Good Math, Bad Math

Friday Random Ten, 11/06

Fri, 06 Nov 2009 14:58:50 -0500

Porcupine Tree, "Kneel and Disconnect": New Porcupine Tree! It's always great to get new stuff from these guys. It's good, but it's not up to the quality of their last two albums. (But given that their last two were utterly amazing, that's not much of a criticism.)
Mind Games, "Royalty in Jeopardy": Some prog that I recently found via eMusic. They've got a sound that I describe as being sort of like a mix between Yes and Marillion. They're very good - I wouldn't put them in the top ranks of neo-prog, but they're not at the bottom either.
Riverside, "Cybernetic Pillow": Now, these guys, I would definitely put in the top ranks of neo-prog. Riverside is a Polish prog-rock band, formed by members of a couple of other heavy metal bands. They're absolutely brilliant. This track is off their album "Rapid Eye Movement", which I'd recommend as a first Riverside album.
Marillion, "Hard as Love (acoustic)": This is the version of "Hard as Love"" from their recent acoustic album. HaL was one of their louder, poppier, catchier tunes - a Marillion rocker. To call this just an acoustic mix doesn't do it justice. They took the basic bones of the song, and completely rebuilt it. It's an amazing change. The acoustic version swaps the bridge and the chorus, completely changing the fell of the structure, and turning it into something that's almost a ballad. Amazing, and much better than the original version of the song.
Thinking Plague, "This Weird Wind": Thinking Plague is a group that I have a hard time describing. To me, they sound like a very out-there post-rock group with classical influences, but I've been told that they call themselves a "Rock in Opposition" band. What they are is a distinctly peculiar ensemble. They've got vocals, but they use the singers voice like it's just another instrument in the mix - it's not leading the song in any way, it's just part of the music. The music itself is frequently atonal, with a very peculiar sound. The guitarist sounds very much like one of Robert Fripp's GuitarCraft students - but when I mentioned that in the past, he showed up in the comments saying "Who's Robert Fripp?" I love Thinking Plague, but I have a hard time recommending them - they're so strange that most people won't like them. If you're a big fan of both neo-progressive rock and 20th century classical, then definitely give them a listen.
EQ, "Closer": IQ is back! IQ is a progressive band that got started around the same time as Marillion. Also like Marillion, they started off sounding like a Peter Gabriel-era Genesis rip-off, but they've evolved their own very distinct sound over the years. They're absolutely fantastic - I'd put them up in the top of neo-progressive bands with Marillion and the Flower Kings. And they just released a new album, which is absolutely fantastic.
Sonic Youth, "Rain King (live)": Very typical Sonic Youth - strange tonality. Loud. Tons of hidden complexity. Brilliant. And performed live! No studio tricks here.
Kayo Dot, "The Useless Ladder": Another very hard-to-describe band. Roughly, they're what you get when a progressive metal band decides to start writing 21st century classical chamber music. Very, very highly recommended.
Red Sparrowes, "And By Our Own Hand Did Every Last Bird Lie Silent In Their Puddles, The Air Barren Of Songs As The Clouds Drifted Away. For Killing Their Greatest Enemy, The Locusts Noisily Thanked Us And Turned Their Jaws Toward Our Crops, Swallowing Our Greed Whole": It took me longer to type the title of that than it did to listen to it. Red Sparrowes is a really excellent post-rock band. But frankly, this track just annoys be because of the damn title.
Rachel's, "A French Gallease": A beautiful track by my favorite of the classically-leaning post-rock ensembles.

Orbits, Periodic Orbits, and Dense Orbits - Oh My!

Thu, 05 Nov 2009 12:16:18 -0500

Another one of the fundamental properties of a chaotic system is dense periodic orbits. It's a bit of an odd one: a chaotic system doesn't have to have periodic orbits at all. But if it does, then they have to be dense.

The dense periodic orbit rule is, in many ways, very similar to the sensitivity to initial conditions. But personally, I find it rather more interesting a way of describing key concept. The idea is, when you've got a dense periodic orbit, it's an odd thing. It's a repeating system, which will cycle through the same behavior, over and over again. But when you look at a state of the system, you can't tell which fixed path it's on. In fact, miniscule differences in the position, differences so small that you can't measure them, can put you onto dramatically different paths. There's the similarity with the initial conditions rule: you've got the same basic idea of tiny changes producing dramatic results.

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Free Energy From Air? Sorry, no.

Mon, 02 Nov 2009 14:22:49 -0500

After the fiasco that was my flame against the downwind faster than the wind vehicle, you might think that I'd be afraid of touching on more air-powered perpetual motion. You'd be wrong :-). I'm not afraid to make a fool of myself if I stand a chance of learning something in the process - and in this case, it's so obviously bogus that even if I was afraid, the sheer stupidity here would be more than enough to paper over my anxieties. Take a look at this - the good part comes towards the end.

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The Hallmarks of Crackpottery, Part 1: Two Comments

Wed, 28 Oct 2009 11:25:32 -0500

Another chaos theory post is in progress. But while I was working on it, a couple of comments arrived on some old posts. In general, I'd reply on those posts if I thought it was worth it. But the two comments are interesting not because they actually lend anything to the discussion to which they are attached, but because they are perfect demonstrations of two of the most common forms of crackpottery - what I call the "Education? I don't need no stinkin' education" school, and the "I'm so smart that I don't even need to read your arguments" school.

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Chaos and Initial Conditions

Mon, 26 Oct 2009 22:07:15 -0500

One thing that I wanted to do when writing about Chaos is take a bit of time to really home in on each of the basic properties of chaos, and take a more detailed look at what they mean.

To refresh your memory, for a dynamical system to be chaotic, it needs to have three basic properties:

Sensitivity to initial conditions,
Dense periodic orbits, and
topological mixing

The phrase "sensitivity to initial conditions" is actually a fairly poor description of what we really want to say about chaotic systems. Lots of things are sensitive to initial conditions, but are definitely not chaotic.

Before I get into it, I want to explain why I'm obsessing over this condition. It is, in many ways, the least important condition of chaos! But here I am obsessing over it.

As I said in the first post in the series, it's the most widely known property of chaos. But I hate the way that it's usually described. It's just wrong. What chaos means by sensitivity to initial conditions is really quite different from the more general concept of sensitivity to initial conditions.

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Back to Chaos: Bifurcation and Predictable Unpredictability

Tue, 20 Oct 2009 10:20:07 -0500

So I'm trying to ease back into the chaos theory posts. I thought that one good way of doing that was to take a look at one of the class chaos examples, which demonstrates just how simple a chaotic system can be. It really doesn't take much at all to push a system from being nice and smoothly predictable to being completely crazy.

This example comes from mathematical biology, and it generates a graph commonly known as the logistical map. The question behind the graph is, how can I predict what the stable population of a particular species will be over time?

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Sorry, Denise - but God didn't make numbers

Mon, 19 Oct 2009 15:54:52 -0500

I was planning on ignoring this one, but tons of readers have been writing to me about the latest inanity spouting from the keyboard of Discovery Institute's flunky, Denise O'Leary.

Here's what she had to say:

Even though I am not a creationist by any reasonable definition, I sometimes get pegged as the local gap tooth creationist moron. (But then I don't have gaps in my teeth either. Check unretouched photos.)

As the best gap tooth they could come up with, a local TV station interviewed me about "superstition" the other day.

The issue turned out to be superstition related to numbers. Were they hoping I'd fall in?

The skinny: Some local people want their house numbers changed because they feel the current number assignment is "unlucky."

Look, guys, numbers here are assigned on a strict directional rota. If the number bugs you so much, move.

Don't mess up the street directory for everyone else. Paramedics, fire chiefs, police chiefs, et cetera, might need a directory they can make sense of. You might be glad for that yourself one day.

Anyway, I didn't get a chance to say this on the program so I will now: No numbers are evil or unlucky. All numbers are - in my view - created by God to march in a strict series or else a discoverable* series, and that is what makes mathematics possible. And mathematics is evidence for design, not superstition.

The interview may never have aired. I tend to flub the gap-tooth creationist moron role, so interviews with me are often not aired.

* I am thinking here of numbers like pi, that just go on and on and never shut up, but you can work with them anyway.(You just decide where you want to cut the mike.)

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Saturday Recipe: Chicken Mole Enchiladas

Sat, 17 Oct 2009 13:37:45 -0500

I forgot to take a picture of this dish - so Physioprof, shut up :-)

I don't even pretend that this is an authentic mexican mole. It's something that I whipped together because I felt like a mole, and I worked from very vague memories of a mole recipe I read years ago, and ad-libbed this. So it's absolutely not authentic - but it is yummy.

Ingredients

2 pounds chicken breasts, bone in.
One large onion, diced.
2 cloves garlic, minced.
1 teaspoon coriander powder.
1 teaspoon cumin powder.
1/4 teaspoon cinammon powder.
1 teaspoon mexican oregano.
1/2 teaspoon epazote.
1 chipotle pepper in adobo sauce, finely minced.
1 large dried ancho chili pepper.
1 dried serrano chile pepper.
One can diced tomatoes.
2 ounces dark chocolate, chopped.
1/4 cup tequila.
1 dozen corn tortillas, lightly toasted.
1 tablespoon whole almonds.
chicken stock.
Cheese. (I use cheddar; you should use a mexican queso blanco, but I don't have access to a decent one.)

Instructions

Put a pan on high heat. When it's good and hot, start adding chicken thighs, skin side down, to the dry pan. (You're going to get fat from the chicken skin.) Brown them well on both sides, then remove.
Reduce the heat to medium, and add the onions to the pan with the chicken fat. Stir, and let them cook for several minutes until they're translucent.
Take the dried peppers, remove the seeds, and crush/chop them finely. (Depending on the peppers, they may be brittle, in which case you'll need to just crush them in a mortar and pestle; or they may be leathery, in which case you'll need to mince them.)
Add the garlic, chipotle, and dried chilis to the onions, and let them cook for about 3 minutes.
Add the tequila, and let it cook until most of the liquid has evaporated.
Add the can of tomatoes, the cumin, the cinammon, and the coriander. Stir it to mix, and then re-add the chicken. Add chicken stock until the the chicken is covered.
Let it simmer on medium-low heat for about 20 minutes.
Turn off the heat, and remove the chicken from the sauce. Set it aside and let it cool.
In small portions, move the sauce to a blender, and puree it to a smooth sauce.
Put the pureed sauce back into the pan, and turn the heat on low. Let it simmer for another 10 minutes.
Pull the chicken meat from the thighs, and shred it. Move it into another pan. Add a couple of tablespoons of the sauce, a cup of chicken stock, and simmer it for half an hour.
Shred one half of a corn tortilla, and the almonds into the blender. Add just enough chicken stock to cover them, and puree until smooth.
Add the pureed tortilla and almonds into the sauce, and stir them in. Let it cook until the sauce starts to thicken.
Lower the heat on the sauce to low. Add the chocolate to the sauce, and stir until it's melted and well-blended in.
Taste the sauce, and add salt, black pepper, and sugar to taste.
Toast the tortillas lightly until they're softened.
Into each tortilla, spoon a couple of teaspoons of the shredded chicken, roll it, and then put it into a baking dish.
Spoon the sauce over the fill tortillas. Don't overdo it - you want them nicely coated, but not drowned.
Shred cheese over the top of the sauce.
Bake the casserole with the tortillas for 30 minutes at 350 degrees.

Serve it with a nice mexican rice and beans.

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Humans not yet Perfect? There must be a god involved!

Thu, 15 Oct 2009 16:14:16 -0500

First, a quick status note: the blog has been really slow lately because I fell behind schedule on my book, and I've been putting all of my free time into catching up. I'm finally pretty much caught up, so I should have time to get back to the Chaos theory posts. I need a few days of study time to get myself back up to speed, and then some actual good contentful posts should start showing up.

In the meantime, for your entertainment, I've been looking at a really silly website that was sent to me by a reader with entirely too much free time on his hands. It's another one of those supposed proofs of the existence of God and the correctness of fundamentalist Christianity. In a typically humble (and ungrammatical) fashion, the site is called "4 Step Perfect Proof for God of the Bible, above all other claims on the uncreated creator". And to give the author a miniscule amount of credit, it's not an argument that I recall seeing before. It's a crappy argument that I haven't seen before, but at least it's a sort-of novel crappy argument that I haven't seen before.

The basic idea of it? The fact that we are not perfect means that we must have been created by a perfect God. Is it me, or is there something a bit weird about that argument?

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Saturday Recipe: Home-Made Roasted Tomato Salsa

Sat, 10 Oct 2009 12:10:59 -0500

Lately, friday's have just been too busy for me to get around to posting a recipe. So I decided to switch my recipe posts to saturday. I'll try to be reliable about posting a recipe every saturday.

I tried making homemade salsa for the first time about about two months ago. Once I'd made a batch of homemade, that was pretty much the end of buying salsa. It's really easy to make, and fresh is just so much better than anything out of a jar. When it takes just five minutes of cooking to make, there's just no reason to pay someone else for a jar of something that's not nearly as good.

This recipe isn't much to look at. It's a tomato salsa - it looks pretty much like a salsa you'd buy in a store, except that it's a paler pink, because the tomatoes weren't cooked down. But in terms of taste, it's an absolute knockout.

The original version of this recipe came from Mark Miller's Salsa cookbook., which is a fantastic little book. But since I first made it, I've made enough changes that it's really a very different salsa. Obviously, I like mine better :-).

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The Conservative Rewrite of the Bible

Thu, 08 Oct 2009 14:55:38 -0500

This is really off-topic for GM/BM, but I just can't resist mocking the astonishing stupidity of the Conservapedia folks.

I'm sure you've heard by now that Andy Schafly and his pals are working on a "new translation" of the bible. They say that they need to do this in order to remove liberal bias, which is "the single biggest distortion in modern Bible translations". You see, "translation bias in converting the original language to the modern one" is the largest source of what they call translation errors, and it "requires conservative principles to reduce and eliminate".

Plenty of people have mocked the foolishness of this. So many, in fact, that I can't decide which one to link to! But what's been left out of all of the mockings that I've seen so far is one incredibly important point.

What the "Conservative Bible Project" is doing is not translating the bible. It is rewriting the bible to make it say what they want it to say, without regard for what it actually says. These people, who insist that every word of their holy texts must be taken as absolute literal truth without interpretation -- are rewriting their bibles to make it say what they want it to say.

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Friday Random Ten, 10/2

Fri, 02 Oct 2009 15:39:51 -0500

Dead Soul Tribe, "Goodbye City Life": mediocre prog metal. Not bad, but nothing special either.
Dave Matthews Band, "Lying in the Hands of God": I know, lots of people think I'm crazy to like DMB. But I do. And I find this song terribly depressing. One of the members of the DMB was an amazing saxaphone player named LeRoi Moore. Moore's saxaphone play was absolutely fantastic - incredibly skillfull, tasteful, with a huge range. Moore was killed in an auto accident, and his place was taken in live shows by Jeff Coffin from the Flecktones. Coffin is, in my opinion, a godawful gimmicky player with no taste, no style, and who knows one volume setting: way too loud. This track uses old samples of Moore from before he died - the last time we'll get to hear his beautiful playing.
Marillion, "The Space" (electric): this one is actually a double. I just got the digital version of Marillions new album, which consists of acoustic rewrites of a selection of their old songs. This is one of the tracks that they chose. The original version is from "Season's End", the band's first recording with Steve Hogarth as the lead singer. It's a great song - one of the best from that album. The original version is very interesting - because it's recognizably Marillion, and yet there's a huge difference to the sound of the song compared to the stuff they'd been performing with Fish on vocals - and that basic difference emerged all at once on this album, and stayed with them through the dozen albums since. Like I said, it's classic Marillion, with beautiful transitions, elegant instrumental breaks, intricate structure. A lovely song, which is carried by Hogarths vocals, Kelly's keyboards, and Rothery's electric guitar.
Marillion, "The Space" (acoustic rewrite): An amazing difference. From an incredibly dense electric song, to a sparse, intimate acoustic. It's not just an acoustic remix, but a really deep rewrite of the song. The rhythm of the vocals has changed. The main vocals are now sung mainly against acoustic bass guitar and a but of rythmic chunking on the guitar. Everything is much more syncopated. It's hard to believe it's the same song. I need a few more listens - but I think I actually prefer this newer version - the rhythmic changes and the sparse arrangement just increase the emotional impact of the song. It's really quite impressive.
IQ, "Breathtaker": Bit of a jarring change after the acoustic version of "The Space". But IQ is one of the very best neo-progressive bands out there. Like Marillion, they started off as a Genesis sound-alike, but grew into their own sound. Great song, from "Subterranea", the IQ album to buy if you've never heard them before.
Isis, "From Sinking": Post-rock, from one of the harder/louder post-rock bands. Isis is a bit of a harder listen for many people, because they include death-metal-style screeched vocals, which can really grate. But their overall sound is brilliant - it's worth getting over the vocals to enjoy them.
Dirty Three, "Feral": Another big transition, but still post-rock. Dirty three is a mostly-acoustic post-rock ensemble from the more classical end of the spectrum. Their compositional style is much more minimalistic than a lot of others. But it's beautiful stuff. Highly recommended.
The Flower Kings, "Flight 999 Brinstone Air": What can I say about the Flower Kings that I haven't said before? THey're a neo-progressive band that's fit to drop the neo - they could stand up well next to pretty much any of the original wave of prog in both quality and creativity. This is a typical instrumental track from them. If you've never listened to the Flower Kings, give them a try. It's pure brilliance.
Isotope 217, "New Beyond": This is hard to classify. It might be sort-of progressive rock. It might be sort-of odd Jazz fusion. I just don't even know where to put it. It's a recent acquisition, and to be honest, I haven't formed a firm opinion of it yet. (That could be good or bad. Much of my favorite music is stuff that I wasn't sure about at first. I tend to like things that challenge me as a listener, and so that sometimes means listening a few times to absorb it.)
Abigail's Ghost, "d_letion": Abigail's Ghost was recommended to me by a reader as an American neo-prog band that I'd probably like. Unfortunately, I'm really not wild about it. I don't know if this album is typical of their sound. But I really don't like this one.

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Sloppy Dualism on Bad Astronomy

Fri, 02 Oct 2009 11:36:51 -0500

In the history of this blog, I've gone after lots of religious folks. I've mocked lots and lots of christians, a few muslims, some Jews, some newagers, and even one stupid Hindu.

Today, I'm doing something that's probably going to get me into trouble with a lot of readers. I'm going to mock a very well-known atheist. No, not PZ. As much as I disagree with PZ, as far as I can tell, he's consistent about his worldview.

Over at Bad Astronomy, Phil Plait has been a major voice for skepticism and a vocal proponent of atheism. He has, quite rightly, gone after people of all stripes for foolishness and silly supernaturalism. He's frequently talked about how silly he thinks religion is. All well and good.

But Phil just really screwed up. And I've got to call him on it.

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Information vs. Meaning

Mon, 21 Sep 2009 12:55:37 -0500

If you regularly follow comments on this blog, you'll know that I've been having a back-and-forth with a guy who doesn't know much about information theory, and who's been using his ignorance to try to assemble arguments against the Kolmogorov-Chaitin information-theoretic measure of information in a string. In the course of doing that, I came up with what I think are some interesting ways of explaining bits of it, so I thought I'd promote it to the top-level to share with more readers.

To be absolutely clear up front: I'm far from an expert on K-C theory. It's something that I find incredibly fascinating, and I've read a lot of Chaitin's work. I've been fortunate enough to meet Greg Chaitin a bunch of times when we both worked at IBM, and I've attended a bunch of his lectures. But this isn't my main area of expertise, not by a long-shot.

If you don't know any K-C information theory, then you can look at my introduction here. The rest is beneath the fold.

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Two Dimensional Pathological Beauty: SNUSP

Thu, 10 Sep 2009 12:41:21 -0500

I'm currently away on a family vacation, and as soon as vacation is over, I'm off on a business trip for a week. And along the way, I've got some deadlines for my book. So to fill in, I'm recycling some old posts. I decided that it's been entirely too long since there was any pathological programming 'round these parts, so I'm going to repost some of my favorites.

Todays programming language insanity is a real delight - it's one of my all-time favorites. It's a language called SNUSP. You can find the language specification here, a compiler, and an interpreter embedded in a web page. It's sort of like a cross between Befunge and Brainfuck, except that it also allows subroutines. (And in a variant, threads!) The real beauty of SNUSP is its beauty: that is, programs in SNUSP are actually really quite pretty, and watching them run can be positively entrancing.

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