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.
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
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.
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
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?
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
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.)
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
- 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.)
- 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
- 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.
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?
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 :-).
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.
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
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
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.