"At one point, Paulos claims that the computer scientist Gregory Chaitin’s work shows that a formal system can only generate information whose complexity is less than its own. A dozen or so pages later, Paulos says the mathematician John Horton Conway’s work shows that sources of complexity need not be complex. The reader might be forgiven for smelling a contradiction where none really exists."

I think this might be your area (but I've forgotten). Is there a layperson's explanation for this?

It's gotta fit inside the margins of a comment box, though.

Since George Bush talks to God all the time I must assume there is such a thing. Presumably an elderly white male with a long beard.
But what is religion? To me it is primarily a creation myth. It could also be argued that the big bang theory is just another creation myth. Now physicists are saying that there are as many as eleven dimensions and that the big bang was caused by one dimension coming into contact with another dimension. Certainly there are proofs that the big bang occurred, the expansion of the universe discovered by Hubble as in the Hubble constant as well as the left over heat radiation that has been measured, a supposed fossil of the big bang itself. Still, it is just a theory and the proofs are circumstantial. It is interesting that the laws of physics break down as physics approaches the actual moment of the big bang itself. Then of course there are fractals that some mathematicians have called the thumbprint of God, whatever. Personally I find the big bang theory lacking as it does not actually explain where the original singularity came from in the first place except of course the clashing dimensions idea. My favorite theory is that it is impossible for nothing to exist and that something can indeed be born of nothing of which there is some mathematical proof I believe. I am not sure that I want everything explained as when you take the mystery out of life it ceases to be as interesting.

Donald Johnson:
http://cs.umaine.edu/~chaitin/bonn.html

Eat it up.

Also useful is the Wikipedia page on Chaitin's incompleteness theorem, which has a brief proof outline:
http://en.wikipedia.org/wiki/Kolmogorov_complexity#Chaitin.27s_incompleteness_theorem

Donald: I haven't read the book, but I assume Chaitin refers to Kolmogorov complexity (his life project), the notion that the information contained in a string of symbols should be measured by the length of the shortest computer program that generates it. It's a neat notion (intellectually) but not very useful in practice (these measures are typically undecidable).
So, in the Chaitin sense, the decimal expansion of pi reveals very little complexity because one can produce it with a very short computer program.

Conway refers to a very different kind of complexity -- a predictive kind,
whereby something is complex if tiny perturbations cause huge effects (as in chaos). It is possible to generate such systems in a very simple way: 10 lines of computer code will get you a chaotic system of enormous "complexity" (in the predictive sense). Like all these pictures of fractals you've seen, Mandelbrot sets, etc.

Of course since you forced me into, I have to mention the 3rd kind of complexity: the only one that really for a computer science theorist like me, and that's computational complexity.
Here the idea is that something is complex if it takes too much time to compute it. For example, playing large sudokus is "complex" in this sense.

It's the most important kind because (1) I get paid to work on it, and (2) it's the key to the security of e-commerce and other such things that filthy capitalists worry about.

don't forget irreducible complexity: if it can't be written as the product of two simpler animals, then it was designed by space aliens.

I've never heard the Bohr quote before. (Nils or Aage?) Maybe Einstein was right, but God plays horseshoes instead....

Anonymous,
Talking about something I know nothing about--as usual--but I think my brother the quantum physicist would have an issue with you calling the big bang theory "another creation myth." (I bring him up because we had a conversation about these very issues last month.)

A myth is by definition unprovable; a theory, at least in the context of the Big Bang, must be provable. Furthermore, myths do not change in the face of new information; scientific theories do.

Scientific theories are not, then, what scientists believe, as if scientists were just another group of acolytes, with ideas no better or worse at explaining our world than any other group's. Scientific theories are constantly refined in the face of experiment; and if new information does not verify them, they are at least changed, and sometimes simply scrapped.

I say this not to chastise you, Anon, but to weaken a dishonest argument often employed for political ends.

Carry on, everybody, as you were.

The Mathematical Theory of George Bush in the converse relation to the TAXPAYER. {short program} (U+I)= paying 4 it.

Thanks, Bernard. I've read enough of the popular level explanations of those things to be able to follow you, but wasn't sure what the reviewer meant.

And he's right about how it might be misinterpreted. I've got a friend, a fellow Christian and and also a believer in ID (which I hasten to add I'm not) who's constantly on the lookout for apparent "contradictions" of that sort.

Mike of the Beatles Angle,
You misunderstand me or perhaps I just don’t write in clear manner. I am a fan of science so please do not think I am defending the creationist crowd. I do understand the difference between a myth and a theory however I do believe that there is a similarity between the two as both are given as an explanation for the existence of the universe, an explanation of our origins. No offense to your brother but as far as I am concerned I don’t have much faith in the big bang theory. What if for example it was merely a local phenomenon and the universe is far huger than we know with the scientific data we have? With our present instruments we can see what, about 15 billion light years into the past so we say the universe is about 15 billion years old. But when you think about it that is only what we can see now so who knows. As for your comment about being dishonest that was just a tad unkind on your part.
And actually what I dislike is when scientists bring religion into their science as in the thumbprint of God and that sort of thing. It is almost like we just cannot shake off those religious ties no matter how hard we try.
As exhibited in your utter faith in science that is when science becomes more like a religion, no? The fact is we may never know why the universe exists, it is a possibility you know, we may not just be smart enough to figure it out, gasp. As for science being the answer to everything that as well has religious overtones. Science may not be the answer to everything at all. These are just some things I like to think about so there is no reason for you to be offended by them. However I do admire you charging in like the Calvary to defend science against all critics.

God plays dice, not horseshoes...and frequently he throws snake eyes.

Oh, poor Anon! I absolutely did not mean to call you "dishonest"! Apologies for any offense. What I meant was that I think Creationists often take advantage of others' willingness to "live and let live" or at least entertain all opinions. I have to occasionally remind myself that it's okay to come out strong for what I think is right. So that's what I was doing, in the guise of a response.

Your response makes good sense. I use scientific theories for what they are good for, and religious beliefs for what THEY are good for. Apollo in his chariot does not explain how an airplane flies, but we'd be lesser without it. (And vice versa, of course.)

The thing I like most about science is that it provides for a limitless future of knowledge. Sooner or later, every theory changes--and I think that's a strength, not a weakness. I've no doubt that the Big Bang will be discarded eventually, or changed so fundamentally that it would seem very strange to us were we around in say, 200 years. We may never know the TRUE what and why of the Universe--but it's the hunt for knowledge that fascinates and excites me.

Anyway, sorry if I seemed harsh. It wasn't intentional.

"A general problem with much of Western theology in my view is that the God portrayed is too small. It is a god of a tiny world and not a god of a galaxy, much less of a universe." --Carl Sagan

Noble Mike of Angle
How nice that you misread half of what I have said but that is understandable since for you there are only two ways of looking at things apparently which is either religious or science. I would say I was sorry that I offended you this time but it would not be true. However I am glad you enjoyed my response. I agree with you about the strengths of science but that does not mean science is above criticism. If it were it would not be very scientific now would it? Since this discussion(?) has reached the point of farce of epic proportions there seems little reason to continue with it. I am sure we can all rest easier knowing that your battle for truth, justice and the American way shall never falter. You can put your fangs away now but please in the future remember your blood pressure.

"No, but I've heard it works even for people who don't believe."

Pray in one hand and piss in the other and observe which one gets wet. That is science.
Continue pissing in one hand and praying in the other til both hands get wet. That is faith.

The problem for Bohr is that while it is true that it sometimes 'works' for people who do not believe, it also fails often for the people who do believe.

Or, in other words, Blaise, pardner, I'll take the fucking bet.

MY RELIGIOUS BELIEF IS that WE can find the roots of OUR present situation in OUR failure, as a nation, to ARREST AND JURY TRY Richard Nixon once he left office and OUR not taking a hard look at those around him, those whom WE see today.
MY FAITH IS that WE as AMERICAN TAXPAYERS have learned a lesson and ARREST AND JURY TRY this crowd when they leave office. (am I wrong to believe?)

Sometimes a joke is just a joke.

I like how "Anon" tells Mike this:

"How nice that you misread half of what I have said but that is understandable since for you there are only two ways of looking at things apparently which is either religious or science."

And then refuses to explain exactly what Mike allegedly misread. Run away! Run away!

I am reminded of Henry Wadsworth Longfellow's poem about The Village Blacksmith (the connection to horseshoes is that manufacture of horseshoes was a major component of a blacksmith's work).

UNDER a spreading chestnut tree
The village smithy stands;
The smith, a mighty man is he,
With large and sinewy hands;
And the muscles of his brawny arms
Are strong as iron bands.

His hair is crisp, and black, and long,
His face is like the tan;
His brow is wet with honest sweat,
He earns whate'er he can,
And looks the whole world in the face,
For he owes not any man.

Week in, week out, from morn till night,
You can hear his bellows blow;
You can hear him swing his heavy sledge
With measured beat and slow,
Like a sexton ringing the village bell,
When the evening sun is low.

And children coming home from school
Look in at the open door;
They love to see the flaming forge,
And hear the bellows roar,
And watch the burning sparks that fly
Like chaff from a threshing-floor.

He goes on Sunday to the church,
And sits among his boys;
He hears the parson pray and preach,
He hears his daughter's voice,
Singing in the village choir,
And it makes his heart rejoice.

It sounds to him like her mother's voice,
Singing in Paradise!
He needs must think of her once more,
How in the grave she lies;
And with his hard, rough hand he wipes
A tear out of his eyes.

Toiling,—rejoicing,—sorrowing,
Onward through life he goes;
Each morning sees some task begin,
Each evening sees it close;
Something attempted, something done,
Has earned a night's repose.

Thanks, thanks to thee, my worthy friend,
For the lesson thou hast taught!
Thus at the flaming forge of life
Our fortunes must be wrought;
Thus on its sounding anvil shaped
Each burning deed and thought!