Sam's Posts

Classical music's obsession with the past

noreply@blogger.com (sam post) — Tue, 10 May 2016 19:45:00 +0000

There are some things I like about the culture of classical music, and some things I really, really don't. For instance, I love the idea that music is more than just an accompaniment to something else (like a movie), and more than mere entertainment. Though this obviously isn't exclusive to the type of music we call classical, I still see it as one of the prominent features of classical music, what motivates it and defines it, since the actual music can't really be fit into any one single category or united by any style or idea.

(Just like the music itself, it's hard to fit "the culture of classical music" into a single box, since it's different to different people. Nevertheless, I maintain that for better or worse, the common understanding of the words "classical music" in the world today is more or less a definition of a type of listening setting and a set of conventions, though these conventions aren't universally agreed on or anything like that.)

Anyway, what I don't like is that classical music tends to bring along an obsession with the past—preserving it, reproducing it, elevating it. Now, don't get me wrong, I love music from the past; how else would I have made it through 20+ years of education in Western music? There's a lot of great music out there, and I think it's well worth keeping around for the next hundred, thousand, million years.

But there's also a lot, lot, lot of music that was written in Europe between 1600-1900 (give or take), and listening to it comes with an opportunity cost of keeping up with something more current. If you try to listen to all of the music from this period, you're necessarily missing out on a lot of other music, and you're necessarily going to hear a lot, lot, lot of music that kinda sounds like Mozart, Bach, or Beethoven, except that it's not nearly as good. Like, say, this!

I didn't have to look very hard for this, by the way. All I did was go to WETA (my local classical radio station) and pick literally the first thing on the playlist for today. The rest of the list is littered with other music that, at its best, is mildly pleasant, and at its worst, is incredibly boring.

I have nothing against Carl Friedrich Abel. I'm sure he was a nice guy. I'm sure there's something interesting about him, to an academic somewhere in the world. But is this the music that people who have any sort of direction over the future of classical music should be promoting? What makes this music worth playing, worth listening to?

I understand that radio stations are playing to their audience, and that I never contribute to them. But I do believe there is some top down influence on people's preferences. (And I would contribute to the station if it weren't so terrible and made more creative selections.)

I imagine the executives of WETA claim they are carrying on a proud and longstanding tradition of a certain variety of Western music, but really they're just peddling mediocrity. What brings Abel to the airwaves is the convenient-but-not-at-all distinguishing fact that he happened to write music the kinda sounds like Mozart (if you're half-asleep) written around the same time and place as Mozart. Is that a reason to listen to a piece of music? I say no. Overall, they (institutions like WETA) make it difficult, as an omnipresent standard-bearer of classical music in the DC area to forge a future for concert music that is interesting, diverse, enjoyable, and dynamic.

(Full disclosure, they sponsor the music where I teach; obviously this post does not reflect the opinions of the school and would probably horrify them. Sorry, Levine!)

Excellent sheep in music education

noreply@blogger.com (sam post) — Sun, 24 Apr 2016 17:45:00 +0000

In 2014, a former Yale English professor published a provocative book following an essay in the American Scholar. His central idea: the elite institutions of American higher education, from high-priced secondary schools to prestigious universities, increasingly value, encourage, and churn out students who are very good at jumping through hoops on a path to achievement (so-called "excellent sheep") without engaging in real intellectual risk-taking and discovery. Though I felt somewhat differently about my own experience at an elite institution, there is one subject where I felt and continue to experience exactly what he's talking about: music education.

Music education, of course, comes in many different strains and variations, and within any system or institution there are always exceptions. But any student in a traditional classical performance program will recognize the excellent-sheep-ist attitude that propels us from conservatory preparatory programs through college and graduate school, funneling many of us (in some sense, the lucky ones) into orchestras and competitions after graduation. To put it bluntly, a traditional instrumental music education is largely and predominantly about execution as opposed to creation: how to execute precisely, exactly, and perfectly the music on the page in front of you.

Full disclosure: I am a piano teacher at a school that is very much part of the system I'm writing about, though it is better than most, and moving in the right direction. But I am part of the problem too. Another disclosure: obviously there are times and situations where execution is paramount (especially in large ensembles). But that doesn't mean it needs to be the singular focus of an education.

First, we teach children to read music and show them exactly what all the symbols mean in front of them. We teach them technique and exercises so that they have the freedom to play anything, but if that anything is written down in front of them, then we generally demand they play it a certain way.
I can hear some of my friends and colleagues crying out, "but there's so much room for creativity in different manners of execution!" And that is true, but even there the role of creativity, of personal artistic freedom, is often minimized in service to the original creator of the music.

Think I'm simplifying? Don't believe me? Let's look to some authorities of classical music. Sviatoslav Richter is widely considered one of the greatest pianists of the 20th century, and he described his thinking thusly: "The interpreter is really an executant," (emphasis mine), "carrying out the composer's intentions to the letter. He doesn't add anything that isn't already in the work." It wasn't hard to find this blog post from renowned cellist Lynn Harrell about his frustration with students' imposing—get this!—their own wills on musical performances. Other examples explicitly urging forth excellent sheep from the Internet abound.

The philosophical problem with these types of views, though dominant in the conservatory world, are several, but in practice they tend to fuse everyone's playing together, encouraging a sameness across the world of music. A performance in this view is less an act of creative expression than a fact-finding mission, a piece of detective work. Is that really what we want?

Ironically, Richter himself came up with some of the bizarre and enigmatic performances of the music of Brahms, Schubert, etc., and that's what truly made him a great pianist, at least for me. In fact, is there any artist, musician or otherwise, performer or otherwise, for whom anyone holds the highest admiration, merely for playing exactly by the rules and strictures handed down from above?
Thankfully, I've had some wonderful teachers in my own education, but I believe it's time for classical music to reckon with its authoritarian attitude and priorities. A music education should emphasize execution in the service of expression. It should include spontaneity, improvisation and creation, in addition to tradition. How to do that? Coming up next time...

Speed Reading, Chess, and Playing by Ear

noreply@blogger.com (sam post) — Sat, 16 Apr 2016 17:16:00 +0000

Recently I've taken to starting recitals by playing popular jingles from TV or radio shows. It's fun to see who else in the audience listens to Serial or NPR, or is familiar with the Champion's League theme (come on people, it may be the most widely-recognized music on the planet). Admittedly, it's also to win over the audience and impress them right off the bat, because rattling off something by ear is unusual and seldom taught in the world of (so-called) classical music and traditional music education (a topic for another time).

At the intermission of one show, someone asked me: can you play anything by ear, instantly? The answer is a definite and emphatic no, but the question reveals a lot about people's misunderstanding not just of music, but of human cognition and the limitations of memory.

People assume that playing music by ear is difficult because amateur listeners (and even amateur musicians, see: educational issues above) are not used to identifying pitches or the distances between them. Sadly for us musicians, identifying notes is only the first and easiest hurdle to clear when trying to learn music by ear. Remembering and rattling off a piece, armed only with the ability to identify pitches, would be like memorizing a poem by remembering the sequence of letters. The real problem is not identification but information reduction, taking a whole slew of sound and unconsciously reducing it to larger abstract musical components.

Think about the process you would go through in memorizing some lines of text to write out later. First, let's keep it simple, and imagine you just had to learn a single sentence, like, "What is your favorite piece of music and why do you like it?" Piece of cake, right?

But what if the line were in a foreign language that you didn't know ("Cila është pjesa juaj e muzikës dhe pse nuk ju pëlqen?" **from google translate, possibly not accurate)? In that case, your best bet would be remembering the sequence of letters that make up the spelling of the phrase. Think how difficult that might be for even a few words, how much more work, and how prone you would be to mistakes. Even worse, if you misremembered even just a couple of letters, it might distort the meaning or render the phrase completely meaningless. You couldn't remember it accurately with a single glance, even though remembering any of the individual component letters or words on their own might not be difficult at all. (In a language with different symbols, things would be an order of magnitude more difficult, though in principle the same: remembering any single letter in Arabic might not be too difficult, but good luck with a string of them).

The difference is, in your native language you don't have to remember the individual letters—or even words—that make up the phrase, but only a single concept (or two) of favorite-music-ness. If you mis-remembered the exact wording, you would still easily reproduce something that preserved the meaning ("What's your favorite piece of music and why do you love it so much?").

I was reading this morning (pretty quickly, but not that quickly) about speed-reading in the New York Times, and the problem is the same (though one level of abstraction higher). I used to think if my eyes could just move faster through text, I could read faster. But the limiting factor in reading isn't the speed of cramming letters and words into your brain through your eyes, it's remembering, keeping track of, and making sense of what your eyes are sending to your brain. Turns out, most people can only keep track of 5-9 "concepts" at a time, and so reading is really an exercise in grouping words into concepts, absorbing them, and then moving on. People who can "chunk" the most words into a single abstract idea or concept, then, will tend to be faster readers.

The go-to example in psychology textbooks is memory for chess positions. People used to think master chess players had great memories because they could remember an entire chessboard much more accurately than amateur players, but it turns out expert players are no better (or only slightly better) at remembering a randomly arranged board than amateurs. They're better with boards from real games because rather than store the pieces and their positions one by one, they store the board in relation to other "types" of positions they've seen before, and so only have to remember a few ideas, rather than all 32 pieces' positions.

I know very little about chess, so I can't really explain what those "types" are, but what I do know a lot about is music! And the process for learning something by ear is very similar, only the "types" of things you have to remember are music-specific instead of chess-specific. Identifying this pitch or that pitch from something you hear is essential, but it's only as helpful as remembering that the word "what's" starts with a w, or that white bishop is in position a6. In other words, it's a total red herring and completely misses the point. What's helpful in reproducing a musical phrase is reducing it to something close to something you've heard before and stored in memory already from hearing and categorizing thousands of times already, to a series of harmonies and rhythms and patterns that you already know.

One final story to clear up a musical misconception about absolute, or perfect, pitch. Absolute pitch is the ability to identify the pitch class of a sounded note (a, b, c, etc., basically, where it is on the piano). People sometimes think of absolute pitch as a great musical gift, and it doesn't hinder anything, but it's also, again, a red herring in terms of musical cognition. Example: a classmate who had absolute pitch in one of my music classes in high school. We were learning to identify different chord types (major, minor, etc.) by sound and by sight (hearing them or seeing them written down on the staff). Just as a point of reference, most of my beginner piano students can learn to do the sound identification task without too much difficulty. But rather than listen to the quality of the chord overall in the sound training, my fellow student would try to hear all the pitches individually, write them down, and then determine what type of chord was played by sight. In other words, instead of reducing the information, she was multiplying it! Like a great speller declaring, "I'll remember the phrase 'what's your favorite piece of music and why' by spelling it out each time, rather than storing its meaning." Moral: absolute pitch plays little to no role in musical memory since it generally doesn't help reduce information at all.

And even relative pitch (the ability to identify relationships between two pitches), while important and more valuable than perfect pitch, is only the first small step in learning to play by ear, since it, too, only aids the identification of pitches, but not necessarily the ability to store and remember those relationships.

Trump Appealing to Broad and Diverse Coalition of Assholes, Survey Shows

noreply@blogger.com (sam post) — Mon, 24 Aug 2015 07:36:00 +0000

Although many have "drawn comfort from the belief that Donald J. Trump’s dominance in the polls is a political summer fling", a new analysis shows that he is building a broad and diverse coalition of douchebags, jerks and straight up assholes to maintain his position at the top of the Republican primary field.

Trump draws enthusiasm from people of varying ideological, political and demographic backgrounds, but the data suggest his supporters do in fact fall squarely into one category: total dicks.

Republican Party strategists are particularly impressed at Trump's ability to unite this emerging and powerful voting bloc. "Sure, we're been courting the asshole vote for years," said one Republican insider. "But with his wishy-washy attitude toward attacking defenseless homeless people, Trump is setting a new bar."

Carl Tomanelli of Londonderry, N.H. counts himself among Trump's supporters. "People are starting to see, I believe, that all this political correctness is garbage," he said. "I think he’s echoing what a lot of people feel and say." Added Tomanelli, "And by people, I mean, you know, sexist and xenophobic jackasses."

Lisa Carey said, "As inappropriate as some of his comments are, I think it’s stuff that a lot of people are thinking but afraid to say. And I’m a woman." Continued Carey, "And, as you can clearly tell, I've thought through the consequences and wisdom of having the man responsible for the safety and well-being of over 300 million citizens casually blurt out the inappropriate things that other people are thinking."

In general, Trump's women supporters cited his willingness to be a total douche toward Mexicans as paramount to any policy concerns, while his sexist male enthusiasts pointed to an egregiously demeaning attitude toward women as key to their unconditional support.

Study: literally looking at a single pie chart increases support for action on climate change

noreply@blogger.com (sam post) — Thu, 13 Aug 2015 18:40:00 +0000

Ah, climate change policy. Forever frozen in a political standoff, impossible to move toward a consensus. Or is it?

Today I came across this study on PLOS via a link from the Times. As with most scientific papers, the core message is obscured by technical details and jargon (Gateway Belief Model??), but the takeaway is simple and powerful: inform people of the overwhelming scientific consensus that human-caused climate change is real, and their belief in that consensus, along with support for public action, increases. Democrats and Republicans alike. Voila!

The method of the experiment, likewise, was really basic. Step 1: ask people what their estimation of the state of the scientific consensus is around climate change (only 12% accurately put the consensus above 90% on initial questioning) along with a few other simple questions—whether they're worried about it, whether they support public action, etc. Step 2: inform them of the actual scientific consensus (via one-sentence script, pie chart, or convoluted metaphor). Step 3: repeat step 1.

I'm surprised this paper hasn't received more press, precisely because most of what you read about political opinions (not that this issue is actually political, of course!) suggests that you can't change people's mind on charged topics: people filter new information to confirm what they already believe and even harden their views in the face of conflicting evidence. I feel like I'm constantly barraged by articles in the media about the impossibility of shifting anyone's attitudes on any important, consequential topic by supplying information.

Take this recent example of an experiment about people's attitudes toward gay marriage. The study got a ton of attention because everyone was so shocked that talking to people (appeared to) succeed in shifting their attitudes on gay marriage. This American Life did a whole show about it! The study's conclusions were also really narrow: only protracted, personal and empathetic conversations were effective in changing people's views (as opposed to reading a prepared script or set of facts). Furthermore, it turned out the entire dataset was fabricated, so it's possible no one's views changed at all.

That's why this climate change study is really encouraging, and kind of shocking. Caveats: it's just one experiment and the results, while robust, are modest (4 point mean increase in people's belief, on a scale of 1-100, that humans are causing the climate to change, and 1.7 point mean increase in people's belief that people should be doing more to reduce climate change). Still, that's pretty good for one sentence, pie chart, or metaphor.

What's going on? Are people more open to new facts and shifting their views than previous research suggests, or is climate change different from other political issues associated with complete and utter intransigence like abortion, evolution in education, gun control, etc?

I'm guessing it's a little of both, but mostly the latter. Unlike abortion, evolution, or gay marriage, climate change denial isn't a result of core philosophical or theological beliefs, even loosely defined. It's not even a longstanding political divide (the first President to propose cap and trade climate legislation was George W Bush). Which suggests that elite political opposition to climate change policy, far from an inevitable result of climate change denial, may actually be a principal cause. That, at least, is the simplest explanation for people's ignorance of the scientific consensus in the first place.

So, ya know, in case you were wondering:

Serial's fallacies and how we fell for them

noreply@blogger.com (sam post) — Fri, 19 Dec 2014 15:50:00 +0000

At the beginning of Serial, Sarah Koenig and Ira Glass convinced me I was in for a wild ride. I was supposed to live Koenig's back-forth-experience of doubt and conviction. Adnan is innocent—no, he's guilty! Every episode, a new telling clue, a new revelation!

Little did I know Koenig and her producers had no idea how to incorporate new evidence with their prior beliefs. They fell prey—repeatedly—to the prosecutor's fallacy, giving undue weight to new discoveries, trying to pull us along as they changed sides again and again. Unfortunately for them, the basic story never changed. At the beginning, there was no physical evidence against Adnan, and the whole case against him came down to Jay's credibility. In the end, there's no physical evidence against Adnan, and the whole case against him comes down to Jay's credibility.

Whenever Koenig was convinced of his innocence, something new—the Nisha call!—would change her mind. When she was almost convinced of his guilt, something different—the Aisha call!—would change it back. In the last episode, my frustration reached its peak when Dana—the "logical" one—summed up her understanding of the case with one telling instance of the prosecutor's fallacy. She argued that, despite the utter lack of evidence incriminating him, Adnan most likely killed Hae because the string of events that took place on the day of Hae's disappearance just make more sense that way, and are so unlikely if Adnan is innocent. I mean, if there's only a 10% chance that all of those unlucky coincidences would happen in the case of Adnan's innocence (the Nisha call, lending Jay his car and phone, asking Hae for a ride), then that means there's a 90% chance he did it, right??

Wrong. Turn that same argument on someone who wins the lottery. It's immensely unlikely, after all, for someone to win the lottery. But maybe she cheated. She's much more likely to win by cheating! There's only a 1/1000,000 chance of winning in the case of not cheating, so clearly, cheating is the more "logical" explanation.

The problem is with treating new pieces of evidence—winning the lottery, potentially unlucky coincidences—in isolation, rather than weighting them by prior likelihood. Yes, one is more likely to win the lottery by cheating, and yes, the Nisha call makes more sense if Adnan is guilty, but the prior probabilities in this case—of cheating at the lottery, of Adnan committing murder—are low. And that's what Koenig was missing throughout Serial, at every turn, in weighing evidence for or against Adnan.

And of course, there's a foolproof way to incorporate new beliefs with old ones: Bayes' rule, the most misunderstood of mathematical truths.

Or

For instance, consider Dana's mental calculation at the end. She's looking at these coincidences more or less in isolation, as if they make up most of the case against Adnan (which, aside from Jay's questionable testimony, they kinda do). That is, she's considering the probability of Adnan's guilt (A) given the coincidences (B). Dana incorrectly equates this probability with P(B|—A), probability of B given not A, or the probability of those coincidences, given that Adnan is not guilty, which is of course low. Let's say 10% for the sake or argument. But as you can see, the two things are just not equivalent (this is the prosecutor's fallacy, more or less).

Let's estimate the other quantities reasonably. Let's imagine P(B|A), the probability of all of these unlucky things happening in the case Adnan is guilty, is high, say, 70%. (I wouldn't say 100%, even for the sake of argument, because why would Adnan call Nisha in the course of a murder?? All these things happening together is unlikely, even if Adnan is guilty).

Then there's P(A), the prior estimation of probability that Adnan murdered Hae, before we consider the evidence at hand. This has to be low, because Dana is using these coincidences to weigh Adnan's story against Jay's. And aside from that story, what reason do we have to believe Adnan committed the murder? Not much. So let's say this is 20% (still an overestimation, as well, I would say).

This leaves P(—A) = 1 - 20% = 80%, and our calculation is: (.7)*(.2) / [(.7)*(.2) + (.1)*(.8)] = .64

After weighing the evidence of these coincidences, our subjective probability that Adnan is guilty goes up, as we would expect. But not as high as we would think. Definitely not to 90%, as Dana kinda-sorta-implies but without any numbers. And I would argue that the 10% for P(B|—A) we chose was too low anyway, since we know Adnan had other potential reasons for lending his phone and car to Jay, and we know there are other possibilities for how the Nisha call could have happened. (And I don't know why they kept considering the cell tower evidence, since my understanding is that the tower just isn't that closely related to the location of the call).

This same process seemed to take place over and over again in Serial. Something new would come up, and Sarah Koenig would overstate its significance. Adnan stole money from the mosque: maybe he has the personality to commit murder. Aisha called Adnan when he was high at Jen's house: Adnan had a reason to be acting scared of the police. These may have made for compelling drama early on, but ultimately, turned Serial into a frustrating experience, because after the first few episodes, nothing of any substance happened or changed. The case against Adnan was comically thin all along, and the producers of Serial failed to break the story down much further than that.

In the end, it all came down to your P(A), your estimation of the prior likelihood of Adnan committing the murder after considering the basic evidence, and so everyone's opinion pretty much lined up with whom they believe more, Adnan or Jay. And in that sense, the whole series was a massive exercise in confirmation bias.

Dick Cheney to Senate: Nobody Out-Evils Dick Cheney

noreply@blogger.com (sam post) — Tue, 09 Dec 2014 18:51:00 +0000

In scathing comments regarding the recently released Senate Intelligence report on the CIA's torture of detainees, Dick Cheney lambasted the committee for ignoring his "singular role" in creating "the policies, culture and dubious legal cover" for the CIA's interrogation techniques.

While the report contends that CIA interrogators acted without authorization and outside the legal bounds of the programs approved by the Bush administration, Cheney insists that he was behind the torture of the terrorist suspects all along. "This idea that detainees were waterboarded, deprived of sleep or subjected to 'rectal hydration' without my knowledge is absurd, since everyone knows I practically invented rectal hydration," said Cheney.

Insisting that he would have "personally waterboarded every detainee in US custody, guilty or innocent," Mr. Cheney dismissed the claim that the CIA acted as a rogue agent in the aftermath of the September 11th attacks.

"Look, I think it's become pretty clear the most outrageously terrible ideas from the last Presidential administration were my idea. Nobody at the CIA could have come up with anything this ill-conceived and ineffective," said the former Vice President, adding, "Nobody out-evils Dick Cheney."

Newly Discovered Fossil—and Science—Could Prove Problem for Creationists

noreply@blogger.com (sam post) — Fri, 07 Nov 2014 16:46:00 +0000

As the Washington Post reports, researchers have discovered a fossil that they claim—along with the entirety of the scientific literature of the past 150 years—could be a headache for Biblical Creationists.

The new fossil may, along with multiple lines of converging evidence from fields as diverse as paleontology, biology, astronomy, genetics, physics and geology, finally provide strong evidence against the hypothesis that the world was created in its present form as little as 10,000 years ago.

"Sure, we have plenty of evidence from carbon dating that the earth is billions of years old," said lead researcher, Ryosuke Motani. "The theory of continental drift makes it pretty clear that the earth has changed quite a bit over that time. Once you get into the biology, you've got evidence from molecular genetics, comparative anatomy of homologous traits, not to mention the distribution of various branches of the tree of life around the globe, to name just a few."

Added Motani, "but until today, we didn't really have a smoking gun."

Multiple scientific observers have expressed hope that, along with many cases of observed evolution in nature and in laboratories, and in addition to numerous already-discovered fossils that appear to be the intermediate stages between marine and land-dwelling animals, the newly discovered fossil will be the straw that breaks the camel's back in the Creationists' argument.

"We truly believe that Creationist fundamentalists the world over will finally yield on this," an assistant researcher said. "...especially after they consider that nothing in the last century of scientific investigation has produced any shred support for their hypothesis."

A spokesman at the Creation Museum in Petersburg, Kentucky said they will take a "very close look" at the group's forthcoming research paper before deciding their next move.

Podcast! The Music Post is here

noreply@blogger.com (sam post) — Mon, 20 Oct 2014 16:40:00 +0000

The Music Post is here! It's a podcast dedicated to discovering what makes great music great.

Listen to the first episode above, or right click here and select "save link as" to download directly.

You can also find episode two and all future episodes here, and subscribe on iTunes here.

Should be available for subscription on iTunes within a few days!

Okay, now why would I do such a thing?

In the past five years, I've played a lot of performances, and received a lot of feedback from audiences. A fair amount of this feedback comes in the form of praise for the feat of performing, things like "That looked so difficult" or "I can't believe you memorized that whole piece." Of course, I appreciate this type of praise, but as a musician, it's definitely not what I'm going for, because music, after all, isn't a sport. It's art.

What I'm really shooting for in a performance is to have the audience fall in love with whatever I'm playing, to seek it out. I know I've really, truly connected with an audience when people say something more like "That piece was so great! Where can I listen to it again?"

Even more effective than simply playing, I've found that walking people through a piece, pointing out features and motives, beautiful moments, is the surest way to get them to connect with it and seek it out later. Even more so than my playing, people appreciate these mini-explanations of the music I'm playing (or at least, that's what they claim!), telling me they've never been able to listen more closely or more attentively.

So I figure why restrict that to the recital hall? It scales perfectly well to a podcast, where you can listen while you drive, cook, or get ready for bed.

Hope you enjoy!

Art of Fugue, cont'd: which instruments?

noreply@blogger.com (sam post) — Tue, 07 Oct 2014 01:33:00 +0000

Of the many mysteries surrounding the Art of Fugue, perhaps the most practical regards the instrumentation: Bach leaves no indication of what instrument(s) he had in mind in composing the piece. Perhaps it was just an oversight, or perhaps he thought it was so obvious, he didn't need to even write down the instruments. More likely, though, Bach was purposefully evasive and ambiguous, leaving the door open for numerous readings.

There's evidence to support multiple sides of the debate. The piece is written entirely in "open score," instead of on a grand staff as was most typical for keyboard music. On the other hand, various details suggest that Bach heard it on a keyboard (the fact that it's possible to play). For many people, Bach’s failure to explicitly commit to an instrumentation—along with his failure/reluctance to indicate tempos/dynamics/phrasings in the vast majority of his compositions—is a weakness or an unfortunate omission, opening this work, and all the works of Bach, to “wrong” interpretations and gross manipulations.

But for me, it’s a strength, and maybe even a sign of Bach’s foresight and growing wisdom in his old age. Why commit his final masterpiece to any single instrument or ensemble when the world of music is always changing, adapting to new trends? If a piece is to be timeless, it should adapt too, and this is exactly what the Art of Fugue, and all of Bach’s music, has aged so magnificently well. It’s the difference between “No state shall discriminate on the basis of race” and “No state shall deny its citizens equal protection of the laws.” The former may have been essentially what the drafters of the 14^th Amendment had in mind, but it would have been overly rigid, with no room for an evolving standard of equality.

Questions of history and constitutional law aside, though, the practical question remains: what instrumentation best suits this piece? Few works have been the subject of more variety of interpretation. You can hear the Art of Fugue played on piano, harpsichord, organ, harmonium, string quartet, brass quartet, and recorder quartet, guitar and trombone duo (seriously), among others.

The advantage of the quartet versions is obvious: each player can give his full attention to a single voice, giving them each an independence that should—in theory at least—be impossible for a single keyboard player to execute.

On top of that, compare moments like 0:38 in the video below to 0:34 in the video above. On the piano (though not the organ, to be discussed next time), you can't sustain notes. Once you play a note, it immediately starts to disappear. This is a huge disadvantage, in general, but even more so in the Art of Fugue, in places like this one. This moment brings back the main theme for the entire piece in a soaring soprano line, but on piano, it can be a little, well, disappointing.

Then again, what we gain from hearing from four instruments' individuality and attention, we can easily lose in unity of vision and overall coherence. It's mighty difficult for one person to keep track of four voices, but at least that person is in full control and able to present one single vision of the music in question.

And then there’s the inescapable fact (for me, at least) that this music just doesn’t quite sound right played on strings or brass instruments. The main difference is in the quality of articulation on these instruments vs the piano, harpsichord, or organ. On the latter instruments, it’s impossible to play with a true legato, or smoothness between the notes. Every note is marked by a clear and definite beginning, unlike in string instruments (where the bow can continue moving between notes), or winds and brass (air keeps flowing). This fact is something we pianists work incredibly hard to overcome or compensate for, but it’s this place in between, the illusion of legato that’s not quite there, that makes our instrument perfect for contrapuntal writing. The quick-moving notes in the string parts have to be separated to be heard at all, but as such, they're too articulated, where on piano they can be with a more singing quality.

There are lots of other considerations, of course, and it depends on a lot on which number of the Art of Fugue we're talking about, as well as who exactly is playing. But perhaps not surprisingly, as a pianist, I think this music sounds best on a keyboard (and apologies to all brass player friends, but the brass quintet just doesn't work, at least not the one I linked above). But where I’m firmly convinced that much of Bach’s keyboard music sounds best on piano, specifically, I can’t say I’ve come to the same conclusion for the Art of Fugue. More on that next time.

For the record, this is my favorite non-keyboard version yet:

The Hypnosis of Bach's Art of Fugue

noreply@blogger.com (sam post) — Thu, 25 Sep 2014 16:32:00 +0000

A little over a year ago, I was driving along unsuspectingly when I switched on the car radio. Immediately I was taken, entranced by the incessant, interwoven lines of a four-part fugue played on the organ. I knew it could only be Bach, and moments later, when the original theme emerged in sustained and soaring whole notes in the soprano line, I knew it was from the Art of Fugue. Somehow, I had never heard any except the first, second, and fourth movements, or "Contrapunctuses," from one of Bach's last, culminating masterpieces. Sitting in city traffic is not usually the time or place we associate with profound experiences, but such was the power of Contrapunctus 9—and of Glenn Gould's playing—that I'll never forget those few minutes.

I went home and listened to more of the same recording, and was shocked at what I'd been missing. I know a lot of Bach's music, and have been lucky enough to perform a good chunk of it as well: the Well-Tempered Clavier, many of the dance suites, the Italian Concerto. When I played the Goldberg Variations, I kind of thought I had conquered the most difficult, the most complex, the pinnacle of them all. Little did I know the Art of Fugue is like the Goldberg Variations on steroids. In the words of Angela Hewitt, "it makes the Goldberg Variations sound like child's play."

So when a fellow pianist proposed last spring that, together, we learn the whole thing, I enthusiastically-and-somewhat-naively accepted the challenge. Over the next month, I'll attempt to describe the piece and my experience grappling with, learning, and playing it.

These pieces are different from anything Bach wrote. They are beautiful, yes, and they can entertain, certainly. But at their best, they overwhelm, they awe, and they mesmerize.

Of course, if you don't know this music, what are you waiting for? Go listen!

The whole project consists of eleven fugues, plus four canons, plus six more "mirror" fugues, plus the final, colossal-yet-tragically-unfinished quadruple fugue, all labeled with the somewhat more generic Latin "Contrapunctus," for "counterpoint."

Why the obsession with fugues? Bach was the unquestionable master of counterpoint. No one has been (or will for all eternity be) able to combine music of multiple independent parts to better entice and challenge the human brain. That's why listening to Bach's music can sometimes be "difficult": there's usually no one thing going on (no "melody") that draws your ear to the exclusion of other parts of the music; there is, rather, a bunch of melodies all at once, constantly vying for your (and the poor keyboard player's) attention.

But the payoff is enormous. To the extent that our enjoyment of art comes from subtly recognizing patterns, contrapuntal music provides a whole layer or dimension on which to built those patterns. And fugues—pieces defined by one (usually) to a few recurring musical ideas, twisted and transformed to varying degrees of recognizability—provide the perfect medium for a true craftsman to demonstrate his mastery of counterpoint. And Bach was the greatest craftsman of all.

The first fugue is smooth, filled with a feeling of emptiness and desolation. It never departs from the key of d minor yet never stands still, continuously in flux, with no clear structural boundaries or moments of repose. It is in one sense the simplest piece of the whole set, yet it is mysteriously elusive. Whereas the other fugues will draw heavily on increasingly elaborate technical feats of fugal style—stretto, inversion, augmentation and diminution—as well as an elaborate chromaticism that was a hundred years ahead of its time, this fugue is propelled by nothing more than its simple subject, which serves as the inspiration for all that follows.

After that, the the music grows in technical and harmonic complexity, as well as sheer density, culminating—at least temporarily—in the obsessive, relentless and truly manic Contrapunctus 11.

The four canons and six mirror fugues are even more esoteric in style, but underscore Bach's incredible ability to mold his music to his thematic ideas. (The mirror fugues, by the way, are kind of exactly what they sound like: each has a right-side-up version, and an upside-down version, to be presented separately in their completion...pretty incredible!).

But none of them matches the dignity, solemnity and profundity of the final fugue (Glenn Gould's all-time favorite, by the way)....

Perhaps it is not the easiest piece to become acquainted with, and doesn't exactly make for easy listening. But be careful: the Art of Fugue is apt to consume you as it has done for me over these past couple of months. And the best is yet to come!

Alex Ross Missed the Point

noreply@blogger.com (sam post) — Tue, 09 Sep 2014 15:16:00 +0000

Having just read Alex Ross's typically eloquent essay from last week's New Yorker (hoping my opinion is still relevant a week later), I can't help but wonder whether he's missed the point.

Ross talks about the joys of scanning his collection of CDs, of reading the old liner notes, of the personal connection he feels to each recording by virtue of its real, physical existence. He laments the economics of online streaming, where royalty payments are so pathetic, only the artists who have no need for them can hope to earn anything from them. (Aside: I was legitimately excited last month when my Spotify income surged to $1.95.) Certainly, he realizes that not everyone agrees: "If I were a music-obsessed teen-ager today, I would probably be revelling in this endless feast, and dismissing the complaints of curmudgeons."

But the problem of the cloud reaches deeper than Mr. Ross realizes. All nostalgia and ethics aside, listening to music from the cloud changes the perceptual experience of listening. Technology has shortened and divided our attention in many ways, and listening to music is no exception. And that's bad news for classical music in particular.

CDs, LPs, and cassette tapes: music in these forms is (or was) a commitment. You made a decision to buy a recording and spent your hard-earned money on it. Any time you wanted to listen, you had to decide that you would listen, what you would listen to, and physically go through the motions of starting some sort of listening device, while remaining in the same place for the duration of the recording. Listening was expensive, not just because it cost money, but in the cost of setting it up and parking yourself somewhere to hear it (or carrying around a massive portable player).

One of my very first recordings was a cassette of the Bach inventions. Cassettes were terrible, of course, but they were great because I couldn't skip ahead in the tracks: they forced me to listen all the way through.

At that point I probably only had three of four classical recordings to choose from (along with a handful of Madonna and Alanis Morisette tapes). Every time I bought or received a new CD, it was an event! I always listened religiously until I knew the new recording inside out.

Sometime in middle school, I jumped on board the technological bandwagon (at the time, this consisted of acquiring something called a "MiniDisc") that allowed me to splice different parts of different CD tracks together. I thought this was great! I could finally take my favorite moments of every piece of music and listen to them next to each other, basking in the continuous ecstasy of musical climax after climax. But of course, things didn't work out that way, because a musical moment's power comes with context. Much of the power of the end of Beethoven's 7th Symphony, or Mahler's 2nd, or any piece, comes from all the buildup before it, and trying to cheat my way to that kind of musical epiphany was shortsighted and naive.

In college, I swung back in the other direction. Having bought a record player and inheriting a bunch of my parents' old records, it was like elementary school all over again, and I could listen for long stretches of time. Maybe listening to LPs was a waste of time at a university (sorry parents!), but once I went through the tiresome routine of removing a record, cleaning it, and putting it on, I was certainly going to try my best to enjoy it and absorb everything it had to teach.

Listening today takes neither time nor money. MiniDiscs never rose to popularity, but what replaced them is more efficient and much easier to use (and much, much cheaper). On its face, this seems great! I doubt I ever would have bought six different recordings of the Marriage of Figaro, but I do have them all in my Spotify. But every time I want to listen to something new, the number of choices is mind-boggling. And humans don't always deal with choices intelligently. If I don't like something new right away, I don't usually follow through and listen to it again, the way I always would with a new CD, until I was absolutely sure I didn't like it.

Streaming makes it easy, too easy, to listen to music. We can listen any time, anywhere, for whatever tiny duration we choose, without taking our attention from whatever other task we might be engaged in. If you're listening to Ke$ha and Taylor Swift, that's probably okay. Pop music can survive a five minute attention span. But "classical" or "art" music requires sustained engagement and attention in order to be fully appreciated and understood.

Cloud listening has the potential for good, but it doesn't lend itself to true listening. Unfortunately, that's what classical music depends on. The only solution: fight back against our habits!

teaching backward, calculus, part 1

noreply@blogger.com (sam post) — Fri, 23 Nov 2012 22:14:00 +0000

Some (admittedly limited) experience teaching math and physics in high school has led me to believe that the standard approach to teaching calculus is misguided. The way we typically teach math, the solutions all come first, and then we teach students why those solutions exist. But problems always precede solutions in real life. Why not in the classroom?

Calculus was developed as a solution to a very specific problem: the motion of objects through space. Though its applications range far beyond that problem, that original problem remains by far the best way to approach calculus since everybody already has intuition and experience with moving objects.

In a better world, then, calculus will always be approached from a physical perspective, since everyone already (sort of, at least) understands how things move around. Here's how. [This is, incidentally, what I did in the first day of AP physics class, but as you'll see, it's not terribly complicated, and (hopefully) most anyone can follow it.]

Imagine you're standing around with a stopwatch on a road that conveniently has length measurements posted all along it, and a car drives past you. Your task is to measure how fast the car is going the instant it passes the mark that's right at your feet. How do you do it?

Well, speed is just a measure of how far the car goes in some unit of time, say, a second, so you can just start your watch as the front wheels pass the mark by your feet, and then mark off where the front wheels of the car are when the watch reads exactly one second. (We can ignore the fact that, perceptually, this might actually be a difficult task...imagine you have some helpers or something). Let's say it's gone 10 meters, as marked on the road. Then it's speed is just 10 meters / 1 second=10 meters per second. Right?

Almost. What you've measured is the car's average speed over one whole second. But remember we want to find the speed of the car the instant it passes by your feet. Let's say it passed you by quite slowly but then managed to speed up incredibly quickly and travel 100 m by the time your stopwatch reached the one second mark. You wouldn't conclude that it was going 100 meters per second when it passed you.

So, you say, okay, let's not measure the distance it travels in a whole second after it passes me, as it can speed up, slow down, and do all sorts of crazy things in that time! Let's measure the distance it goes in just a tenth of a second!

This approach will have the same problem, but it's definitely getting us closer to what we want. The car can speed up or slow down in a tenth of a second just as it can speed up or slow down in a whole second, but it can't speed up as much! What you'll end up measuring though, is the average speed of the car over one tenth of a second. That's probably closer to the speed we're looking for.

Okay, so make it a hundredth of a second, or a thousandth! Well, you're getting the idea. No matter how small you make the time interval over which you're measuring, the car will always move some finite distance over that time interval. You can basically think of the speed as the distance you travel in some tiny time interval, divided by the time interval. If the car goes 10 millionths of a meter in 1 millionth of a second, then it's speed is very well approximated by .000001 meters/.0000001 seconds=10 meters per second.

[Now, if you want to be more precise, the above definition of speed doesn't quite cut it (but it's close enough, so you can probably skip this paragraph). Really, you take all these different tiny time intervals, say a thousandth, a millionth, a billionth, and a trillionth of a second, and mark off where the car is after each time interval. You find the average speed associated with each time interval as we did above for one second and one tenth of a second. If they're the same, great! You're done. That's your speed. But even if they're different, you'll notice that as you make the time interval smaller and smaller and smaller, the speed you calculate will get closer and closer to some value. That's the speed.]

Congratulations, you now more or less understand the idea behind the derivative—one of calculus's two essential ideas! In this case, what we were looking for was the speed. But here's how we found it: we took the change in position (how far the car moves) and divided by the time interval, meanwhile shrinking the time interval so that it was arbitrarily small. In math jargon, this looks like

where x stands for position, t stands for time, and the Greek letter delta means "change in." This, then, we re-define as the derivative of position with respect to time. We solved our problem, and we generalized our solution to a definition, which will be very useful later on!

In the next post, I'll discuss the standard approach to calculus a little more thoroughly.

No, the electoral college is not a good system

noreply@blogger.com (sam post) — Tue, 06 Nov 2012 17:59:00 +0000

Oh come on, obviously you can't think about anything but the election today anyway! You might as well keep reading, even though you probably already agree. Do not be attempted to check nytimes or cnn, as the election results are still not in. And don't worry, Fivethirtyeight still has Obama above 90%.

Anyway, yesterday, courtesy of Sarah (hi Sarah!) I was pointed to this interesting argument in favor of the electoral college (update! see this one from today in Slate, especially point 1 which is basically the same as the previous link). At first it seemed persuasive. But then I realized the entire argument rests upon a basic flaw of sampling and statistics!

Weingarten says that a close election in 1 or 2 states is a manageable disaster, but a close election nationally would be an unmanageable disaster because every vote would be contested, not just every vote in FL, or every vote in OH, or whatever. This is an appealing point—it would be a nightmare if the campaigns were suing for votes all over the country—but it ignores the fact that the likelihood of a close and contestable election in the statistical sense (explained below) decreases sharply with the number of votes cast. A 0.5% margin of victory nationally is equally likely to, but much more robust, than a 0.5% margin of victory in any one state. A more precise formulation of this same idea: if a candidate wins by 0.5% in a single state, it's much more likely that his victory in that state is a result of random vote-counting errors than if the candidate wins the national popular vote by 0.5%.

How much more likely? It depends on the relative size of the state vs. the national population, but the general relationship is that the statistical robustness of a given margin of victory grows like the square root of the sample size. So if a state has 1/100th the voting population of the country as a whole (like, say, CT), then a given margin of victory is equivalent to a national margin of victory that's only 1/10th as large (since 10 is the square root of 100).

The margin of victory of Florida in the 2000 election was about 500 votes out of over 5 million, or less than 0.01% of the total votes cast. In order for a national victory in the popular vote to be as narrow statistically, it would have be a margin of less than 0.002%, or just 3000 votes out of about 140 million. Although one Presidential election has been this close (1880), it was way back when the population was much smaller, and that election was dubious for lots of other reasons. And no other popular vote result before or since has been anywhere near as questionable. In general, it remains true that the chance of a close election in one or more decisive electoral states is much more likely than the national popular vote being similarly questionable. Therefore a national popular vote is a much more reliable way to arrive at a clear, decisive winner.

Weingarten's other argument is that the electoral college ultimately legitimizes the electoral process by amplifying the margin of victory, since the winner typically wins a much larger fraction of the 538 electoral votes than of the total votes cast. But this contention seems neither desirable, nor true for any election that's close enough for it to really be an issue. Again, think back to the election of 2000. In that year, the election went to Bush by a mere 537 votes! Does that really legitimize the electoral process? No, it makes it seem incredibly arbitrary, because a national popular vote victory will simply never be that close!

Of course, as far as I know, no state has ever been decided that narrowly either, and so it was probably a one-time fluke as well. But the basic point remains: a narrow-enough margin to be dubious in a decisive electoral state is more likely than a narrow-enough margin nationally, because of the much bigger vote sample nationally.

And then there's all those other traditional reasons to dislike the electoral college. But I won't get into that.

Time to call some Ohians!

Teaching Backwards

noreply@blogger.com (sam post) — Mon, 29 Oct 2012 22:54:00 +0000

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

noreply@blogger.com (sam post) — Mon, 29 Oct 2012 18:22:00 +0000

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

noreply@blogger.com (sam post) — Thu, 28 Jun 2012 04:32:00 +0000

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?

Well, if we can accurately predict the number of goals in a match with a weighted coin experiment, then clearly we’ve formed our opinion about the nature and flow of the match, somewhat falsely, based on the final score. We wouldn’t congratulate a coin tosser for getting 10 heads in 90 minutes with the weighted coin, would we?

Now I’m not trying to say that this is completely true, that soccer is purely a game of chance, nor does what I looked at (so far) say anything about the relative share of the goals for the two separate teams. Nevertheless, the results are suggestive of the “over-attribution” effect I pointed out in an earlier post: people think that teams who score goals played well and vice versa, even in the face of lots of conflicting evidence.

Now for some basic probability. (Skip if you’ve ever taken statistics, or are bored.) The number of heads in our little experiment (or goals scored in a real match) is of course is a fixed number. Toss a coin 90 times (once for each minute of the match), and get heads once, or twice, or zero times, or ten times. If you perform this experiment a billion times, you won’t get a single result, but a billion results that we call a distribution the number of heads: maybe 10 million zero’s, 20 million one’s, etc. The fraction of the time the experiment resulted in zero, one, or two heads , etc. is a good estimate of the probability that you would get that number of heads in any single experiment.

Luckily we don’t have to really do all that work tossing coins, ‘cause someone worked out the math for us! If the coin has a fixed probability of landing on heads on each toss, we can calculate the probability that we will get zero, one, two (etc.) heads in an entire match using a common probability distribution for rare events (the Poisson distribution).

We can test, then, whether a sample distribution of goals in soccer matches matches the Poisson distribution. Long story short, it does. Very well, in fact! As samples, I used each of the last six seasons of the English Premier League, individually and compiled into one sample (that's 2280 matches), and each of the last 3 World Cups and European Championships (collectively, for a representative sample). Each sample matches the Poisson distribution—the same one that we would get with a weighted coin, remember—extremely well!

There are other intriguing and unexpected results, however. For the English Premier League seasons, one fact jumps out from the data: the number of 1-0 games is massively over-predicted by the probability model, meaning that a first goal in a game actually makes a second goal much more likely. This result is true for each season individually and is also statistically significant.

As you might guess (and as I hypothesized), this is not true for international tournaments like the World Cup and European Championship, where 1 goal games are slightly but not significantly underpredicted.

The larger point remains, though, that soccer is a probabilistic game. I wish that it had more chances and more goals. An important effect of the probabilistic nature of soccer, which I’ll have to expand on another time, is that the randomness in goal-scoring also affects the randomness of the outcome, or result, of the match.

Now there’s a lot of other stuff to do with this statistical modeling. Here are some other ideas. First, is this effect unique to soccer? I would guess that hockey follows the same distribution, but baseball does not.

The next thing to look at, though, might be the effect that the first, second, or third (etc.) goal has on the result of the match. ESPN is fond of showing us idiotic statistics like the fact that the team that scores first has a great record in Euros, or World Cups, or whatever. Of course! In a game with so few goals, every goal matters. It would be much more interesting, in an ongoing 1-0 game, to show us the record of the team that scores second, since it is also extremely good. 1-1 game? Then show us the record for teams scoring third! My next question would be whether the first/second/third goal matters more than the simple probability model would predict. These are more interesting questions, I think….and also harder to gather and analyze data for, unfortunately…we'll see what I can do.

more thoughts on euro 2012 houghts on euros

noreply@blogger.com (sam post) — Thu, 28 Jun 2012 04:24:00 +0000

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.

With that in mind, Del Bosque would be crazy not to start Pedro in the final instead of Negredo. He may not have as much of an impact as a starter as he does coming on in the 70th minute, but he's been excellent both times he's played, and was by far Spain's biggest threat today when he came on (along with Navas), giving them a huge edge in extra time. The 90 minutes, and especially the second half, were pretty woeful for Spain on the whole. Pedro and, to a lesser extent, the other two substitutes, really changed that.

Let's hope Germany and Italy both play as well today as they did in their quarterfinals. Could be a great match, or at least, a decent one. If either team performs well, they should go into the final with real confidence against shaky Spain, and make it a competitive final. It'd be nice to end the tournament well!

An offside conundrum

noreply@blogger.com (sam post) — Tue, 19 Jun 2012 23:55:00 +0000

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

noreply@blogger.com (sam post) — Tue, 19 Jun 2012 21:42:00 +0000

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

noreply@blogger.com (sam post) — Tue, 12 Jun 2012 02:16:00 +0000

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

noreply@blogger.com (sam post) — Sat, 09 Jun 2012 19:48:00 +0000

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

noreply@blogger.com (sam post) — Fri, 08 Jun 2012 22:46:00 +0000

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!!

noreply@blogger.com (sam post) — Tue, 24 Apr 2012 16:25:00 +0000

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

noreply@blogger.com (sam post) — Tue, 07 Feb 2012 03:39:00 +0000

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.
Now that's a strange fact! It's not as if there aren't artists out there today, whom I love and admire from live performances, making recordings of their own. But they never seem to capture my interest in quite the same sustained way, and I almost never return to them after a few listenings. Why is that?

Before I jump to any unusual conclusions, I should note that the effect could be one of mere selection bias: the recordings that survive to this day (or to my childhood) from the more distant past are exactly those that were more popular. In addition, because recordings weren't as common in the past, the artists who were releasing recordings were more likely to be "good" in whatever sense makes them more popular. Maybe I haven't made the time to effectively sort through all the modern recordings that are being made to find the ones that would be my favorites. Add to that the fact that, as I mentioned in my last post, I find it difficult to set aside time anymore to listen to something all the way through, maybe it's not too surprising that I get bored easily with new releases.

But with those caveats in mind, though, I suspect that something more nefarious is ultimately responsible! After all, I've been to piano recitals that I absolutely adore, and heard other people rave about live performances that they found truly breathtaking, from people like Stephen Hough, Radu Lupu, Piotr Anderszewski, Alfred Brendel, Richard Goode (who gave the best recital I've personally ever heard live), and yet, when I hear the same music from the same pianist through the lens of the recording studio, it's never quite the same.

If we grant the truth of this alternative hypothesis, there are still a few possible explanations, none of which I find particularly satisfying.

1. Recordings are inherently worse than live performances. Expecting them to be as good is silly. According to this hypothesis, then, if I had ever heard Glenn Gould or Richter play live, I would have been, compared to their recordings, simply, blown away.

If this is the case, then why is my taste so skewed to pianists from mid-century? Were they really better? If so, why?

2. Something about making a recording in a studio sucks the life out of a performance, and modern recording techniques have only exacerbated this trend.

But Glenn Gould was possibly the worst offender (at least, as bad as he could have been at the time) for stopping, cutting, splicing and dicing his recordings. But I still love many of them.

3. Something about recording technology, which is supposed to give us better, purer sound quality as time passes, actually makes modern recordings less appealing.

If this is the case, then modern live recordings should be comparably uninspiring to modern studio recordings.

4. Maybe I'm the problem, and I just like the static hum or low clarity of old recordings. But why? Maybe I (and others like me?) are biased toward recordings that have the same type of sound (in some sense) as those that we listened to and loved most growing up. If that's true, then transferring modern recordings to less sparkling analog formats should make them sound better to me.

Of course, the real answer could be any and all of these four, or none of them. But they are reasonably testable...