Behe's Dreadful New Book: A Review of "The Edge of Evolution"

I’ve gotten my hands on a review copy of Michael Behe’s new book, “The Edge of Evolution”. The shortest version of a review is: Bad science, bad math, and bad theology, all wrapped up in a pretty little package.
As people who’ve followed his writings, lectures, and court appearances know, Behe is pretty much a perfect example of the ignoramus who makes a bad argument, and then puts his fingers in his ears and shouts “La la la, I can’t hear you” whenever anyone refutes it. He *still* harps on his “irreducible complexity” nonsense, despite the fact that pretty much *every aspect* of it has been thoroughly refuted. (The entire concept of IC is a pile of rubbish; the entire argument about IC is based on the idea that evolution is a strictly additive process, which is not true; there are numerous examples of observed evolution of IC systems, both in biology and in evolutionary algorithms. But none of these facts makes a bit of difference: like the energizer bunny of ignorance, he just keeps going, and going…)
Anyway, the new book is based on what comes down to a mathematical argument – a mathematical argument that I’ve specifically refuted on this blog numerous times. I’m not mentioning that because I expect Behe to read GM/BM and consider it as a serious source for his research; even if I were an expert in the subject (which I’m *not*), a blog is *not* a citable source for real research. But I mention it because the error is so simple, so fundamental, and so bleeding *obvious* that even a non-expert can explain what’s wrong with it in a spare five minutes – but Behe, who apparently spent several *years* writing this book still can’t see the problem. (In fact, one of the papers that he cites as *support* for this ridiculous theory contains the refutation!)

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The Disgrace of Memorial Day

Today is Memorial Day, and I feel compelled to say something about it.
We’re in the middle of a horrible and pointless war. A war that we started, based on a bunch of lies. Since we did this, we have caused the deaths of hundreds of thousands of innocent Iraqis, and thousands of American soldiers. And we did it for no reason.
As the situation has grown progressively worse, and more and more people have been maimed and killed, we’ve heard an endless drumbeat from Bush supporters: me must support the troops!
I support American soldiers. As the son of a WW2 veteran, I grew up with a lot of respect for soldiers. People who join the military voluntarily give up many of the freedoms that we take for granted, and allow themselves to be put into situations that people like me can’t even really begin to imagine. We ask the members of our military to go and put themselves into a situation where they have to pick up a weapon, point it at someone, and kill them in cold blood – because they’re a member of the enemy’s army. We ask them to put themselves into a position where other people are going to try to kill them. These are horrible things, things that most of us can’t even really contemplate. Because my father put himself into that situation many years ago, he understood what it meant, in a way that I can only imagine.
When soldiers go to war, they’re taught to dehumanize the enemy. They don’t do that because they’re bad people. They do that because they have to: normal people, sane people, can’t pick up a gun, look through its sights at another human being that they don’t know, and pull the trigger and watch them die. People put into that situation hesitate – and hesitation in battle costs lives. As horrible as that sounds to us sitting in our comfortable homes, that’s what must happen to create effective combat soldiers.
When we ask people to do that on our behalf, we take on a great responsibility. We are asking them to do terrible things, things that will, under the best of circumstances, leave deep emotional scars. What happens when we put them into the hell of war is our responsibility. When we send them to war, we are obligated to respect the kind of sacrifices that we ask them to make; to make sure that we only ask them to do it an a cause that’s truly worthy of the price that they will pay; and to care for them and their families after the war is over.
In this war, that hasn’t happened. We’ve asked people to kill and die for no good reason; and while doing it, we have consistently neglected the soldiers we put in harms way, and the families that they left behind.
Our president criticizes people who want to get our soldiers out of harms way as “not supporting the troops” – while opposing funding for medical care for soldiers, housing wounded people in rat-infested hell-holes, denying financial assistance to them and their families. He talk about sending people back into combat three and four times as “support”. He sends them to die, and never attends a funeral, never watches the coffins coming home, never takes any responsibility for the horrors he’s inflicted on them and their families. He works hard to oppose things as simple as funding medical care for returning soldiers. But people who fight him on that, he tars as “not supporting the troops”.
He’s given the orders to teach them them to torture people, given the orders to tell them to torture people, and them blamed them for doing it. The horrors that he has chosen to inflict on them are, in his eyes and the eyes of his supporters, unimportant. He feels no responsibility for what he’s made them do. He’s sent near-children to the front lines, and watched as they’re punished for following his orders, while pardoning – or even rewarding the people who created the policies and gave the orders.
We should honor and respect the people who make sacrifices for our country. Instead, we spit on them, and call it support.
Today is memorial day, the day when we are supposed to remember the people who gave their lives for our country. And instead of honoring them, we’re sending more of them to die for no good reason, in a phony pointless war. Honoring them means making sure that we never ask them to sacrifice themselves unless there is a real need. We deserve to be deeply ashamed of what we’ve permitted in our names. On this day when we honor them, we should be begging them for forgiveness, for what we made them give, and what we made them do.
And meanwhile, our president’s idea of celebrating memorial day is giving a five minute speech, and then rushing off to his barbecue.

The Axiom of Choice

The Axiom of Choice
The axiom of choice is a fascinating bugger. It’s probably the most controversial statement in mathematics in the last century – which is pretty serious, considering the kinds of things that have gone on in math during the last century.

The axiom itself is quite simple, and reading an informal description of it, it’s difficult to understand how it managed to cause so much trouble. For example, wikipedia has a rather nice informal statement of it:

given a collection of bins each containing at least one object, exactly one object from each bin can be picked and gathered in another bin

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The Axiom of Infinity

The axiom of infinity is a bundle of tricks. As I said originally, it does two things. First, it gives us our first infinite set; and second, it sets the stage for representing arithmetic in terms of sets. With the axiom of infinity, we get the natural numbers; with the natural numbers, we can get the integers; with the integers, we can get the rationals. Once we have the rationals, things get a bit harder – but we can get the reals via Dedekind cuts; and by transfinite induction, we can get the transfinite numbers. But before we can get to any of that, we need a sound representation of the naturals in terms of sets.

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We’ve been having some problem with popups showing up on scienceblogs. It’s not deliberate: Seed does not accept popup ads. But it appears that one snuck in somehow, but no one is sure where it’s coming from.

If you see a popup on GM/BM, please do me a favor, and post a comment here telling me:

  1. Who the popup was for,
  2. What ads appeared on the page when the popup popped up.

The sooner we figure out where the popup is coming from, the sooner we can get rid of it.

The Axiom of Extensionality

Some of the basic axioms of ZFC set theory can seem a bit uninteresting on their own. But when you take them together, and reason your way around them, you can find some interesting things.

Let’s start by looking at the axiom of extensionality. Pretty simple, right? All it does is define what set equality means. It says that two sets are equal if, and only if, they have the same members: that is, a set is completely determined by its contents.

How much more trivial can a statement about sets get? It really doesn’t seem to say much. But what happens when we start thinking through what that means?

The way we normally think of sets, they’re collections of objects. So, imagine a set like {red, green, blue}, where the three values are atoms: that is, they’re single objects, not collections. What does the axiom of extensionality say about that? It says that red, green, and blue are not atoms?

Why? Well – let’s look at the axiom of extensionality again: (∀A,B: A=B ⇔
(∀C: C∈A ⇔ C∈B)). So – does red = blue? Well, if they’re atoms, then
yes, red=blue, because nothing is in red, and nothing is in blue. Since neither has any members, they’re equal.

In fact, if we follow that reasoning through, there’s only one possible atom: the only set with no members is the empty set. So anything else we want, we’re going to have to represent using some kind of collection.

As a result of that, along with the axiom of specification, we can show that the axiom
of the empty set is actually redundant. After all – the axiom of specification basically
says that if you can describe a collection of values by a predicate, that collection is a class. So take the predicate P(x)=false; that’s a set with no values. Also known as the empty set. So the empty set exists, and it’s the only set with no members – aka the only atom.

The Axiom of Pairing

The axiom of pairing is an interesting beast. It looks simple, and in fact, it
is simple. But it opens up a range of interesting things that we’d like to be able
to do. For example, without the axiom of pairing, we wouldn’t be able to formulate the
cartesian products of sets – and without cartesian product, huge ranges of interesting and
important areas of mathematics would be inaccessible to us. (Note that I’m saying that
pairing is necessary, not that it’s sufficient. You also need replacement
to get the projection functions that are part of the usual definition of the cartesian

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