You say that, however, there is still no convincing scientific explanation for irreducible complexity in evolution. Interestingly, this paradox is exemplified best by the irreducible complexity in the nature of the eyes
> irreducible complexity in the nature of the eyes
There have been several papers published that outline how eyes could have evolved via a series of incremental steps.
I don't have references handy[1], but the process is thought to go something like this:
1. The earliest, primitive animals were tiny. Think small worms and the like.
2. Soft-bodied creatures are always at least somewhat translucent to light, at least to a certain depth: a few millimeters at least. Just shine a torch through the thin part of your hand between your thumb and forefinger! Similarly, this is why you know it is daylight or not even with your eyelids closed.
3. If a nerve in the brain of a primitive creature contains a chemical that is both neurologically active and light sensitive, then even without any "eye structure" at all, it can detect lightness and darkness. Melatonin is thought to be a candidate for this chemical. This can happen by accident but is immediately useful for seeking shelter, escaping a "sudden shadow" (predator), detecting day/night cycles, etc...
4. If those nerves migrate closer to the surface of the skin, then they receive more light, and the sensitivity becomes directional. The most obvious thing is for a spot to develop on top of the head, which is still seen in many creatures today!
5. Having multiple such spots over an area, sensitivity increases.
6. If that light-sensitive patch becomes concave[2], then this provides crude directional sensitivity. The more concave it becomes, the more accurate the direction sense, until it invaginates completely to form a cavity with a small hole as the pupil -- a pinhole camera. There are creatures living today with similar primitive eyes!
7. If the cavity becomes filled with a transparent variant of the skin, then it can be protected from filling up with dirt, etc...
8. If this transparent flesh has uneven index of refraction, it can focus light. This is a primitive lens.
9. Etc...
You get the idea. Essentially, every step can occur incrementally, providing benefits at every step, and these steps are littered throughout the tree of life, we just have to put the steps back in order to see the timeline.
