Saturday, September 19, 2009

A New Weasel

At Uncommon Descent, W. Dembski presents us with a new weasel: Someone with the name Oxfordensis programmed years ago two Pascal versions.
The interesting aspect: In contrast to the usual weasels - as discussed in the earlier posts - not every letter is changed with a certain probability in this program, but exactly one letter is changed in each child. Here, the word change is used loosely, as with a probability of 1/27, no letter is changed at all.
Mathematically, this is easier to handle: the transition matrix of the corresponding Markov process gets sparser...
And you have only one parameter which can be changed: the size of the generation.
If I had any reader he may ask himself: Does this algorithm latch? Well, the pic provides the answer: it depends :-)
And here are some values for the probability that the program will show a change to the worse during a run of the program, depending on the size of the population:
  1. 99.999 %
  2. 98.485 %
  3. 83.879 %
  4. 55.944 %
  5. 30.008 %
  6. 14.071 %
  7. 6.168 %
  8. 2.649 %
  9. 1.137 %
  10. 0.491 %
  11. 0.214 %
  12. 0.094 %

So, even with a generation size of one hundred children, one in two hundred runs will show that this algorithm doesn't latch - it's not what W. Dembski and R. Marks describe as a partitioned search.

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