Argument from irreducible complexity
The concept of irreducible complexity is that a structure formed in an organism is too complex to have formed in gradual steps, or that a complex structure couldn't have formed in gradual steps because the structure is useless in anything but a complete state.
The eye is often cited in these arguments due to its high complexity. However a possible evolutionary course for the eye has been produced, which due to the nature of this argument, refutes the argument.
The steps that the eye evolves through are as follows (and are diagrammed in the picture):
1. A simple photosensitive nerve
2. A concave depression which allows for directional sensitivity
3. A spherical enclosed area with a pinhole input point, which allows for more precise directional sensitivity
4. A transparent humor develops inside the enclosed area.
5. A lens forms, allowing for the focusing of input light
6. Tertiary structures form, including irises which greater increase the capability of the eye.
The first possibility is that it could have evolved for a different reason. It has been pointed out that a typical pump is of similar design and uses 10 of the parts used in the final flagella outboard motor. They argue that there are 30 extra parts in the final motor, and that the parts in question are used entirely differently from their original purpose. They ask how such an outrageous event could occur to make these things change purpose. It's possible that they adapted to a different purpose and added parts because such was advantageous to do so, a possibility that they dismiss completely.
The second possibility is that it evolved incomplete. Only some parts of it were changed at a time. Because even slight jiggling is preferable over no motion at all. They claim that such is impossible because lacking a single part an outboard motor won't work. However what they overlook is that it doesn't work as well. Parts of the outboard motor can be removed and still have it do something, perhaps not as much as the entire engine together, but even just whirring engines are better than none at all from an evolutionary perspective.
Wikipedia Wikipedia has a number of arguments against irreducible complexity on its page, including detailed sources and links to other arguments.
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