Control-X: Polygonal numbers

Polygonal numbers belong to one of the somewhat arcane branches of mathematics that concern themselves with the physical representation of abstract concepts. Which is to say, while I imagine there is some aesthetic pleasure to be had in determining a series of polygonal numbers, it seems unlikely that there's any deeper mathematical truths to be unearthed in the process. It's math for beauty's sake, or order's -- a manifestation of the mathematician's desire to calculate all that can be calculated, for the purpose of itemizing existence to the fullest extent possible.

A polygonal number, according to Wikipedia, is any number that can be arranged as a regular polygon. Which is to say, n is a polygonal number if you can take n pebbles, or seeds, or -- in extreme mathematics -- hippos, and arrange those n physical objects into a regular polygon (i.e. a square, or a triangle, or a pentagon).
For any given polygon, there are a series of corresponding polygonal numbers that can make said regular polygon. These series always begin with one, and then proceed upwards: for example, you can make a triangle of hippos with one hippo, with three hippos, with six hippos, with ten hippos (pictured), with fifteen hippos, and so on. So the series of polygonal numbers for a triangle goes 1, 3, 6, 10, 15...

There is a formula, of course, for determining a polygonal number. If s is the number of sides in one's polygon, then the formula for the nth polygonal number in the series of polygonal numbers for an s-gon is:




Midway through the first semester of my freshman year of college, I was alarmed to discover that I could no longer learn math.

I had always been an excellent math student throughout elememtary school and high school. Though I fancied myself an artsy type -- a future writer, or maybe an editor, or possibly a jazz trumpeter, or perhaps a director, or maybe if all the cards played out right an actor -- I always scored higher on the math sections of standardized tests than the verbal sections. In seventh grade, I chose not to take advanced math, as the class met at a time I otherwise would have science with the foxy, low-cut-dress-wearing Miss Holton; this entirely rational decision would have long-lasting ramifications for my academic career. Not taking advanced math in seventh grade meant I went through middle school and high school on the standard mathematics track, with algebra in 9th grade, geometry in 10th, algebra 3/trig in 11th, and pre-calculus in 12th. I aced most of these classes, finding math a subject I could breeze through without breaking much of a sweat.

However, toward the end of senior year, I had some trouble with pre-calculus -- particularly with series theory. I remember loving the concept of factorials -- it was fun to envision eight factorial as 8!, pronounced simply by shouting the number eight -- but having difficulty with the formulas used to calculate them. I chalked these problems up to senior laziness and my antipathy toward Mr. Young, my pre-calculus teacher, who had scuttled my somewhat lame attempt, toward the end of senior year, to land on the varsity baseball team despite not having played organized baseball in four years.

But once I reached college, and calculus, I realized that I was now studying math at a level I was incapable of comprehending. At first I tried to blame the problem on my teaching assistant's impenetrable Chinese accent, but I soon realized that even when classmates explained the lessons to me in unaccented English I still didn't understand a single thing they were saying. It was as if the agreement I'd had with numbers all my life had been revoked, and suddenly those simple numbers were behaving in all sorts of odd ways. New rules and formulas sloughed from my memory, and math seemed like a difficult foreign language -- one in which I was taking some kind of advanced grammar seminar, despite not knowing the basic rules of speech.

I got an F on my first calculus test, the first F I'd ever gotten on a test in my life. In a panic, I took advantage of my friend Jamie, who had seized on our mutual safe unavailability -- she had a boyfriend in San Diego, I a girlfriend in Madison -- to nurture a freshman-year crush on me. She was a nice girl, but more critically to my fortunes, she was a math major, and we spent endless Platonic (Leibnizian?) nights with her patiently explaining calculus to me in terms more appropriate to a fourth-grader. When I needed a break, I'd play Nintendo baseball while she kept score in a scorebook she would utilize that spring as the scoreboard operator for our college's baseball team. I got an A on my second calculus test, and an F on my third. My grade -- in my mind, really, my entire academic future -- rested on my final exam.

Jamie slave-drove me through my studying, forcing me to put off the Nintendo World Series until such time as she was satisfied I could swing better than a C on the final. It worked: I got a B+, secured a C+ in the course, and never took math again. A subject that once was as easy as breathing disappeared forever, to be pulled out only occasionally when I needed to use basic cross-multiplication to convert fractions to percentages. Chief Toasohcah would never again be a part of my life.

Here's what I don't quite understand about polygonal numbers. The rules, as detailed in Wikipedia's definition, are such that the polygonal number series for a hexagon goes like this:



Why, in order for a number to qualify as a polygonal number, doesn't the number in question need to fill up the polygon? Why isn't the second hexagonal number seven, instead of six? Why isn't the third nineteen, instead of fifteen? Doesn't it seem something of a violation of the orderly nature of mathematics? Doesn't it all seem kind of arbitrary?

What happens to all those extra hippos?

Jamie moved back to San Diego at the end of freshman year, shortly after she slid a journal detailing the mortifyingly sexual fantasies she'd been having about me under my dorm room door. She remains the only girl who's ever been obsessed with me, even if she was obsessed not with me, really, but with the idea of a romantic escape from her doomed relationship. Soon my high school relationship started following the roller-coaster pattern of my relationship with calculus, but this time it all ended in disaster. Jamie got married, and then divorced. We fell out of touch.

I got married too, and seven years later had a daughter. She, my wife, and I make a nice little triangle together.

Control-X: Samboy Lim

Written by a passionate fan of retired Filipino basketball player Avelino "Samboy" Lim -- or possibly by Samboy Lim himself -- today's random Wikipedia entry makes me desperate to find video of Samboy Lim in action.





The entry is so outlandishly rich in praise that I like to imagine the president of the Samboy Lim fan club (again, possibly Samboy Lim himself) sitting in his apartment in Manila, typing feverishly away:

Samboy is an impact player who can dominate the game by penetrating to any stone wall defense. He uses his speed and hangtime to create a impossible shots. With his dare-devil high flying drives to the basket, sharp outside shooting and all out hustle, Samboy electrified the crowd for decades. He earned the monicker "The Skywalker" and "The Dragon."

The author sits back, wipes his face, takes a drink of water. He rereads the graph he just typed, and shakes his head, unsatisfied. There must be more, he mutters. There must be more he can say to help readers of Wikipedia understand the majesty of Samboy Lim.

Samboy was unstoppable in his time. He had heart. And for some time, he was the most popular player in the PBA after Robert Jaworski. Samboy is best remembered as the only player getting a standing ovation and applause from the crowd (even of the opposing team) every time he walks up to the officials table to enter the game.

His eyes fill with tears. Oh God! he cries. Why can't they just understand everything that Samboy Lim means to him? He pounds his desk, paces the room, smokes a cigarette. When he sits back down, though, his pathetic words mock him. They don't do justice to the awesome force that was Samboy Lim, soaring above his opponents in his blue San Miguel Beer jersey. The author pulls up his socks, praying that this imitation of Samboy's signature style might inspire him to dazzling heights of prose, graceful and beautiful as Samboy Lim himself:

Samboy was so unstoppable that isolating him, during the time that isolation plays are allowed in the PBA, would mean an automatic two points or an and 1 situation. He could break down defenses like bowling pins even if he is matched-up with an import.

The author sits back. He smiles. Yes, he thinks. Yes, that was it. Yes, thank God.

The Philippine Basketball Association features, currently, nine teams, each of which is named after the team's primary sponsor. (One team, for example, is called the Santa Lucia Realtors.)





This means that team names and identities have always been malleable and volatile, based on the whim of the marketplace and the marketing department. From 1975-1977, for example, a team in the PBA was called the 7-Up Uncolas, perhaps the only time a professional sports team has been named explicitly for what it is not. Say what you want about the players on that team, but they were not cola.

It's hard to get a gauge on the quality of play in the PBA. My best guess is that it's akin maybe to a mid-major conference in NCAA Division I, or maybe Division II. The best dunker in the PBA seems to be a player for the Air 21 Express named Niño Canaleta. He can be seen in the PBA's 2005 Slam Dunk Competition in this YouTube clip:





Canaleta is 6'8", which seems reasonable if a little on the small side for a forward, and his dunk -- a fairly good one, but nothing amazing by NBA standards -- blows away the crowd, the announcers, and the guy who posted this YouTube clip. "He's in a class by himself," a commentator says, awestruck, when Canaleta finishes.





American players can play in the PBA, though each team, per a recent New York Times piece, is restricted to one "import," who must be 6'6" or smaller. Teams apparently replace imports with surprising frequency; when the league playoffs began, according to the Times piece, the Red Bull Barakos replaced their import, Quemont Greer, with another player, despite the fact that Greer was the team's leading scorer, averaging 27 points per game. At DePaul University, Greer averaged 18 points per game during his 2004-2005 senior season. So competition in the PBA is, say, 50% less challenging than in Conference USA.





According to the Times, Darvin Ham was also not quite good enough to make it in the PBA. "'I averaged a double-double over here with like 16 and 12,'' Ham told the Times, griping about PBA press releases claiming he was a disappointment. ''These articles the PBA is putting online are like propaganda.'' Ham, who has averaged 2.7 points per game in his eight year NBA career, lasted three games with his team, the Talk 'N Text Phone Pals.

Samboy Lim still plays in the occasional PBA Legends game. And like any sports league, the PBA has its rabid fans. This blogger loves Samboy Lim, and it's fun to read his post just to see the over-the-top hoops jargon used by every American sports blog you've ever read employed to describe players you've never heard of:

Of course, Jolas is the fourth-quarter man, so he promptly hit a big three for his team's go-ahead basket. I guess these things never change. There was Benjie kicking the ball out to Ronnie (Magsanoooc, threeee poiiiints!!!), Ato Agustin hogging the ball, Allan Caidic posting up smaller guards, and of course, Alvin and Jerry sharing the same front court, perhaps for the last time ever. Allan Caidic won the MVP for Baby Dalupan's team, after which his counterpart Robert Jaworski joked in the post-game interview, "Ah, pinagbigyan lang namin sila."

Pinagbigyan lang namin sila, indeed.

Control-X: Dirkjan

According to Wikipedia, the title character of the impenetrable Dutch comic strip "Dirkjan" is "a loser who stumbles through life." Like "Doonesbury," "Dirkjan" started life as a college strip featuring collegiate sidekicks and a familiar university setting, and only upon syndication did creator Mark Retera attempt to broaden the strip's appeal by moving its main character into the world at large.





"Dirkjan" brings to mind the golden age of American comic strips -- not the 1930s, when the broadsheets ran "Little Nemo" every week, but the late 1980s, when "Bloom County," "Calvin and Hobbes," "The Far Side," and "Doonesbury" all appeared in the Milwaukee Journal's Green Sheet every afternoon. I learned everything I know about the 1960s and 1970s from "Doonesbury"; I still remember most major events of the 1980s as refracted through the lens of "Bloom County." I even filled scrapbooks with clipped-out copies of particularly crucial "Bloom County" cartoons, believing sincerely that future generations would treasure the opportunity to see first-hand the pale green "originals" of such epochal comic events as Opus's death by balloon-wheelchair, or his wedding to Lola Granola.





Endless inches have been written about the decline of the comic strip in American newspapers, most snappily by Scocca and MacLeod in Baltimore City Paper's treasured (and defunct) Funny Paper column. But between the Prophet Mohammed cartoon furor and "Dirkjan," it seems that things aren't much better in the Netherlands.




Reading a foreign strip like "Dirkjan" feels off-kilter, with the familiar rhythms of comic beats only barely breaking through my lack of Dutch language comprehension. In the strip pictured here, the entire first panel of the strip is wasted as a character -- seemingly Dirkjan's landlord, although it's unclear why he's wearing oversized clown pants -- asks Dirkjan and a roommate to come with him. In the second panel, the clown-pantsed landlord mentions that he's found a hair in the shower, and declares that the hair is not his own.

The third panel's punchline is an utter mystery to me. Altavista's Babelfish translates it: "With that red capsule nose he had still something comically." Perhaps this is a reference to the clown-pantsed landlord, who may at one time have worn a large red nose? Perhaps the "comically" should be translated "funny," and this is some Dutch-specific play on the well-worn cannibals-cooking-a-clown gag, "Does this taste funny to you?" It's unclear.

Wikipedia links to this site, which offers two Flash-animated Dirkjan bits, both of which are a tiny bit funny, and benefit from their relative lack of Dutch dialogue. Both seem to imply that Dirkjan, the character, is not your garden-variety comic loser -- in fact he seems so moronic as to nearly qualify as being in a persistent vegetative state. Dirkjan is visited by a clown at his (very European-looking, depressing block) flat, and sits mutely through the clown's performance? The gag is that next door, a harried mother waits impatiently at her child's birthday party as the promised entertainment never arrives. But I found myself wondering not at the joke, but at the depth of Dirkjan's idiocy, that he would never question the idea that a clown would visit his flat and put on a private performance just for him -- and that he would watch the performance silently, never smiling, never responding in any way. (Though I suppose his clown-pantsed landlord may have deadened Dirkjan to the appeal of clownly antics.)

Or are we to take away from the gag not Dirkjan's idiocy but his loneliness? That the long barren stretch of his endless days has been interrupted by a surprise visit from a floppy-shoed stranger with a unicycle and juggling balls? That despite the joy such a show should bring, Dirkjan realizes that even this pleasure is temporary -- that soon the clown will depart, unicycle packed carefully away, and Dirkjan will be left alone with his Continental despair, his tiny head sinking lower and lower into his chest, as a future of three-paneled misery stretches out before him?

According to Wikipedia, Dirkjan is also a "notorious leprechaun abuser." But I don't think he abuses leprechauns out of bigotry, or hatred. I think he does it to feel something. To feel anything.