involuntarily; and that, segundo, this reflex was caused by emotionally tinged surprise. 
Such associations are to some extent conventional, and thus vary across cultures.  Part of the value of such digestible and repetitious reading as the Hardy series, is to inculcate such simple mappings.  To accomplish this does initially require the learner to pay attention to immediate context:  as, a preceding

There beneath the Christmas tree stood a shiny red roadster.

followed by

“Jumpin’ Jehoshaphat!   This is the best present ever!”

in which case the jaw-drop manifests surprise plus delight;  or else

There on the kitchen floor lay Aunt Gertrude, bound and gagged.

followed by

WTF ?!??!!!”

(well, not that exactly), in which case the concommittant to surprise is rather dismay.

Surprise is the common factor, and persists for all later instances of falling jaws, even in the absence of such circumambient clues.   That there exists some attendant emotion  is likewise a given, with some (surprise, dismay) being much the most common, and others being almost ruled out (perplexity, embarrassment, boredom).  What objectively occasions the surprise in each new instance can be described as a matter of simple statistics, derived from such considerations as the relative likelihood of encountering a beribboned roadster on Christmas morn, versus a fruitcake, say, or a set of Lincoln logs (or, for adults of a Glengary Glen age, a set of steak-knives);  and whether Aunt Gertrude is a conventional reserved sort of elderly lady, or whether, rather, she is given to bouts of self-bondage, like that MI6 agent whose corpse was found found in his bathtub.  Such frequency-profiles are of course relative to culture, and their calculation and application go beyond the content of the immediate sentence under interpretation, but they are soon solidified into background assumptions tacitly available to anyone competent in the culture, and need not be specifically keyed by the ambient text.
In time, one accumulates great hordes of such things, no longer needing any contextual guidance to interpret such conventional gestures as

Frank slapped his forehead.
Iola blanched.
Clint’s eyes narrowed.
Wolfe frowned and polished his glasses.

and so on and so forth.   As one’s literary experience proceeds, other, no longer culture-wide but character-specific physical indicia may be acquired:

Merlin’s thumb tingled.

(Cf. “By the pricking of my thumbs, something wicked this way comes.”)  But once acquired, their interpretation is straightforward, and purely local.


Consider, now, a character  not from any series, and whose acquaintance we have only just begun to make, in a character-crowded tapestry, the novel Martin Chuzzlewit:  to wit, Tom Pinch.  And consider this line, appearing isolated in a paragraph all by itself:

Mr Pinch opened his eyes wider, and looked at the fire harder than he had done yet.

Whatever can this mean?

[Note:  I shall pause here, pending future leisure to expand, and meantime let you ponder this, and to seek its context if you will, in Chapter 6.]

Tom has recently been sent to fetch Martin Chuzzlewit fils at the inn, to be Mr Pecksniff’s new architectural apprentice.  When we first meet him, coming in from the cold on a frosty night, he too engages in a bit of hearth-staring:

The stranger became thoughtful, and sat for five or ten minutes  looking at the fire in silence.

Here the significance of the action is quite different from that which applies in Pinch’s case.  Yet, different in a deep way, which requires psychological excavation to uncover:  not different in the merely algebraic way whereby x may denote, now 2, now ½, or his may be co-indexed, now by Frank (“…stroked his chin”), now by Rico (“… hefted the Lugar in his hand”).
Though born to wealth and privilege, Martin has recently been evicted from the good graces of his elderly uncle and theretofore-presumed bequeather-to-be.  And since (like half the characters in Dickens, it sometimes seems) he is otherwise an orphan, he has seen his “Great Expectations” (Martin’s phrase; where have we heard that before?)  evaporate before his eyes (which, had he been a Hardy Boy, would have “popped” at the news, along with his plummeting jaw).  He is accordingly a great fire-starer, by way of absorbing the warmth he feels to be his due, and of brooding upon his wrongs.  Here we see him later, at it again, with poor Pinch huddling on a neighboring footstool:

Beyond that, Martin is not (yet) a deep character, further than what we have seen, and indeed is typical of Dickens as being sharply (though, to a beginning reader, somewhat subtly) delineated, repeatedly bodying-forth a certain trait of character.  This is the sort of thing that has led some critics (unjustly I believe) to dismiss the Dickensian menagerie as caricatures.   It is likewise part of Dickens’ craft, to throw this character’s essence into greater relief, by means of characteristic physical gestures;  further, in the case of Martin, by the juxtaposed contrasting figure of Tom Pinch, who is something like Martin’s dual or inverse.  Where Martin was born to privilege, Tom was born to none.  Whereas Martin continually frets at any crumb that might be missing from his own bounty, Tom is grateful -- truly, deeply grateful -- for any scrap that might fall from the table of his betters.  (Dickens offers a literal picture of this, in Tom’s delighted feasting upon the wilted leftovers of the departed Misses Pecksniff.)
Tom Pinch is more of a puzzle -- more of a mystery.   On the face of it, he is a simple fellow, almost a simpleton;  certainly that is the opinion of the various Pecksniffs.  But there are a deep roots to Tom’s humility, to which the instincts of a Christian will quicken.  He is less a village idiot, than a Holy Fool.

And now these polar opposites are confronted.  Martin speaks casually, heedless of his snubs towards Pinch.  Pinch, from his good heart, never quite perceives these, just as he does not from the Misses Pecksniff.   Martin’s pretentions are likewise dutifully seconded, just like those of Pecksniff.  (Martin on his family’s failings, which fortunately “haven’t descended to me”; he must “be very careful that I don’t contract ‘em.”  “’To be sure,’ said Mr Pinch. ‘Very proper.’”)   But at length, Marvin’s account of his haughty rebuke to his elder relative, is too much for poor Tom to swallow whole.  It is his glimpsing that flash of Satanic pride -- that non serviam -- which sets Pinch to staring, wide-eyed, sightlessly, into the fire:  into the depths of the fiery pit.

To resume the mathematical metaphor:   This ignispective image is visually equivalent for Martin as for Tom, but means something a bit different.  It represents, if you will, the punctual intersection of two life-curves;  and its meaning in momentum-space is given  not by the locus alone, but by the tangent.

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