Wednesday, February 09, 2011

Chuck III

OK, so, here's the deal (with myself): I am not reading the AV-Club discussion of Chuck versus the Honeymooners, nor watching Chuck versus the Role Models, until I write up my own (eagerly awaited) impressions on them. Why am I doing this? Because, you see, the world clamours for my, undiluted and unaffected, thoughts on this year-old episode, and will not be content if they hear only me parroting the Onion party line, or if they see me in the depths to which I am sure I will sink once I see that the Chuckwriters (it's one word, see? Because it looks sort of like chuckwagon, see? No, I don't get it either) cannot sustain for long the mood that they have created—for I am sure that they (indeed, anyone) cannot, for reasons that I will outline *. Why am I telling you about it? Because I really want to watch another episode—I skipped my usual Monday-evening viewing in pursuit of my austere goal, and do not want to have to skip Wednesday's, too—and so I want you to understand why if today's post seems a bit hurried.

Although you are by now clamouring to see these much-ballyhooed thoughts, I remind you that I feel no shame about spoilers; my post will be to no end if I pepper it only with vague clues to what I actually mean, and so I am just going to assume that those of you who want to preserve the surprise will do so now.

Now that the spoiler-avoiders are gone: Chuck and Sarah, huh? I will admit that I thought that we'd be consigned to glances-and-throwaway-SOs forever, because such is the model for will-they-or-won't-they shows; but, after plenty of close calls, in Chuck versus the Other Guy we got a very definite commitment from Sarah. I would have been on tenterhooks for the it's-all-part-of-the-spy-game come-uppance, where was revealed that this was just a gambit to get Chuck to perform (ahem) or some such disappointment, except that TVTropes had already revealed to me that the relationship was to be. (One of these days I will get under control my instinct to go out and read all about a TV show in which I am interested, especially if I am watching old episodes—really, one of these days—but, until then, I will be stuck in such positions as my current one, where I know full well, for example, how Season 6 of House will end, and am hoping that I will manage to forget.)

So, since I have declared my love for Chuck's treatment of love, and since Chuck versus the Other Guy was definitely focussed on the Chuck–Sarah relationship after a long near-abandonment, why not write about that one? Well, because it was unsatisfying, treating love only in a very clichéd fashion; the principals, after much longing, pull in for a passionate kiss, we fade to black, hurrah, hurrah. Sure, the show has successfully positioned us so that that kiss is very satisfying, but in so doing it seems only to be setting us up for a fall: screenwriters are very good at the passionate initial outbursts of love, but seem to have very little idea about what happens after. Well, OK, they seem to have some idea what happens immediately after, and, in fact, that's part of what bothers me—has no one ever experienced a kiss that does not lead directly (after a fade to black if necessary) to the bed? Apparently not, if one believes the tale of life told by television and the movies. Indeed, my first hint that Chuck might have something more to offer than the standard tale of unrequited love was Chuck versus the Imported Hard Salami, during which the now-couple's first kiss (which surprised me as much as it did Chuck!) was followed by a very dramatic sort of generalised interruptus with the return of Bryce Larkin. An original plot device?—hardly, but remember that my admiration for Chuck focusses on its character development, not on its subtle command of narrative. (Actually I have just realised that I may be lifting even this judgement from elsewhere; the TVTropes summary says

… the appeal of Chuck comes from … well-realized characters with surprisingly genuine emotional lives ….

Well, anyway. Chuck and Sarah's non-interrupted kiss on Chuck versus the Other Guy, particularly the look on Chuck's face as he realised his luck, was sweet, but it was hardly enough to re-kindle my enthusiasm for a relationship that I think Season 3 has badly mistreated over-all. (More on that shortly *.) COG did offer one particularly bright spot, though: when Sarah is expressing her relief over Casey's news, she says “you're still Chuck, you're still my Chuck”, and the ‘my’ is so tender that I'm choked up—choked up now, writing about an episode of a pop television show! Well, that tells me that the writers and actors are doing something deeply right, if I care so much about the relationship of fictional characters that one word between them can have that effect on me. Then … “shut up and kiss me”, really? There go my hopes for a new TV perspective on romance.

Thus it was that my hopes were low going into Chuck versus the Honeymooners. The beginning of the episode didn't do much to raise those hopes, but neither did it lower them; while I would appreciate some romance rather than an instant trip to the bedroom, there is no denying that Chuck and Sarah have waited a long time for this (including enduring what the AV Club calls “the saddest IOU of all time”), and so I cannot begrudge them their pleasure at the beginning—especially since, once their frolicking is done (or temporarily on hold), they … well, how do I put this delicately? They talk. This is another place where I think most movie accounts of love fall down; you can be quite confident when you sit down for a romantic movie that it won't be long until it's time for the get-to-know-one-another music montage, and, though it seems to be common to excuse this laziness, I am not so forgiving—to me, the writers who resort to this trope have effectively thrown up their hands and said “we have no idea what people in love talk about, and we would prefer not to have to figure out something”. The conversations that Chuck and Sarah have are relatively mundane—well, in some respects, they are not mundane at all, as, after all, they are talking about evoking the wrath of a government body with deadly global reach; but, if one ignores the subtext, much of the dining-car conversation is little more than “what shall we do for our summer vacation?”; but it is a fact of life that not all conversations in a relationship will be scintillating, and I appreciate the honesty of a show that acknowledges this.

Well, then the spy stuff starts, and Casey and Morgan show up, and, OK, this is a spy show and not a travel show, and I do not complain; but really I could have watched a whole episode of such conversations—indeed, I say that with complete confidence, because, in essence, I did, twice, in Before Sunrise and Before Sunset, films that are in sharp competition for the top two spots in my pantheon. That is to say, sure, I enjoyed the hijinks of Chuck and Sarah's repeated exploits while cuffed together, and I appreciated that Chuck finally had his chance to fight back-to-back with Sarah as he wished he could have while watching her and Bryce (during Chuck versus the Nemesis, I think); but the quiet contentment on Sarah's face as she listens to Chuck's candidate for her favourite song, and, even better, the fact that that favourite song is another Nina Simone song, was what made this episode my favourite of Chuck so far by a long shot. I laughed, and I gasped, both aloud, while watching it, both in the middle of the Pizza Inn where I was having dinner—and I think that's about all that I can ask of a TV show.

* You know what? Now that it comes time, having finished my disquisition on what I liked, to elaborate on these my gripes and complaints, I find that recalling the episode in this detail has robbed me of the will to do it. You will have to wait for another day to hear my discontent; today I am content.

An exercise in visualisation

Many people think that the only neighbourhood of a dense subset of \(X\) must be the entire space \(X\). There's a counter-example that's so easy it's all one can think of afterwards, so that one soon forgets how hard it is to visualise: let \(q : \mathbb Z_{> 0} \to \mathbb Q\) be an enumeration of \(\mathbb Q\), and consider \(U_1 := \bigcup_{j \in \mathbb Z_{> 0}} (q_j - 1/2^j, q_j + 1/2^j)\). Clearly, \(U_1\) is a neighbourhood of the dense subset \(\mathbb Q\) of \(\mathbb R\). (Actually, this is two counterexamples for the price of one, since \(\mathbb Q\) is also co-dense.) The Lebesgue measure of \(U_1\) is then at most \(\sum_{j = 1}^\infty 1/2^{j - 1} = 2\); in particular, it's not all of \(\mathbb R\).

I forget where I first saw this. It is too easy to think that you are picturing \(U_1\), by envisioning a collection of blobs; so try visualising its complement instead. This is a closed subset of \(\mathbb R\), of infinite measure, that contains no intervals. This is maybe not so scary if you're used to visualising, or imagining that you've visualised, the Cantor set, but it's still pretty strange.

That's not the visualisation exercise. Instead, I ask you to visualise the following, drawn from Oxtoby's book. Notice that the construction of \(U_1\) can easily be generalised to give, for any \(\varepsilon > 0\), a neighbourhood \(U_\varepsilon\) of \(\mathbb Q\) of measure at most \(2\varepsilon\). Now consider \(G := \bigcap_{i = 0}^\infty U_{1/2^i}\). This is a neighbourhood of \(\mathbb Q\) whose ‘biggest radius’ \(1/2^i\) shrinks to \(0\), so it must be just \(\mathbb Q\), right? No. Notice that each \(\complement U_{1/2^i}\) is the complement of an open, dense set in \(\mathbb R\), hence is (closed and) nowhere dense; so \(\complement G = \bigcup_{i = 0}^\infty \complement U_{1/2^i}\) is of the first category in \(\mathbb R\). If we had \(G = \mathbb Q\), then \(\mathbb R = \mathbb Q \cup \complement G\) would again be of the first category; but Baire assures us that it is not.

It is easy to see where the reasoning goes wrong—since the intervals that go into the construction of each \(U\) are badly overlapping, the ‘largest radius’ need not actually be shrinking to \(0\) as we expect—but not, or at least not for me, easy to get any idea what \(G\) actually looks like. Thoughts?

UPDATE 2011-02-09: Note, incidentally, that \(G\) is also a Lebesgue-null set. It is obviously uncountable (or else the above argument would go through essentially unchanged), but it must be a very small sort of uncountable. I wonder if assuming that it has the cardinality of the continuum is equivalent to the Continuum Hypothesis?

Saturday, February 05, 2011

Chuck redux

Do you know how to pronounce ‘redux’? I don't, and, although the answer is trivially easy for me to find out, nonetheless I don't; somehow it's fun to have these questions in life—that or I'm lazy. Well, if it's pronounced ‘reducks’ (as in “he ducks when the crane first comes at him, and then he reducks on the return path”), then the title is almost a rhyme; but if it's pronounced ‘redo’ (as in “the first test subject wasn't too good at reducking, so we need to have a redo”), as I have been sometimes assured that it is, then the title doesn't rhyme at all. (Unless, that is, you pronounce ‘Chuck’ as ‘Chew’, in which case you are a very special flower.) Perhaps even more interesting, to me, than its pronunciation is its meaning; I always assumed, in my optimistic, faux-amis-prone style of guessing at meanings *, that it was akin to ‘reduced’—which, I know, makes no sense at all, since, for example, Apocalypse Now Redux is an extended, not shortened, version of the film—but actually it means ‘revisited’. My reader, you know this, I am sure; but I did not, and so you can share with me in the delight of shedding a bit of ignorance. I'm still not looking up the official pronunciation, though.

Well—that ‘well’, I picked it up from Garrison Keillor, I think, and now I cannot get rid of it as an all-purpose segue—I ended last night's very long entry by lamenting my tendency to write about what I wanted to write, so let me do my best to curtail that tendency (and the attendant footnotes, also copied, these from DFW) and dive right into today's topic: Chuck! Revisited, and, possibly, reduced!

Diving right in: Chuck is, you may have heard, a spy show, but I want to advance the thesis that it is not. Indeed, when I say that I want to write about the show but that I might seem to be duplicating the AV Club's work, in fact there is no such worry; the AV Club is concerned with recounting and analysing plots, and this activity interests me almost not at all, since the plots are thin and flimsy things—so why am I such an addict? We all have our weaknesses for cultural garbage, but this is not, I think, one of the times that I am indulging that weakness. Nor is it the cheesecake, which, actually, doesn't appeal to me at all—“yes, right,”, you respond, “tell us another”, but, really, there is a point when the pandering becomes so comically obvious that it's hard even to enjoy it qua pandering. No, it is this very simple fact: this is a show about two very rare themes, friendship and love.

Perhaps now you are snorting with derision at the idea that these are rare themes; indeed, buddy shows (is that what we call them? There must be a name, but TVTropes lets me down here) and romantic movies are perhaps two of the most reliably visited genres to be found. Yes, but think about the friendships and the romances that you see in these shows—are they anything like any you have ever had? They intersect, a tiny bit, with true life, or else no one would relate to them and no-one would watch; but also there is a reason that one refers to television- and movie-watching as escapism. They leave out the boring bits of everyday life, and, really, my dedication to cinéma v&ecaute;rité is not such that I need to see that (although David Lynch can do it beautifully; I always squirmed with impatience at the scenes in Lost Highway where the Balthazar Getty character, whose name I now forget, is simply lounging around in his backyard, trying to come to terms with this part of his life that he cannot remember and of which no-one else will speak—it is a crucial moment but everything is internal, and there are so few cues onto which the stimulation-craving viewer can hang); but, perhaps more importantly, they seem almost obliged to seize on certain well worn tropes and inflate them to proportions that are meant to be, and often are, humorous or involving, but that in the end inevitably ring hollow.

Am I, perhaps, suggesting that Chuck is free of such tropes? I certainly am not (ahem); it has its share, and this, combined with the aforementioned flimsy plots, gives critics most of their ammunition against it. My feeling, though, is that the show is deeply authentic in its depictions of these two central themes, friendship and love; and this is what keeps bringing me back to it, despite the morass of Season 3, and this is why Chuck versus the Honeymooners struck such a chord with me that I decided to revive this long-dormant blog just to write about it. Which I will. Soon.

* I was about to call this activity ‘etymologising’, but I really meant something like “semanticising based on etymology”, or would have meant that if ‘semanticising’ were a word. Anyway, I was going to describe it as something “my optimistic, I-can-guess-your-meaning-based-on-appearance etymologising”, but then I realised that I was transgressing against Larry Wall's injunction against an I-can-make-anything-an-adjective attitude.

Friday, February 04, 2011


This used to be quite a good blog. I was reading some old posts the other day, though what brought me here I don't recall, and came across some musings on Magritte, and, wow, that's not a bad analysis—not, by any stretch, art criticism, but there are interesting ideas, and that hysterical (in the sense of overwrought, not funny) essay by Hillier was well worth recalling (I had completely forgotten ever digging it up, and indeed don't remember, nor am reminded by the post, what brought it to my attention; probably it was just a Google-hit when I was looking for a freely available copy of La reproduction interdite).

OK, it used to be a good blog, and then the shininess of this platform, and the feeling of celebrity that comes of having a reader or two, both wore off, and I was distracted by other endeavours (of which—but, no, I've said it too many times already; let me just do it in lieu of making further promises) but felt too guilty simply to leave it behind, and so I followed the slow sad death spiral of unwanted blogs everywhere, making desperate grabs for topicality—not to say that I didn't care about the ouster, for I really did, but what useful commentary was I adding with that sad pun?—and increasingly rare updates with promises of more to come, and—uh, OK, you know what? I just looked back over the archives, and at least it wasn't that long a death spiral, as apparently I managed to keep most of the promises to myself rather than posting them here. Well, there goes some of that guilt.

(By the way, speaking of death spirals that aren't so very spiral-y, one finds that already in my very first post I was jealously eyeing a snappier URL that was occupied only by 8 posts made over the course of 5 months, and which was for that minor reason forever—3 years at that point, and 8 years now *—denied to me. Well, I suppose that I am not now in a position to complain about Google's failure to evict blogsquatters.)

Anyway, reading over those old entries made me want to make some more postings of interest, rather than little once-a-year checkings-in; and I figure that there is no better way to revive the subtlety and erudition that were once the hallmarks of this blog than by discussing television. That's right, Chuck! “But wait,” you say, you my faithful reader, “suppose that we are willing to indulge you in the idea that weighty and ponderous discussions of television shows as if they held some cultural weight are somehow a way to make your come-back in style. So suppose. Are you not nonetheless merely duplicating existing work, especially since”—and here you indulge in a bold, but correct, guess—“you intend only to talk about old episodes?” Yes, reader, you are quite correct, I will be duplicating existing work—indeed, work that I am reading myself, running off after each episode with such eagerness that I'm sometimes not sure which I enjoy more of the episode or analysis—but here is the twist: I will do so badly ****. I should also warn you that I will issue spoilers with stunning cavalierness, feeling myself justified by the fact that the episodes I'm watching are new only to me. (Of course, this attitude can be abused; I was reminded just yesterday of this by a Harry Potter spoiler—OK, maybe only technically, but still a spoiler; cultural Neanderthal that I am, I have not read beyond HPOoP.)

Actually, I stumbled on the AV Club blog only after I'd already watched a few episodes of Chuck, and I was shocked; here I thought that I had seen an episode that—actually, you know what? I have no memories of what I thought after watching the first few episodes, none at all. I remember that I enjoyed it, scarcely a stretch given that I have been consuming it at a steady clip ever since, and I remember that it struck me that it had certain unique qualities, but in retrospect I have no idea what they were. “A unique perspective on geek culture”?—I was about to write something like that. Well, what do I know about geek culture? I'm a mathematician; I'm not even the cool kind of geek. (I do know that I was inordinately proud of myself for catching the Zork reference, but I'm pretty sure that it was not on that basis that I decided to continue.) Anyway, whatever it was, it was enough for me to keep watching, and so I was shocked to read Steven Hyden's vitriolic take on it. I couldn't resist reading ahead, and it may well have been Steve Heisler's much happier perspective that led to my current addiction. It's a bit funny to be following through the will-they-or-won't-they drama—I mean NBC and picking up new episodes, obviously—after it's long since unfolded, with obvious result.

Hi, reader! Do you know what I've just done? I've just spent about an hour writing, not what I wanted to write, but about what I wanted to write; and now I am out of time, but I am actually rather pleased with this post, light on content though it is, because I'm writing again (such as it is), and I've really missed that. Almost certainly I will lose my momentum, and forget what I wanted to say, and not be able to find the mood, but surely I won't leave a post like this hanging as I did all the others, right? Surely I've righted that tailspin, no? Well, maybe. Let's see.

* A group of my graduate-school classmates and I got together, after all our classes (or, rather more significantly, all our exams) were finished, not just for the quarter but forever—most everyone, I guess, gets to say that at some point, but it is perhaps a particularly compelling moment for a professional academic—and sat down to go through our notes and see what is the biggest number that was mentioned explicitly in a mathematician's education. It was 5 ** .
** Achieved twice, once in the proof of the Vitali covering lemma *** and once in a discussion of non-Abelian, simple groups.
*** About this number, a classmate asked “Is that really 5?” (meaning, is it just some random number that's big enough, as when one takes δ = ε/30); and the instructor, flustered, replied “It is 5. 5 is 5. 5 is not 3.”
OK, technically, it was the order of the Monster, which was mentioned in an off-handed way once, but that doesn't make for such a good story.
**** Remind me some time to talk about my indecisiveness over the grammatical function of colons. No, I won't do it now, no matter how you beg!