Teaching Backwards

One of the most difficult things about teaching math and science is avoiding the temptation to teach everything backwards.

The backward approach roughly follows the same standard scheme, as exemplified in every textbook ever (and far too many classrooms): introduce an idea, term, or a definition, and then explain what it means, how it's relevant, and how to do "problems" or answer "questions" using it.

For example, most high school math textbooks come to a chapter titled "trigonometry" or something like that, give definitions of the trigonometric functions (sine, cosine, tangent, etc.), and then proceed to show how useful they are in solving problems involving triangles.

Later in the chapter, in the section titled "the sum and difference formulas," the book gives the sum and difference formulas for sine and cosine, before giving the proofs, and before even stating a relevant question that would require the sum and difference formulas.

Unfortunately, this approach completely eliminates any and all creative insight into the very real problems at hand, and leaves the student with no reason or desire to acquire that insight. It's as if the definitions of the trigonometric functions were handed down by God, followed by a set of problems to solve that require them.

In the real world, of course, everything happens in the opposite order: definitions don't lead to problems. Problems and questions lead to insights, which lead to generalizations, which eventually lead to generalizations and definitions. Someone tries to find the distance between two points knowing their respective distances to a third point and one of the angles. After studying geometry (or even before), most students have an intuitive sense of how to approach this problem, and with some care and coaxing, you can get them to "discover" the law of sines. But if they learn trigonometry from a standard textbook, they'll never even get the chance, because there it is before the problem is given!

Most students can learn to use and manipulate trigonometric functions fine by the backwards method, but its flaws aren't merely aesthetic. If a student has no sense for the scope of a problem he or she is trying to solve, what reason does he or she have to remember the trigonometric functions beyond the next test, or the SATs? For most students, the sum and difference formulas are something to memorize and then forget, rather than a beautiful solution to a seemingly intractable problem.

On the first day of my 4th grade science class, I handed the students a sheet with just three questions: What is science?, Why do we care about/study science?, and How do we study science? Their answers were revealing and kind of depressing (also somewhat hilarious). How do we study science? Why, from science books of course! Why do we study science? So that if we need something to fall back on, we can be science teachers!


These students, like so many, have completely missed the point (so far at least!). Maybe some of them will miss the point either way. But it seems more likely that the things they learn will leave enduring memories if they have to confront the same problems that the people who actually discovered and developed them had to confront. At least that way, they get some sense of what math and science are really about!

Not-Romney for President

All the media back & forths of this Presidential campaign have somewhat obscured a few basic truths about the Republicans and their ideas for governing the country. Yes, we all know Romney has changed his mind on almost every issue, and nobody knows how he would govern. But the narrative and motivation of his candidacy still rest on a few paradoxical ideas about government and the economy.

The first is the "government can't fix your problems, so elect me to fix all your problems" fallacy. It's worth stepping back every once and a while and realize that this makes no sense. The Republicans have been hammering Obama for four years for directing his focus away from "job-creation," while arguing that the government should do less to create jobs. Less government is certainly a coherent ideological position, but not a good way to make jobs in a recession.

The next contradiction: lower taxes will encourage more people to work, which will bring down unemployment. Huh? This wouldn't even make sense if the US economy were somehow lacking for people looking for work. And anyway the problem is precisely the opposite. To the extent that lower taxes would encourage more people to work (which may not even be the case anyway), they would obviously increase unemployment since there aren't enough job openings for all the people looking for jobs anyway.

And lastly, the deficit. People seem to forget that there's a very specific reason to fear government deficits and debt: higher interest rates. Government debt isn't some vague but inherently evil entity that will erode Your Children's Future if not tackled Right Away. Your children will be richer than you! They'll pay back your debt fine!

On the other hand, if people fear the government will become insolvent and therefore unable to back its debts, then they demand higher interest rates, and these higher rates make private investment a less attractive alternative by comparison. That would be bad. But with interest rates on treasury bonds lower than ever, there's just no reason to make an issue of short term deficits.

And don't even get me started on foreign or social policy.

soccer, chance, and attribution, continued

As I argued in an earlier post, football is an inherently probabilistic game. Here I’d like to expand a bit on what I mean, and look at some (preliminary) evidence.

Clearly, everyone realizes that chance and luck play some role in soccer (indeed, in any sport). I’d like to argue that it plays a rather larger, and more specific role than we might think. In particular my hypothesis is that we can predict the distribution of goals in a soccer match and over a number of matches with a fixed-probability model. Imagine a soccer game is like a series of coin tosses of a very, very unfair coin. In each minute of a soccer match, we toss a coin that has about a 1/35 probability of landing on heads. How many times will it land on heads?

My hunch is that that the number of heads you get in this experiment is the same as the number of goals you get in any given soccer match, which (if true) means that in every minute of a soccer match there’s more or less a fixed probability that one or the other team will score.

This isn’t what we expect, or what conventional wisdom would predict. We like to think that in a 0-0 soccer game, the teams just didn’t attack very well, or defended very well, or both, and that in a 4-3 game, the opposite is true. Those teams really came out with attack-minded tactics and didn’t play defensively at all! And they did brilliantly, too! Right?

more thoughts on euro 2012 houghts on euros

I have to admit I succumbed to the hype of Euro 2012. I was excited to watch soccer every day, to watch some of the best teams and the best players on earth. But the tournament has, overall, been a disappointment. Let's admit it: too many of the games that were, on paper, decent match-ups, have been colossal bores. Starting with Germany-Portugal and continuing through to Portugal-Spain today, the games have been low-scoring (lowest since euro 96 overall), defensive-minded, and lacking general excitement. Even a game like Italy-England, which, to be fair, actually had quite a bit of attacking play and lots of chances (mostly for Italy), ended up with no goals at all. For me it's another sign that football, as a game, simply cries out for more goals. It's becoming a game of who can hold on to slim leads, rather than a game of who can attack the most and create the most chances. In all the rule changes I've suggested over the years for soccer, of course, I've never written about the most obvious, most consequential, and least likely to change in the near future: make the goals bigger. But that's for another time.

As for yesterday's semifinal, a few comments. First, Portugal did, in truth, defend brilliantly through the 90 minutes. Spain certainly were not at their best, and seemed to lack a lot of energy, but even a weak Spain team usually dominates possession and creates a lot more than they did. And people tend to look back (as I've mentioned before) when a team gets a clean sheet and claim that they defended well even if they just, in fact, got lucky, but in this case it was no meager stroke of luck. Portugal did what no team in the tournament had done thus far: they defended high up the pitch and denied Spain's defenders time to play the ball out. Teams have tried this against Barcelona, most notably Man. Utd in the 2009 champions league final, or Madrid in various Clasicos, but it usually doesn't work because if you apply high pressure to such a skilled team, you're vulnerable to quick attacks when the team breaks that pressure. But Spain were unable to do that, lacking, most notably, someone quick to run at defenders through midfield. They don't have a Messi, and until late in the game, they didn't even have a Pedro. Iniesta can usually take up this role, but he was unusually subdued.

An offside conundrum

If you've read anything I've written about soccer before, you probably already know that perhaps nothing annoys me more than when a team is falsely penalized for offside. So in a surprising turn of events, I'll be writing today about a new problem: the offside rule as currently interpreted allows for certain plays that should be sanctioned for offside. As you might, expect, two recent examples from Euro 2012 motivate this post: Bendtner's first goal for Denmark against Portgual, and Jesus Navas' goal for Spain against Croatia. The offside rule should be clarified so that these types of goals don't count.

The "Laws of the Game" state that a player is guilty of an offside violation if two conditions are met: 1) He is in an offside position when the ball is last touched by a player on his team, and, 2 "He is involved in active play by [either] interfering with play, interfering with an opponent, or gaining an advantage by being in that position."

Now back to the two goals I linked above. In the first, Bendtner is in an offside position when the ball is initially crossed to Krohn-Deli. He is clearly not in an offside position when Krohn-Deli heads the ball back across to him. On the initial cross, he is neither interfering with play, nor interfering with an opponent. But surely he gains an advantage by being in an offside position at that moment. If he weren't in an offside position, he would be closer to both Pepe and Bruno Alves, who could more easily track him and mark him on the following play. Now it turns out that both Bruno Alves and Pepe are giant ball-watchers, and simply turned their heads and watched as the play unfolded, in this case. However, even if they were decent defenders, they wouldn't have been able to get back mark Bendtner and prevent the goal, precisely because Bendtner was already closer to the goal. Thus, according to the clear and obvious meaning of the words in the offside rule, Bendtner is guilty of offside.

But wait! Since the offside rule is so complicated, FIFA appends a whole section to the "Laws of the Game" clarifying its interpretation. As you can see if you care to look at page 109-110 (that's right) in this PDF, you'll see that precisely this type of play, is deemed "not an offside offence." In fact, the phrase "gaining an advantage by being in that position" is furthermore defined to encompass only two specific situations, namely being an offside position when a teammate makes an effort on goal that rebounds off the goalpost or the goalkeeper.

That's it! Of course, FIFA can define the rules as it wants. But is it really "fair" in some more objective sense to allow these types of plays to proceed and not be offside? Well, by now you probably know what my answer is! To help you see why I think so, take the situation to its logical extreme. Imagine that one striker on an attacking team is camped out in the opposing team's penalty area (cherry-picking, as we say). Surely, the other team doesn't have to mind him when the ball is in the other half, since he's so far offside! That's the whole point of the offside rule, to essentially eliminate that player from relevance! But clearly, as the rule is currently interpreted, the defending team does have to mind the cherry-picker, because of the following possibility (illustrated in the awesome image below). Imagine a long, well-timed through pass is played toward the defending team's corner flag. One attacking player, who was already running toward the corner when the ball was played, chases it, and is tracked by a single defending player. But not all the defending players were running back when the ball was played because they weren't similarly tracking penetrating runs. But what would normally be a defensive situation totally under control, as the player running toward the ball is under pressure even if he gets to the ball first, is now a very worrying situation, because the attacking player can make a simple pass across to his teammate who is now waiting, onside, inside the penalty area, without a defender anywhere in sight! This is analogous to the goals linked above; according to the rules, the play is not offside, but clearly, it should be, because the cherry-picking player in fact compels the defending team to defend him, in a manner completely contrary to the spirit of the offside rule (and, indeed, to the most reasonable interpretation of the language of the rule).

what's the point of the goal-line referee? re: ukraine-england

More thoughts to come as an overall reaction to the conclusion of the group stage of Euro 2012. But for now, the question that should be on everyone's mind (who just watched the final matches in group D): how did the goal-line referee miss that ball going over the line? I'd use this example as more support for my idea that the goal-line referee is essentially a giant misuse of precious refereeing resources. If there are extra referees in a football match, they should help call offsides, since these calls are missed much more often and, though less tangibly so, have a much bigger impact on the final outcome of matches. In addition, as we see here, even having a goal-line referee doesn't guarantee that goal-line calls will even be made correctly! Several talking points here.

First off, the obvious: England fans will be quick to point out that the play should have been ruled offside much earlier on. So maybe it's not such an unjust outcome that it wasn't ruled a goal. Fine. That doesn't interest me so much right now.

More interestingly, I wonder about two things: 1) the positioning of the goal-line referee, (is he really standing in the best position to judge whether the ball has crossed the line? NO) and 2) the training or instructions given to the goal-line referee (was he trained to stand where he was standing? Lamentably, probably. Was he directed as to how certain he should be that a goal has been scored in making the call for a goal? Probably not?)

For the first point. You'll notice if you watch this video or any other that shows the play in question (the link will probably be removed for copyright by now), that the goal line referee is standing right on the goal line, with his line of sight along it. Now some basic trigonometry should enough to convince you that, since the goalpost has finite thickness, standing here will not allow the referee to clearly see the entirety of the ball crossing the line even if it has, because his view of the ball is partially obstructed by the goalpost. In addition, because in order for a goal to be scored the ball has to cross the goal post from his line of sight, there will necessarily be a discontinuity in his view of the ball. Now he sees it, now he doesn't, as it crosses the goal line. This means, even when the ball goes in the goal, it's harder to follow from this view.

So where's a better place to stand? Closer to the fucking goal, and slightly behind the goal line, to have a better view of the ball. Standing right next to goalpost, slightly behind it, would allow the referee to rely on depth perception, instead of merely using line of sight, to see when the ball has crossed the line. This strikes me as a much better system.

As for the second point, how certain should the goal line ref be that a goal has been scored? Certainly 100% is too high a burden. I'd assume that if he was given any instruction by FIFA, it would be of the "beyond a reasonable doubt" variety, but more likely he was left to decide for himself. But of course, any close call, especially one that happens on the goal line so quickly, comes with a large degree of uncertainty. The best criterion to use in this case is a 50/50 judgment. As long as the goal line referee, who by assumption, is the best positioned to make the call, believes there is above a 50% chance that a goal has been scored, he should call a goal. My hunch is that the referee in this case maybe thought it was a goal, but wasn't sure, so refrained from calling it. What a shame! Would've made for a fine finish.

the tournament so far, quick reaction

After having seen 6/8 initial games (missed Croatia-Ireland and England-France, some initial thoughts and predictions:

1. Favorites: Spain are still my favorites to win it, but only marginally, well below 50% probability. My next pick would be (perhaps surprisingly) the Netherlands (you heard it here first!), who, after being the butchers of WC 2010 came out to play this time around. If they can build some confidence and get out of the group of death after the initial defeat, they will be formidable opponents. Technically they looked quite good and created a lot of clear opportunities. Sneijder played a really impressive game in particular. I hope van Persie can find his form again after a woeful start. Though it's just as likely he and his team will do what the great Dutch teams of the past have always done best: play beautiful soccer and choke under pressure. It will be key for them to come out in the next game and not believe what everyone said about their first game, that they played poorly and need to reinvent themselves. If they play the same way, they'll have a great chance of beating Germany and Portugal and winning the group.

 For Spain, well, they can continue to play with 6 midfielders and could even win the tournament that way with odd goals from Silva, Iniesta and Fabregas, but more likely they'll need Torres or Llorente to score at some point. Especially with Pique and Ramos not looking particularly comfortable with each other at the back (never having played together as a central defense pairing), they'll need more than the 1 goal a game that basically won them the World Cup. Not sure if that's gonna happen. On the other hand, Iniesta really stepped up as Spain's most dangerous player...if he keeps playing like that, he could be the player of the tournament and they won't need a striker.

2. Pleasant surprises: Italy held their own against Spain and are my other pick to advance from Group C. Ukraine were also impressive in midfield and attack (though perhaps not so much in defense, as they were quite lucky to escape with the victory in the end). But in a competitive tournament, home support can make all the difference. Russia also looked formidable in their first game, but the Czechs were awfully poor in defense, so I'll be watching their match closely tomorrow.

3. Disappointments: Portugal and Germany both looked lackluster. The Germans could well pull it together, but their midfield play was surprisingly vertical. Muller stuck to the right flank, Podolski to the left, leaving Oezil to be the only real creative force for them. They'll need more, particularly from Muller, to reclaim the exciting form they showed at the World Cup. I don't see the Portuguese advancing, and it'll be another disappointment for Ronaldo in a major tournament.

netherlands-denmark

The Netherlands were upset today by Denmark, despite playing well and creating some great chances. Full credit to Denmark, who took their opportunity, defended well and kept the ball when they needed to, threatening on attack throughout the second half as well. Sometimes you play well and still lose. That's football, right?

It always hurts me a little bit to see a team play well and lose, but what was really frustrating this afternoon was the inane but predictable commentary. Throughout the second half, they couldn't stop saying how poorly the Dutch were playing, how they were so uncreative and couldn't create any chances to score. Which was, simply speaking, false. This is a common mistake that people make watching soccer: they always align their opinions about how well the teams are playing with the scoreline. But the thing about soccer is, those two different aspects of a game can diverge pretty dramatically. In this case, if van Persie had brought his shooting boots, Robben or Huntelaar had converted their chances, the commentators would have been singing Dutch praises, talking about how their tactics were brilliant and how they really had the will to win. If someone had watched the game with the 30 second sequence that included the Danish goal cut out, they would have predicted that the Dutch were the ones that had scored, not the reverse.

In the end, soccer is a game not just of two teams and their quality of play on a given day, but of individual players, individual moments, and chance. People will try to construct ad hoc narratives to fit the results of matches, especially in short tournaments where every result is crucial, but these shallow analyses are an annoying disservice to the teams and players involved.

Euro 2012: it begins

Now that the dust has finally settled over the tragedy of the Champions league semifinal (and final), it's on the Euros and a chance at redemption (for the game of soccer, that is). A few things to note as the tournament gets rolling:

1. The European Championship is probably the best tournament there is, in terms of the actual football being played, given the concentration of high-level games over the course of a single month. Sorry FIFA, but the Euros offer higher quality play, with fewer teams, and all of them just incredibly good. The World Cup is great for spectacle, but the North American, African and Asian confederations still lag behind Europe and South America and dilute the overall quality of play. (The very best matches are at the club level, but are distributed sparsely throughout the season, only when the very best clubs play each other.)

2. The past four years have been the era of Spanish-style attacking football, with Spain winning the last two international tournaments and Barcelona dominating (to a greater or lesser extent) the club level in Europe. After Guardiola's recent retirement, people in the football world have been talking about how he has changed the game for the better by making the attacking, passing, free-flowing style a staple. Though he deserves enormous credit, Barcelona and Spain were already in ascendance before he took over.

One thing that has contributed enormously—but invisibly, given that no one ever talks about it—to this ascendance is the improvement in the enforcement of offsides over the past decade. People say that soccer needs video review technology. Well, video review has already made an extreme difference, just not in the way people thought it would. Several years ago I watched the 1974 World Cup final, a classic match between Germany and the Netherlands. I was shocked to find that, in those days, players were called offside on plays that, today, most people would recognize as clearly onside. But nobody could rewind the tape in those days and see what was really going on: defending players stepping up after a ball was passed to an attacker, thereby making the play look offside when in fact it wasn't. I was lucky enough to see, in the age of the emerging DVR, how often assistant referees wrongly called offsides because of the the time it took to shift their attention from the source of the pass to the player in question, combined with the flash-lag effect.

The improvement in offside calls (or, mostly, non-calls), while vastly underestimated by players and commentators alike, makes good timing and fast attacking play a much more rewarding tactical option. In possibly the greatest soccer performance of all time, Barcelona's 2010 5-0 massacre of Madrid, 3 of Barcelona's goals were barely onside. Ten or even five years ago, all or at least a couple of them would have been called back before the players even had a chance to finish, and the game would have been much different.

In both of today's matches, crucial non-offside calls played a critical role, not in the results themselves, but in the play of the match overall. In Poland-Greece, the pass that led to Greece's penalty and Scezny's sending off was a very close call, as was the Czech Republic's goal against Russia. These aren't just isolated incidents. They happen game after game after game, and they are slowly having less of a negative impact on the game.

Game on!

Big game today!!

On the eve of the crucial Champion's League semifinal second-leg, I found myself wondering last night about how much professional sporting events actually matter, for me personally, and for others more generally. Perhaps because it's an interesting question. Perhaps because my anxiety about the game today is extremely high! Will my life be awesome if Barcelona beat Chelsea? Will it really be terrible if they lose?

After all, who cares? My team wins, my team loses, life goes on, right? Right?! Does it really make a difference to my day-to-day existence whether Barcelona win the Champions League, at all? Or to anyone's, besides the players and managers, people close to them, and the people who live in the actual cities involved?

A lot of research in positive psychology suggests that people are pretty terrible at predicting what will bring them happiness in the future. Sure, I think the game today is important, but will I really care tomorrow, the next week, or the next month, if the result goes my way? Or will it be like buying an expensive car or winning the lottery, where the resultant happiness might diminish quickly and never really live up to my expectations at all?

The question calls for a bit of reflection about how past sporting events. Have they really provided any lasting happiness, or even, somewhat scarily, become a real part of my identity? My initial inclination is to answer with an emphatic yes, both for single events (Iniesta's goal in 2009, anyone?) and the longer arcs of team performances, like DC United in the late 90's or US national team in 2002. And the disappointments are salient as well, like the 1998 World Cup. How can they really feel so important, so many years later?

The answers have serious implications for human psychology and biology. Loyalties to sports teams are evidence of our clear desire to segment into groups and reinforce the differences between groups. This is most obvious in our support for national sports teams, where supporting one's country is a secondary manifestation of national identity. Support for local sports teams makes sense for similar reasons. But in the era of globalization, more and more people identify with teams on the other side of the globe, and that's where the real puzzle lies. Sometimes the choice of loyalties is arbitrary, sometimes it's not. But once we've chosen sides, we rarely change, and we seek evidence to confirm our choice in moral terms, however tenuous or dubious.

One time one of the players on my own team took this sentiment a bit too far, urging me and our fellow-teammates to focus on and intensify our dislike for the individual members of the opposing team for extra motivation. In context, this seemed reasonable: the other team really did seem like an unpleasant bunch of people. But, any one of us could have easily been on the other team (they weren't much different in background from us, and even if they were, would that make it any different?), and if we had been, we would have been saying the same thing about the players who we were, in fact, playing with and liked. Our sentiments weren't completely arbitrary in this case. It made sense to be loyal to the teammates we knew well and had forged strong bonds with; but at the same time, the circumstances for forming separate teams was largely arbitrary, a mere consequence of where we decided to go to school.

As I've argued before, outcomes in soccer games also contribute to my personal narrative about the game itself, and I'm sure this is true for many other players and fans as well, even neutrals. I really, really want Barcelona to win because their winning helps reduce cognitive dissonance I feel about the game of soccer itself. It makes the game seem relevant not only as a competition but as an art, and helps fuel my hope that it will continue to be a worthwhile artistic endeavor. For me, this is often the most important factor, and Barcelona may be the team, throughout its history, that contributes most to this narrative of soccer as a sport with artistic meaning.

But luckily, the game of soccer is unlikely to change significantly as a result of today's match. When all is said and done, Barcelona will still four of the best attacking players on the planet in Fabregas, Iniesta, Xavi, and of course, Messi. Three of them are younger than 28, and they seem unlikely to leave Barca anytime soon. Whatever happens today, they'll be back next year!!

life and tragic death of recorded music, part 2

Recently I read this lovely article (subscription required, unfortunately) by pianist Jeremy Denk in (but what else?) the New Yorker, and it reminded me to follow up on this post about recordings and music. In the article, Denk describes how the process of recording is inherently stressful and tortured, more so than performance, because of the finality of the product, as well as the expectation and possibility of perfection (in some sense, at least!).

A while after writing that last post I realized a somewhat surprising fact about the recorded music that I love and cherish: it is, almost without exception, all recorded before 1985.

math

For about half of a (school) year now, I've been teaching math at a private school in CT. How to teach math is kind of a hot topic, what with the school reform movement and the lagging achievement by Americans in the sciences. So far, I've struggled to accommodate, or consolidate, two basic philosophies about how children should learn math. It's made for quite a tumultuous experience! I'd say, on average, I spontaneously re-think the lower school math curriculum at least on a monthly basis.

On the one hand, there's the Tiger-mother-inspired, "achievement"-oriented approach to math instruction, which is based largely on the theory that kids—for the most part—learn unconsciously, and need to practice something in order to acquire a certain skill level. On this theory, math is something not to be too much enjoyed, but to be drilled and internalized. It is, in another words, a set of basic skills involving numbers and computations that, once practiced and learned, will set a solid foundation for future quantitative endeavors.

On the other side of the coin, we have the idealist philosophy on math instruction.

authenticity and performance practice, part 1?

To follow up on the earlier post about my recital.....Here are some thoughts expanded from this short introduction I gave before playing Mozart, which you can see here.

Authenticity is a problematic concept when it comes to all art. In the world of classical music, the problem is especially important to address because most of what we do as musicians is reproduce the music of others. We don't typically own, at least in a strictly philosophical sense, intellectual property over our performances, since they're written by someone else. Unfortunately, as the classical music scene struggles with evolving standards of intellectual property involving the internet and duplication, it simultaneously struggles to evolve out of an antiquated and damaging mindset involving all that music in the public domain!

It's one of those things that, if you operate outside the world of classical musical performance, you'll probably say either "huh?" or "who cares?!", and maybe you're not totally wrong. But maybe you would care more if the world of classical music performance weren't so bogged down in its silly performance practices!

Before writing anything more witty about it, I feel I have to lay down the groundwork for what I want to say.

new pieces

I recently played a recital at the Levine School of Music in Washington, DC. On the program were many of my own pieces. I had to learn them a bit too quickly for my liking, so the performances aren't exactly polished, but representative enough of the compositions that I hope you'll give them a listen if you weren't there! Here they are, with the notes I wrote for them.

Notes on the original works performed tonight:

I've been trying to compose music, on and off, since I was very young. I wrote quite a few “model” compositions—works modeled specifically after the styles of past composers—in college, but I was only ever satisfied with one of them. It wasn't until just over a year ago that I managed to compose with any consistency—or any general success (though I suppose the jury is still out in that regard). The Silent Night fantasy, which you will hear tonight, was cobbled together in two days, one year ago, in the run-up to my recital in this same hall last December, and revised this fall. The Fugue from the Prelude and Fugue in D major, after Bach was written in 2007, when I was a junior in college. The Star-Spangled Banner Fantasy was written in the last week of June, just before this year's 4th of July, while the rest of the pieces were written from September onward.

These pieces were written obsessively and unpredictably, in fits and starts. At times, I would sit down, intent on working on them, and nothing would happen at all. At other times, needing sleep, I would stay awake as long as the ideas kept flowing. All in all, (too) many of them came together in their final form about two weeks ago. You may believe that since I wrote these pieces, they should be easier for me to play, when in fact, the very opposite is true. Because these pieces have in many cases been through multiple revisions, it has taken extra time and care to delete the past versions from my memory and muscle memory, and replace them with the new ones. Accordingly, I put aside my originally ambitious plan to complement my own pieces on this program with other pieces that were new to me, in favor of some music that I'm more comfortable playing.

When you hear my music, you might miss the influence and inspiration of one “composer” if I didn't give her due diligence. Gabriela Montero is not only my favorite living pianist, but a truly brilliant composer, though her “pieces” are all improvised. Since I discovered her improvisations two years ago, they've been a revelation for me. She improvises with the skill of a jazz player, but in a huge range of styles. She can take any tune, from any time, and turn it into something completely different, all seemingly instinctively and almost without conscious thought or foresight. Her playing was critical to making me realize how rhythmic and textural variety can add so much, can indeed completely change the character, of a simple melodic or harmonic idea. She made me realize also that composing is just as much a physical act as a cerebral one. So much of the music I've written came about not from thinking, but just from putting my hands on the keys, seeing what came out, and then refining it.

The “style” of these compositions, if I may claim have the authority or perspective to comment

on them, is eclectic, but they share a conservative outlook, a debt to past styles that is extremely uncommon in modern “classical” music. A good friend of mine heard another one of my pieces (not being performed today), which I wrote and performed in June, and criticized it on the grounds that it “sounded like a hybrid of Mozart and Schubert.” My immediate thought was, that's a criticism?! But at the same time, I feel such a need to justify the existence of this music, that I suspect deep down, at least a part of me shares his criticism.

The question he raises is a serious one, and gets at the heart of what we consider the value of art. Is it, at its core, an aesthetic experience, or do we care about authenticity, about the meaning behind the experience? On the one hand, I believe that music is just music, and all that matters is how it sounds. If it sounds good, it is good, and if it sounds vaguely like Mozart or Schubert, then it's probably really good. People like to say there's no point in writing music in Classical style (capital c-Classical denoting a system of form and harmony in common practice in Europe from roughly 1750-1830) because we already have the music of Mozart, Haydn, Beethoven and Schubert. But if, tomorrow, we discovered a trove of previously unknown, mature works by any of the above, is there any doubt that they would

dominate concert programs all over the world? That if Mozart had lived another 30 years, he wouldn't have written hundreds more works that we would still be playing today? Perhaps this is an irrelevant thought experiment, mostly because I don't claim to be capable of writing music that could be mistaken for that of any of these composers. But that doesn't mean that music that sticks to old styles has to be strictly imitative. Each of the above found a way to express himself within a set of rules that gave his music structure and definition, and I think that's what all composers, indeed all artists, strive for.

That being said, only one of the pieces you'll hear tonight was conceived specifically to sound

like music from a by-gone era (the prelude and fugue that opens the second half). I haven't set out, generally, to write music in any specific style, but rather to play only that which I find good enough to be worthy of repetition. Still, the things I write have a habit of sounding as if they were written for another century, , which, at least superficially, defies the idea that music is a reflection of the culture and the times in which it was conceived. I think people who would make this claim confuse the normative with the positive, the idea that music is inevitably looking back, a reflection of its time, vs. the idea that it must be, in a predictable way, reflective of its time. Nobody in 18th century Europe knew how Classical style was especially suited to its time and place. All I can reflect on in my own music is my own philosophy regarding music; if I am so lucky, perhaps one day people will see some connection to the world in which I lived. But to me, it doesn't much matter.

Sam Post

December 20th, 2011

The Life and Tragic Death of Recorded music

I've already decided on an early New Year's resolution: listen to music. Seems so simple, right? In truth, it is deceivingly difficult, maybe impossible.

I mean, does anyone listen to music, for long stretches at a time, without undertaking any other distracting task, except in a concert setting? Put on a CD or turn on your ipod or other cloud-playing device, sit down and just listen with no other short-term goals in mind?

I suppose maybe most people never did this; certainly very few people, if any, do it today. But I used to do it all the time.