The Frozen Tundra

I was invited by a friend to golf yesterday at Dyker Beach Golf Course in Brooklyn. The invitation came a few weeks ago, when it seemed like winter would never arrive and late-November temperatures were hovering in the low 50s. But as Saturday approached, the foursome exchanged emails and phone calls wondering if there was a certain temperature threshold below which it would be stupid to golf. The forecast predicted it would be around 40 degrees, with an Accuweather Real Feel Temperature (TM) in the low 20s. The course is in the shadow of the Verrazano-Narrows Bridge, just off the ocean, so we could expect a brisk sea gale blowing in our face. We dithered around about postponing it, and I was finally told by the organizer to stop being a big girl's blouse and just golf already. So I went. I hoped it would be horrible enough that I could get some funny stories out of it.

It was really, really cold. It wasn't as bone-chillingly cold as I was afraid it would be, but it was cold. A friend who, like me, was born in Wisconsin gets angry when I whine about the cold, her logic being that I should be inured to low temperatures. And being from Wisconsin, she says, I have a reputation to uphold. But I think that because I endured 18 frigid years in Wisconsin, I’ve earned the right to complain about the cold for the rest of my life.

So when you're golfing in very cold weather, it naturally affects your game. For instance, in order to stay warm enough not to die, you have to wear enough clothes to seriously hamper your swing. Which turns out to be a blessing, because after every errant shot someone could strip off some article of winter wear and exclaim, “God, these earmuffs totally screw up my peripheral vision” or whatever.

The course actually looked pretty majestic, with leafless trees stretching over bright green fairways, grown through that unseasonably warm autumn. The ground was rock-hard, such that tees snapped in half when you tried to get them into the earth. Also, divots were not an issue. The frozen tundra really benefited my game, because as a golf player, I make a great singles hitter. I have an awkward swing, and I send sharp grounders up the middle, like Ichiro. Yesterday I would hit one of my topspin screamers off the tee and the ball would just roll and roll, finally coming to a stop often as far down the fairway as the worst of my playing partners' drives.

One guy brought a thermos full of hot tea. We belittled the fourth guy, who failed to show up. We all golfed terribly, though I golfed a little more terribly than everyone else. It was nice not having a foursome immediately behind us breathing down our neck; inspired by that leisure, we took multiple cracks at some of the trickier shots with which we were faced. Inevitably, my mulligans were worse than the awful shots that had inspired them, so that made me feel like my golf skills have already peaked.

As we approached the ninth tee we asked each other if there was interest in playing eighteen. Nine was fine, we decided. We all really felt like we’d proved ourselves just by showing up.

May Be Qualified

I owned Prince's Sign 'O' the Times on vinyl, which makes me seem like a much cooler kid than I actually was, as I didn't like most of the songs and found the whole thing -- all the peace signs, Prince's mustache, "The Cross" -- a little bit embarrassing. One song I wore out, though, was "I Could Never Take the Place of Your Man," an expertly crafted pop-rock song that tells a simple yet (to a 14-year-old boy, anyway) utterly fantastical story. The singer meets a beautiful woman in a bar who is crying because her husband left her. She sizes him up and immediately wants him. "I asked her if she wanted to dance," Prince sings, "and she said that all she wanted was a good man, and wanted to know if I thought I was qualified." The singer is flattered, and admits that he "may be qualified for a one-night stand," but he does the noble thing and refuses. "I could never take the place of your man," he sings, sadly yet firmly.

To a 14-year-old whose only previous relationship was a one-week muddle at (no lie) band camp, this story was endlessly fascinating. What was frustrating to me about the song was that Prince was singing it from a position of privilege. I read his nobility as slyness, because when you're Prince, it's easy to do the right thing and turn down a hot woman who needs a long-term relationship, because you know full well that in the next bar will be another, hotter woman who needs casual sex. Because I didn't even know how to talk to girls, I knew that if, by some miracle, I ever found myself with such a dilemma it would be a lot harder to be noble. I spent a lot of time dreaming myself into analogous situations, in which beautiful ninth grade girls left their boyfriends and came crying to me. It was enjoyable to imagine myself as noble. But it was much more enjoyable to imagine myself as not. I can, I can, I can take the place of your man.

There's something hypnotic about the rhythm guitar riff and keyboard line in this song, the way they climb the ladder for four measures and then slide down the chute for four more. Two songs that I later came to love echo this chord progression, and when I listen to the Mountain Goats' "Going to Georgia" and Superchunk's "Detroit Has a Skyline" I'm filled with a wistfulness for my teenage self that likely was not the intention of those songs' writers. "Going to Georgia" is fierce and openhearted; "Detroit Has a Skyline," especially this acoustic version, is elegaic and personal. Neither one has anything to do with my teenage romantic frustration. But that's how I read them now, thanks to their accidental echo of a perfect song written by Prince twenty years ago.

Prince: "I Could Never Take the Place of Your Man"
from Sign 'O' the Times (1987)

The Mountain Goats: "Going to Georgia"
from Zopilote Machine (1993)

Superchunk: "Detroit Has a Skyline (Acoustic)"
from Hyper Enough EP (1995)

The Top 25 Sports Lists of the Past 25 Years

What makes a great sports list? Is it inclusiveness? Glibness? Groundless authority? Ability to inspire email-forwarding? All of the above!!! Readers looking for an argument love 'em. Hacks desperate for a column depend on 'em. In honor of a quarter-century of awesome sports lists, I've put together the ULTIMATE list of sports lists! Here it is... The Top 25 Sports Lists Of The Past 25 Years!

25. The Infinite ERA Club
Sean Holtz, Baseball Almanac, 2003
Who doesn't remember where they were when this list was first released? Baseball is a game of numbers, so why not celebrate the pitchers whose season or career Earned Run Averages stand at the number to end all numbers: Sideways 8.

24. Dives Not Recognized by the Olympic Diving Committee
Peter Schoof, mcsweeneys.net, 2001
A forward 3 1/2 somersault with the hand clap from the 'Friends' theme song in a pike position.

23. Most Eligible Palm Beach Polo Ponies, 1986-1987
Muffy Turlingstone, Palm Beach, FL, 1986
A snapshot of a era gone forever. #1: Dipsy-Doodle. This chestnut dynamo has a firm carriage and wonderful deep-brown eyes. A really, really neat horse.

22. Top Ten Hockey Fighters of All Time
As voted by the readers of hockeyfights.com, 2004
The authorities on hockey fights speak: the most fearsome brawler in hockey history is the Blackhawks' and Red Wings' Bob Probert.

21. 1984 Draft Winners and Losers
Jock Stewart, Sandy, OR, 1984
You can't go to a bar in Portland without hearing people still laugh about this list. Delightfully misguided: The Trailblazers can be pretty thrilled about their pick of Sam Bowie. Size wins in the NBA. Rumor has it Stewart eventually moved to Chicago to avoid the constant catcalls.

20. Ted Williams' 20 Greatest Hitters
Ted Williams, 1994
The Splendid Splinter created his Hitters' Hall of Fame in Hernando, FL, and named as its inaugural class the players he believed to be the 20 greatest hitters of all time... not counting himself, of course.

19. Best Baseball Players of All Time
Charlie Brown, 1982
A list from all our childhoods. Still gives me a warm feeling in my heart. #1: Joe Shlabotnik.

18. Chester vs. Shrewsbury Town Top Ten Matches
Chas Sumner, Chester, UK, 2003
Surely the most accurate document of British football infatuation is this list of the best ever matches between two teams no one cares about. 30 September 1911. The first competitive fixture and Chester win comfortably thanks to a hat trick from Lol Cook. Chester go on to beat Northern Nomads and Wrexham but are eventually eliminated by Stockport County.

17. The 50 Greatest Players in NBA History
National Basketball Association, 1997
In honor of the 50th anniversary of the NBA, the league named its all-time greats. Still hard to believe Scottie Pippen made this list.

16. Top Ten Other Unconfirmed Rumors About Mike Piazza
The writers of "The Late Show With David Letterman," 2002
#9. His number, 31, is also the number of bat boys he's strangled."

15. Top Ten Feats We'd Like to See
Jeff Merron, ESPN.com, 2003
J.J. Redick shooting 100% from the line? Ichiro hitting in 57 straight games? Future sports records, unveiled, by the listmasters at ESPN.com. Merron in particular is a list machine; he spouts off two or three a week, never anything less than professional.

14. Courtney Walsh's Six Best Performances
BBC Sports Online, 2001
In honor of Jamaican bowler Walsh's 500th Test wicket, the BBC runs down his six greatest Test matches. Full of charming and incomprehensible cricket lingo. Having recorded 6-62 in the first innings, he was given the new ball second time round and responded by dismissing Navjot Sidhu, the first-innings centurion, for a duck.

13. Left-Handed Catchers
Sean Holtz, Baseball Almanac, 2002
A classic sports list: it illuminates something we never knew about a sport we thought we knew everything about. Have you ever seen a left-handed catcher?

12. Longest Field Goals By Female Kickers
P.S. Luchter, 2004
Creepily comprehensive. 30 yards: Kara Snitger (Cedar Cliff HS, Camp Hill, Pa.), halftime of Big 33 (Penn. v Ohio) HS All-Star Game, 7/24/2004 to win college scholarship. Going to Pittsburgh.

11. Fans in Section 8-J Whose Heads I Would Like to Bash In
Ralph Stevens, Cleveland, OH, 1979
#2. That guy in the rainbow wig who's blocking my view of the visiting end zone.

10. Most Influential Bowlers of All Time
Larry Paladino, Bowling Digest, 2001
What finally landed it on the list was this quote from #1 Larry Weber: "Come to think of it, I haven't bowled on a submarine."

9. Inside-the-Park Grand Slams in Baseball History
Sean Holtz, Baseball Almanac, 2002
Holtz scores again with this compendium of a surprisingly common baseball event, an inside-the-park home run with the bases loaded. In September 1901, Brooklyn's Jimmy Sheckard accomplished it twice in two days. Who doesn't love baseball lists like this? So useless, yet so delightful?

8. Kelly Slater's Pro Surfer 2 Top Ten Wishlist
The Editors of SportPlanet.com, 2001
How much do you care about you surfing videogame? The authors of this list care a lot. As it stands now the surfer simply lies there on his board and waits for a wave to magically appear. He can't sit up and look around, his paddling abilities seem limited, and if he duck dives the wave the next one comes just as quick in the same fashion as the first. Degree of passion outweighs the lack of initial capitals.

7. Obvious Fouls I Cannot Believe These Referees Did not Call
Jonathan Farmer, Chapel Hill, NC, 1996
#4. They're just mauling Antawn Jamison down there! C'mon, call that!"

6. Top Ten Athletes of All Time
Jeff Merron, ESPN.com, 2004
An ambitious attempt to combine all sports lists into one. But Dave Winfield ahead of Bo Jackson?

5. Responses to Reporters
Don Carman, Philadelphia Phillies, 1990
Phils pitcher Don Carman posted his boilerplate answers to reporters' questions on his locker midway through the 1990 season. #12: "This team seems ready to gel." Rasheed-esque.

4. Manchester United's Top Ten Offseason Targets
The editors of Manchester Online, 2003
They could buy and sell you. Shevchenko also apparently has the most complicated contract in world football.

3. Top Five Passers in the NBA
Allhiphop.com message board user IrishPride, 2004
Two words: Vlade Divac. Authoritative and inarguable. One of the best no-commentary lists ever made. Those who argue with IrishPride are fools.

2. Best High School Football Teams in the North Shore Conference
The Whitefish Bay High School Pep Squad, Whitefish Bay, WI, 1988
#1. The Whitefish Bay Blue Dukes!!!!!!!!!! #2. Everyone else.

1. Top 10 Sports Lists of the Past Year
ESPN.com staff, ca. 2002
The clear winner. Groundbreaking. Initiated a revolution in listmaking. True list-lovers -- those who know that sporting events find their grandeur not in their competition but in the arbitrary ranking that occurs afterwards -- still get goosebumps when they see this list.

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.