Monthly Archives: December 2008

Book Review: The Manga Guide to Statistics


I recently got an offer from someone at No-Starch Press to review the
newly translated book, The Manga Guide to Statistics. I recieved the book a couple of weeks ago, but haven’t had time to sit down and read it until now.

If you haven’t heard of the “Manga Guides”, they’re an interesting idea. In Japan, comic books (“Manga”) are much more common and socially accepte than they typically are in the US. It’s not at all unusual to see Japanese adults sitting in the subway reading Manga. Manga has a very distinctive artistic style, with its own
set of common artistic conventions. The Manga Guides are textbooks written as
Manga-style comics. In this case, it’s an introductory text on statistics.

The short version of the review: terrific book; engaging, thorough, and fun. Highly recommended. Details beneath the fold.

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Tips for NYC Tourists

As a daily commuter into NYC via Metro-North to Grand Central Terminal, followed by two subways to my office, I go through one of the busiest transit hubs anywhere twice a day. Since it’s tourist season, I also get to see lots of silly things tourists do. And since I live here and love the city, I’ve got a few suggestions, both of things to not do, and things that you shouldn’t miss. So, based on my observations, here are a few tips for NYC tourists this season.

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Friday Random Ten

  1. Elizabeth and the Catapult, “Golden Ink”: a mellow track from a very
    good NY area band. This really isn’t one of my favorites of their songs. It’s rather on the dull side.
  2. Miles Davis, “Ray’s Idea”: Miles is one of the great geniuses of the 20th century. What more need be said?
  3. Do Make Say Think, “Hooray! Hooray! Hooray!”: DMSY is one of the very
    best post-rock ensembles you’ll find. They’re another group that overlaps with
    Godspeed You Black Emperor, and they approach the brilliance that is Godspeed.
    This is a nice mellow track, with some lovely steel guitar playing.
  4. The Tangent, “Photosynthesis”: great neo-progressive stuff. This band started off as a collaboration between Roine Stolte of the Flower Kings and
    Andy Tillson. This is off the first Tangent album after Stolte and Tillson had a falling out. The band still features some members of tFK, but the writing is now
    pretty much all Tillson. They’re an excellent band, but I did prefer their sound with Stolte.
  5. Marillion, “Splintering Heart”: the best track off of a frankly lousy
    Marillion album.
  6. Gogol Bordello, “Not a Crime”: Gypsy punk rock, with brilliant fiddle
    playing. What could be cooler than that?
  7. Mel Brooks, “Springtime for Hitler”: A song from one of the most brilliantly offensive shows of all time. The original movie remains one of my very favorite movies. Come on, how can you not love the blue blankie? Or Mel Brooks stepping out of a dance line to sing “Don’t be stupid, be a smarty, come and join the nazi party?”
  8. Marillion, “Throw Me Out”: something off of Marillion’s new double album. I love this album. It’s the best thing from Marillion in ages. I can’t stop listening to it. This is why I love Marillion. Brilliant songwriting, amazing technical performances, music loaded with feeling, and those astonishingly wonderful Marillion transitions. Even a short little song like this manages to be just
    brilliant, with so many little treasures hidden in it.
  9. Pink Floyd, “The Dogs of War”: It’s a damn shame that David Gilmour got control of the Pink Floyd name, and chose te release so much crap under it. He’s a wonderful guitarist, but frankly, he’s a pretty rotten songwriter. All of his compositions have this dull droning quality to them. This is typical. There’s some nice guitar work in the live version, but the song itself is just dreck.
  10. Happy the Man, “Maui Sunset”: I was delighted when I heard Happy the Man was getting back together. I wasn’t so delighted once I heard what they did. It’s got all of the technical qualities of good progressive rock: complex melodies and harmonies, interesting chord progressions, complex and irregular rythyms. But it’s cold. It sounds like music performed by a computer. There’s not a trace of humanity to it. Technically brilliant, but ultimately remarkably dull.

Why Math?


So, why math?

The short version of the answer is remarkably simple: math provides
a tool where you can, without ambiguity, prove that something is true or false.

I’ll get back to that – but first, I’m going to make a quick diversion, to help you understand my basic viewpoint on things.

This blog actually started in response to something specific. I was reading
Orac’s blog “Respectful Insolence”, and
he was fisking a study published by the Geiers, purporting to show a change in the trend in autism diagnoses. Orac was attacking it on multiple bases, but it struck me
that the most obvious problem with it was that it was, basically, a mathematical argument, but the math was blatantly wrong. It was making a classic statistical analysis mistake which is covered in first-year statistics courses. (And I mean
that very literally: when I was in college, I lazily satisfied some course requirements by taking a statistics course given by the Poly Sci department, and
in statistics for political scientists, they covered exactly the error made by the Geiers in November of the fall semester.) It struck me that while there were a lot of really great science bloggers – people like Orac, PZ Myers, Tara Smith, and so on – that I didn’t know of anyone doing the same thing with math.

So I started this blog on Blogger. And my goals for the blog have never changed. What
I’ve wanted to do all along is:

  1. To show people the beauty of math. Math is really wonderful. It’s
    fun, it’s beautiful, it’s useful. But people are taught from
    an early age that it’s useless, hard, and miserable. I want to show
    otherwise, by describing the beauty of math in ways that are approachable
    and understandable by non-mathematicians.
  2. To help people recognize when someone is trying to put something past
    them by abusing math – what I call obfuscatory mathematics. Because so many people don’t know math, hate it,
    think it’s incomprehensible, that makes it easy for dishonest people
    to fool them. People throw together garbage in the context of a mathematical
    argument, and use it to lend credibility to their arguments. By pointing
    out the basic errors in these things, I try to help show people how to
    recognize when someone is try to use math to confuse them or trick them.
  3. To show people that they use and rely on math far more than they think.
    This relates back to the first point, but it’s important enough to
    justify its own discussion. Lots of people believe that they can’t
    understand math, and avoid it like the plague. But at the same time, they’re
    using it every day – they just don’t know it. My favorite example
    of this is from my own family. My older brother had a string of truly horrible
    math teachers, and was convinced that he was horrible at math, couldn’t
    understand it, couldn’t do it. You couldn’t even try to teach it to him,
    because he was so sure that he couldn’t do it that he’d psych himself out
    before he even started. But he’s a really smart guy. When he went to college,
    he studied music. I visited him at one point, and was watching him do an
    assignment for his music theory course, where they were studying something
    called serial composition. He was analyzing a musical score – and what
    he was doing to analyze it was taking determinants of matrices in mod-12
    arithmetic! Of course, he didn’t know that that was what he was
    doing; instead of the numbers 0 through 11, he was using the notes of the
    musical scale. But it was taking a determinant, just using a different
    symbol set. He had no trouble doing that; but try to teach him to compute
    a percentage, and he’ll insist not just that he can’t do it, but that
    he’s incapable of learning to do it. That kind of thing is
    all too common – people do math every day, without knowing it. If they
    understood whata they were doing, they might be open to learning more,
    to being able to do more themselves – but because they’ve been taught
    that they can’t do it, they don’t see that they do.

This will come around back to my basic point; keep reading below the fold.

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The Real Bozo Attempts to Atone: Why the DDWFTW Car Works

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So, as I said in the edit to my previous post about the wind-driven cart, I seriously blew it. The folks who pointed out the similarity of the cart to a tacking sailboat were absolutely correct. The guys who built this cart, and recorded the demo were absolutely right, and I was stupidly wrong, in multiple ways. First of all, I thought this was a really simple system. I couldn’t possibly be more wrong about that – this is anything but simple; in fact, it’s a remarkably interesting and elegant demonstration of how complicated and counterintuitive fluid dynamics can be. Second, I completely misunderstood the simple mechanics of the device; I originally thought that the propellor was spinning in the opposite direction – and I completely missed it when people repeatedly tried to explain that error to me. And third, I completely screwed up my own mathematical model of how something like this works.

So – to repeat: the guys who did the demo of this are clearly not bozos; the only bozo in this situation is me, for screwing it up so badly, on so many levels. I sincerely apologize for calling them bozos and mocking them. I made a whole series of really stupid errors, and took an unreasonably long time to recognize that fact.

It should be obvious that there’s some way to go downwind faster than the wind, because as so many people pointed out, sailboats do it. It was frankly stupid of me to even argue about this – it’s really pretty boneheadedly obvious. The question never should have been “can it be done?”, but rather just “does this device do it?”

And the answer to that is “Yes”. This thing does do it. It’s not magic, it’s not perpetual motion. In fact, it’s really astonishingly simple, once you realize that the behavior of things moving through air is quite different from the simple rigid system that it appears to be equivalent to.

In this post, I’m going to try to do two things:

  1. Explain the faulty reasoning that led me to think it couldn’t work, and why it’s wrong.
  2. Explain why the thing really works.

In another post later this week, I’m going to try to explain why I think the mathematical element is so important. There’s a ton of people who’ve got devices that really look convincing, and that have really convincing arguments for why they should work; only they don’t, because they’ve missed something.

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In case anyone’s interested, I’m currently fooling around with Twitter. If you’re interested, I’m user-id MarkCC. Feel free to ping me if you’ve got an interesting twitter feed that you think would interest me; I’m still building up my list. Eventually, if I find it useful, I’ll put a Twitter sidebar here on GM/BM.

Another Bad Metric Error: Wages vs. Labor Costs

It’s just been a week for metric errors. Via Media Matters comes an impressive list of stories in the media about the automobile companies financial problems, where they cite labor costs as a major issue. So far, so good. But in virtually every story about this, you’ll find a statement along the lines of: “union workers make $71 an hour in wages plus benefits”.

In many cases, they even go so far as to specifically compare that figure as wages to other companies. For example, this quote, from a conservative talking head:

“When you’re paying $73.73 an hour to those people with salary and benefits and your competition is paying $48 to its workers, you’re going to get your butt kicked in the marketplace unfortunately.”

Here’s the problem with that. The roughly $70/hour figure is a statement of labor costs, not wages. What’s the difference?

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Wind-Powered Perpetual Motion

(NOTE: It appears that I really blew it with this one. I’m the bozo in this story. After lots of discussion, a few equations, and a bunch of time scribbling on paper, I’m convinced that I got this one wrong in a big way. No excuses; I should have done the analysis much more carefully before posting this; looking back, what I did do was pathetically shallow and, frankly, stupid. I’m sincerely sorry
for calling the guys doing the experiment bozos. I’ll follow up later this weekend with a detailed post showing my analysis, where I screwed up, and why this thing really works. In the meantime, feel free to call me an idiot in the comments; I pretty much deserve it. I’m leaving the post here, with this note, as a testament to my own stupidity and hubris in screwing this up.)

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This has been quite the day for the bad math; I’ve encountered or been sent a bunch of real mind-numbing stupidity. Unfortunately, I’m too busy with work to actually write about all of it, so as I have time, I’ll pick out the best tidbits. Today’s example is a fascinating combination of perpetual motion and wrong metrics.

Via BoingBoing comes a bunch of bozos who believe that they can create a “wind-powered” vehicle that moves faster the wind that powers it.

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If you measure the wrong thing, you get the wrong answer: Down's syndrome in Britain

One of the blogs I read regularly is Ben Goldacre’s “Bad Science”. I recommend
it highly. (Which reminds me that I really need to find some time to update my blogroll!) In saturday’s entry, he discussed a BBC Radio documentary that described how Britain is becoming a much more welcoming place for Down’s syndrome babies.

Ben did a good job of shredding it. But I also wanted to take a stab, focusing on
the mathematical problem that underlies it, because it’s a great example of two very
common errors – first, the familiar confusing correlation and causation, and
second, using incorrect metrics.

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Public Key Cryptography using RSA

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The most successful public key cryptosystem in use today is RSA – named for its inventors Rivest, Shamir, and Adleman. I first learned about RSA in grad school from one of my professors, Errol Lloyd, who was one of Ron Rivest’s students. Errol is without a doubt the best teacher I’ve ever had (and also a thoroughly nice guy). If you want to go to grad school to study algorithms, you frankly couldn’t do better than heading to Delaware to work with Errol. I have very fond memories of Errol’s class where we talked about this. He’s got a way of teaching where he doesn’t come out and tell you anything; what he does is ask questions that lead you through the process of figuring it out yourself. That’s an incredibly effective way to teach if you can carry it off. Personally, I can’t. And I’ve never known anyone except Errol who could do it for a topic like RSA encryption!

Anyway, moving on… In general, public key cryptosystems are based on problems that are easy to solve computationally in one direction, but really hard to solve computationally in the other. In the case of RSA, the basic underlying problem involves prime numbers: if you’ve got two really large prime numbers, then multiplying them together is easy; but if you’ve got a number that’s the product of two really large primes, factoring it is very hard.

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