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.

Paths: "we apologise, but it avoids writing 'induced' about 600 times"

Somewhere between the marathon chess matches, the wide-eyed tourist photography, dinner, the operas and incidental books, breakfast and tea, and talking about the aforementioned (although not at a regular or prolific rate, my readers will attest), some work gets done.

A quick update on the status of the various classes that have come to my attention. I don't remember precisely where we were last time and somehow I don't want to look it up. So, beware repetition.

• Introduction to Algebra, which induced a long discussion on the word "introduction," which along with cousins "basic," "elementary," "trivial," "easy," and so on does not seem to mean what the mathematicians think they mean. This got ditched in favour of two other classes at the same time. Same goes for Introduction to Analysis, except that it only overlapped one other class. While you're pretending to laugh at yet more ironic pedantry, let me observe that I was never taking Introduction to [Differential] Geometry, for I knew from the start that I wanted to take the other class at the same time, meaning that none of the three basic classes introduced by the department have done anything for me. Thanks for the thought, guys; fire the goobers who arranged your schedule. Moving on.


• Langlands Correspondence and Representation Theory are the two overlapping the first above. I have a hazy recollection of mentioning this along with a bit of the sentimental side.


• Algebraic Geometry, this time for real, not fake, not "introduction," not pretending to be "basic," is what induced me to let Analysis drop by the side this term. The trouble here, however, is that it's not an introductory class. Fortunately, due to a remarkable confluence of events, beginning with the fact that the class only meets once a week and ending with the professor's plane touching down an hour too late, it's been suspended for most of a month -- reconvene mid-November. I say this is fortunate because it will give me a little time to look up what all those words mean.


• Discrete math is very interesting. The instructor is a resident professor named Paul Seymour; he is doing this class for the fall and another in the spring. In each case the topic of the class is a theorem he and his various teams have proved -- "Strong Perfect Graph Conjecture" (now "Theorem") for the fall, "Graph Minors Theorem" for the spring. This is neither amok vanity nor petty parochialism. Rather it happens that this man has to his name a couple of the biggest, splashiest results in graph theory. Selah. Is this not why one goes to such a school in the first place? Just to hear this man talk is breathtaking. It's not just the rapid dictation of diagrams and arguments or the hundred-fifty-page paper sitting on the desk that constitutes his lecture notes, not that he frequently checks it. It's the chit-chat about how he used to work just on graph minors, then started on induced subgraph problems, then got a grant for his team to study Berge graphs with an eye to the Strong Perfect Graph Conjecture, spent months studying the things, proved a nice result, found out someone beat them to it by just weeks, and anyway went on to solve a major outstanding problem.

In summa, it's sunny out these days even when it's raining.

Zwischenzug

Apparently it's raining a lot here.

I didn't notice. But I did spend some time watching the rain fall. It feels very soothing, somehow.

But they do have rotten drainage and water pooling everywhere. A colleague told me his roof is leaking -- he's on the second of three floors. I think this is how Torontonians feel when they come to Vancouver and it snows and the city shuts down.

While we're here, a few more gargoyles, which give the relative worth of various specimens of the animal kingdom. These are the last two from the local gymnasium.

Ape with a book

Scholar with a book

Tigers: "old New Jersey in that far-off jungle land"

I hope the subtext from previously-quoted tidbits like the cherubim iconography and the Grotesque Tour of Princeton Campus and is clear: these people are nuts. And from the long-standing "what are they" question below -- that it's a stylish nuts.

But in this vein aside from the tiger-siss-boom-ahh! I think I've not justified my seeing tigers everywhere. So let me tell you about these people and their tigers. They have tigers everywhere. Most of the following I shot just while I was out taking pictures for the statues of the previous post.

(Now that I've figured this thing out, every picture is a thumbnail. The large versions vary a lot in size; only three are over 400kb, most of the rest under 200kb. Not that it matters with every single person in North America having broadband. But scroll down, because I still don't know why there's white space in front of my tables.)

	They have roaring tiger gargoyles, stone fixtures silently challenging passers-by give up the watchword.
	There are many of them on this building, interspersed with more traditional undead-goat motifs.
	Naturally it would be tedious to see the same face everywhere, so they have stylised mutant tigers, too. Or maybe this one is a man with a tiger mask; the structure of the jaw looks a little unclear and there's something suggestive about the eyes. There are a few other types, too.
	They don't have tiger door-knockers, just for the obvious reasons, but they make up for by putting overtop of a door a relief of tiger with ring hanging from snarling jaws. Or, say, more than one door. Note the whiskers on this guy.
	Here's a slightly more traditional-looking relief: just some mighty animals sitting next to a shield, a classical chivalric tableau. Apparently I wasn't standing flush when I took some of these. Shameful.
	Or, for the stalwart conservatives on campus, a yet-more-traditional rendering, complete with Latin 'motto' (VET NOV TESTAMENTUM, "new and old testament"). But what are those bizarrely contorted, ephemeral figures growing from the back? Someone tells me monkeys, and a shower of leaves. This is the most surreal tiger carving I've seen, although I've heard about one with a tiger and two cannon (!).
	Before we move on, the mother of all tiger gargoyles. This one hangs near the 'footballer' gargoyle seen here previously.
	Of course they have large bronze statues, too. These are Bengal tigers, male and female, 133% actual size. Guess how I found that out. Yeah, that's right.
	"All right," you say to me. "So they've got a few little stone trinkets and a statue or two and they cooked up some informational brochures on the subject. That a fixation does not make! -- no, not even the creepy anthropomorphic one." Fair enough. Let's move onto Exhibit B:
	This highly creepy metal statue stands taller than I. It was installed just a few years ago, at the north entrance of the stadium, shortly before a big game, I guess, demonstrating the longevity and potency of the fad.
	By the way, while we're here, you may recall that the stadium is adjacent to the math building. (As in, fifty-second-walk entrance-to-entrance adjacent.) I'm sure you know what I was thinking when I heard that there were actually huge metal tigers next to a building next to Fine Hall -- so also what treatment I had in mind for these thrice-blasted (not enough times, apparently) trees in my way.
	Moving on, to Exhibit C, we have one of the exhibits in the Frist Campus Center, a social hub: the skeleton of a Bengal tiger, eternally pouncing. Below it is a little statue of an actual bengal. And to the right?
	Showing their fine sense of history, they also obtained the skeleton of a sabre-tooth tiger. Below it, too, another statue showing what (they think) the tiger actually looked like. Never mind the apparently lack of connection; let's take a gander at that dedication plate.
	Right -- so that's the guy who made the statues. And below it, they have taken the opportunity afforded by this juxtaposition to summarise a few of the contrasting features between the Bengal and the extinct sabre-toothed tiger Smilodon.
	I sense the point is about made, so we'll finish this little tour with a phenomenon which I think speaks quite eloquently for itself. The store was closed at this point, so I don't actually know what this book is about.

Yes, the last few pictures were taken separately from the others, at night-time. Yesterday I was organising my tiger photos and thinking it was a shame that I didn't have a picture of those skeletons to 'seal the deal', as it were; when I came across them originally I didn't have my camera on me. It was about 8 o'clock and I was feeling vexed up until I realised that it is not a fifteen minute walk to get there. Suddenly I felt an incredible thrill, and infused with a giddy anticipation at brazenly flouting the most basic habits of my youth I immediately gathered my bag and umbrella. Then I realised I should put on a warmer shirt, since it is getting a little nippy these days.

Finally, I should share this little passage I came across, which sheds a small amount of light on the subject of last entry's mystery.

Blair Hall (1897), the first Gothic dormitory built on campus [there was a decision around this time to adopt Gothic architecture for future buildings --BKF], was given by and named for University trustee John Insley Blair. It was designed by Walter Cope and John Stewardson.... Between Blair and Little is a gateway planned by the architects, linking the two halls. The Daily Princetonian told its readers in September 1899, "The tigers, four feet in height, which will besurmount the posts of the gateway between Blair and Little, will be the finest pieces of carving connected with the building." These two bellowing stone beasts, installed in 1902, were the first free-standing tigers to appear on campus. They sit up facing west, propping up shields, each atop its own gatepost.

So, it seems we now besurmount our quandry.

Before we sign off, one last item I can hardly resist. Since there are no references to New Jersey in the extant literature, and certainly not as the jungle it clearly is not, you may guess something about the titular quotation. Yes, here it is, from the "can't-make-this-up" file, the Princeton Jungle March:

Way down in old New Jersey in that far-off jungle land,
There lives a Princeton Tiger, who will tat right off your hand.
But when he gets in battle with the other beasts of prey,
He frightens them almost to death, in this particular way:
Wow... Hear the Tiger roar. Wow... rolling up a score.
Wow. Better move along, when you hear the Tiger sing his jungle song.

(Kenneth S. Clarke, '05, Carmina Princetonia centennial ed.)

Particularly peculiar.

Tigers: "more in heaven and earth than is dreamt of"

They provoked interest and speculation unprecedented at Sun-Drunken. What do they mean? Who made them? What are they? Tigers? or prototigers? Lionesses? or not even mammals? Hybrid gone deformed? Groundhogs? or beavers? Giant prehistoric beavers? Obscure Japanese cinema amok on otherwise dignified campus?

Because a man knows to give the people what they want, here it is, no more nauseatingly wimpy polemics against bad lock design (I swear those clowns are half-way to a KUCA, specifically, the "useless" half, missing only the necessary irony) and bureaucrats: up close and uncut, you see what I see. These below are real thumbnails; click through for the massive (650-850kb, 1700x2270) originals.

Note the distinctly non-flat tail, sleek skull with slanted eyes and swept-back ears, and characteristic growl with saber-like fangs. Contrariwise, the pose of course is very distracting, and I didn't realise they could have haunches like that, nevermind the protruding bellies.

Here's a real tiger for reference, courtesy of Google (and, uhh, Associated Press, apparently).

But, you know, as much as I make light of them, in truth I'm envious. I wish I could have obscure and bizarre statuary. Couldn't really move them around with me, though.


On a related subject: Ever since I found Gargoyles of Princeton: A Grotesque Tour of the Campus (I keep telling you about these people) I've had that "gotta-catch-em-all" one gets when just the right triviality comes along over which to obsess. Granted this was just last night; but the fact that I went out the very next day to snap some shots suggests I am just as Orpheus in the underworld. So now I've got fifty pictures of miscellaneous gargoyles. I think I'll make a checklist. Here's a sneak peak, one of the weirder gargoyles. This "see-it-or-disbelieve-it" gargoyle is on the local gymnasium. (Also a thumbnail.)

World Around Us: "the unexamined life is not worth living"

The other day, looking in a certain vicinity for a particularly well-hidden building -- the local medical clinic -- I came across this specimen:

Truly, a building much like any other (I did not take more pictures to prove it, but maybe you can believe in the local homogeneity), and clicking for a larger version won't show you much more. But there is a little bit of something, dirt maybe, on the stone face above the door, obscured by the harsh sunlight? Take a closer look -- is it -- yes, it is -- huh!

Just hanging there, like you have to bargain with acolytes to enter and receive the cryptic wisdom of Apollo, ΓΝΩΘΙ ΣΑΥΤΟΝ!

know thyself!

Judging by the postings on the billboards inside, this building does not belong to the Classics Department but instead to the biologists. I bet they always use the door on the other side, just to avoid blushing walking under this thing.

Another incongruity I walk by every day:

Seems someone in the Class of 1879 didn't get the memo: "Lions out, tigers in."