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Darwin's Eye: Bait and Switch
In The Origin of Species, Darwin admitted that the complexity of the human eye presented a problem for his theory. Having correctly used the word complexity at the outset, he did not use it again but instead switched the discussion to adaptation and natural selection.
It is true that random mutations and natural selection lead to a steady increase in adaptation over many evolutionary steps. What needs to be explained, however, is the increase in complexity, not the increase in adaptation.
The proposition that an increase in adaptation entails an increase in complexity can be disproved if a single counter-example exists. The development of bacterial resistance to streptomycin is such a counter-example (Lee Spetner, Not by Chance, Judaica Press, New York, 1998, p. 141).
Thus Darwin in no way solved the problem of the complexity of the human eye.
A possible, suitable definition of the word complexity of an organism is the least number of pieces of information in a list that would be needed to specify the organism completely enough to enable a copy to be constructed from the information in the list alone.