Friday, September 23, 2005

A Math Post!

The evolution news is a bit thin today, though you might want to have a look at this statement from the American Astronomical Society supporting the teaching of evolution.

So, what the heck, how about a random math post? Math is just filled with things that can bring a smile to your face and make you say, “Gosh, that's really clever!” Why not share a few of them? If it goes over well, perhaps I will make this a regular feature.

Let's think about addition. If I have two numbers, let's call them x and y, then I can add them together to produce a new number, which I will call z. This fact can be expressed by writing x+y=z.

Addition is something you do to two numbers. You take one number, add it to the second, and that is all. But sometimes we like to talk about adding three or more numbers. What does this mean? Well if I want to evaluate something like a+b+c, I would proceed by first evaluating a+b and then taking the result and adding it to c. In other words, the problem of adding three numbers can be broken down to two separate steps, where in each step I am only adding two numbers.

By the same token, I can add n numbers by carrying out n-1 separate additions, where at each step I am only adding two numbers.

Perhaps there's another concern. In evaluating a+b+c, do I need to worry about the order in which I carry out my additions? The answer is no, which you probably already knew. We can write

a+b+c = c+a+b = b+c+a,

and all of these expressions are equal to the sum obtained from adding the three numbers in any other order. Since the image of our numbers shifting their positions back and forth is vaguely reminiscent of what commuters do in shifting their positions from home to work, we refer to this phenomenon as the commutative property of addition.

What happens if I try to add infinitely many numbers?

Sounds like gibberish. Addition, as I have said, is something you do to two numbers. It is meaningful to talk about adding together arbitrarily large finite collections of numbers, but only by breaking the process down into many smaller steps. But all the small steps in the world will never allow me to add infinitely many numbers. And even if I do manage to add them all up, won't I just keep getting larger and larger numbers without bound?

Perhaps not. Suppose I want to evaluate the following sum:

(1/2) + (1/4) + (1/8) + (1/16) + (1/32) + (1/64) + ...

I am trying to add up all the fractions with one on top and a power of two on the bottom. I have included the parentheses only for ease of reading.

I could reason as follows: If I add up the first two fractions I get

(1/2) + (1/4) = (3/4).

If I added the first three I would get

(1/2) + (1/4) + (1/8) = (7/8).

If I continued in this way, I would find that the sum of the first four fractions is 15/16, the sum of the first five is 31/32, the sum of the first six is 63/64, and the sum of the first n fractions is 2 to the n-th power minus one over 2 to the n-th power.

If I line up these fractions I produce the following sequence

3/4, 7/8, 15/16, 31/32, 63/64, ...

Since every term in this sequence is obtained by adding up a small part of the original series, we refer to this as the sequence of partial sums.

If you stare at that sequence for a while you might notice that each fraction is a little closer to one than the fraction before it. Indeed, by adding up more and more of the fractions in my sequence, I can produce sums that are as close to one as I wish. And from there it's easy to take the plunge and write:

(1/2) + (1/4) + (1/8) + (1/16) + ... = 1.

So if I want to add up infinitely many numbers I carry out the following steps: I add the first two numbers, and jot down the sum. I add the third number to that sum, and jot that down as well. Then I add the fourth number to that new sum, and jot it down. I keep doing this. Then I stare at the sequence of sums that I have produced, and try to determine if it's getting closer and closer to something. I refer to that something as the sum of the infinite series.

Thus, it is now meaningful to talk about the sum of an infinite series.

That's the good news. The bad news is that most of the time your infinite series will not add up to anything. Just try evaluating 1+2+3+4+5+... and you'll see what I mean. Even if it does add up to something, it is usually next to impossible to figure what, exactly, the sum is. If you manage to evaluate this sum:

1 + (1/8) + (1/27) + (1/64) + (1/125) + …

(note that the denominators are all perfect cubes) you will instantly become very famous. (Hint: The sum is known to be irrational).

An infinite series that actually adds up to something is said to converge. Otherwise it is said to diverge. The convergent series are the especially interesting ones.

When confronted with an infinite series, the first question you ask is whether it converges or diverges. Towards that end, there are a variety of tests you can perform that, if they work, will resolve the question. Here's an especially simple one: For there to be any hope that your infinite series converges, you must have that the terms of your series are getting smaller and smaller and smaller.

Otherwise there would be some (possibly tiny) number x with the property that infinitely many terms of your series are larger than x. And if that is the case, then the sum of your series will have to be larger than the sum of infinitely many x's. But no matter how small x is, if you add it to itself enough times you will get very large numbers indeed.

Alas, it is possible that the terms of your series get smaller and smaller, but your series diverges anyway. The most famous example is:

(1/2) + (1/3) + (1/4) + (1/5) + ...

This is known as the harmonic series, and it is a standard exercise in freshman calculus to devise at least three different proofs of its divergence. That means that if you add up enough terms in this series, you can produce a sum that is larger than any number you care to name. (Curiously, if you throw out all of the fractions whose denominators are not prime numbers, the series still diverges. But that's another post).

Adding up infinitely many numbers is not quite the same thing as adding up finitely many numbers. Which might make you wonder how much of your intuition about finite addition remains true when you consider infinite addition.

For example, suppose I have a convergent series in which all of the terms are positive, and I decide to add up the terms in a different order. Will I necessarily get the same sum? Or is it possible that when I discuss sums of infinite series, I must give up the commutative property?

The answer is that I will, indeed, get the same sum. Very comforting.

But what if I throw negative numbers into the mix? For example, consider the following series:

1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + ...

It turns out this adds up to log 2. The expression “log” denotes the natural logarithm; i.e. the logarithm taken to the base e.

(It is possible that in your school days you learned that natural logarithms are denoted “ln” The reason we do not use such an unpronounceable abomination here is that, as far as mathematicians are concerned, base e is the only game in town. It is also possible that you learned that logarithms to the base ten are called, “common logarithms”, a locution so foul I'm sure it exists solely to raise the blood pressure of professional mathematicians. But that's yet another post).

The series above is called the alternating harmonic series, for reasons I trust are obvious. It converges. But if we dropped all the minus signs we would have the harmonic series, which we know diverges.

Let us call such a series conditionally convergent. That means that the series converges, but if you dropped the minus signs (take the absolute value, in math parlance) from all the negative terms you would have a divergent series.

I ask again: If you take a conditionally convergent series and rearrange the terms, can you be certain that they will add up to the same number? To be specific, if I rearrange the terms in the alternating harmonic series, will they still add up to log 2? Or is there a danger that they will add up to something different?

This time the answer is that they might add up to something different.

Actually, it's far worse than that. Hand me any real number and call it x. Positive, negative, rational, irrational, it doesn't matter. I can rearrange the terms of any conditionally convergent series so that the sum is precisely x.

I'm not kidding.

I heard this fact for the first time in a real analysis class in my sophomore year of college. Real analysis (sometimes called “advanced calculus”) is basically calculus, but where you pay attention to proving everything rigorously. The professor was lecturing like gangbusters, and I was dutifully jotting everything down, word for word, in my notes. I was struggling to keep up, when suddenly he tossed off the fact that you can rearrange a conditionally convergent series to make it add up to anything you want. He did not elaborate, and by the time I had lifted my head out of my notes he was on to a different topic. I figured I must have heard him wrong. But I hadn't, it really is true.

Let's see how the trick is done.

Suppose you have a divergent series. Then by adding together sufficiently many terms, you can produce a sum bigger than any number you care to mention. But what would happen if you removed the first one hundred terms from this series? The answer is that the series would still diverge. What if you removed the first billion terms of the series? No effect. In fact, there is no way you can remove finitely many numbers from an infinite, divergent series and produce something that converges.

After all, the finitely many numbers you removed must add up to something finite. If the infinitely many remaining numbers likewise added up to something finite, then the sum of the whole series would simply be the sum of those two finite quantities. And that contradicts the assumption that the series diverges.

Now consider a conditionally convergent series. It is really two series in one: There is a series of positive numbers and a series of negative numbers. By applying logic similar to the argument from the last paragraph, we see there must be infinitely many of each. Furthermore, both of those series must diverge individually. I will ask you simply to take my word for it.

One final observation: Since we are assuming the series converges, we know that the terms in the series must get smaller and smaller and smaller. It follows that the positive numbers and the negative numbers, each taken by themselves, must also be getting smaller and smaller and smaller.

Now take all your positive numbers, arranged from largest to smallest, and put them over here and take your negative numbers, similarly arranged, and put them over there. We are now ready to rearrange our series.

Pick a number. Five sounds good. I will now rearrange my series to produce a sum of five.

Go to your stash of positive numbers, and keep adding them to your series until their sum is just greater than five. We know this is possible, since the series of positive numbers diverges.

Now go to your stash of negative numbers, and take just enough of them to bring your sum down to something smaller than five.

Now return to the positive numbers, and take enough of them to make the sum larger than five once more. Since we have only removed finitely many numbers from our divergent series of positive terms, we know this is possible. Furthermore, since the positive numbers are getting smaller and smaller, the amount by which we overshoot five will be smaller this time than last time.

Return to the negatives, and once again bring the sum down below five.

Since the series of positive and negative terms each diverge individually, w know we can do this forever. Add enough positive numbers to lift your sum over five, then enough negative numbers to bring you below five, and on and on. The amount by which we overshoot or undershoot five will keep getting smaller and smaller.

In this way, our sequence of partial sums will shift, pendulum-like, from being above five to being beneath five, and so on. In the limit it will have to converge to five. The result is a series that adds up to five.

Obviously, we could modify this argument to achieve any sum we desired.

Gosh, that’s really clever!

The process by which we sum up infinitely many numbers seems like a simple extension of basic arithmetic. It isn’t. Strange, counter-intuitive things start to happen when we consider infinite sets. These are the sorts of oddball things that attracted me to math in the first place. Hopefully I managed to communicate some of that here.

Thursday, September 22, 2005

The Darwin Conspiracy?

Browsing in Barnes and Noble yesterday, I came across The Darwin Conspiracy by John Darnton. This is a novel. The plot summary on the jacket reads as follows:

In this riveting new novel, best-selling author John Darnton transports us to Victorian England and around the world to reveal the secrets of a legendary nineteenth-century figure. Darnton elegantly blends the power of fact and and the insights of fiction to explore the many mysteries attached to the life and work of Charles Darwin.

What led Darwin to the theory of evolution? Why did he wait twenty-two years to write On the Origin of Species? Why was he incapacitated by mysterious illnesses and frightened of travel? Who was his secret rival? These are some of the questions driving Darnton's richly dramatic narrative, which unfolds through three vivid points view: Darwin's own as he sails around the world aboard the Beagle; his daughter Lizzie's as she strives to understand the guilt and fear that struck her father at the height of his fame; and that of present-day anthropologist Hugh Kellem and Darwin scholar Beth Dulcimer, whose obsession with Darwin (and with each other) drives them beyond the accepted boundaries of scholarly research. What Hugh and Beth discover - Lizzie's diaries and letters lead them to a hidden chapter of Darwin's autobigoraphy - is a maze of bitter rivalries, petty deceptions, and jealously guarded secrets, at the heart of which lies the birth of the theory of evolution.

With The Darwin Conspiracy, John Darnton again delivers a stunning tapestry of history and imagination, a galvanizing novel.

I bought it, of course. One suspects it has as much connection to reality as the movie Amadeus, but heck, I liked that movie!

Perhaps I was too impulsive. Over at Amazon (linked to above), I find that Publisher's Weekly had this to say:

Darwin's theories have been under attack since he first published The Origin of Species in 1859, but this grandly ambitious novel goes a few steps further to intimate that he was a fraud—and a murderer.

And later:

Stilted dialogue, perfunctory romance and expendable subplots make for a rough voyage, but Darnton (Neanderthal) puts real passion into his historical imaginings and recreations: the revelation of the “true” origin of the theory of evolution is particularly inspired and more than enough to sustain another Darntonian bestseller.

Well, that doesn't sound good.

However, I also found this review by Deane Rink. I know nothing about Mr. Rink, but according to the author bio at the start of the article, he has worked for PBS, The American Museum of Natural History, and National Geographic, among other places. I also noticed that he wrote a favorable review of Richard Dawkins' book A Devil's Chaplain. That tends to make me trust him. He writes:

John Darnton has stuck to the facts as they are known, and projected hypothetical answers for the gray areas in this new novel. Readers familiar with Darwin’s life and the furor that The Origin of Species caused will be amused by Darnton’s solutions, unless they take them to be assertions of fact. Readers unfamiliar with this episode in the history of science will learn much about the wars between science and religion that were fought in the 19th Century, and no doubt notice that some of the same battles continue to be fought today.

He concludes with:

This is a painless way to learn some crucial history of science without wading into dry and pedantic tomes. The reader will be surprised at the conjectural outcome, but also quite possibly satisfied. Darnton handles these issues without pandering to the irrationalities of the modern critics of Darwin, most of whom are driven by their immutable faiths. He once again proves that fiction can illuminate fact in ways that fact itself cannot. (Emphasis Added)

Anyone out there know anything about this novel? Did I get suckered into buying creationist propaganda, or did I buy a first-rate piece of historical fiction?

Multiple Universes

The cover story of the current issue (October 2005) of Astronomy magazine is about the growing consensus among physcists that our little place in the cosmos is simply one universe in a larger multiverse. This cuts right to the heart of one of ID's main arguments: that cosmological “fine-tuning” can only be explained as the direct result of an intelligent designer. If there are an essentially infinite number of universes, each with different fundamental constants, then chance alone is an adequate explanation for why our universe has just the constants it does.

The article, by Steve Nadis, is not freely available online, so here are a few excerpts:

More than 400 years ago, the Dominican monk Giordano Bruno was burned at the stake for making a heretical claim: that our universe was inifnite and contained an infinite number of worlds.

Today, cosmologists arguing a similar point - that our universe is but one of many universes comprising a larger “multiverse” - are hoping for a better fate, maybe even a Nobel Prize. There is growing acknowledgement among physicists and astronomers that this idea, outlandish as it sounds, just might be true.

One picture emerging from cosmology, astronomical observations, and particle physics is that there's a lot more to the universe than we can see: The universe is not only vast, extending far beyond the visible portion, it may be composed of distinct, exponentially large regions with wildly divergent features. For all practical purposes, these realms could be regarded as separate universes within an all-embracing multiverse.

While schemes exist for multiple or parallel universes, one promising approach reflects what Haravrd physcicist Nima Arkani-Hamed calls “the confluence of things now pushing us toward the notion of a multiverse.”

These include: measurements that indicate the universe's expansion is accelerating; empirical tests that bolster the inflationary universe scenario; thoeries of eternal inflation that suggest an endless number of Big Bangs; and recent developments in string theory that show how to design universes with widely different properties. Collectively, these developments support the proposition that on the largest scales, diversity, not uniformity, characterizes our universe.

Later on we find this:

Eternal inflation creates a different kind of universe than the simple sphere we once envisioned. Think of Swiss cheese instead. Each hole represents a bubble universe; the cheese represents the space between the bubbles and is expanding faster than the speed of light. Not only do the bubbles get farther and farther apart, new bubbles keep forming withn the cheese - the result of new Big Bangs popping off in a never-ending chain reaction. Eternal inflation doesn't just produce an oversized hunkof cheese; it produces a multiverse.

How convincing is this scneario?

“Many, no doubt, would call it a house of cards, but from my point of view, it looks very plausible,” says MIT's Alan Guth, generally credited as inflation's inventor. Inflation has been very successful in making predictions - flatness, homogeneity, and scale-invariance - for the part of the universe we can observe, he says, “which means we should also take seriously its predictions for parts of the universe we can't observe.”

Indeed. As I recall, I said something very similar in this blog entry, and took some grief in the comments for it. Nice to have Guth on my side.


As scientists, adds [MIT physicist Max] Tegmark, “We're not testing the general idea of a multiverse. We're testing inflation - a mathematical theory that predicts a multiverse and all kinds of other stuff.” So far, inflation has passed all empirical tests to date, but the idea faces even more rigorous challenges coming later this decade and beyond.

“We still have no idea whether these is one universe or many,” says [Cambridge University astronomer Martin] Rees. Yet at a 2003 Stanford University conference, he was confident enough of the multiverse's existence to stake his dog's life. Stanford's Andrei Linde went further, claiming he would put his own life on the line.

The article has much more to say, including some stuff specifically about the anthropic principle. I recommend picking up a copy (or at least reading it in the bookstore, leaning against the newsstand).

As I read the article I was mostly thinking about just how pathetic the ID folks really are. The fine-tuning of the universe for life is something that needs to be explained. One possibility is to hypothesize that we are part of a multiverse, a conclusion that follows logically from tolerably well-established principles of modern physics. This possibility only requires us to hypothesize that the sorts of forces that led to our Big Bang led to other Big Bangs as well. There is absolutely no argument, beyond personal incredulity, against the idea, and the theorists investigating the possibility are routinley led to other important discoveries for their troubles.

Another possibility is to invent, out of whole cloth, an intelligent agent fundamentally different from any known intelligent agents. This intelligent agent would have unfathomable, supernatural powers. There is absolutely nothing in the way of direct evidence for the existence of such an agent. And if you further hypothesize that this agent is omnipotent and omnibenevolent, there is evidence against his existence (the problem of evil and suffering). Choosing this possibility leads to no insight into any physical process. A physicist choosing this path continues to do research in spite of his belief, not because of it.

I'm with the folks who, by sheer hard work and brain power, are trying to figure out how things really work. Choose the God cop-out if you wish, but stop pretending there's anything scientific about your conclusion.

Wednesday, September 21, 2005

Is Education the Answer?

Brian Leiter links to a recent New York Times article in this post at his blog. The article itself is now only available for a fee in the Times archives, but Leiter produces the following excerpt:

American adults in general do not understand what molecules are (other than that they are really small). Fewer than a third can identify DNA as a key to heredity. Only about 10 percent know what radiation is. One adult American in five thinks the Sun revolves around the Earth, an idea science had abandoned by the 17th century....

Dr. Miller, who was raised in Portsmouth, Ohio, when it was a dying steel town, attributes much of the nation's collective scientific ignorance to poor education, particularly in high schools. Many colleges require every student to take some science, but most Americans do not graduate from college. And science education in high school can be spotty, he said.

“Our best university graduates are world-class by any definition,” he said. “But the second half of our high school population - it's an embarrassment. We have left behind a lot of people....”

Lately, people who advocate the teaching of evolution have been citing Dr. Miller's ideas on what factors are correlated with adherence to creationism and rejection of Darwinian theories. In general, he says, these fundamentalist views are most common among people who are not well educated and who “work in jobs that are evaporating fast with competition around the world.”

But not everyone is happy when he says things like that. Every time he goes on the radio to talk about his findings, he said, “I get people sending me cards saying they will pray for me a lot.”

There's no doubt that science education could be far better than it is in this country. But it is naive to think that improvements in public education by themselves will put much of a dent in the seemingless endless tide of ignroance that has swept the nation in recent years.

Everything mentioned at the start of this excerpt is taught in science classes. Everyone learns in school what molecules are, that the Earth orbits the Sun, that DNA is the key to heredity and what radiation is. That's not the problem.

The problem is that for many kids in this country, the things they learn in school are not reinforced outside of school. If you never hear anything about science outside of school the facts you learn in the classroom will quickly slip your mind. The same goes for any other subject.

And when it comes to science specifically, a lot of kids are leanring things outside of school that are completely wrong. The typical child in a fundamentalist home hears, from the time he is little, a huge amount of false information about what science is and what it's findings are. The best public education system in the world could not fight that.

This is an anti-intellectual society that values neither teaching nor learning. Between public libraries and the internet it is easier to obtain information than ever before, but too many people refuse to make use of these resources. The article complains that we are leaving many people behind. Well, a lot of people are perfectly happy to be left there. At some point, they are responsible for their own ignorance.

Tuesday, September 20, 2005

ID Debate at BU

William Dembski is reporting on a forthcoming debate he will be participating in at Boston University. Representing the forces of evil and darkness will be Dembski and Edward Sisson. Defending sunshine and goodness will be Eugenie Scott and James Trefil.

Actually, the official topic of the debate, according to Dembski, is whether ID should be taught in conjunction with evolution. Seeing as how the official position of the Discovery Institute (the pro-ID think tank of which Dembski is a senior fellow) is that ID should not be taught in schools, it will be an interesting debate indeed.

Incidentally, if you want a good illustration of just how creepy and demented some of Dembski's admirers are, have a look at the comments. For example, here's “Ben Z:”

It seems to me that neither Eugenie Scott nor James Trefil are qualified for a real debate on ID. They’re just going to go for the same old boring objections.

Of course, this particular debate, apparently, is about the teaching of ID and not its scientific merits. Leaving that aside, Eugenie Scott has a PhD in anthropology and has been a major player in evolution/creation disputes for decades. James Trefil, meanwhile, is a professional physicist with particular experience in science education. Mr. Z. finds them unqualified to discuss the subject.

From the other side, Edward Sisson is a lawyer who describes himself (in his contribution to Dembski's anthology Uncommon Descent) as an interested layperson. Qualifications indeed.

Meanwhile, “mechanicalbirds” offers the following:

J. P. Moreland’s critique of naturalism is probably the best out there today. As good a job as all the ID guys are doing, I’m not sure that the battle can really be won until scientists on both sides examine the philosophical foundations that underlie all scientific enterprises. Even though ID isn’t a movement limited to Christianity (or theism, for that matter), I don’t think it is possible for scientific knowledge to even be justified outside of the Christian theistic framework. We’ll see.

Right. So scientists who are not Christians, which is to say most scientists, are simply being irrational. The arrogance of these people is breathtaking.

Museums Fight Back Against Organized Creationism

Today's New York Times has this article about the steps natural history museums are taking to deal with aggressive creationists:

Lenore Durkee, a retired biology professor, was volunteering as a docent at the Museum of the Earth here when she was confronted by a group of seven or eight people, creationists eager to challenge the museum exhibitions on evolution.

They peppered Dr. Durkee with questions about everything from techniques for dating fossils to the second law of thermodynamics, their queries coming so thick and fast that she found it hard to reply.

After about 45 minutes, “I told them I needed to take a break,” she recalled. “My mouth was dry.”

That encounter and others like it provided the impetus for a training session here in August. Dr. Durkee and scores of other volunteers and staff members from the museum and elsewhere crowded into a meeting room to hear advice from the museum director, Warren D. Allmon, on ways to deal with visitors who reject settled precepts of science on religious grounds.

I love that last line. The article's author is Cornelia Dean, who is one of the best reporters on evolutionary issues in the business.

The description of Dr. Durkee having to deal with questions coming thick and fast on a wide variety of topics matches my own experiences dealing with young-Earthers. Most YEC's don't actually care about the subtleties of thermdynamics or paleontology. For them, these subjects exist to provide talking points in these sorts of encounters. They probably didn't hear a word Dr. Durkee said.

From the other side, scientists often find it hard to deal with creationists precisely because they are naturally reticent to discuss scientific disciplines outside their area of expertise. A biologist is naturally going to be reluctant to talk about thermodynamics, for example. Creationists, unencumbered by any desire to understand the subjects they are discussing, labor under no such difficulties.

The article is not very long. Go read it!

Monday, September 19, 2005

Brayton on Dembski

A week ago I posted this entry in which I reviewed some of the recent posts from William Dembski's blog. My conclusion was that Dembski seems to be coming completely unhinged.

As if to confirm my conclusions, Dembski has since written several more dopey, delusional posts. Happily, Ed Brayton has saved me the trouble of eviscerating them myself:

When IDers hire actual PR firms to sell their ideas, that doesn't suggest anything negative about ID. But when evolution advocates write a letter to a school board advocating evolution, he calls that an undue focus on PR and suggests that this proves something wrong with evolution. Dr. Dembski works at a seminary; one would think he'd have stumbled across the biblical concept of not pointing out the splinter in someone else's eye when one has a log in their own by now.

That's he conclusion. Now go read the rest!

Evolution and Buddhism

Today's New York Times has this interesting review of the Dalai Lama's new book, The Universe in a Sinlge Atom:
The Convergence of Science and Spirituality

Actually, the most interesting part of the review is its opening sentence:

It's been a brutal season in the culture wars with both the White House and a prominent Catholic cardinal speaking out in favor of creationist superstition, while public schools and even natural history museums shy away from teaching evolutionary science.

That's wonderfully blunt, and makes a nice contrast with the overly respectful coverage of ID the Times has sometime provided in other articles.

As for the Dalai Lama, he's certainly a lot more sensible than many of the religious leaders in this country:

But this book offers something wiser: a compassionate and clearheaded account by a religious leader who not only respects science but, for the most part, embraces it. “If scientific analysis were conclusively to demonstrate certain claims in Buddhism to be false, then we must accept the findings of science and abandon those claims,” he writes. No one who wants to understand the world “can ignore the basic insights of theories as key as evolution, relativity and quantum mechanics.”

Sounds good. Might have to check this one out. But the reviewer, George Johnson, does sound a cautionary note later on:

But when it comes to questions about life and its origins, this would-be man of science begins to waver. Though he professes to accept evolutionary theory, he recoils at one of its most basic tenets: that the mutations that provide the raw material for natural selection occur at random. Look deeply enough, he suggests, and the randomness will turn out to be complexity in disguise - “hidden causality,” the Buddha's smile. There you have it, Eastern religion's version of intelligent design.

It's hard to comment without having read the book, but Johnson's brief description sounds considerably better than what the ID folks say. It seems like the Dalai Lama is suggesting simply that we have more to learn about evolution; that our perception of randomness in the course of evolution might simply reflect our imperfect understanding of genetics.

If I'm interpreting him correctly, that's far more sensible than what the ID fokls say. The Dalai Lama is telling us we have more to learn. The ID folks are telling us that they have proved mathematically that at some point God waggled his finger and caused something to happen, and any failure on your part to acknowledge that obvious fact simply reflects your irrational predilection for atheism (and probably homosexuality and Communism to boot). That's a big difference.

Alas, the rest of the paragraph is more troubling:

He also opposes physical explanations for consciousness, invoking instead the existence of some kind of irreducible mind stuff, an idea rejected long ago by mainstream science. Some members of the Society for Neuroscience are understandably uneasy that he has been invited to give a lecture at their annual meeting this November. In a petition, they protested that his topic, the science of meditation, is known for “hyperbolic claims, limited research and compromised scientific rigor.”

Oh well. That one's annoying. And it's definitely annoying that he's been invited to address the Society of Neuroscience. Does he, er, know anything about neuroscience?

New Creation Watch Column

Part Two of my column about probability and evolution is now avaialable at CSICOP's Creation Watch site. Enjoy!

In part one I considered the classic anti-evolution arguments based on probability theory, and showed why they failed. In part two we disucss why it is no improvement to add “specification” to the mix. We also examine some of the ways probability theory can be used legitimately to shed light on evolution.