In Order To Give A Man A Fish, You Must First Teach Him How To Eat It

A couple weeks ago I got to spend an evening with Haley and Gabe in Boston discussing various things that probably bored Haley to tears (sorry!), but at least Gabe found interesting. One of Gabe’s shticks is that art should do a better job of conveying important ideas and concepts to its consumers. His favorite example of this (of everything?) is The Wire.

I want to push back on this a little bit – an alternate title this post might be “In Which I Attempt To Troll Gabe Into Coming Back To The Internet At Least In Small Doses And In A Totally Responsible Fashion Which Won’t Disrupt His Life And Waste His Time And Also Into Maybe Writing Something Interesting” but it just didn’t seem catchy enough.

Let’s take the premise at face value – that art should try to convey useful, meaningful concepts to its consumers. This seems reasonable as at least one of the things art should do. Well, it’s reasonable so long as art can convey these concepts. But can it? At face value, the answer is obvious – of course it can! The Matrix taught a generation that their perceived reality is possibly not even real. Inception did this for another generation.

But this dodges the question by avoiding the steel man: can art realistically convey new concepts to people often? Or efficiently? It’s easy to be less sanguine about this question.

A good example here is a concept from economics (and elsewhere) called elasticity. The price elasticity of demand, for example, is the % change in the quantity of a good demanded caused by a 1 % change in the price. There’s an ambiguity here though – are these percentages computed by using the original price and quantity as the base? The new price and quantity? Or maybe the average of the new and old price and quantities? Different textbooks and instructors make different decisions here, and students often get lost in a formula that doesn’t at all seem intuitive. Conveying the concept of elasticity at a high enough resolution that the recipient can understand the math is hard.

Unless they already know calculus. In terms of calculus, price elasticity of demand is dQ/dP * (P/Q), or in other words the derivative of demand with respect to price times the ration of price to demand. We can rearrange this equation as (dQ/Q)/(dP/P) in order to make it look more like percentage changes. If a student already knows calculus, it’s often very easy to explain elasticity to them – the ambiguity about base percentages goes away through the magic of calculus, and learning calculus already taught them about rates of changes. It’s also really easy to explain acceleration (the derivative of velocity) or jerk (the derivative of acceleration) or a whole host of useful concepts from a wide variety of disciplines.

I’m not just saying it’s better to teach a man to fish than to give a man a fish – as Gabe told me in Boston there’s some low hanging fruit to be grabbed just from giving people fish, and I agree. Some of the people you give fish to may have starved after all! But there’s something else going on here – not everyone knows how to eat fish. The fish eating novice might not chew thoroughly and miss the small bone tucked in the flaky goodness, resulting in some discomfort, post traumatic stress syndrome, and a lifetime devoid of fish. This, I contend, is a potential problem with trying to give someone the concept of elasticity who has never had calculus. Fundamentally, this is a really hard thing to do in such a way that requires no work on the recipient’s end.

Perhaps this is why Gabe reveres art which successfully conveys important, meaningful, and difficult concepts well – precisely because it’s so difficult. But I must ask the question, was is really that successful? Or did the people who got the concept already have the equivalent of calculus under their belt? Consider The Wire. As Robin Hanson notes:

The overall moral of the story seems to me largely libertarian.  A renegade cop effectively legalizing drugs in one area works out great, and the show’s writers have a Time oped supporting drug law jury nullification.  Dire consequences follow from child labor and prostitution being illegal.  The police, courts, prisons, schools, and city hall are unrelentingly corrupt and dysfunctional, because voters don’t much care.  In the background of the story, industries managed mainly by private enterprise, such as stores, hotels, shipping, and cars, seem to mostly function well.  Private newspapers look bad, but mainly because readers don’t much care.

Apparently, however, many see The Wired as calling for more government.  At a Harvard symposium on The Wired, many panelists said the answer was more funding.  Simon was there:

The wire is about a world in which people are worth less. … We depicted a world in which market forces always have their say and in which capitalism has triumphed, and marginalized labor – it makes labor cheap. … What we have here is a market-based [world]; capitalism has been the God.  To even suggest that there should be some social compact along with the capitalistic forces, to mitigate any of that, over the last twenty-five years, has been political suicide. … We are only getting the American that we’ve paid for, no more, and God damn it, we deserve it.

– See more at: http://www.overcomingbias.com/2008/10/the-wire.html#sthash.WTsGobX2.dpuf

To many people, The Wire illustrates all the reasons why capitalism caused the problems of Baltimore and other cities. Any understanding of market forces goes over their head. But to libertarian leaning economists like Robin and Alex Tabborak, The Wire is obviously illustrating how market forces work and the problems that arise when we ignore these forces. We can give these men fish; they already know calculus.

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Accidental Trial by Fire

An Aeon piece by Dimitris Xygalatas has been making the rounds describing how hazing and other rituals involving sacrifice or pain, physical or psychological, often serves as a sort of prosocial glue that keeps groups together and functioning well. Xygalatas goes as far as to measure the heart rates of people involved in a fire walking ritual, and finds that he can predict how closely related two people are in their social network — e.g. spouse vs. close friend vs. stranger — just by patterns in their heart rates throughout the night. This insight helps explain vast swaths of social behavior, from fraternity hazing to why people go to concerts. Do read the whole piece for better context and more convincing evidence.

What struck me while reading the piece is how many of these prosocial rituals are almost accidental in our modern lives. We seem to be forming strong social bonds with strangers in a random, haphazard fashion rather an with the people we’re likely to have extended contact with — e.g. family or local community members. I can really only speak to my own experience here, so I started listing the various painful “rituals” I’ve participated in to get a feel how true my intuition was. I’ll list mine below, but I encourage you to list yours in the comments.

  • Enduring long (3 hours +) trips and spending too much money to play in Magic: the Gathering tournaments, often missing other important obligations as a result.
  • Enduring less long trips and spending even more money to play in paintball tournaments, often missing other important obligations as a result. Also, getting shot is physically painful and the most painful occasions are more likely to occur in these tournaments.
  • Graduate school – especially core courses and qualifying exams.
  • Concerts – it’s hot, smoky, hard to see, uncomfortable seating, often had to travel a long distance, etc.
  • Various outdoor activities (but only sometimes) – camping, fishing, etc. At their worst, it’s way too hot or way too cold, it’s unpleasantly wet, and there’s sometimes an element of danger. Sometimes they require quite a trip too.
  • A small underground boxing club in high school
  • High school itself. School itself.

What stands out to me about this list is the number of items that are or are attached to some hobby that requires time, money, and travel and aren’t typically things you do with your family and non-hobby friends – how many people are willing to travel for hours to get shot at with paint filled pellets or play a card game? But looking at the list, a smaller proportion of them have the accidental nature than I expected. Traveling and enduring pain for hobbies that few in your family/community participate in does seem like a stereotypically modern behavior. Is anyone aware of any evidence one way or another?

Another thing I noticed is how many are associated with school. School is traumatic in a lot of ways (raise your hand if you’ve ever had a nightmare about somehow making a huge mistake at school), and ever notice how so many people feel such a strong connection to their alma mater? Perhaps the modern social order is held together by school and hobbies.

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The Old Evidence Problem

I’m in the middle of writing up a post sketching a some ideas I have about Bayesian inference in order to stir up a hornet nest – in particular to prod the hornet queen, David Chapman. In the process, I ran across this old blog post by Andrew Gelman discussing this (pdf) paper by Bandyopadhyay and Brittan criticizing one form of Bayesianism – in particular the form espoused by E.T. Jaynes. One of the issues they bring up is called the old evidence problem:

Perhaps the most celebrated case in the history of science in which old data have been used to construct and vindicate a new theory concerns Einstein. He used Mercury’s perihelion shift (M) to verify the general theory of relativity (GTR). The derivation of M is considered the strongest classical test for GTR. However, according to Clark Glymour’s old evidence problem, Bayesianism fails to explain why M is regarded as
evidence for GTR. For Einstein, Pr(M) = 1 because M was known to be an anomaly for Newton’s theory long before GTR came into being. But Einstein derived M from GTR; therefore, Pr(M|GTR) = 1. Glymour contends that given equation (1), the
conditional probability of GTR given M is therefore the same as the prior probability of GTR; hence, M cannot constitute evidence for GTR.

Oh man, do I have some thoughts on this problem. I think I even wrote a philosophy paper in undergrad that touched on it after reading Jaynes. But I’m going to refrain from commenting until after I finish the main post because I think the old evidence problem illustrates several points that I want to make. In the mean time, what do *you* think of the problem? Is there a solution? What do you think of the solution Bandyopadhyay and Brittan propose in their paper?

Edit: Here’s a general statement of the problem. Suppose we have some well know piece of evidence E. Everyone is aware of this evidence and there is no doubt, so P(E)=1. Next, suppose someone invents a new theory T that perfectly accounts for the evidence – it predicts is with 100% accuracy so that P(E|T)=1. Then by Bayes’ rule we have P(T|E)=P(E|T)P(T)/P(E) = P(T), so the posterior and prior are identical and the evidence doesn’t actually tell us anything about T.

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The Mark of an Ergodic Crab

I. Chasing ergodic crabs

Yes! Ergodicity is interesting and very useful. At least in statistics. Don’t ask me what physicists do with the thing though. Those guys are crazy. The problem with ergodicity is that it’s pretty complicated. Go ahead, take a look at the Wikipedia page, I’ll wait a minute.

Ok, good. The math geniuses are gone now. You know the type – they can look at some math they’ve never seen before and understand it in minutes. Right now they’re busy proving theorems about ergodic flows on n-dimensional locally non-Hausdorff manifolds. And twitching at that last sentence. You and me? We’re going to learn about ergodicity with a pretty crabby extended metaphor.

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What is statistics?

I put the call out on twitter for ideas for my first post, and Gabe asked this:

I suppose I did ask for statistics questions. This one is a bit tough to answer because, like I hinted at on twitter, a wide variety of things get called statistics by the people doing them, statisticians do an even wider variety of things, and to muddy the waters even more, lots of things that typically get categorized as statistics often are also categorized as other things like machine learning or computer science. I suppose I should blame the computer people.

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