Tuesday, February 21, 2006

On being a moron

When Red State Rabble pointed out the strangeness of Bill Dembski's use of The Bible Code (a wildly popular work of fiction) as support for ID, DaveScot (at Billy's Blog) blew a gasket ("moron" was tossed about). RSR has some fun with the swicheroo that happened to that post, and the pride in a nickname well-earned.

Not to be outdone by my fellow Kansas blogger, I present a section on Specified Complexity from a PDF paper on Specification. Billy Dembski writes:
To see how all this works, consider the following example from Dan Brown’s wildly popular novel The Da Vinci Code. The heroes, Robert Langdon and Sophie Neveu, find themselves in an ultra-secure, completely automated portion of a Swiss bank (“the Depository Bank of Zurich”). Sophie’s grandfather, before dying, had revealed the following ten digits separated by hyphens: 13-3-2-21-1-1-8-5. Langdon is convinced that this is the bank account number that will open a deposit box containing crucial information about the Holy Grail. We pick up the storyline here:

The cursor blinked. Waiting.

Ten digits
. Sophie read the numbers off the printout, and Langdon typed them in.

ACCOUNT NUMBER:
1332211185
When he had typed the last digit, the screen refreshed again. A message in several languages appeared. English was on top.
CAUTION:
Before you strike the enter key, please check the accuracy of your account number.

For your own security, if the computer does not recognize the account number, this system will automatically shut down.

Fonction terminer,” Sophie said, frowning. “Looks like we only get one try.” Standard ATM machines allowed users three attempts to type in a PIN before confiscating their bank card. This was obviously no ordinary cash machine….

“No.” She pulled her hand away. “This isn’t the right account number.”

“Of course it is! Ten digits. What else would it be?”

“It’s too random.”

Too random? Langdon could not have disagreed more. Every bank advised its customers to choose PINs at random so nobody could guess them. Certainly clients here would be advised to choose their account numbers at random.

Sophie deleted everything they had just typed in and looked up at Langdon, her gaze self-assured. “It’s far too coincidental that this supposedly random account number could be rearranged to form the Fibonacci sequence.”

[The digits that Sophie’ grandfather made sure she received posthumously, namely, 13-3-2-21-1-1-8-5, can be rearranged as 1-1-2-3-5-8-13-21, which are the first eight numbers in the famous Fibonacci sequence. In this sequence, numbers are formed by adding the two immediately preceding numbers. The Fibonacci sequence has some interesting mathematical properties and even has applications to biology.]

Langdon realized she had a point. Earlier, Sophie had rearranged this account number into the Fibonacci sequence. What were the odds of being able to do that?

Sophie was at the keypad again, entering a different number, as if from memory. “Moreover, with my grandfather’s love of symbolism and codes, it seems to follow that he would have chosen an account number that had meaning to him, something he could easily remember.” She finished typing the entry and gave a sly smile. “Something that appeared random but was not.”


Needless to say, Robert and Sophie punch in the Fibonacci sequence 1123581321 and retrieve the crucial information they are seeking.

This example offers several lessons about the (context-dependent) specified complexity
Including that it is fictional?

I confess that I have never read The Da Vinci Code. This little sampler doesn't impress me. Setting aside the point that the Fibonacci sequence is a bad password (as silly as the fact that every combination lock in a physics or math department either uses pi or e), there are a lot of interesting numerical sequences. A truly random sequence of numbers is likely to hit some interesting sequence, especially if sequence doesn't matter.

What are the odds that a random sequence will exactly match the Fibonacci sequence? Small. What if you allow the square numbers, or triangular numbers? How about the digits of pi, or of e? Prime numbers? One plus a prime, one minus a prime? There's a whole The Encyclopedia of Integer Sequences. It has more than 5,000 entries. What are the odds that a random sequence of numbers will match one or more of those sequences? Enormous.

This is the Panglossian paradigm at work. The numbers rearrange to the Fibonacci sequence, and so they must have been a rearranged Fibonacci sequence. Bacterial flagella must be vaguely like outboard motors (rather than like jet engines, or paddle wheels) because everything is for the best in this best of all possible worlds.

Maybe Dembski should spend less time with fiction and work on actual science. He might learn something.