head of Tyrannosaurus Rex A Horse Race to Beat Dembski's "Universal Probability Bound"

Thomas D. Schneider, Ph.D.

Summary: A horse race is run between Dembski's horse, the so-called "universal probability bound", and the Evj program. Who will win?

As discussed in The AND-Multiplication Error, William Dembski claimed that there is a so-called "universal probability bound" which cannot be beaten, especially not by evolution:

"Randomly picking 250 proteins and having them all fall among those 500 therefore has probability (500/4,289)250, which has order of magnitude 10-234 and falls considerably below the universal probability bound of 10-150."

-- William Dembski, No Free Lunch: Why Specified Complexity Cannot Be Purchased without Intelligence. Rowman and Littlefield Publishers, Lanham Maryland, 2002. page 293

Let's see if we can obtain this "universal probability bound" using the Evj program. First we need to set things up:

Pushing Beyond Dembski's Bound

Can we really break way beyond Dembski's bound? By decreasing the site width, we can pack more sites in. The current Evj (version 1.25) has a limit of 200 sites:
Parameter Value
population: 512 creatures
genome size: 2048 bases
number of sites: 200
weight width: 5 bases (standard)
site width: 5 bases
mutations per generation: 1
The evolution came to 0 mistakes by 12703 generations, with Rsequence = 4.27 bits. Let's use Rfrequency = 3.36 bits for a total of 671.23 bits. 2671.23 = 1.15×10202 This is not yet double the orders of magnitude of Dembski's bound, but it is 50 orders of magnitude greater! It is getting close to the 10-234 that Dembski mentioned. A little more effort should crack that too given that the evolution above works quickly because the site width is small. Here's the image: Beating Dembski's `Universal Probability Bound' using Ev
- screenshot3 It looks a little different because I ran it on a Mac G4, OSX 10.4.2, while the above were run on a Sun computer. Java gives the same results on both.

Let's go even further. Since Rfrequency = log2G/γ, can increase the information by increasing G. Evj 1.25 limits me to genomes of 4096. But that makes a lot of empty space where mutations won't help. So let's make the site width as big as possible to capture the mutations. ... no that takes too long to run. Make the site width back to 6 and max out the number of sites at 200. Rfrequency = 4.36 giving 871 bits.
Parameter Value
population: 64 creatures
genome size: 4096 bases
number of sites: 200
weight width: 6 bases (standard)
site width: 5 bases
mutations per generation: 1

It worked: Beating Dembski's `Universal Probability Bound' using Ev
- screenshot4 The probability of obtaining an 871 bit pattern from random mutation (without selection of course) is 10-262, which beats Dembski's protein calculation of 10-234 by 28 orders of magnitude. This was done in perhaps an hour of computation with around 100,000 generations.

Conclusion

Dembski's claim that evolutionary processes cannot beat the "universal probability bound" are shown by Evj program runs to be false. It took a little while to pick parameters that give enough information to beat the bound, and some time was wasted with mutation rates so high that the system could not evolve. But after that it was a piece of cake.

Notice what I'm doing here. A lot of people say that Intelligent Design claims cannot be tested because they are not science. That's wrong, some of the claims can be tested. But as shown above, and elsewhere on this web site, the claims are demonstrably false. Therefore these claims will not become part of science.

I did learn an interesting lesson from this. (Note that I learned it, not the ID types!) The final binding sites take a long time to mutate because exact hits must be found in certain spots. Thus a high information content binding site may not appear rapidly. If we imagine that sites appear initially as a single control element, then they would have high information content. These would not evolve easily. So it seems more likely that gene duplication of the recognizer occurs, there is decay of the recognizer and that sites tend to have low information content initially. That means they would bind all over the genome and then the excess would be swept away gradually. Also, the threshold seems to restrict the finding of sites when it has a high value. So perhaps the evolution would run faster if one could force the threshold to zero. This is an option on our wish list and it probably simulates the natural situation closer.

References

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Schneider Lab

origin: 2005 Oct 13
updated: 2012 Mar 08
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