What is irreducible complexity? When you have a system in biology such that the
intermediate step creates an apparently USELESS system and ONLY the FINAL step results in a USEFUL system. (From Michael Behe) That is what is meant by irreducible complexity.
For example, one not taken from nature. If you build a house. The separate parts don't add up individually into anything meaningful. At different stages, the parts are intermediate. When all of the parts are complete, you have a house.
But is there any way for a complex system to evolve?
Some recent findings a physicist at Caltech wanted to know if he could teach digital organisms how to add, when they didn't know how. Ok, what is a digitial organism? A digital organism is a self-replicating computer program that mutates and evolves. They are used as a study tool of the dynamics of Darwinian evolution. They can be used to test or verify specific hypotheses or mathematical models of evolution. This is closely related to the area of artificial life.
So what happened? At first he presented numbers to them at recurring timed intervals. They were not able to do anything at first. However, each time a digital organism replicated,on occasion one of its command lines might mutate. These mutations allowed an organism to process one of the numbers in a simple way. Thus an indifferent organism might acquire the ability simply to read a number, for example, and then produce an identical output. This would change to characteristic of the organism, from indifference to attentive.
In followups one of the things the scientist did was to reward the digital organisms by speeding up the time it took them to reproduce. If an organism could read two numbers at once, he would speed up its reproduction even more. And if they could add the numbers, he would give them an even bigger reward.
Within six months, the organisms were able to perform many number operations. They were able to evolve on order but the astonding fact was that they evolved in ways that were not initially programmed like taking input, storing it, manipulating it, and producing output.
See http://discovermagazine.com/2005/feb/ for a full story.