The Future of Credibility: “everything is what it is because it got that way”

It's Pandaemonium. I came to praise it, not to bury it.

In his tendentiously-titled Consciousness Explained, Daniel Dennett suggests an outline of a theory of the generation of speech. His outline is expressly directed against the classical notion that when I say something it is because I mean it. More precisely, he is arguing against the claim that there is necessarily within me a Central Meaner, perhaps that being myself or else a kind of homunculus, who holds safe the semantic meanings that I intend, and against which all my attempts to frame utterances are compared for semantic fidelity.

Imagine a great horde of senseless daemons, he says to us, rather than a single central homunculus, each with a phrase or piece of a phrase to suggest. These pieces are mere “found objects” and most are senseless or irrelevant. Irrelevant to what? -- to some kind of goal being held, but, crucially, not necessarily a semantic goal. (Dennett gives an example caricature of a person responding to hostility, starting with the angry flush “Go on the offensive!” and passing through “Cast aspersions on some aspect of his body!” on the way to “Say: 'Your feet are too big!'”. He assures us that we can then go home and curse ourselves for not having thought of a wittier retort.) All these “word-daemons” compete to put their mark on each others' candidates for a verbal utterance, and the stream of language they generate is adjudicated over, “yes or no”-style, by a horde of equally senseless “content-daemons.” This chaos does not end when the daemons together have assembled something that meets a Central Meaner's review. Rather, the putative semantic intention is itself modified by the judgments of the content-daemons upon the candidate utterances of the word-daemons.* The intention is “drawn” through an abstract semantic space toward the candidates, just as the candidates are drawn to the intention. What one has is not a kind of bureaucracy but (in Dennett's terminology) Pandaemonium, and it is “a process that is largely undesigned and opportunistic.”

This, if I may remark, is not a model that would have been taken too seriously as recently as the mid-nineteenth century. It is a thoroughly post-Darwinian conception, this supposition that all this chaotic variation can with only subtle environment constraints and interactions nonetheless construct something complex, something with significance, an utterance with a Meaning. Dennett directs this schematic model against the suggestion that the need for a Central Meaner would give necessity to the opposing theory of consciousness that he calls the Cartesian Theatre, (which is, roughly speaking, the idea that there is a single [physical or abstract] place where consciousness “all comes together”). In doing so he links our naïve sense that there must be a Cartesian Theatre to explain our experiences with our naïve presumption that there must be an agent's design behind anything complicated. There is indeed a commonality between them: both are a kind of turtle-stacking. (Check out the graphic on that page!)

We therefore stand properly advised that in our new century we will brook no contention anywhere that sophistication mandates design. To now pass instantly from the ontologically profound to the perhaps merely interesting, and to keep up to the promise of the title and opening paragraph of this post, we in particular note that in the new society of the Internet there is no compulsion to subscribe to a Central Content Provider.

This is a change from the old model, the model of cable television and publishing houses, where the expense of broadcasting mandated a few powerful players. To be sure, Peter Mansbridge isn't going anywhere, but there's a reason why he's now reading out viewer e-mails on the air each night. It's spelled out in this article, which was first published in a magazine and only later reprinted in the author's blog – so don't hold it against it, that it didn't come from a Central Content Provider, that in fact you (maybe) first heard about it from my pointing it out.

For this is the basis for our Internet Pandaemonium: if you know me and trust me, if I have credibility, then my endorsement of content brings that content to your attention. If you agree it's view-worthy, you refer your own close neighbours to it. If not, it need not branch any more along that path, but remember that my other readers might feel differently. The more it's passed around, the more credence and significance it gains in the greater community: some memes gain tremendous attention, or tremendous notoriety, as any longtime Internet reader can verify. As for where that content came from before -- maybe I found it purely by chance, or from another blogger whom I read, who may himself just be another citizen marking out prose or maybe someone with a mission to find selected or special content, like a museum curator, or from a newspaper or other kind of dedicated, professional content provider. (As exciting as our new century is, we would be too reckless by half to lose our professional content providers: they still deserve our respect, even if their roles are changing.) In this particular case it's all-of-the-above: the article I just linked to isn't the link I followed to that blog. This fellow's blog is in my queue pending final decision on whether I should bookmark – add him to my trusted content providers. The ultimate origin of the article, for our purposes, is the author's blog, (strictly speaking, this origin is in the sense that “eukaryotes come from prokaryotes” rather than “eukaryotes come from primordial soup”, to anticipate parenthetically some ideas from the sequel); but every blogger is an author waiting for his work to be cited and to come to prominence, possibly as part of a greater content-complex (an organelle in a eukaryote). It doesn't happen often: the price, the scarce resource that demands differential survival (speaking so as to continue to anticipate), as always comes from the opportunity cost of a person's limited attention-bandwidth for consuming media. So most bits of content don't achieve total renown, but rather roam and hover between heaven and earth. (Mostly around earth: renown like flight is very expensive to support.)

Now let me make good on those anticipations. I used that word -- memes. If you've never heard it, maybe as always the Wikipedia summary can be helpful. In short, an idea is a meme, or more precisely an idea at the size that can be replicated. It might be as small as an idiom of language or the refrain of a song or as big as the text of a book. This is in analogy to the way that a gene is some span of codons in DNA, not of fixed length but rather defined in terms of its being able to be selected for or against. A gene is supposed to do something meaningful to the phenotype, which is either fit or not according to the environment, and this by backward-translation is a selection pressure against the various genes in the gene pool. The notion of a meme is, I believe, an idea whose time has come. Of the increasing number of contemporary popular works on the subject I can't sanction or sanction any, since I haven't read them. I can, however, (not to use my pulpit to promote too many more books) both on general and specific principles recommend Richard Dawkins' The Selfish Gene, which to my mathematician's eye reads not so much as a book about biology as an extended worked example to support a nearly-axiomatic theory about differential survival of replicators. (This description is not meant to put you off it: that's good praise!) The memes, the so-called New Replicators that “live” not in space but in peoples' minds (hence why they're new – not so long ago there weren't any minds), are first introduced by that name in Dawkins' 1976 book, although I imagine the notion was anticipated by other authors previously.

With the meme as part of our vocabulary, more or less everything we've described so far today takes a single shape. They're all stages of memetic evolution.

And while we're here, what about that Wikipedia? I cited it so casually to give a reference to memes, but isn't that where Wikipedia itself came from – some kind of memetic evolution? Take a listen to this talk by the Wikipedian progenitor himself and decide whether it sounds like the same thing. Not to be tendentious myself but I think it does: each Wikipedia article is itself a meme complex adapted under the pressure of its editors and its editors' minds – that last meaning, perhaps, the memes living in the editors' minds? So a Wikipedia article is a complex adapted to the memetic environment that the editorial community represents. If you think the situation is disqualified because the editors are agents with intentions, remember the parable of the Central Meaner: those intents themselves are memes, or perhaps more precisely certain products of memes (in the sense that the phenotype of an animal is a product of its genotype).

This is encouraging in the sense that it seems this is an example of memetic evolution, but, to get back to the original objection of the last paragraph, if we were inclined to be suspicious of the memes and the prospects for memetic evolution, the fact of a Wikipedia citation about them is not going to be terribly convincing. The mere fact of the citation is mere question-begging! On the contrary, it is good and well, we imagine, to say that animals rose from natural selection; but why is it that we suppose the conditions are present in our world of discourse to make possible a memetic evolution by “natural” selection, even if we believe (“in our new century”) that this is possible in principle?

For if the conditions are not there, a Wikipedia citation must surely be a deeply suspicious thing. Supposing that daemons can make wisdom just by nattering suggestions is no better than saying that monkeys can write Hamlet given typewriters nor than saying a mammal came about by accident. Even Plato knew, despite not having Darwin's idea as a counterexample, that sophistication does not imply an agent's design; but chance alone does not gain sophistication without selection pressures causing differential survival. (The “nonrandom survival of randomly varying replicators,” in Dawkins' one-sentence summary.) So rose the animals, and so rise the meme complexes – supposedly. But is there or can there be really such a thing as the so-called “wisdom of crowds”?

What, for example, to make of such a famous experiment as Kasparov v. The World? Let me recall the circumstances of this event to you. In Summer 1999, Microsoft sponsored a chess game played (at correspondence time control, about one move per day) on their website. Garry Kasparov, recently having regained his status as the invincible champion with spectacular triumphs at Wijk an Zee and Linares in the first quarter of the year, commanded the White pieces, (with the assistance of his usual seconds). Captaincy of the opposing Black forces was given to – everyone who showed up: any person could log on to the MSN Gaming Zone and submit a vote for their team's play. The move with a plurality of votes would be the one made. The match was not so uneven as it sounds: four strong junior players were enlisted to provide brief recommendations to The World team, and still more strong players volunteered, including Alexander Khalifman, who went to Las Vegas in Fall 1999, while the game was still being played, and there won the FIDE World Championship. (At this time, the world championship was still a divided title, and Kasparov refused to play in FIDE's events.) Or perhaps after I, and Dennett and Darwin, praise Pandaemonium you might think the game unfairly balanced in the other direction?

No, it was not so. After several months of tough play, during which at times all three outcomes (win, lose, draw) seemed equally plausible, Kasparov was victorious, (in a queen-and-pawn endgame). Is this the logical triumph of expertise? I would be quick, in my Platonic prejudice, to think it so: understanding trumps grasping because that's what understanding is. Similar one-versus-many contests have been held, albeit with less fanfare and publicity, and they have often been decided for the expert and not the putative wisdom of the mob, but far from always. More recently, Arno Nickel, who holds the ICCF (international correspondence chess federation's) grandmaster title, bested the computer Hydra, by a score 2.5-0.5, in correspondence games; and this unthinking computing beast the same creature of awful power that beat Mickey Adams 5.5-0.5 over the board! But Nickel too has lost a game against The World, in the form of the community on the website ChessGames.com; it concluded in January of this year.

So what to make of all this? In a phrase, it's the difference between a mob and a crowd. Fickle folly can be incendiary, but it knows not how to aim itself nor cares what it burns. If a man leads a mob, it is at most as wise as he, and often less. Irina Krush, one of the World Team coaches Microsoft hired in the match against Kasparov, expressed her displeasure when some of her mob's decisions decided against her and Khalifman. A mob can beat Kasparov if Khalifman can. After it gave such a tremendous fight it is ungenerous, to say a minimum, to put that World Team closer to the monkeys than to Shakespeare, but one idly wonders if simply the presence of better tools, like a ChessBase wiki to replace the primitive forum design of the MSN Gaming Zone, might have made the difference.** Anyway, it's quite possible that to beat Nickel in correspondence games is more impressive than to beat Kasparov, so the proper tools have surely been developed. But the lesson is clear: It is the networking of the crowd that sets the stage for the miracle of memetic evolution, and not the noisy, violent hub-bub of the mob.

And, to get back to our Wikipedia problem after an extended parable, a fringe article is only as good as its first and only editor-progenitor, but a well-eyed treatise is a tremendous thing – as long as Wikipedia itself is properly built to encourage the right selection pressures. Remembering the talk, the last pieces come into place. You have administrators, (Dennett's content-daemons, the judicial counterparts to the word-daemons striving to craft prose), and they, of course, don't need to be experts in the article subject areas, no, not in anything but encyclopaedia mediation, -- and then, more or less, the “undesigned, opportunistic” process of evolution can start. Alexander Khalifman is a tremendous “chess expert,” but that's a word-daemon: he isn't on the right ontological level to exploit a Pandaemonium to challenge Garry Kasparov.

After so much chatter, let us remind ourselves that – it is a fait accompli; Pandaemonium is already here! It came in the form of the blogosphere and YouTube and other networking sites. (Pre-Internet models suffer from limited connectivity and content distribution – somewhat deficient for good examples of a functioning Pandaemonium, and so every film studio executive dreams of that rare word-of-mouth buzz.) Bloggers write and post content and link to each other; YouTube users have schematic personal pages on which they can, in addition to posting their own videos, link to particular other videos or to other users' personal pages. This is the minimum requirement. It doesn't have to be one or two sites in particular, and may not be in future. Indeed the Internet crowd can sometimes be fickle in its endorsement (the various blog-hosting services all rise, compete, and fall among themselves). What's important is just the structure on which the community builds itself, and any sufficiently self-connecting framework could do. From there we little daemons, simultaneously both word- and content-, we take care of things themselves.

And quite well, too. So ends my speech of praise.


(Endnotes.)

* For example, consider the "seductive turn of phrase." Where did the title "The future of credibility" for this entry come from, anyway? It's apparently a play against an earlier entry entitled "The end of credibility," (which, if you're looking for it, was the last of "Three Short Comments from Princeton"). Is this really the best I can do? The two entries don't seem to have a lot to do with each other, other than being about blogging. Maybe they're both about content distribution, from two different sides. Maybe it's just a weak play on words. But it has such a hold that the word "credibility" even gets a mention a little later, in the middle of a very important paragraph. There's supposedly an abstract semantic idea that this paragraph is to communicate, and that idea is independent of its instantiation in text, but in particular the "trust metaphor" to explain the low-level links between blogs is directly connected to this curious title. Can I say which came first in my thinking? For surely the meaning of the text would not be quite the same with a different metaphor.

In other examples, a "seductive turn of phrase" becomes its own justification, divorced from any external semantic concept. An easy way for this to happen is from grammatical ambiguity, say due to excessive editting for style over content.

Incidently, the titular quotation, "Everything is what it is because it got that way," is from D'Arcy Thompson's "On Growth and Form." (Peter Medawar called this "the finest work of literature in all the annals of science that have been recorded in the English tongue." I haven't read it. It's about 1200 pages, which is rather longer than this post.) It is a little more obviously connected to the technical side of the subject matter.


** Everyone who has ever spent a little time slumming on a forum whose theme yields to certain frequently-asked-questions knows that Sisyphus himself hadn't such a futile task. I have examples in mind, but they're such dangerously contagious and stultifying memes I don't dare quote them – they're the memetic equivalent of the flu.


Postscript. Sorry about all the broken links; I've fixed them. They were there because I was composing this entry in a word processor (for the obvious reason) which was automatically turning all the quotation marks into smart-quotes (that angle toward text, like “...”) rather than the (uniformly-oriented, like "...") quotation marks that one needs to put in HTML tags.

Happy Assyrian New Year

Tomorrow will be a wonderful day. I'll wake up and check the news and know that don't-believe-a-damn-word-you-read-online day (aka 1 April) is as far away as it possibly could be.

This day is painful. Yesterday FIDE (the world chess federation) did YAST (yet another silly thing -- I won't explain that thing, it doesn't have a good length-of-exposition to payoff ratio) and apparently said they weren't going to fix it, or something like that, and there was a protest from the Indian Chess Federation, advocates of the injured party, Vishy Anand, and now Chessbase is reporting that FIDE has reversed its position, except the article in question was published on 1 April, and these Chessbase guys are incorrigible pranksters, they really delight in it -- I mean, they're usually more obvious about it, but I read this thing, this news report, and I'm even doubting the factual basis -- and if I had that kind of doubt when reading a newspaper, why would I waste my time with that? Editorial indiscretion, what a bother.

But, you know, it's more like next week that I'm free, because today's debris will still be there tomorrow. For days yet I'll be checking the dateline of everything I read.


Postscriptum primus. Last entry updated today [1 April] with some pictures, because we haven't had any pictures in a while.

Postscriptum secundus. Turns out they were serious. "I never doubted you," said C-3P0, "much."

Postscriptum tertius. Turns out a lot of people doubted them too :

The day we published our April Fool's prank we also carried an important news item: in view of wide-spread protests FIDE had decided to correct their April 2007 rating list and to include the Morelia/Linares event in the calculations. This, many readers believed, was the April Fool's joke. In fact a colleague had told us on the previous evening that he intended to use it as his prank: "FIDE admits error, vows to correct it immediately" was the hilarious article he was working on. On April 1st we received irate messages from him accusing us of poaching his joke. It took a while to convince him that the FIDE decision was for real.

Well. There it is.

Postscriptum quartus, (since, hey, we've followed up on our story a couple times already.) Thanks to the nonflat nature of the Earth and the roughly Copernican character of our solar system, it turns out that Vishy Anand thought the first part was a prank, until he was informed likewise by a vast number of concerned well-wishers. (Take that, medievalism.) I had no idea they celebrated Assyrian New Year in India.

Schachmaschinen: "a horse, a horse, my kingdom--"

An item on the list of Things Everyone Knows: that, without qualification, computers are better than humans at chess. Ever since Kasparov lost the first game of the original 1996 match against Deep Blue it's been downhill for chesspeoples looking to protect their mystique. It seems the Royal Game is fit just for calculators. Whereas in the 19th century it was held that a master's gift was for inspiration and fantasy, and optimism so reigned it was felt that a player could in the most seeming-rotten position discover some extraordinary resource to save the day --

-- or so the chess mystifiers and hagiographers tell us. I would doubt it, except that not too long before Everyone Knew that all functions are continuous and with one or two silly exceptions differentiable and so forth, which is a right bit of fantasy itself -- albeit abetted by ambiguity in the meaning of the operative terms.

Anyway, Kasparov lost the game, then stormed back to win the match 4-2 (+3=2-1), winning the sixth game in a particularly gruesome manner; he was in such high spirits as to spontaneously agree to a rematch during the press conference; and then next year came and crumbled in front of the world, losing the 1997 rematch 3.5-2.5 (+1=3-2) after another particularly ignoble sixth game, dual to the previous match; and that was it, chess is something you can calculate, and, incidently, all the hopes of the early AI pioneers that it would take real intellect to make a fine mechanical chess machine -- just vapour, like so much else.

But one didn't have to be a chess mystifier to know it just wasn't so. The computers were still weak relative to the best, demonstrably so, to those wanting to take enough time to demonstrate it, even if it was long past the time a humble patzer could hope to score a few points off his laptop any more than off a flesh-and-blood master, and Kasparov's loss was far from convincing.

So despite Deep Blue's "retirement" the experiment continued. The computers got better. Man still had some triumphs; for example, Ilia Smirin's 2002 match against four leading programs, which he won, 5-3 (+2=6-0). The game against "Gambit Tiger" was particularly curious and prompted one commentator to remark ironically that although computers were superior in strategy to humans, we could still overpower the machines tactically, (as Smirin did in a dubious position).

Fast-forward to 2004, with two high-profile matches between leading players and leading machines: Kramnik v. Fritz and Kasparov v. Junior. (You can always tell which side is computer by the goofy name, and which side human by the Russian name.) In the former Kramnik looked to be coasting to an easy victory before dropping two points in the second half to end 4-4 (+2=4-2), once simply hanging a piece and once playing a slightly speculative combination with a very deep refutation which the machine very impressively found. In the latter things looked up when Kasparov cooked the machine in a knife fight in the first round, then slightly down when in a later game he overlooked a mating attack from the machine, then slightly askew when in the final game he agreed to a draw in an unbalanced position -- in front of millions (maybe), since the game was televised on ESPN (!). Ending up at 3-3 (+1=4-1), one could be forgiven for having lost almost all interest in Man-Machine matches.

Then, of course, there was Hydra, which pretty much made it mandatory to lose all interest. ("Lasciate ogni interesse, voi ch'entrate"?) Finally the knowledge that the tail wags the dog came true with a painful demolition in Adams v. Hydra. (Finally not a Russian, but still, to be sure, a world-class talent. For the record, Smirin is Israeli.) This travesty took place just a few months ago and saw the bon vivant Englishman lose 5.5-0.5 (+0=1-5). Ugh. Even worse, the prize fund was structured so that money only came for scoring points (unusual: usually the purse is split in some specified way to the winner and loser of the match, irrespective of the score), so for enduring this drubbing poor Michael Adams picked up only 10 thousand. (For comparison, Kasparov and Kramnik pocketed mid-six-figure sums for their labours -- minus pay to their seconds, and so forth.)

Finally, today started the second annual (so far) Man v. Machine tournament in Bilbao, Spain. Three men, all former "world champions" (so to speak; they comprise an Uzbek, a Ukrainian, and a -- Russian), against three leading programs, two microprocessors you too could own (Fritz and Junior) and one supercomputer (Hydra, again). Care to guess the day's score? Yes, that's right.

Certain chess fans might note encouragingly that all is not yet completely lost: correspondence chess players, who play games over duration of months instead of hours, sending moves by post, still know how to take the machines' measure. But this wagging wolf will just give a desultory woof!. It's all true. If a chess titan spends months preparing for a match, then we'll watch it, for sports' sake. But these sideshows are dispiriting.

Math jokes: "your lie when you said to me, 'I did this only as a game'"

Famous math-joke punchlines: "Ah-ha, a solution exists!," "thus reducing it to a problem previously solved," "totally true but completely useless," "assume we have a jabberwock," where a jabberwock makes the problem trivial, "there is at least one borogrove at least one side of which is mimsy," and so on. If you've never heard them, you've not been listening to math jokes, you sensible fellow.

But there are others, call them sporadic math jokes (that's one of them), which don't fit into the mold. Those punchlines above are jokes about mathematicians more than math; the closest I can think of to the latter is "let epsilon be less than zero," which presumably is completely cryptic to non-mathematicians (that's the whole joke, not the punchline), or maybe one of the waitress jokes ("one-half x squared,... plus a constant," "in characteristic two"). Here's another one that bridges the gap:

A mathematician keeps a diary. It reads:

• Monday: Tried to prove theorem.
• Tuesday: Tried to prove theorem.
• Wednesday: Tried to prove theorem.
• Thursday: Tried to prove theorem.
• Friday: Theorem false.

Sometimes it's just one of those weeks.

It cuts even more when the "mathematician" is a student and the "theorem" is an assigned exercise. Sometimes this happens, quite by accident, even on an exam (oops! -- I've seen a couple of these), say if a little hypothesis gets left out or if the problem is copied without discrimination from another source.

On the opposite side, firmly in "not funny," are Stiller's monsters. Computer scientists who play chess and have too much computing power sitting idle engage in the following project: to enumerate and evaluate all legal chess positions with some small number of pieces, say, five or six or seven. You can download complete six-man tablebases, as they're called; that's the two kings plus four other pieces. They'll only cost you several gigabytes. It will also be extremely boring to blindly wander through them, although in normal chess praxis from time to time it would be helpful to have a computer program capable of not just crunching moves with grandmaster vision but of perfectly evaluating every six-man endgame.

In the famous rematch Deep Blue v. Kasparov the machine had six-man tablebases, and it must have weighed on Mr. Kasparov's mind that if the board got too light with material the computer would begin to play not just mortal chess but mathematical perfection, as though announced on the trumpet from the throne of god, or if you prefer, gleaned from the immodest prostitution of the Platonic Form of Chess itself.

And god and Plato can be inscrutable: this is where Stiller's monsters come in. They're a couple of six-man endgames, winning for one side, but where the shortest forced win is around 250 moves; they're named for the man who first enumerated the six-man endings and found them while looking for long forced wins. In the linked article, Tim Krabbé writes:

They are beyond comprehension. A grandmaster wouldn't be better at these endgames than someone who had learned chess yesterday. It's a sort of chess that has nothing to do with chess, a chess that we could never have imagined without computers. The Stiller moves are awesome, almost scary, because you know they are the truth, God's Algorithm - it's like being revealed the Meaning of Life, but you don't understand one word.

The seven-man tablebases of course will be downright huge, but a couple of endgames, like KRRN v. KRR (king-rook-rook-knight versus...) have already been worked out. There is a position in this class which is winning for the superior side but it takes 290 moves to prove it. The last ten or so, mind you, are pretty easy; but the first ninety have to be perfect.

It's the dark side of discrete math. Sometime's there's an obscure obstruction to a general claim ("theorem false") and sometimes ("file under Stiller's monsters") it's true but you have to beat the devil to prove it.

Classes: "will to the thinkability of all things"

I've been trying out the local wireless internet service. I take the laptop down to Fine Hall and watch chess in the afternoons. In case you haven't heard (huh), the 'world championship' (long story) is taking place right now, in Argentina. (No more games played in east Siberia being over before I wake up in Pacific time zone.) As I type it's mid-evening here and Topalov seems about to pick up his second win in as many rounds -- against Leko and Anand, respectively, canonically described as the principal competition, which one would think would put him far ahead of the pack (twelve rounds remaining notwithstanding). It seems Topalov is playing like a man possessed, not exactly by Caissa, but with boundless fight -- today he refused to take back the exchange he sacrificed even when it seemed that he no longer had any compensation, just, somehow, to keep fighting. And it seems to have paid off, as Anand proves that not even Anand can play fifty moves of perfect chess. What an allegory: "If I can't be right, at least be bold--"

Which brings me to the list which has dominated my attention for the past week:

• Analysis -- since the instructor was still unable to manipulate the digits of his hand, he -- got someone else to teach the class. It turns out that there is a class in algebraic geometry basically at the same time which I might go to instead. I had some notion that I should take some analysis-type class with an eye to that part of the general exam, but the overlapping of material seems to be non-existent, to the extent where one hardly even needs to recall the material salient to one side to execute the tasks on the other. So it looks like I just spend some time with Folland or Rudin (textbooks) sometime between now and next October (or whenever).


• The Very Bad Characteristic -- a very pleasant surprise. It seems this class will be very accessible and very interesting. It is only too bad that it is so early in the morning, I can hardly wake up early enough to eat breakfast, make and drink my tea, walk over there, and so forth. (Today one of these got cut out. "Walk over there" wasn't it.)
  
  While there is a lot of mathematics that I enjoy -- I don't hold with those who disparage commutative algebra or whatever -- I've a special fondness for Galois theory, (roughly speaking the study of symmetries of algebraic numbers), which I first learned as an impressionable young undergraduate. It is the most beautiful mathematical theory I have known, something which by the maxim "excess is proof of itself" demonstrates a fortiori that there is beauty in mathematics. To work on a problem in this field would be satisfying, indeed; and that it relates deeply to the study of algebraic geometry, the field I'm slighting when I say "most beautiful," well,...
  
  Something, as we say in our reserved language, to keep an eye on.


• Representation theory -- which I attend because my advisor is teaching it and it seemed like the politic thing to do. I think by the end I may be believing that "to impress this person" is one of the classically idiotic reasons to do something. Or some reflection along these lines (append some caveats and provisos). It is not yet clear where we are going with this theory so I'll soldier on for now, especially since my resolve to stay with the class in the previous bullet point means I won't be able to attend the "introduction to algebra" class further.
  
  The trouble is that it feels like everyone else in the room is there because they're Really Serious about representation theory, whereas I'm halfway there on a lark, not a total lark, I like it fine, but it's pretty far from being a career interest of mine. It's a pervasive feeling, though.


• Discrete math -- seems like a lot of fun, as discrete math often is. Rapid-fire graph theory. In the afternoon but not late enough that I can take a nap after the morning classes.

That's about where it lies. I bought some books online (what a miraculous form of commerce), and picked up a little something else, too -- Verdi's Rigoletto, and, under the hypothesis that the neighbours don't like Verdi like I like Verdi, some headphones. Not "extremely good" ones but not disposable, either. Seems like pretty good sound, right down to the singers' steps on the stage and the coughs in the audience.

Got to keep entertained here, you know.

I'm sitting here, kind of in disbelief, because it seems like Topalov may manage not to win after all. Such a sad story. Sitting partly entranced by what is happening and partly because Blogger is undergoing maintenance, preventing me from submitting this for the moment. Fortunately, I still don't know what's going on in Morozevich's game. Yet mysteries of the universe. ("--try to solve them, but can you? -- nope; they're mysteries.")