Monthly Archives: July 2009

Friday Random Ten, July 31

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  1. Russian Circles, “Youngblood”: post rock, in the Mogwai style. Very nice stuff. Not the
    most exciting PR band around, but good.
  2. The Flower Kings, “World Without a Heart”: typical FK. Since I pretty much worship the ground
    that Roine Stolte walks on, you can guess what I think of this.
  3. Darcy James Argue’s Secret Society, “Transit”: would you believe sort-of progressive
    big-band jazz? That’s pretty much how I’d describe this. Big band jazz is not my usual cup of tea, but
    this is damned impressive, and a good solid listen. Definitely very cool stuff.
  4. Naftule’s Dream, “Yid in Seattle”: Naftule’s Dream is an alternate name for a wonderful
    Klezmer group called Shirim. When they’re doing weird stuff, they record as ND; when they’re doing
    traditional, they record as Shirim. ND is klezmer the way that John Zorn and his radical jewish
    culture guys play it. Wild stuff. Brilliant.
  5. Sonic Youth, “Leaky Lifeboat (for Gregory Corso)”: a track from the newest Sonic Youth
    album. This actually sounds more like older SY. In general, they’ve mellowed a bit over
    time; in particular, they’re last album had fewer rough edges. This one keeps the smooth
    production, but brings the edge back to the sound. SY just keeps getting better.
  6. The Tangent, “The Ethernet”: the Tangent started out as a collaboration between
    Roine Stolte of the Flower Kings, and Andy Tillison of Parallel or 90 Degrees. Stolte eventually
    quit, leaving Tillison running the band. It’s completely replaced Po90D as Tillison’s main band.
    It’s not quite up there with tFK, but it’s damned good.
  7. Keith Emerson Band, “Prelude to Hope”: This is an astonishing track. It’s Keith Emerson
    playing something beautiful and subtle. I’m a big Emerson fan. He’s a brilliant pianist.
    I love his style, and I usually love his compositions. But my opinion of him in the past was that
    if anyone were to suggest that perhaps he should try being a bit more subtle, he’d
    be likely to bash their head in with a sledgehammer, put the body through a wood chipper,
    collect up the bits and burn them to ashes, and then piss on the ashes – just to make sure
    that he made his point clear. And yet… This is a beautiful, subtle piece of playing, from
    a frankly terrific album.
  8. Echolyn, “Lovesick Morning”: Echolyn is one of my favorite recent discoveries. They’re
    not exactly a new band – they formed in the early 90s, broke up in 95, and then reformed
    a couple of years later. But they’re a thoroughly excellent neo-progressive band, with a very
    distinct sound. They don’t sound like they’re trying to be Genesis, or the Flower Kings, or Yes… They
    sound like nothing but themselves.
  9. Frank Zappa, “Drowning Witch”: Typical Zappa. Very strange, wonderfully erratic
    but great music, and incredibly silly lyrics delivered in that strange Zappa style.
  10. Dream Theater, “Wither”: Dream Theater’s newest. DT is a great progressive
    metal band. Their last few albums were a bit uninspired in my opinion. This one is really
    quite good. Unfortunately, this is one of the weaker songs on the album. Not bad, but not
    exactly what I’d choose to try to turn someone on to Dream Theater.

Bill O'Reilly on Life Expectancy: Dumbest Man on Earth?

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An alert reader just sent me, via “Media Matters”, the single dumbest real-life
video clip that I have ever seen. In case you’ve been living under a rock, Bill O’Reilly is
a conservative radio and TV talk-show host. He’s known for doing a lot of really obnoxious
things, ranging from sexually harassing at least one female employee, to sending some of
his employees to stalk people who he doesn’t like, to shutting off the microphones of
guests on his show if he’s losing an argument. In short, he’s a loudmouthed asshole who
gets off on bullying people.

But that’s just background. As a conservative commentator, he’s been going off on
the evils of Obama’s supposedly socialist healthcare reform. That’s frequently
taken the form of talking about how horrible medical care is under Canada’s
socialized health system. One of his viewers wrote in to him about this. And
the insanity follows.

The question came from a viewer named Peter from Victoria, BC, who asked: “Has anyone noticed
that life expectancy in Canada under our health system is higher than the USA?”

Bill’s response:” Well, that’s to be expected Peter, because we have 10 times
as many people as you do. That translates to 10 times as many accidents,
crimes, down the line.” Delivered, of course, in BillO’s trademark patronizing
style.

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Friday Recipe: Chinese Potstickers (aka Jiao Zi)

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dumpling.png

My wife is chinese. So in our house, comfort food is often something chinese. For her, one of her very favorite things is dumplings, also known as pot-stickers. They’re time consuming to make, but not difficult. They’re really delicious, well worth the effort. They’re best with a homemade wrapper, but that’s not easy. If you go to a chinese grocery store, they sell pre-made dumpling wrappers with are pretty good. Not as good as homemade, but more than adequate. The wrappers are circular, and about 2 or 3 inches in diameter.

These are traditionally made with ground pork. But I don’t eat pork, so I use chicken thighs. Definitely make sure you use thighs – to come out right, the meat inside can’t be too lean – it needs to have some fat in it. Thighs work really nicely; breasts, not so much.

When my wife stuffs them, this recipe makes around 30 dumplings. If I’m stuffing them, it’s more like twice that – she somehow manages to stuff an amazing amount of filling into each dumpling. If I try that, I can’t close ’em.

Ingredients

  • 3 boneless, skinless chicken thighs.
  • 1/2 medium sized head of napa cabbage (about 1lb).
  • Thinly sliced green parts of two scallions.
  • 1 tablespoon Oyster sauce.
  • 1/4 teaspoon sesame oil.
  • 1-2 tablespoons soy sauce (to taste)
  • A small dish of cold water.
  • Dumpling wrappers.

Instructions

  1. Put the chicken thighs and the oyster sauce into a food processor. Pulse until you’ve got what looks like coarsely ground meat.
  2. Finely mince the cabbage. Don’t do it in a food processor – that’ll just pulp it. You want it minced into little pieces.
  3. Fold the cabbage, soy sauce, and sesame oil into the ground meat.
  4. Now you’ve got the finished filling. Take a wrapper, put a dollop of filling into the center of the wrapper. Lightly brush the edges with water, and then fold the wrapper in half, sealing the edges. (The really correct way of doing it crimps it so that it actually looks like a crescent moon, and stands up by itself. But I have no idea how to explain that! And it tastes good even with the lazy fold.)
  5. Keep doing that until you run out of either wrappers or filling.
  6. Heat up a shallow frying pan on medium to medium-high heat. Cover the bottom with oil. You want enough oil to fry the bottom of the wrappers, but not enough that they’re swimming in it. And you only want the bottom to fry. (Don’t use a wok for this. This is one of the only times that I’ll ever say that about chinese cooking – but you really want a flat bottomed pan.)
  7. Put the dumplings into the pan in shifts. You don’t want them too close together, or they’ll stick to one another. Let them cook for one or two minutes, until the bottom is a nice dark brown.
  8. Take about 1/2 cup of chicken stock, dump it into the pan, and immediately cover the pan tightly. Let it cook like that until almost all of the stock evaporates. Then take the dumplings out, and put them in a serving bowl. They’ll stick to the bottom a bit; pry them up gently with either a spatula or tongs. (There’s a reason that they’re called pot-stickers!)
  9. Keep going in batches until they’re all cooked.
  10. Serve them with a dipping sauce. Spoon a bit of sauce over each dumpling right before you eat it.

There are a ton of dipping sauces you can use. My own favorite is:

  1. about 1/4 cup of clear rice vinegar
  2. About 1/4 cup of soy sauce
  3. 1 teaspoon of sugar
  4. one clove of crushed garlic, finely minced.
  5. One slice of ginger, crushed and finely minced.
  6. Greens of one scallion finely minced.
  7. One drop of sesame oil.
  8. One half teaspoon of sambal or sriracha chili sauce.

These little suckers are seriously good eating. They’re sort of like potato chips, in that once you start eating them, you can’t stop. So make a lot!

If you really want to make homemade wrappers (which is a lot of work, but which makes these wonderful little things so much better that you’ll never go back to store-made wrappers), there’s a great recipe for them in Ming Tsai’s “Blue Ginger” cookbook.

Bad Healthcare Cost Models Produce Silly Results (anyone surprised?)

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This morning, my good friend Orac sent me a link to an interesting piece
of bad math. Orac is the guy who really motivated me to start blogging; I
jokingly call him my blogfather. He’s also a really smart guy, not to mention
a genuinely nice one (at least for a transparent box of blinking lights). So
when he sends me a link that he thinks is up my alley, I take a look at
the first opportunity.

Today, he sent me a link to a guy who claims to have put together
a mathematical model showing that it’s impossible to create a national
healthcare system without rationing. The argument is a great example
of what I always say about mathematical modeling: you can’t just
put together a model and then accept its results: real mathematical models
must be validated. It’s easy to put together something that looks
right, but which produces drastically wrong results.

The common way of saying it is “Garbage In, Garbage Out”. I personally
don’t like that way of describing it – because in the most convincing examples
of this, it looks like what’s going in isn’t garbage.

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High School Reunion: New comment thread

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We’ve been having some load trouble with the ScienceBlogs server, and the
400+ comment over on the high school reunion thread seem to be resulting in a lot of timeouts. In an attempt to reduce the number of errors, I’m closing the thread on that post, and asking folks to post any new comments here.

Friday Random Ten, July 17

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  1. John Corigliano, “Fantasia on an Ostinato”: Corigliano is absolutely my
    favorite modern composer. He writes stunningly beautiful music. This is a wonderfully
    subtle piece: unaccompanied solo piano. Just incredible.
  2. Isis, “Not in Rivers, But in Drops”: The transition between the last one
    and this just about scared me out of my seat. From solo piano to loud, heavy
    post-rock. Once the shock of the volume change was past, I love this track. Isis
    is a really fantastic group.
  3. Dirty Three, “Amy”: Dirty Three is another interesting transition. DT is another
    post-rock, but from the opposite end of the post-rock spectrum from Isis. DT is mostly
    accoustic, heavily classically influenced post-rock. Most of their studio work doesn’t have
    the energy or the focus of a band like Isis, but it’s still very good stuff.
  4. Trans Am, “(Interlude)”: from post-rock to math rock. Trans Am is a pretty neat
    little band. Not nearly as good as some of the others in my collection, but definitely fun.
  5. Jadis, “Need to Breathe”: Finally, some neo-prog. Jadis is a new neo-progressive
    group that’s heavily influenced by Marillion. They’re pretty good. Not great, but good.
  6. Broken Social Scene, “Our Faces Split the Coast in Half”: a big disappointment. I heard Broken Social Scene being interviewed on NPR. They’re a Canadian collective, which has
    some overlap with the deities of postrock, “Godspeed you Black Emperor”. The bits they played
    live sounded great. But when I got one of their albums, it’s profoundly dull. Pretty much
    the only time I ever listen to it is when it comes up in a random playlist, and then
    I usually wind up skipping past.
  7. Echolyn, “The End is Beautiful”: very good neo-progressive rock. Maybe a tad on the emo side,
    but the quality of the musicians more than makes up for that. Seriously good stuff,
    very highly recommended. Includes a really beautiful fugue section.
  8. Gong, “Magdalene”: Brilliant prog-rock, with nothing neo about it. Gong has been
    together since the 70s (although I just recently found out about them). They’re one of the
    most amazing bands I’ve ever heard. Very strange, very silly at times, but always
    musically brilliant. They’ve got unusual instrumentation – very woodwind heavy for a rock
    band. I can’t recommend them highly enough.
  9. Alan Holdsworth, “The Sixteen Men of Tain”: Alan Holdsworth is someone who’s music
    I simultaneously love and hate. The guy is, without a doubt, one of the most skillful
    and artistic guitar players ever. He can play fast or slow with every note being crisp
    and perfect. He can play rock, jazz, and classical guitar with equal skill. And yet,
    most of the time, he leaves me cold. He’s like a guitar playing machine – perfect in every
    mechanical way, but somehow, his playing just totally lacks humanity.
  10. The Flower Kings, “The Blade of Cain”: The perfect ending for a FRT: my
    favorite band, the Flower Kings. These guys are the neo-progressive band
    to watch. Brilliant composition, brilliant performances. They come closer to musical
    perfection than any other rock band I’ve ever seen or heard. I found a youtube clip
    of them performing this track live, so you can get a sense of what I mean, which is below.

Chaotic Systems and Escape

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nbody.jpg

One of the things that confused my when I started reading about chaos is easy to explain using what we’ve covered about attractors. (The image to the side was created by Jean-Francois Colonna, and is part of his slide-show here)

Here’s the problem: We know that things like N-body gravitational systems are chaotic – and a common example of that is how a gravity-based orbital system that appears stable for a long time can suddenly go through a transition where one body is violently ejected, with enough velocity to permanently escape the orbital system.

But when we look at the definition of chaos, we see the requirement for dense periodic orbits. But if a body is ejected from a gravitational system, ejection of a body from a gravitational system is a demonstration of chaos, how can that system have periodic orbits?

The answer relates to something I mentioned in the last post. A system doesn’t have to be chaotic at all points in its phase space. It can be chaotic under some conditions – that is, chaotic in some parts of the phase space. Speaking loosely, when a phase space has chaotic regions, we tend to call it a chaotic phase space.

In the gravitational system example, you do have a region of dense periodic orbits. You can create an N-body gravitational system in which the bodies will orbit forever, never actually repeating a configuration, but also never completely breaking down. The system will never repeat. Per Ramsey theory, given any configuration in its phase space, it must eventually come arbitrarily close to repeating that configuration. But that doesn’t mean that it’s really repeating: it’s chaotic, so even those infinitesimal differences will result in divergence from the past – it will follow a different path forward.

An attractor of a chaotic system shows you a region of the phase space where the system behaves chaotically. But it’s not the entire phase space. If the attractor covered the entire space, it wouldn’t be particularly interesting or revealing. What makes it interesting is that it captures a region where you get chaotic behavior. The attractor isn’t the whole story of a chaotic systems phase space – it’s just one interesting region with useful analytic properties.

So to return to the N-body gravitational problem: the phase space of an N-body gravitational system does contain an attractor full of dense orbits. It’s definitely very sensitive to initial conditions. There are definitely phase spaces for N-body systems that are topologically mixing. None of that precludes the possibility that you can create N-body gravitational systems that break up and allow escape. The escape property isn’t a good example of the chaotic nature of the system, because it encourages people to focus on the wrong properties of the system. The system isn’t chaotic because you can create gravitational systems where a body will escape from what seemed to be a stable system. It’s chaotic because you can create systems that don’t break down, which are stable, but which are thoroughly unpredictable, and will never repeat a configuration.

Very off topic: Why I won't be at my high school reunion

This comment thread has gotten long enough to start causing some server load problems. As a result, I’m closing the comments here, and I’ve added a new post where discussions of this past can continue.

If you’re not interested in completely off-topic personal rambling, stop reading now. This is very off-topic. But I wanted to say this once, and I wanted to do it in a way where I had some control over the publicly viewable responses. I will not be following my usual commenting guidelines here – anything which I consider to be abusive will be deleted, with no warning.

I graduated from high school in 1984. Which means that this year is my graduating class’s 25th year reunion. As a result, a bunch of people from my high school class have been trying to friend me on facebook, sending me email, and trying to convince me to come to the reunion.

I don’t feel like replying to them individually, which is why I’m writing here.

As pretty much any reader of this blog who isn’t a total idiot must have figured out by now, I’m a geek. I have been since I was a kid. My dad taught me about bell curves and standard deviations when I was in third grade, and I thought it was pretty much the coolest damn thing I’d ever seen. That’s the kind of kid I was. I was also very small – 5 foot 1 when I started high school, 5 foot three my junior year. Even when I shot up in height, to nearly 5 foot eleven between junior and senior year, I weighed under 120 pounds. So think small, skinny, hyperactive, geek.

Like most geek kids, I had a rough time in school. I don’t think that my experience was particularly unusual. I know a lot of people who had it worse. But I think that it was slightly worse than average, because the administration in the school system that I went to tolerated an extraordinary amount of violent bullying. Almost every geeky kid gets socially ostracized. Almost all get mocked. In fact, almost all face some physical abuse. The main determinant of just how much physical abuse they get subjected to is the school administration. And the administration at my school really didn’t care: “Bruises? He must just be uncoordinated and bumps into things. Broken fingers? Hey, it happens. We’re sure it must have been an accident. What do you want, an armed guard to follow your kid around?”

In high school, I didn’t have a single real friend in my graduating class. I had a very few friends who graduated a year before me; I had a few who graduated one or two years after me. But being absolutely literal, there was not a single person in my graduating class who came close to treating me like a friend. Not one.

Like I said before, the way I was by my classmates in high school was pretty typical for a geek. At best, I was ignored. At worst, I was beaten. In between, I was used as a sort of status enhancer: telling people that you’d seen me doing some supposedly awful or hysterical thing was a common scheme for getting ahead in certain social circles. In the most extreme case, someone painted a swastika onto the street in front of my house with gasoline, and lit it. (In autumn, in a wooded neighborhood.)

I’m can’t even pretend that I wasn’t an easy target, or that I didn’t respond in a way that encouraged my tormentors. I was a hyperactive geek. My social skills were awful. I don’t think that I deserved the way that I was treated; but at the same time, I do think that my hyperactivity and my lack of social skills both helped make me such a good target, and discouraged anyone from intervening on my behalf.

But I don’t think that that excuses anyone who abused me. It doesn’t excuse the bastards who made up stories about me. It doesn’t justify the people who threw me against walls. It doesn’t explain the guy who broke my fingers, because he wanted to know what it would sound like. And it doesn’t absolve the people who watched, and laughed while that happened.

Now it’s twenty five years since I got out of that miserable fucking hell-hole. And people from my high school class are suddenly getting in touch, sending me email, trying to friend me on Facebook, and trying to convince me to bring my family to the reunion. (It’s a picnic reunion, full family invited.) Even some of the people who used to beat the crap out of me on a regular basis are getting in touch as if we’re old friends.

My reaction to them… What the fuck is wrong with you people? Why would you think that I would want to have anything to do with you? How do you have the chutzpah to act as if we’re old friends? How dare you? I see the RSVP list that one of you sent me, and I literally feel nauseous just remembering your names.

The only positive thing that ever came out of my time with you people is that my children are studying karate. My son will, most likely, have his black belt by the time he finishes fourth grade. He’s a hyperactive little geek, just like me. He’ll probably go through some social grief, just like I did. But when some fucker like one of you tries to lay a hand on him or one of his friends, he’ll beat the living crap out of them. One of the mantras that his karate school follows is: Never start a fight, but if a fight starts, always be the one to finish it. And that’s what he’ll be able to do. To definitively finish any fight that anyone starts with him in a way that will teach his abusers and their cohorts to stay the fuck away.

And that’s all that I want from you. Stay the fuck away from me. I don’t want to hear about your lives. I don’t want to know how you’ve changed since high school. I don’t want to hear about your jobs, your spouses, your children. I’ve got a good life now, and I cannot imagine a reason in the world why I would pollute that world with contact with any of you.

Strange Attractors and the Structure of Chaos

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sage0-1.png

Sorry for the slowness of the blog; I fell behind in writing my book, which is on a rather strict schedule, and until I got close to catching up, I didn’t have time to do the research necessary to write the next chaos article. (And no one has sent me any particularly interesting bad math, so I haven’t had anything to use for a quick rip.)

Anyway… Where we left off last was talking about attractors. The natural question is, why do we really care about attractors when we’re talking about chaos? That’s a question which has two different answers.

First, attractors provide an interesting way of looking at chaos. If you look at a chaotic system with an attractor, it gives you a way of understanding the chaos. If you start with a point in the attractor basin of the system, and then plot it over time, you’ll get a trace that shows you the shape of the attractor – and by doing that, you get a nice view of the structure of the system.

Second, chaotic attractors are strange. In fact, that’s their name: strange attractors: a strange attractor is an attractor whose structure has fractal dimension, and most chaotic systems have fractal-dimension attractors.

Let’s go back to the first answer, to look at it in a bit more depth. Why do we want to look in the basin in order to find the structure of the chaotic system?

If you pick a point in the attractor itself, there’s no guarantee of what it’s going to do. It might jump around inside the attractor randomly; it might be a fixed point which just sits in one place and never moves. But there’s no straightforward way of figuring out what the attractor looks like starting from a point inside of it. To return to (and strain horribly) the metaphor I used in the last post, the attractor is the part of the black hole past the even horizon: nothing inside of it can tell you anything about what it looks like from the outside. What happens inside of a black hole? How are the things that were dragged into it moving around relative to one another, or are they moving around? We can’t really tell from the outside.

But the basin is a different matter. If you start at a point in the attractor basin, you’ve got something that’s basically orbital. You know that every path starting from a point in the basin will, over time, get arbitrarily close to the attractor. It will circle and cycle around. It’s never going to escape from that area around the attractor – it’s doomed to approach it. So if you start at a point in the basin around a strange attractor, you’ll get a path that tells you something about the attractor.

Attractors can also vividly demonstrate something else about chaotic systems: they’re not necessarily chaotic everywhere. Lots of systems have the potential for chaos: that is, they’ve got sub-regions of their phase-space where they behave chaotically, but they also have regions where they don’t. Gravitational dynamics is a pretty good example of that: there are plenty of N-body systems that are pretty much stable. We can computationally roll back the history of the major bodies in our solar system for hundreds of millions of years, and still have extremely accurate descriptions of where things were. But there are regions of the phase space of an N-body system where it’s chaotic. And those regions are the attractors and attractor basins of strange attractors in the phase space.

A beautiful example of this is the first well-studied strange attractor. The guy who invented chaos theory as we know it was named Edward Lorenz. He was a meteorologist who was studying weather using computational fluid flow. He’d implemented a simulation, and as part of an accident resulting from trying to reproduce a computation, but entering less precise values for the starting conditions, he got dramatically different results. Puzzling out why, he laid the foundations of chaos theory. In the course of studying it, he took the particular equations that he was using in the original simulation, and tried to simplify them to get the simplest system that he could that still showed the non-linear behavior.

The result is one of the most well-known images of modern math: the Lorenz attractor. It’s sort of a bent figure-eight. It’s dimensionality isn’t (to my knowledge) known precisely – but it’s a hair above two (the best estimate I could find in a quick search was in the 2.08 range). It’s not a particularly complex system – but it’s fascinating. If you look at the paths in the Lorenz attractor, you’ll see that things follow an orbital path – but there’s no good way to tell when two paths that are very close together will suddenly diverge, and one will pass on the far inside of the attractor basin, and the other will fly to the outer edge. You can’t watch a simulation for long without seeing that happen.

While searching for information about this kind of stuff, I came across a wonderful demo, which relates to something else that I promised to write about. There’s a fantastic open-source mathematical software system called sage. Sage is sort of like Mathematica, but open-source and based on Python. It’s a really wonderful system, which I really will write about at some point. On the Sage blog, they posted a simple Sage program for drawing the Lorenz attractor. Follow that link, and you can see the code, and experiment with different parameters. It’s a wonderful way to get a real sense of it. The image at the top of this post was generated by that Sage program, with tweaked parameters.