Drably lyrical realism

James Lever on Franzen (LRB):

the book is, among other things, possibly the most lachrymose novel of modern times. There are, in its 560 pages, 26 separate instances of weeping, not counting the many blinked-back tears or suppressed sobs or ‘Tiny pearls of tear … clinging to her eyelashes’ (a formulation so heartfelt it is recycled from page 421 of The Corrections). Meanwhile the final results for our ensemble have come in: Republican go-getter Joey has seen the error of his ways and become an importer of ethically grown coffee. Jessica is a junior editor at a literary publishing house in Manhattan, excited to be publishing ‘an earnest young novelist’. Patty’s rotten sister Abigail has become a successful art-clown in Italy. Patty’s less rotten sister Veronica is an unappreciated but possibly genius-level painter. Patty works with kids; Walter, one supposes, with birds. Richard, ‘busy and successful’, has just completed ‘one of those avant-garde orchestral thingies for the Brooklyn Academy of Music’ and is currently working on scores for art-house movies. And pretty much everyone lives in New York. Now, that’s how life oughta be! At last the question ‘How to live?’, posed throughout the novel, has been answered: we should live like they do in Hannah and Her Sisters. It’s around now that it may dawn on the reader that Freedom has more in common with Richard’s country-tinged, Grammy-nominated middlebrow hit record than Franzen might have intended. This book is ‘Nameless Lake’.

Freedom, like Netherland, is a book I would presumably finish but that I cannot get excited about. Zadie Smith, writing about Netherland and Remainder a year or two ago, got at part of the drabness of "lyrical realism" of the McEwanesque sort, but, if the passages she quoted (or that Lever quotes from Franzen) really are the purplest at hand, what is surprising is how unlyrical, how lacking in "sharp tender shocks," the writing is, despite its elegance. Perhaps the problem with all these books is their quest for "relevance"; I wish there were more of "the sluggish cream wound curdling spirals through her tea" or at least far less of "I was seized for the first time by a nauseating sense of America, my gleaming adopted country, under the secret actuation of unjust, indifferent powers." Or perhaps the reviewers are doing the book an injustice by picking out those bits.

The necessary angle

There is an obvious joke, which I've never actually heard anyone make, re Schrodinger's cat, the measurement process, and "curiosity killing the cat." (This joke would be vaguely appealing because of the role reversal -- it's the scientist's curiosity that kills the cat -- and would fit very naturally in an elementary discussion of quantum mechanics.)

Tangentially, I wonder what it says about my intellectual seriousness that I sometimes get interested in a problem purely because I can think of an amusing title for a talk about it. I started working on (what I thought were) macroscopic tunneling phenomena in superconducting whiskers because I wanted to give a talk titled "Schrodinger's whiskers." (This has the additional advantage of providing a segue into trapped flux in SQUID-like rings, which of course one can call "quantum handcuffs." In the event, the program sort of petered out.) Recently I've been finding it hard to get interested in problems that would not lead to a talk titled "Fear and loathing in the electron gas."

Snips of Jellyfish

I was planning to blog about Kay Ryan -- one of the three or four living poets whose work I actually care about -- but Paris Review just interviewed her so I can put this off for a while:

---

INTERVIEWER

How did you come up with what you’ve called recombinant rhyme?

RYAN

When I started writing nobody rhymed—it was in utter disrepute. Yet rhyme was a siren to me. I had this condition of things rhyming in my mind without my permission. Still I couldn’t take end-rhyme seriously, which meant I had to find other ways—I stashed my rhymes at the wrong ends of lines and in the middles—the front of one word would rhyme with the back of another one, or one word might be identical to three words. In “Turtle,” for instance, I rhyme “afford” with “a four-oared,” referring to a four-oared helmet: “Who would be a turtle who could help it? / A barely mobile hard roll, a four-oared helmet, / she can ill afford the chances she must take / in rowing toward the grasses that she eats.” The rhymes are just jumping all around in there, holding everything together. 

What’s recombinant rhyme? It’s like how they add a snip of the jellyfish’s glow-in-the-dark gene to bunnies and make them glow green; by snipping up pieces of sound and redistributing them throughout a poem I found I could get the poem to go a little bit luminescent.

Local color III: coppery keen slaws

This bit from Humphry Clinker is worth excerpting if only for its concreteness.

I am pent up in frowzy lodgings, where there is not room enough to swing a cat; and I breathe the steams of endless putrefaction; and these would, undoubtedly, produce a pestilence, if they were not qualified by the gross acid of sea-coal, which is itself a pernicious nuisance to lungs of any delicacy of texture: but even this boasted corrector cannot prevent those languid, sallow looks, that distinguish the inhabitants of London from those ruddy swains that lead a country-life — I go to bed after midnight, jaded and restless from the dissipations of the day — I start every hour from my sleep, at the horrid noise of the watchmen bawling the hour through every street, and thundering at every door; a set of useless fellows, who serve no other purpose but that of disturbing the repose of the inhabitants; and by five o'clock I start out of bed, in consequence of the still more dreadful alarm made by the country carts, and noisy rustics bellowing green pease under my window. If I would drink water, I must quaff the maukish contents of an open aqueduct, exposed to all manner of defilement; or swallow that which comes from the river Thames, impregnated with all the filth of London and Westminster — Human excrement is the least offensive part of the concrete, which is composed of all the drugs, minerals, and poisons, used in mechanics and manufacture, enriched with the putrefying carcasses of beasts and men; and mixed with the scourings of all the wash-tubs, kennels, and common sewers, within the bills of mortality.

This is the agreeable potation, extolled by the Londoners, as the finest water in the universe — As to the intoxicating potion, sold for wine, it is a vile, unpalatable, and pernicious sophistication, balderdashed with cyder, corn-spirit, and the juice of sloes. In an action at law, laid against a carman for having staved a cask of port, it appeared from the evidence of the cooper, that there were not above five gallons of real wine in the whole pipe, which held above a hundred, and even that had been brewed and adulterated by the merchant at Oporto. The bread I eat in London, is a deleterious paste, mixed up with chalk, alum, and bone-ashes; insipid to the taste, and destructive to the constitution. The good people are not ignorant of this adulteration — but they prefer it to wholesome bread, because it is whiter than the meal of corn: thus they sacrifice their taste and their health, and the lives of their tender infants, to a most absurd gratification of a mis-judging eye; and the miller, or the baker, is obliged to poison them and their families, in order to live by his profession. The same monstrous depravity appears in their veal, which is bleached by repeated bleedings, and other villainous arts, till there is not a drop of juice left in the body, and the poor animal is paralytic before it dies; so void of all taste, nourishment, and savour, that a man might dine as comfortably on a white fricassee of kid-skin gloves; or chip hats from Leghorn.

As they have discharged the natural colour from their bread, their butchers-meat, and poultry, their cutlets, ragouts, fricassees and sauces of all kinds; so they insist upon having the complexion of their potherbs mended, even at the hazard of their lives. Perhaps, you will hardly believe they can be so mad as to boil their greens with brass halfpence, in order to improve their colour; and yet nothing is more true — Indeed, without this improvement in the colour, they have no personal merit. They are produced in an artificial soil, and taste of nothing but the dunghills, from whence they spring. My cabbage, cauliflower, and 'sparagus in the country, are as much superior in flavour to those that are sold in Covent-garden, as my heath-mutton is to that of St James's-market; which in fact, is neither lamb nor mutton, but something betwixt the two, gorged in the rank fens of Lincoln and Essex, pale, coarse, and frowzy — As for the pork, it is an abominable carnivorous animal, fed with horse-flesh and distillers' grains; and the poultry is all rotten, in consequence of a fever, occasioned by the infamous practice of sewing up the gut, that they may be the sooner fattened in coops, in consequence of this cruel retention.

Of the fish, I need say nothing in this hot weather, but that it comes sixty, seventy, fourscore, and a hundred miles by land-carriage; a circumstance sufficient without any comment, to turn a Dutchman's stomach, even if his nose was not saluted in every alley with the sweet flavour of fresh mackarel, selling by retail. This is not the season for oysters; nevertheless, it may not be amiss to mention, that the right Colchester are kept in slime-pits, occasionally overflowed by the sea; and that the green colour, so much admired by the voluptuaries of this metropolis, is occasioned by the vitriolic scum, which rises on the surface of the stagnant and stinking water — Our rabbits are bred and fed in the poulterer's cellar, where they have neither air nor exercise, consequently they must be firm in flesh, and delicious in flavour; and there is no game to be had for love or money.

It must be owned, the Covent-garden affords some good fruit; which, however, is always engrossed by a few individuals of overgrown fortune, at an exorbitant price; so that little else than the refuse of the market falls to the share of the community; and that is distributed by such filthy hands, as I cannot look at without loathing. It was but yesterday that I saw a dirty barrow-bunter in the street, cleaning her dusty fruit with her own spittle; and, who knows but some fine lady of St James's parish might admit into her delicate mouth those very cherries, which had been rolled and moistened between the filthy, and, perhaps, ulcerated chops of a St Giles's huckster — I need not dwell upon the pallid, contaminated mash, which they call strawberries; soiled and tossed by greasy paws through twenty baskets crusted with dirt; and then presented with the worst milk, thickened with the worst flour, into a bad likeness of cream: but the milk itself should not pass unanalysed, the produce of faded cabbage-leaves and sour draff, lowered with hot water, frothed with bruised snails, carried through the streets in open pails, exposed to foul rinsings, discharged from doors and windows, spittle, snot, and tobacco-quids from foot passengers, overflowings from mud carts, spatterings from coach wheels, dirt and trash chucked into it by roguish boys for the joke's sake, the spewings of infants, who have slabbered in the tin-measure, which is thrown back in that condition among the milk, for the benefit of the next customer; and, finally, the vermin that drops from the rags of the nasty drab that vends this precious mixture, under the respectable denomination of milk-maid.

I shall conclude this catalogue of London dainties, with that table-beer, guiltless of hops and malt, vapid and nauseous; much fitter to facilitate the operation of a vomit, than to quench thirst and promote digestion; the tallowy rancid mass, called butter, manufactured with candle grease and kitchen stuff; and their fresh eggs, imported from France and Scotland.

[NB The "bills of mortality" is a wonderful synecdoche metonym for London. Would be curious to know of any equivalent contemporary phrases. "Within the police blotter" is almost apt for Champaign nowadays but seems unlikely to catch on.]

Sheridan; the blush as local color

I read the usual Restoration plays in an edition that introduced them as clever but heartless precursors of Sheridan and Goldsmith, and now I've read Sheridan's plays in an edition that insinuates that they are bowdlerized and insipid descendants of Restoration drama. (Why don't people edit books they like?) I'm more sympathetic to the latter point of view, at least re Sheridan; Goldsmith is a different kettle of fish altogether, and not Restoration-like at all. (Sheridan, it appears, actually bowdlerized Vanbrugh's Relapse to make it acceptable to a 1760s audience.) Both The Rivals and The School for Scandal are comedies of manners; the plots -- e.g., man woos idiosyncratic woman with comic aunt -- are very much in the mold of Congreve and Wycherley. The plots are clever enough, but both plays are short on spirit and edge; the characters are pretty blah, though I imagine a good actor could make them come to life, and the dialogue, despite stunts like Mrs. Malaprop's malapropisms, never gets off the ground. In general these plays are what one would expect of period pieces -- unlike The Country Wife, which is entirely contemporary.

The difference, it seems, lies in the smut. Are plays without explicit sexual references ipso facto quaint? There's something appealingly reductive about this notion, and it certainly is quite hard to find sexually explicit ancient texts that are boring. I'd venture an alternative explanation, though, which is that the basic dramatic tension in the comedy of manners -- the horror of being cast out of the loop -- depends on social existence being a bit of a tightrope-walk, which requires a degree of cruelty and willingness to ostracize on the part of the "men of sense" (as ostracism would otherwise be empty) as well as a degree of objective danger (as the men of sense must appear sensible). Sheridan's tendencies deprecated the former; the age's conventions prevented the latter, and one is left, in the end, with two halfhearted plays that were unable -- unlike She Stoops to Conquer -- to create a genre to match their temperament.

The School for Scandal is interesting and flawed in the way that Auden found Twelfth Night interesting and flawed: a few of the characters -- in this case, Sir Peter Teazle; in the other, Viola -- exist at the wrong level of seriousness, and intrude rather damagingly into the fabric of the play. Sir Peter is an old man who has married a young woman who is about to start an affair with his hypocritical ward who's "gulled" Sir Peter; in a Restoration play this would have been a purely comic part, but Sheridan lacks the heartlessness to make it work, and there is an entirely jarring degree of pathos to the scenes in which Sir Peter appears -- jarring because he is so much more "real" than the others; because his presence critiques and undermines the scandalmongers; because it is clear that in Sheridan's view the entire "school for scandal" is at some level out-of-date and irrelevant, like the women in Pope:

As hags hold Sabbaths, less for joy than spite,
So these their merry, miserable night.
Still round and round the ghosts of beauty glide,
And haunt the places where their honor died.

And because these facts let the air out of the main action of the play: if sensible people are indifferent to scandal, the activities of scandalmongers can only be so important; but if so almost everything that happens in the play is insignificant.

I should say that by contrast The Critic is an entirely admirable and very funny play, much better than its Restoration model The Rehearsal.

Flat-nose and Horse-thrift

James Davidson has a delightful article in the LRB about Greek names. You should read the whole thing; I wanted to flag this bit, though:

The most famous account of intentionality in Greek naming comes from Aristophanes’ Clouds; Strepsiades explains how he wanted to call his son Pheidonides (‘Of the Line of Thrift’) but his posh wife wanted a Hippos-name to evoke upper-class horsemanship and chariots. So they ended up with Pheidippides. That name (‘Of the line of Thrifty with Horses’?), shared with the famous long-distance runner of Marathon, shows that although the elements of a name might be transparent they might not necessarily make sense when combined.

Of course, sparing-with-horses was a sensible name, to the point of being bizarrely apt, for the guy who ran the original marathon. It is reminiscent of the kinds of things that pop up in Old English poetry, which consists almost entirely of litotes, kennings, and compound epithets. Or the Icelandic sagas -- cf. the habit of calling blood "dark beer," or saying, e.g.,

"He twisted the tail of his cloak around Thorbjorn's throat and bit through it, then snapped his head back, breaking his neck. With such rough treatment Thorbjorn quietened down considerably."

(Not to mention that the Laxdaela saga begins with a guy called Ketil Flat-nose; the Gk. for flat-nose, "Simon," is cross-culturally popular as a name for upper-class twits.)

Gerund Zero

My initial reaction to this Language Log post about gerunds/participles was that it was imagining an ambiguity where none actually exists. I can't remember ever having been puzzled about whether a particular -ing construction was a gerund or a participle; it's generally clear, and (as some of the commenters said) it seems useful to have different names for the noun-functions and the adjective-functions of a given -ing construction.

Upon reflection, however, I've come around a little to MYL's point of view -- gerunds are not, as a rule, echt nouns. This becomes clear when you try to modify them: consider, e.g.,

(a) "Drinking continuously is a good idea" vs. (b) "Continuous drinking..."

These are both essentially idiomatic constructions to my ear; however, if drinking really were a noun, (a) should sound ridiculous. In fact there are probably instances, like "Going on endlessly about grammar will lose you friends," where you really need the adverbial form, though on a traditional parse "going" is a noun qua gerund. The fact that adverbs can modify gerunds appears quite general to constructions with gerunds in them; and -- to my mind -- offers very strong evidence that gerunds are not to be treated as true nouns. (Obviously the entire phrase is still functioning as a noun; the ambiguity is about the order of operations, as one can noun the verb either before or after adding the qualifier, and depending on what one does first the qualifier is either an adjective or an adverb.)

Some constructions w/ gerunds are of course a lot more noun-like than others -- definitely a pluralized gerund is an echt noun. But they do seem to occupy a bizarre syntactic middle ground, along with infinitives and other similar beasts.

The wages of rudeness

Google analytics has started collecting site traffic data; I was amused to find that the two leading non-obvious searches (i.e., other than my name, the blog's name, or a specific poem) that lead here are for "malcolm gladwell is an idiot" (which leads here) and "ezra klein is a hack" (which leads to this STOATUSblog post). Not "asshole loser fame" by any means, but this suggests a more replicable approach to picking up readers. Look out for "Dan Brown is an imbecile," "David Foster Wallace is a moron," "David Brooks is a douchebag," and other bouts of biliousness.

Borges and Local Color

What's odd about Borges's Personal Anthology is how boring it is relative to his collected works. Borges explains in a preface that he's left out stories that were "superficial exercises in local color" (or something like that); what remain are bland and repetitive statements of certain metaphysical positions -- about infinity and idealism and such -- that obviously meant a great deal to Borges but are trite as philosophy. A good example of the sort of thing Borges seems to have liked in later life is "The Other Tiger"; for all I know it's a good poem in Spanish but in translation one finds it drab and obvious. A good example of the sort of thing he did not like is "Tlon, Uqbar, Orbis Tertius."

I wonder if this is due in part to Borges (mistakenly) comparing himself to Kafka. Jonathan Mayhew has a delightful post likening the Oxfordian theory of Shakespeare to a story by Borges or James or Kafka. I would be much more specific: such a story would have been at home among Borges's Ficciones but has very little to do with Kafka. I am not sure, either, that a reader who knew Borges exclusively through the Personal Anthology would have perceived the accuracy of this comparison, as none of the "notes on imaginary books" are in it. It seems to me quite inaccurate to bracket Kafka with Borges at all. Kafka's novels can be understood in textbook modernist terms, as being rather like Macbeth -- successful attempts to find objective correlatives for a certain set of feelings, a certain sense the isolated mind has of its relation to the world. This will not work with Borges as the stories aren't mood-driven. A Kafkaesque situation is a nightmare; a Borgesian situation is an artifact.

The Borges stories I like best (other than the enjoyable but silly stuff in A Universal History of Iniquity) are the notes on imaginary books and two later stories, "The South" and "Averroes' Search," which come off for reasons that might be fortuitous. The general problem with writing "philosophical" literature, as Eliot remarks, is that the philosophy has to be realized -- fleshed out, peopled, colonized -- for the enterprise to work. (One should make an exception for purely frivolous uses, like the Hitchhiker's Guide.) A lot of Borges stories, like "The Circular Ruins," are bad b'se insufficiently real. In later work like "The Aleph," concreteness coexists uncomfortably with philosophical notions, but the philosophy comes off as an exotic and unjustified plot device. But in Tlon, "Pierre Menard" etc., idealism finds an odd but satisfying local habitation in names. Like Swinburne's poems (insert more Eliot here) these stories seem to indicate that there are other worlds than the physical one that are rich and irregular enough to "inhabit" or "realize" ideas in: the world of words and literature, in particular. I wonder, though, if the truth isn't simpler: these stories depend for effect largely on the ability of language to refract ordinary objects, say the moon, "into something rich and strange" -- all literature does, I think -- and lose their charm when there aren't any objects to be looked at. I've expressed vaguely similar sentiments about Stevens in the past, the good bits of his poems are the half-distinct, dazzling images seen out of the corner of the eye, while he's going on about something or other. This is probably a somewhat heretical opinion.

Afterthought on emergence and limits

See this post for context.

A "universality class" is a basin of attraction, i.e., it consists of the set of microscopic models that coarse-grain to a particular fixed point. Universality classes are, of course, equivalence classes -- of sequences of models that coarse-grain similarly. This structure is to some extent analogous to the set-theoretic construction of real numbers from rational numbers (i.e., pairs of integers): a real number x "is" an equivalence class of Cauchy sequences of rationals (i.e., all sequences that converge to x). The analogy is admittedly not very good: the reals have binary operations on them, etc., whereas there isn't really anything analogous for models. However, I think it is good enough to get at the main point: viz. that when one talks about the properties of the set of equivalence classes of rational numbers, one is doing a different sort of mathematics from the theory of rational numbers: the theory is defined on a different set, so very different sorts of things are true -- reduction to lowest terms in one case, the extreme value theorem in the other -- and the "reduction" of one theory to the other is a reduction of analysis, not to number theory, but to number theory plus set theory. It is also well-understood in the mathematical case that the reduction is not useful in that it doesn't help you prove theorems about the reals; its only potential use is in consistency proofs (which are anyhow precluded by Godel's theorems).

A similar statement seems to be true in physics -- the theory of fixed points is a theory of equivalence classes of sequences of models; this is not a reduction of many-body physics to particle physics but rather to particle physics plus set theory on renormalization group flows. The clumpy, highly classified, scale-invariant space of macroscopic objects is not like the relatively smooth landscape of parameters allowed by the standard model (or the "landscape" in string theory): the reduction is "useless" in the same sense as above. This is closely connected to the intuitive point that coarse-graining doesn't preserve distances in parameter space (two very similar microscopic theories can have very different macroscopic limits, etc.), which is why microscopic theories do not constitute explanations of macroscopic phenomena. Batterman is, I think, correct to try to find more formal and precise ways of saying this than just saying that it's a "useful idealization" to think of emergent phenomena as existing -- while strictly speaking this is all that one can say, "useful" is an ambiguous word, and it is worth emphasizing, I think, that emergent phenomena are "useful idealizations" in the same way as real numbers are useful idealizations of the way we talk about rational numbers.

Although I don't understand the holographic principle terribly well, I should note John McGreevy's claim that the (d + 1)-dimensional holographic dual of a d-dimensional model can be understood as a stack of d-dimensional slices of the model at various stages under the renormalization group. (The d+1 dimensional universe has two boundaries: a surface corresponding to the original model, and a point corresponding to its fixed point.) I suspect that this only really works for the "AdS"-like models, which don't describe the large-scale structure of our universe, but it would be neat if the renormalization group had a "physical" interpretation.

Emergence and limits

If you haven't read it yet, I recommend Batterman's article on the philosophical connection between emergent phenomena and singularities. It is nice to have philosophers taking the renormalization-group idea seriously, as this idea has had an enormous impact on how physics is done and interpreted by physicists -- at least by theorists -- but hasn't made it to the pop physics books or the undergraduate curriculum. Batterman correctly observes that physicists understand emergent phenomena in terms of the renormalization group, that the renormalization group concept needs limits (like that of infinite system size) to be made precise, and that the limits lead to singularities; he goes on to make what I think are some misleading statements about the interpretation of singularities. In this post I'll try to run through the usual argument and explain how I think the singularities ought to be interpreted.

I understand emergent phenomena in terms of the following analogy. Suppose you drop a ball onto a hilly landscape with friction, and ask where it will end up a very long time later. The answer is evidently one of the equilibrium points, i.e., a summit, a saddle point, or (most likely) a valley. Two further points to be made here: (1) It does not matter where on the hillside the ball started out; it'll roll to the bottom of the hill. In other words, very different initial conditions often lead to the same long-time behavior. (2) It matters very much which side of the summit the ball started out on; small differences in initial conditions can lead to very different long-time behavior. So what constitutes an "explanation" of the properties of the ball (say its response to being poked) a long time after its release? One possible answer is that, because mechanics is deterministic, once you've described the initial position and velocity you've "explained" everything about the long-time behavior. However, this is unsatisfactory because point (1) implies that most of this "explanation" would be irrelevant, and point (2) implies that the inevitable fuzziness of one's knowledge of initial conditions could lead to radically indeterminate answers. A better answer would be that the explanation naturally divides into two parts: (a) a description of the properties (curvature etc.) of the equilibrium points, and (b) the (generally intractable) question of which basin-of-attraction the ball started out in. In particular, part (a) on its own suffices to classify all possible long-time behaviors; it reduces a very large number of questions (what does the ball smell like? at what speed would it oscillate or roll off if gently poked?) to a single question -- approximately where is it? (Approximate position typically implies exact position in the long-time limit, except if there are flat valleys.)

"Emergent" (or "universal") phenomena are descriptions of equilibrium points, i.e., answers to part (a) of the question. The renormalization group concept is the notion that the large-scale behavior of a many-body system is like the long-time behavior of a ball in a frictional landscape, in the sense that it is governed by certain "fixed points," which can be classified, and that theories of these fixed points suffice to describe the large-scale properties of anything. So, for instance, there are three states of matter rather than infinitely many. The analogue of time is the length-scale on which you investigate the properties of the system -- as you go from a description in terms of interacting atoms to one in terms of interacting blobs and so on -- and the analogue of the "loss of information" via friction is the fact that you're averaging over larger and larger agglomerations of stuff. (All of this is quite closely related to the central limit theorem.)

The role of infinite limits in the former case is obvious: if you start the ball very close to the top of the hill (where, let's say, the slope is vanishingly small), it'll take a very long time to roll off. So the fixed-point idea only really works if you wait infinitely long. However, it's also obvious that if you wait a really really long time and the ball hasn't reached its equilibrium, this is because it is near another equilibrium; so the equilibrium description becomes arbitrarily good at arbitrarily long times. (This is of course just the usual real-analysis way of talking about infinities.) The infinite-system-size limit is precisely analogous: while it only strictly works in the infinite-size limit, this "infinity" is not a pathology but is to be interpreted in the usual finitist way -- given epsilon > 0 etc. Epsilon-delta statements are true regardless of how far the series is from convergence, but they grow increasingly vacuous and useless as epsilon increases; something similar is true with dynamical systems and the renormalization group.

I should explain what this has to do with fractals, by the way. In the case of the ball, a fixed point is defined as a configuration that is invariant under the equations of motion; in the case of the many-body system, a fixed point is a configuration that is invariant under a change of scale, i.e., a fractal. A continuum object is, of course, a trivial kind of fractal; you can't see the graininess of it without a microscope, and it doesn't seem to have any other scale than the size of its container. Systems near phase transitions are sometimes nontrivial fractals -- e.g., helium at the superfluid transition is a fractal network of droplets of superfluid in a bath of normal fluid, or vice versa. Phase transition points, btw, correspond to ridges; if you move slightly away from them, you "flow" into one phase or the other. The association between unstable equilibria and nontrivial fractals is not an accident. Any departure from the nontrivial fractal (say in the helium case) leads to either superfluid or normal fluid preponderating at large scales; if you average on a sufficiently large scale the density of droplets of the minority phase goes to zero, and you end up in one trivial phase or the other.

Read: Evelina

I was talking about Trollope with a well-known physicist last year -- he's a fan, I'm not -- when one of his grad students, who didn't speak much English and hadn't been listening, burst in with "What's a trollop?" I explained that a trollop was a prostitute, whereas A. Trollope was a novelist. Said Trollope fan was outraged at my quip that there are no good English novels between Persuasion and Ulysses (qua novels, that is; Dickens has a lot of virtues, but construction is not among them). Having read Middlemarch, I suppose I have to revise this opinion, which is sad because it was snappy and easily stated.

The Trollope fan also claimed that Fanny Burney's Evelina was superior to Tom Jones; I have now dutifully read it, and concluded that my Trollope problem is that I just don't much care for novelists who aren't eyecatching prose stylists. While neither Trollope or Burney would begin a novel with "Ingenuous debutante Evelina Anville crumpled behind a bush, having been bludgeoned by notable libertine Lord Merton," they aren't Joyce, and the temptation to skim is often overwhelming. Evelina has a lot of nice satirical touches -- esp. the heroine's stay with her bourgeois relatives in London, her reactions to their "vulgarity," and her extreme embarrassment whenever she runs into aristocratic acquaintances -- and is also very good, in ways that anticipate Austen, on how class distinctions and crushes interact. On the whole, though, it doesn't come off. One of the problems is that the same three aristocrats keep popping up absolutely everywhere, which gives the aristocracy the sense of a claustrophobic little club, and acts at cross purposes with the rest of the plot (which is about an ingenue in the big world). Another is that the posh people don't talk credibly; only the "broad," dialect-speaking characters do. A third is the role of "Sir Clement Willoughby" (btw, the names are not clever at all, another stylistic limitation) who is a rival suitor, a seducer, and, more often than not, a plot device. Mostly, though, it's the drab functional nature of the prose, which is a far cry from Fielding or Smollett; while this was inevitable to some extent in a novel written as a young woman's letters -- "it would be odd for a six-year-old girl to display the character of Winston Churchill" -- (a) that's arguably a statement that the novel was poorly conceived, (b) an easy fix, in this case, would have been to include letters written by the other characters, a la Smollett.

Hodge

The OED defines "Hodge" as follows:

1. A familiar by-form and abbreviation of the name Roger; used as a typical name for the English agricultural labourer or rustic.

c1386 CHAUCER Cook's Prol. 12 Euer sie I highte hogge of ware. [Ibid. 21 Oure host seyde I graunt it the, Now telle on, Roger.] 1483 Cath. Angl. 187/1 Hoge, Rogerus, nomen proprium. 1589 GREENE Menaphon (Arb.) 58 These Arcadians are giuen to take the benefit of euerie Hodge. a1700 B. E. Dict. Cant. Crew, Hodge, a Country Clown, also Roger. 1794 WOLCOTT (P. Pindar) Wks. III. 350 No more shall Hodge's prong and shovel start. 1826 in Hone Everyday Bk. II. 1210 You seem to think that with the name I retain all the characteristics..of a hodge. 1885 Observer 13 Dec. 5/3 The conduct of Hodge in the recent election.

I wonder if being hodged is similar to being rogered. (He was rogered unto a hodgepodge.) I also wonder [well, only rhetorically] about whether the next OED will include the standard mathematical sense of "Hodge."

PS to wander into the country and hang out w/ peasants is to be on a Hodge pilgrimage.

Whimbrels; sea-surfaces

Walking along the beach this evening I saw what I think were whimbrels:

I really ought to buy batteries for my camera. I also finally understand what Eliot meant re

Combing the white hair of the waves blown back
When the wind blows the water white and black.

The waves really looked like that. The sea was abnormally fine-textured and matte this evening; although it was sunny, there wasn't the cheap plasticky gloss one associates with the water on nice days.