Kolmogorov Complexity - again




I was your main opponent. You are still mistaken, and apparently have not
yet understood the explanations. Especially the part about Kolmogorov
Complexity being uncomputable and therefore not useful for any kind of
actual filter.

Try going over the response where I provided the proof you requested above,
in which I proved that the probability for a given finite string not being
algorithmically ranndom with respect to a randomly selected Universal Turing
Machine is effectively zero.

Try going over the part where I pointed out to you that this argument,
though true, becomes less and less relevant as the string continues to
increase in size.

You just don't seem to grasp the notion that though non-computable,
the concepts of KC do indeed play a key role in the detection of bias
and the ability to successfully predict the future of a growing string
with better than even odds of success - without knowing the actual
mechanism of string production. This concept can even be applied to
finite strings using a UTM based on a subsection of the finite string
and then seeing if the chosen UTM can successfully predict the rest of
the finite string. This is where the concept of symmetry comes into
play as far as predictability of a subset of 0101010 . . . regarding
the rest of the string. The larger the repetitive pattern of the
subset, inductive reasoning suggests that the odds that the next
characters in the sequence will share the same pattern increase.

Your arguments that knowledge of how the string is being produced is
required before useful bias can be detected or better than even odds
of success achieved by betting on what will come next is simply
mistaken - and obviously so. This is what places like Las Vegas are
built upon and this is the basis behind those that have successfully
beat Las Vegas at their own game. A few famous examples include
betting on roulette after analyzing many thousands of results from a
particular wheel, to determine the bias of that wheel for particular
numbers in the analyzed sequence. Knowledge about how the roulette
wheel actually worked was not needed before the obvious bias could be
detected in the resulting number sequence. This bias was used to win
millions of dollars. KC is related to how the bias was detected as
successfully used. Yet, you yourself said that you wouldn't bet any
money at all on such sequence information?! Go figure . . .

Sean Pitman
www.DetectingDesign.com

.

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