Saturday, October 17, 2009

I wrote a letter to W. Dembski and R. Marks

After reading their article Conservation of Information in Search:
Measuring the Cost of Success
in some detail, I decided to write to W. Dembski and R. Marks, just to hint them to some minor miscalculations: So, they have the chance to get at least the math straight in their peer-reviewed paper.

At, I tried to draw attendance of Willima Dembski to two minor errors in your IEEE paper ''Conservation of Information in Search – Measuring the Cost of Success'':

Could you correct the sign errors in equation (27) and on page 1057, left column, for Q?

More problematic is the next line: you speak about the active information per query, but you calculate the active information per generation, as you drop the factor -2 from Q ~ -2log(L)/log(1-2µ) and so reach

I+ ~ L/log(L) * log(1-2µ) instead of
I+ ~ L/(2*log(L)) * log(1-2µ).

So, I+ should be µ*L/ln(L) and not 2*µ*L/ln(L).

(I stumbled upon this when I calculated my approximation I+ ~ µ*L/H_((1-b)L) for the average number of queries Q ~ H_((1-b)L)/µ )

And there is a little problem with Fig. 2: all the paths seem to start with no correct bits at all - while the math in ch. III-2 assumes that half of the bits are correct.

Let L=100, µ=0.00005:

1. if you use b(eta) = .5 (as in your calculation) Q ~ 92,100 and I+ ~ 0.00109. Then, you should take other paths for your pic

2. if you use b(eta) = 0 (as in you figure) Q ~ 106,000 and I+ ~ 0.000943

The number in your text is I+ ~0.0022. That's wrong in any case.

Di***** Eb**

Don't get me wrong: I don't want to be just nit-picking. One sign error is no big deal, an even number of sign errors cancels itself out :-)
And the factor two? It's at least the same order of magnitude. (And no one know what magnitude is to be expected for active information, so even a factor 100 would not have been easily spotted). And I didn't mention all the inaccuracies in their references' section....

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