Serial's fallacies and how we fell for them

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

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

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

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?

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

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

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!