“Mighty is geometry; joined with art, resistless." -- Euripides
On November 23rd, 2010, the Duke Blue Devils obliterated the Kansas State Wildcats by a score of 82-68. The game was hardly as close as the score makes it seem. It was a really impressive victory -- the Blue Devils (then ranked #1) were playing against a #4 ranked Kansas State team that featured player-of-the-year candidate Jacob Pullen, one of the most electric scorers in the college game and among the best shooters in the country. The Blue Devils were favored in the game, but only by the slimmest of margins and most thought it essentially a road game for Duke despite the neutral site locale. It was thought of as a given that Pullen would drop 20-30 on a permissive Duke perimeter defense, helmed by rookies and youngsters that hadn't quite grasped Krzyzewski's defensive system yet.
Not quite. Pullen shot 1-12 for 4 points, posting what may have been his worst game as a collegiate athlete. And Kyrie Irving? The 18-year-old jitterbug was phenomenal. Beyond phenomenal. A revolution, a revelation, a reincarnation of all that's good in basketball. A vertical Rothko in three shades of blue, disrupting almost every single shot Pullen took and making everything he touched work better. He even had a poor shooting night, missing his two threes and numerous wide-open jump shots off his pet pick and roll sets. It didn't matter. He still dominated. Nothing he did in that game was anything short of a wonder. He had four games of college experience. Four. He was facing one of the greatest scorers in the history of the college game, in his first true away game as a pro. He had jitters, as he later admitted, but it simply didn't matter -- sometimes you're just too good for jitters.
After the game, what was the topic of conversation? It wasn't really about Irving at all. Some highlights, some features, some general pats on the back for a game well-performed. But little focus on how dominant Irving was in the contest, because that simply isn't how Duke teams are traditionally understood -- instead, commentators sprung for the usual well-worn cliches, continuing to beat the drum on the idea that Duke was the most talented team in basketball and nobody was really anywhere close. Unbeknownst to most at the time, this wasn't true. At all. Without Irving, the 2011 Duke Blue Devils were a lacking bunch with scant cohesion, flawed chemistry, and a tenuous grasp of the defensive end of the court -- and even Nolan Smith's flukishly-good season didn't obscure that once Irving went down. By the time he came back at the end of the year, the 2011 Blue Devils had been exposed as something of a fraud, and Irving was relegated to being an everyday Duke player -- good, decent, and maybe a perennial all-star. Perhaps. With his dominance forgotten, his flaws overstated, and his game misunderstood, people continued to assert rank inferiority of a draft class that's ended up being (potentially) quite a bit better than the 2 or 3 that came before it. And Kyrie Irving sat, in wait, ready to be the transformative player that he knew full well he'd be.
Can you be a star when they don't know who you are?
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To most, the world of Mathematics represents a world of abject certainty. The word "always" is key. One plus one always equals two. One gallon of milk will always contain exactly 16 cups. Avogadro's number will always describe the constituent particles of a single mole. Always this, always that. There's nothing inherently wrong with this stance, and indeed, it's a satisfactory description of the lower-level mathematics covered in high school and the lower rungs of college. In that sphere -- the sphere most contend with -- math is little more than a series of stark truths represented through numerous immutable rules. The broader picture, insofar as it's revealed at all, is inevitably watered down. But ever since reading an excellent piece from the always-recommended folks at Berfrois (this time the imitable Barry Mazur, a Harvard mathematician), I've come to finally put words to a thought I had throughout my studies. Once you get to a high enough level, Mathematics isn't about any of that.
It's more about hunting giraffes.
What? No, that's actually what I meant to type. Giraffe hunting. The key to understand here is the exact core of Mazur's point. Much of mathematics can be distilled to the logical skeleton that composes those previously outlined truths -- everything most people need to know, really. But there's a level far beyond that, and in the seedy and sordid world of higher mathematics, the questions become far less concrete and far more intangible. Even if you accept the proposal that the formal structure behind mathematics is inert and extant in the highest and most complete form it will ever be, as most do, you'll be hard pressed to find a mathematician worth their salt that believes the absolute meaning of these structures is comprehensible to us and entirely within our grasp (although some believe computers will eventually fully comprehend it). Yet, at least. Scrabbling to find that meaning is the core of higher mathematics. And when you apply enough abstraction to the thought, you come to an almost existential crisis -- if we're ascribing meaning to structures we've yet to fully comprehend, at what level have we really established that abject certainty mathematics is known for? Sure, one plus one always equals two, if you're working in base ten in the traditional coordinate system. But so much of higher math involves reorienting systems to solve problems too complex to describe in the traditional frame we spend so much time explicating in our youth.
It's something like this -- as a child, you learn how to shoot a perfect free throw. You are shooting 100% from the free throw line. It's beautiful. Amazing. But then the blindfold comes off, and you realize there are an infinite number of other points on the basketball court that your exacting and perfect free throw form can't make a bucket at, and that you need to be able to take the framework of your shot-making from the line and turn it into a flexible monster that can attack from every isolated space on the court, in an all-engrossing infinite sphere of possibility and wonder. You've established one single thing -- you can make a free throw. Now you need to establish everything using the basis of that single thing. It's terrifying! It's challenging! And it's beautiful, in a way. When you're a young and rising mathematically-inclined student, you're given this broad structure and this set of rules, and tasked to analyze them to their absolute completion. You do so. Life goes on, you work hard, and you finally come to some level of satisfaction with this structure. Then a teacher cracks you in the head and makes you realize the almost-too-hilarious truth. Those rules and that structure you'd been taking for granted in all your work? Indeed, those are the problems. The things that are flexible in higher math aren't the values of the numbers or the forms of the equations. It's the rules you used to get there in the first place.
And that's where the whole "giraffe hunting" tidbit comes into play. In Mazur's piece, he describes a giraffe hunt he observed in a documentary. Four men hunt a giraffe for five days, pursuing without adequate food or water their quarry for as long as it takes to catch it. He describes it as "exhausting yourself in the ecstasy of it", getting lost in your hunt. Finally, when you catch the giraffe, you use everything. You thought you exhausted yourself catching the giraffe? Hardly as much as your former prey will be exhausted for meat, bones, ears, hooves, and skin. That, right there, is what you do with higher mathematics. You hunt for the perfect framework for your perfect proof, and once you find it, mathematics cannibalizes your structure and creates dozens of offshoot proofs in attempts to explain increasingly different phenomena. Mathematics is the process of slowly ascribing meaning to the inert structures we can't quite explain or understand, arrived at through the everlasting hunt of various proofs and logical stabs. These proofs inch us closer to a truth that means nothing until we can explain it. The hunt is what defines broader math, and until the blindfold's taken off by an amused old hand late in our undergraduate career, it's rare for one to fully comprehend the enormity of it.
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This isn't meant to be an anti-Cleveland screed. Really isn't. As many are aware, I'm a fan of the Cleveland Cavaliers. I have a Zydrunas Ilgauskas jersey I sometimes wear in support while rooting from my couch. I have Cavaliers pencils. I have a Cavaliers calendar. Kyrie Irving is one of my favorite players in the league -- top 5 at a minimum. This isn't an essay meant to state some sort of snide, backhanded "fact" about Cleveland being a poor showcase for its young star's talent. Think of it through the whole story, instead -- Kyrie Irving went to Duke University, one of the most over-exposed basketball schools in the country. There are millions upon millions of jokes, and most of them hold water. Duke is held up as a standard-bearer, plastered on national television for almost their entire season, and given innumerable extra coverage opportunities that most other schools simply do not get. He plied his trade at college basketball's equivalent of the Lakers.
Despite this -- despite the overexposure, the massive coverage, the big games -- virtually nobody realizes how good Kyrie Irving was as a college student. Seriously! Nobody! When the 2011 NBA draft approached, there was a serious question that floated on talk radio for some time as to whether Derrick Williams or Kyrie Irving was the better bet as an NBA player. Serious questions, by very smart analysts. This was absurd to me, as someone who watched every single minute of Irving's college career and a fair bit of his high school career. I'm not one to exalt Duke players above everyone else, but by GOD, Kyrie was preposterously good. In college, Irving shot 90% from the line, 46% on threes (almost exclusively unassisted!), and shot over 70% on plays off the high pick and roll. You're reading that right -- 70%, with a seven and a zero. He did this all despite using 30% of Duke's possessions when he was on the floor, playing reasonably solid Krzyzewski-style defense, and being the primary target of virtually every team's defensive schemes. Kyrie Irving may have been injured for much of his college career, but he put up numbers that were legitimately historic. One of the best offensive seasons in college history. There shouldn't have been any doubt whatsoever that the man was the real deal. But everyone was shaky on him, and everyone used the "health" card to explain their doubt.
Then you get to his rookie season. Kyrie didn't play a ton of minutes his rookie year -- topped out at just over 30 per game, and he missed bits of the season with a few minor maladies -- but when he played he was undeniably phenomenal. He threw passes that were steps ahead of the defense, often setting up the ball straight in the cradle of an offensive player's shooting motion for a beautiful dish only ruined by the fact that the offensive player was Samardo Samuels. Whoops. His dribble remains one of the most inexplicable wonders the league has to offer, and Irving's speed with the ball is virtually peerless. The form on his shot was legitimately immaculate, and Irving was a few trick shots at the rim and a few injury-tarred games short of a 50-40-90 season -- as a rookie, remember. His defense was poor, although to my eyes, he started the season relatively well on that end. He defended reasonably well in the preseason and only begun to fall off significantly after a minor sprain early in the year, which gives me some manner of hope that he'll recoup strong and rediscover the bulldog defensive tendencies he displayed at Duke.
In short: Kyrie Irving was all manner of remarkable. He was also nowhere near an all-star spot despite playing significantly better basketball than Deron Williams, Luol Deng, or Joe Johnson. National fans seemed to have virtually no investment in his game. He lived in the shadow of LeBron's rookie season, which was ludicrous for many reasons, not least of which being that Irving was putting up the best rookie season since Chris Paul's, and one of the best rookie years for a point guard in the history of the sport. His rookie year OBLITERATED LeBron's in statistics and standard, with about one tenth the hype and one twentieth the recognition.
But I repeat myself.
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The key thought that connects Kyrie to my missive on mathematics is the idea that, on some level, the idea of Kyrie Irving is a relatively inert function. Just like the broader structures we can't quite describe yet. The more I watch of his dazzling NBA play, the more I'm inclined to believe this as an underlying truth rather than a happy coincidence. If Kyrie Irving is an inert function, his own floating Sealand-style island of NBA bliss that exists under its own flag, it stands to reason that on some level it doesn't really matter that we haven't totally figured him out yet, as a collective of NBA fans. Sure, we've got some appreciation for him. But on a broad level, I've always gotten this feeling that the overexposure of Duke in no way properly highlighted the sort of a player Kyrie was for that Duke team. Nor did the overexposure of the 2012 Cleveland Cavaliers in the light of LeBron's all-universe season do all that much to properly highlight the sort of player Kyrie was as a rookie.
And this year? We're staring at a guard who, as a 2nd year player, is poised to finish the year as a blisteringly efficient 25-ish points-per-night scorer that runs a Cavalier offense with brutally poor pieces alongside him like a whirring, well-oiled machine. And yet appreciation is still, as with mathematics, shaky -- there's a vague understanding of Kyrie's structure among the basketball literati as a general collective, a weak understanding of the qualities he brings to the court. It is a weak understanding of what exactly he does that's so phenomenal. There are the little highlight films that show off his beyond-all-reason handle and his "teenage girls weeping" wet shot. There are the little publicity stunts, the Uncle Drew ads and the mushing with Kobe to give people a taste of his brilliant personality. And there are the accolades; the Rookie of the Year voting, his likely All-Star spot this year, et cetera. Each of these inches us closer to full understanding of Kyrie Irving's inherent truth, and the things that make him whole. But none of us quite inch the collective to complete understanding -- not quite.
It does not matter, in mathematics, that we've yet to come to a full consensus or fully discovered the underlying structure we're studying. Some mathematicians are further along than others. Some are still comprehending the basic groundwork they'll need to get any farther -- they're examining the remains of the giraffes that have been hunted before, discovering things that will help them on the next hunt. So too are we, as a people, learning just how we interface on a collective level with a player as good as Kyrie Irving. People have yet to quite grasp how good he is, and indeed, mathematicians have yet to quite grasp the whole truth of the structure that underlines the discipline. And perhaps they never will. But the true joy of examining and following a player like Kyrie is the same as the joy a mathematician derives from his craft -- the joy of a sailor in the age of discovery, setting anchor ashore in a steppe untouched by man and faithfully taking in the details and oeuvre of their surroundings. And that feeling -- that taste of discovery, that thirst for more -- is exactly what keeps a mathematician hungry. It's what keeps the ecstasy present in their exhaustion, the guiding light that sends them off to prove the new proof and discover the new rules. And this elation, this ecstasy of discovery? This sense that the best is just around the corner, imperceptible to even the most hardy of eyes?
That's what it's like to watch Kyrie Irving -- the showman, the structure, the star.
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