I apologize, I hade read your post in a hurry, and believed that you were speaking of the odds for one query, and not for 3.

As you raised the problem, I have checked, and if I am not wrong, the correct solution for 3 trials has to be calculated according to the binomial distribution, and in our case, with p = 1/27 for each trial, the cumulative probability of getting at least one correct solution in 3 trials should be 0,10704669, which is just slightly lower than 1/9 (0,111111111). So, your calculation was approximately correct.

Again, I apologize for misunderstanding your post.

“So my question to you is, if each letter was “fixed” in the way I believe I understand you mean, why did it take until generation 43 to reach the target from one letter distance, instead of generation 41?”

Because, when we are within one letter of the btarget, we still have to get the last letter by random mutation. I am really surprised that Dawkins got it in only two steps!

Apollos:

“I’m supposing that by the time gen 40 was reached, and the target phrase was one letter off, the only letter place allowed to ‘mutate’ was the ‘incorrect’ one.

This would reduce the chances of reaching the target in each generation to 27^-1; or 1/9 for the generations between 40 and 43. Those are pretty good odds, relatively speaking.”

I perfectly agree with the concept, but not with the calculation. When we are within one letter of the target, the chances for each generation are 1:27^1, that is 1:27. Again, I am surprised at Dawkin’s luck.

I have just tried to get that phrase in the GUI. With an estimated median of 98 queries, I have almost always had a worse result (maybe I am particularly unlucky today…). Finally I got a good result, after many attempts: I got it in 64 queries! (Dawkins is still “best player”).

Here is my final history for the last letter:

61. METHINKS IT IS LIKE A WEASEN
62. METHINKS IT IS LIKE A WEASEU
63. METHINKS IT IS LIKE A WEASEP
64. METHINKS IT IS LIKE A WEASEL

By the way, my heartfelt compliments to Dembski, Marks and Atom for the wonderful realization. The GUI is really useful to illustrate tangibly the folly ofbtrying to abtain even a very short piece of specified information by random, unassisted search. You just have to look at the last search line, which in my example still looked as follows:

WGYOHHFRNIOOOQVPBEOZJJGJLS M

after 1120 queries, and will probably look something like that forever!

This kind of tangible examples are perhaps the only way to heal people from “number numbness”.

So my question to you is, if each letter was “fixed” in the way I believe I understand you mean, why did it take until generation 43 to reach the target from one letter distance, instead of generation 41?

I’m supposing that by the time gen 40 was reached, and the target phrase was one letter off, the only letter place allowed to ‘mutate’ was the ‘incorrect’ one.

This would reduce the chances of reaching the target in each generation to 27^-1; or 1/9 for the generations between 40 and 43. Those are pretty good odds, relatively speaking.

Here is the string at generation 40

METHINKS IT IS LIKE I WEASEL

Which Dawkins introduces as “Generation 40 takes us to within one letter of the target:”

He then says “And the target was finally reached in generation 43″

So my question to you is, if each letter was “fixed” in the way I believe I understand you mean, why did it take until generation 43 to reach the target from one letter distance, instead of generation 41?

I believe this quote from Watchmaher should illustrate what I mean

“It now ‘breeds from this random phrase. It duplicates it repeatedly, but with a certain chance of random error – ‘mutation’ – in the copying”
page 47 last para.

If as you suggest all the letter in correct postions were fixed why the need for more then one generation?

And the strings included in the text, out of necessity, must only represent a small fraction of the “population” so I can see how you get the impression the letters are fixed once hit upon.

Thank you.

I’ll re-read that chapter, but can you substantiate via a quote from Dawkins in the meanwhile?