From: David_Bowman@georgetowncollege.edu
<David_Bowman@georgetowncollege.edu>
>Regarding Richard's latest comments concerning my last post:
>
>>> .... Random sequences (i.e. sequences generated by fully
>>>random processes) are both incompressible and maximally complex.
>>
>>Your last sentence should strictly have said that sequences formed by
random
>>processes *tend* to be incompressible and maximally complex, but are not
>>necessarily so. They may, by chance, turn out to have a regular pattern,
and
>>so be compressible. (Sorry to be pedantic, especially as you've
effectively
>>make this point below, but I didn't want anyone to be misled by this
>>sentence.)
>
>Good point. If we were to be even more pedantic we could say that
>sequences formed by random processes tend to be incompressible and
>maximally complex such that the tendency is manifest by a probability of
>the mean maximal compression ratio being significantly greater than 1
>(by some small fixed positive [delta] no matter how small) asymptotically
>approaching 0 in the limit of the length of the sequences becoming
>arbitrarily long.
And to be even *more* pedantic, we should stress that this only applies to
sequences of independent discrete equiprobable random variables, such as
tossing a fair coin. If, for example, we had a biased coin with a 99% chance
of showing a head, then we would get long sequences of heads, which could be
compressed.
[...]
>>It's also interesting to note that Kolmogorov complexity can give a result
>>opposite to that of Dembski's "specified complexity". The first sequence
of
>>coin tosses above has lower Kolmogorov complexity than the second, but
>>higher Dembski specified complexity (with respect to the chance hypothesis
>>that the coins were tossed fairly).
>
>Yeah. I have not extensively read Dembski's writings, but from what I
>have read he does seem to use this notion in opposite ways. The best
>understanding that I have gotten about what he is claiming about such
>"specified complexity" is that in order for something (such as a
>symbol sequence) to have this property it needs to be *both* highly
>compressible *and* still be highly complex.
I don't believe he ever states that a phenomenon must be complex in the
Kolmogorov sense before we can draw a design inference. His criterion
appears to be a purely probabilistic one.
Dembski seems to be quite keen on the idea of complexity, and determined to
drag it in any way he can. In "The Design Inference", he has a whole chapter
about "complexity theory", which seems to serve two goals. One is to justify
his transformation of probability measures into complexity measures. The
other is to justify his so-called "tractability" criterion for establishing
a specification. However, as I've shown in my rebuttal, neither of these
elements of the Design Inference serves any useful purpose except
obfuscation. He could have omitted that chapter from his book and saved us
all some time.
>The only way these two
>opposing properties can be simultaneously satisfied is if the original
>sequence is so *very* long that even after it has been compressed down
>the length of its complexity (which is much smaller than the original
>sequence because of its high compression ratio due to its high
>compressibility) it *still* is very long as a most-compressed sequence.
>Of course this is not the same as his other criterion of using the
>negative logarithm of the probability of a given sequence, since this
>latter value depends on a knowledge of just what the probability
>distribution is for generating the possible sequences, whereas the
>former notion only requires a copy of the actual sequence(es) in
>question.
Quite.
Richard Wein (Tich)
--------------------------------
"Do the calculation. Take the numbers seriously. See if the underlying
probabilities really are small enough to yield design."
-- W. A. Dembski, who has never presented any calculation to back up his
claim to have detected Intelligent Design in life.
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