Saturday, April 30, 2011

Craig: If God Kills Kids, It's OK

Fundamentalists say the darndest things!

But they're not always pretty. Here we have the truly appalling spectacle of William Lane Craig justifying genocide. It's OK, he says, if God does it.

And - believe it or not - Craig is actually a respected Christian philosopher. Doesn't it make you wonder about what one would have to do to lose respect?

Craig is fond of syllogisms, so here's one just for him:

1. All sane beings agree that genocide is wrong.

2. The Christian god thinks genocide is just peachy.

3. Therefore...

Thursday, April 28, 2011

Can Irrational Numbers be Represented in a Computer?

I often see the following claim, or variants of it:

"In a computer (as we understand computers, at least), irrational numbers can't be fully accurately represented."

This one happens to be from Bradley Monton, Seeking God in Science: An Atheist Defends Intelligent Design, Broadview Press, 2009, p. 128, but Monton isn't alone.

This is a common misunderstanding that, I think, has two bases. First, for people without much mathematical training, a real number is inextricably linked with its base-10 (or perhaps base-2) representation. For them, the number π is 3.141592653 ..., as opposed to being defined by an integral or infinite series. Second, people without computational training often don't understand that some infinite objects -- including some base-10 or base-2 representations of irrational real numbers -- are routinely represented as finite objects in computers.

Let's take √2 as an example. Although it is irrational, symbolic algebra systems such as Maple and Mathematica routinely represent √2 "exactly" and allow manipulations with it. For example, if you type

> x := sqrt(2);
> x^2;

into Maple, it will happily return the "exact" answer 2. And, similarly, other arithmetic operations involving √2 will give the "exact" answers:

> expand((123+45*sqrt(2))^3);

3355317 + 2224665 √2;

Similarly, we can manipulate other famous irrational numbers such as e, π, etc, and often get "exact" results. The point is that many of the irrational numbers that people actually care about need not be stored in terms of their base-10 or base-2 representation.

But even if we insist that yes, they must be stored in this way, there can still be finite representations. For example, consider the base-10 number defined by having a "1" in the i'th digit if i is a perfect square (like 1,4,9,16, etc.), and 0 otherwise. Now it is easy to see that this number is irrational. But we can still store it in a finite way (for example, as a function that returns the i'th digit on input i), and do at least some simple manipulations on this representation. For numbers whose base-k representation is encoded by a finite automaton, for example, we can do addition, even if the carries come from "infinitely far" to the right. (This is not trivial.)

In fact, any algebraic number, and many others, can be stored as a finite program that on input i returns the i'th digit. In some cases we can even do this by a very simple recurrence. For example, Graham and Pollak, in a 1970 paper, gave a simple explicit recursion to compute the i'th bit of √2 .

The misguided claim I started with can be fixed. If instead we say, "The base-2 representation of most irrational real numbers is not compressible to a finite representation, so the entire base-2 representation of most irrational real numbers cannot be stored in a finite computer", we would be correct. Here "most" means "all but a set of measure zero". But this is not particularly interesting, since for actual computation we are rarely interested in "most" irrational numbers -- we are interested in the computable ones.

Review of Monton's "Seeking God in Science"

Bradley Monton is a philosophy professor at UC Boulder and a self-proclaimed atheist. He's written a little book (147 pages for the main text, not counting the preface, endnotes, index, etc.) entitled Seeking God in Science: An Atheist Defends Intelligent Design, which I finally had a chance to read. It consists of four chapters:

  1. What is intelligent design, and why might an atheist believe in it?
  2. Why it is legitimate to treat intelligent design as science
  3. Some somewhat plausible intelligent design arguments
  4. Should intelligent design be taught in school?

I'm afraid this book is not very good. Monton comes off as rather naive (displaying little understanding of the abundant and documented dishonesty in the ID movement) and ignorant of science, the history of intelligent design creationism, and its role in the creationism-evolution wars.

The first chapter of the book is devoted to one of my least favorite philosophical games: trying to create a definition for a concept that covers all possible cases, by starting with a definition and iteratively refining it. He spends 25 pages (pages 16-40) playing this game with the concept of "intelligent design" itself, in a tedious and unenlightening way (for example, he even addresses the possibility that God is biologically related to humans!) and here is what he comes up with (italics in original):

"The theory of intelligent design holds that certain global features of the universe provide evidence for the existence of an intelligent cause, or that certain biologically innate features of living things provide evidence for the doctrine that the features are the result of the intentional actions of an intelligent cause which is not biologically related to the living things, and provide evidence against the doctrine that the features are the result of an undirected process such as natural selection."

Now I don't particularly like this game (although it has a long history -- philosophers have enjoyed applying it to "chair", for example), because for almost any definition proposed it is easy to come up with some outlandish counterexample. Still, as a mathematician, I enjoy and admire precision, so perhaps it's not a game completely without value. But after reading his definition I could only mutter, All that work! - and he still has an imprecise and unusable mess.

Unusable, since key terms like "intelligent cause" and "undirected process" are not defined or made rigorous. Could it be, as other commentators have already observed, that when we try to define "intelligent cause" we discover that natural selection itself could be considered intelligent by our criteria? Could it be that intelligence is a continuous measure, not a discrete quality, so that speaking of an "intelligent cause" is essentially meaningless unless the amount of intelligence is quantified?

Mess, because by calling intelligent design a "theory", Monton begs the question.

Imprecise, because this definition doesn't cover much of what the intelligent design advocates themselves discuss. For example, in Dembski's book No Free Lunch, he spends a good 10 pages discussing the case of Nicholas Caputo, an election official accused of rigging elections. Dembski implies that his intelligent design methodology can help resolve the case of whether Caputo cheated. But this case has nothing to do with a "global feature" of the universe or a "biologically innate" feature of living things.

Monton seems rather naive about the intelligent design movement. For example, on page 12, he claims, "As a matter of public policy, the Discovery Institute opposes any effort to require the teaching of intelligent design by school districts or state boards of education." But this claim could only be made by someone who doesn't understand (a) that the Discovery Institute has a long history of dissembling and (b) that intelligent design, as practiced by its leading proponents (Behe, Dembski, Meyer) is largely a negative program of casting doubt on the theory of evolution, or examining its supposed deficiencies. Therefore, Discovery Institute programs like "Teach the Controversy" and "Critical Analysis of Evolution" are, in fact, just covers for getting intelligent design into the classroom. This is abundantly clear to most people who have studied the intelligent design movement in any depth.

Part of the book is devoted to analyzing the views of pro-science philosophers, such as Taner Edis, Massimo Pigliucci, and Robert Pennock. Needless to say, Monton thinks they have it wrong in many ways; they are "sloppy" and "confused". But much of his criticism seems misplaced. For example, he gives the following advice to Barbara Forrest: she "focuses too much on attacking the proponents of intelligent design for the supposed cultural beliefs they have, instead of attacking the arguments for intelligent design that the proponents of intelligent design give". But Forrest has never said that intelligent design advocates are wrong because of their cultural beliefs; rather, she has fearlessly and tirelessly explored the goals and strategies of intelligent designers, as well as the sociological and political connections between intelligent design creationism and the religious right. Monton is apparently unconcerned with these details, and that's his right. But then his criticism amounts to "I don't share your interests", and that's rather pathetic.

Monton is a fan of Laudan, citing the following passage approvingly: "If we would stand up and be counted on the side of reason, we ought to drop terms like "pseudo-science" and "unscientific" from our vocabulary; they are just hollow phrases which do only emotive work for us." I strongly disagree. As I mentioned already, almost any definition or classification is subject to exceptions, but it's still useful to be able to say something is a chair or not a chair, even if we cannot always agree about the boundaries. Science, as a social process, has a number of characteristics, and it is perfectly legitimate and useful to point out that creationism and its modern variant, intelligent design, fail to share many of these characteristics.

There are signs that although he thinks intelligent design merits a book-length treatment, Monton hasn't really grappled with the issues. For example, on page 17, he cites a beehive as an example of a feature of the universe that "indisputably exist[s] as a result of an intelligent cause" and then, in a footnote, says that "It was surprising to me that some readers objected to this line of thought, saying that ... bees ... aren't intelligent." Well, I'd guess that this surprise comes largely from the fact that Monton hasn't really thought deeply about what intelligence is. We now know a lot about algorithms and naturally-occurring tools to perform computational processes, but Monton doesn't seem to know anything about it. But then he has some real misconceptions about mathematics and computing, claiming that computers can't represent irrational numbers. (I've addressed this misconception here.)

Several times in the book, Monton refers to the Newtonian account of physics and argues it has been "refuted". On page 50, he uses it to argue that false scientific theories can still count as science (so if intelligent design has been refuted, it could still be considered science). On page 152, he uses it to argue that false scientific theories are routinely taught in high school science (so intelligent design, even if false, could still be caught). But this black-white classification of theories as either "false" or "not false" doesn't even come close to capturing the status of Newtonian physics. Yes, it doesn't give the right answers for particles moving at high velocity, for example. But I can't think of a single scientific theory that unfailingly predicts the outcome of every single experiment. It is more correct, I think, to view theories and equations as our models of reality and to have a good idea of their shortcomings and applicability. No one uses special relativity to solve simple problems in kinematics; they use Newton and they don't apologize for it. If we classify theories purely as "true" or "false" then we lose the nuance that some "false" theories are pretty damn good and others are worthless.

Chapter 3 summarizes some of the arguments of intelligent design advocates, such as alleged "fine-tuning", the origin of the universe, the origin of life, irreducible complexity, and the simulation argument. There is not really much analysis that is new here, but I found his discussion of the simulation argument the most interesting part of the book.

Chapter 4 addresses the question of whether intelligent design should be taught in school. By "taught in school", Monton means "taught in public high-school science classes" (although he takes two whole pages to explain this - an example of how clunky the writing is). One of the objections Monton addresses is "we wouldn't be teaching a real controversy", and he answers this by citing Michael Behe as an example of a real scientist who disagrees with the scientific consensus. Ergo, there is a real controversy. But if Monton's definition of "real controversy" is "one scientist disagrees" or even "a handful of scientists disagree", then there is a "real controversy" about relativity, heliocentrism, and the germ theory of disease. Indeed, it would be hard to come up with a scientific theory for which there is no controversy in Monton's sense. Monton's position is absurd. There are controversies, and then there are controversies; it's not a black-and-white term. The "controversy" over evolution is exactly like that over relativity: a very small number of experts in the field, and a larger number of cranks, disagree with current consensus. That doesn't mean their objections merit coverage in science class. I'm not opposed to teaching controversies, but let's teach some real ones.

Finally, I'd say that the book, and Monton himself, seems curiously disengaged from the extensive mainstream criticism of intelligent design. To give one illustration, he doesn't cite much of the literature arguing against the claims of intelligent design advocates. Nowhere will you find any mention of, for example, the fine article of Pallen and Matzke (published in 2006 in Nature Reviews Microbiology) -- although other articles of Matzke are cited -- or the article of Wilkins and Elsberry (published in 2001 in Biology and Philosophy). He lists two conferences where he's presented his work, and both of them were hosted by the "Society of Christian Philosophers". Four people are listed as endorsers on the back of his book, and three of them are non-biologist critics of evolution (Berlinski, Dembski, Groothuis). And Monton has a blog, but he doesn't allow any comments on it. I can't help but think Monton's book would have been much better if he had made more attempts to be engaged with those who disagree with him.

Wednesday, April 27, 2011

More Muddled Thinking about the Brain

If you can stand it, read this article by Raymond Tallis, entitled "What Neuroscience Cannot Tell Us About Ourselves".

There are a lot of confident assertions, all presented without any real evidence:

  • "It is unlikely that the gap between neuroscientific stories of human behavior and the standard humanistic or common-sense narratives will be closed"

  • "But there is nothing in the activity of the visual cortex, consisting of nerve impulses that are no more than material events in a material object, which could make that activity be about the things that you see."

  • "neural activity is not about anything and so can be neither correct nor mistaken"

  • "A consistent materialism should not allow for the possibility of memory, of the sense of the past"

And Tallis seems to have no understanding of what "information" is.

But most of the article seems to be gobbledygook. If Tallis were to try to come up with a rigorous definition of words like "about", he might make some progress. By his argument, it makes no sense to count tree rings to determine a tree's age, since tree rings are not "about" the age of the tree.

As Arthur C. Clarke noted, "When a distinguished but elderly scientist states that something is possible, he is almost certainly right; when he states that something is impossible, he is probably wrong."

Sunday, April 24, 2011

Psychic Fail

A photo from New Orleans.

If I were a real psychic, I wouldn't pay for "24 hr. surveillance", as the sign at the left indicates. Instead, I'd just send security guards around at the time I knew people were about to break in.

Neil Postman - Perpetually Clueless

Yesterday I attended a baseball game in Buffalo, NY: the Bisons versus the Lehigh Valley Iron Pigs. There was, as usual, a big video scoreboard in centerfield.

So this clueless quote from Neil Postman, recently posted on Doug Groothuis's blog, is appropriate:

"Media may now be serving as a surrogate for reality, and a preferred one at that. At stadiums throughout the country, huge TV screens have been installed so that spectators can experience the game through TV because TV is better than being there, even when you are there."

Postman has got to be one of the most overrated media commentators ever.

As I commented to my young son, in many ways, watching baseball at a stadium is a much better experience today than it was when I attended my first game in 1967.

It's not that "TV is better than being there" or that it is "a surrogate for reality", as Postman claims - whatever that means.

It's that a big screen offers more information than the scoreboard of 1967: you get the batter's average and other statistics; you get a reminder of what happened earlier in the game when that batter was up; and you get instant replays of interesting plays you might not have fully appreciated or understood the first time around.

Postman never really understood media; his observations are generally self-important, trite, and ignorant.

"Be it Ever So Humble" - a short story by Louise Shallit

Here's a short story entitled "Be it Ever So Humble" that appeared in Story magazine, Vol. 27, No. 115 (September-October 1945) by my mother, Louise Lee Outlaw. I think this may have been the first short story she published in a national magazine, although she had been writing for newspapers since 1938. Although it doesn't display her at the height of her powers, there are some very nice lines.

As an interesting footnote, another story in the same issue was written by Joseph Heller, who, of course, later became famous as the author of Catch-22.

Friday, April 15, 2011

The True Crocker Story

Over at Uncommon Descent, we have more playing the victim, this time about creationist Carolyn Crocker, and probably written by the World's Worst Journalist™.

For the true story about Crocker, go here.

Having Crocker as the "executive director of a think tank on integrity in science" is kind of like having Newt Gingrich as executive director of a think tank on integrity in marriage.

Thursday, April 07, 2011

Religion at the Science Fair

I judged my first science fair yesterday.

There were some good projects, but most of them were a bit disappointing. The main problem was the lack of originality: most were testing hypotheses that were either obviously true or uninteresting. Good original hypotheses are hard to come by, but still...

One student from a local Christian school added evangelical Christian content to her poster and report. The project concerned determining which solvent was the best to remove stains from various materials. At the end, the student thoughtfully reminded everyone that humanity is also "stained" and that the only stain remover was Jesus.

I feel very sorry for this student, who has clearly been relentlessly indoctrinated by her teachers -- and probably instructed to add this kind of unscientific postscript to her display.