Let's begin by talking about Darwin's work, On the Origin of Species. Darwin was hoping to explain what no one had been able to explain before, which was how the variety and complexity of the living world might have been produced by simple natural laws. This idea is called the theory of evolution by natural selection.
Darwins 5 observations:
1) All species of organisms show variation among individuals
2) Atleast some of that variation is heritable
3) Natural Resources are limited for any given specise, and there will be more offspring in every generation than can make it to the reporductive age
4) There must be some competition for resources within the population; some individuals will outcompete others
5) Some individuals must have a competitive advantage over others in the conditions that prevail at any given time
Conclusion: Those individuals with a competitive advantage will leave more offspring than those without the advantage. The variation that gave them that advantage will be passed on to their offspring and will therefore become more common in the population.
Even though this was an elegant idea, the basis of life was as yet unknown to scientists.
Many of those scientists at that time (Darwin's era) viewed the cell as a simple glob of protoplasm.
Now, we have seen that the cell is run by machines- literally machines made of molecules. There are molecular machines that enable the cell to move, machines that empower it to transport nutrients, and machines that allow it to defend itself.
The main difficulty for Darwinian mechanisms is that many systems in the cell are "irreducibly complex".
Irreducibly complex system : a single system that is necessarily composed of several well-matched, interacting parts that contribute to the basic function, and where the removal of any one of the parts causes the system to effectively cease functioning (Behe 2001).
An example of this would be a mechanical mousetrap like the one you would find in a hardware store.
Typically, such traps have a number of parts: a spring, a wooden platform, a hammer, and other pieces. If one removes a piece from the trap, it can't catch mice. Also, without the spring, or hammer, or any of the pieces, one doesn't have a trap that works half as well as it used to, or a quarter as well; one has a broken mousetrap, which doesn't work at all (Behe 2001)
Irreducible complex systems are very difficult to fit into a Darwinian framework, for a reason insisted by Darwin himself.
Darwin said in the Origin, "if it could be demonstrated that any complex organ existed which could not possibly have been formed by numerous, succesive, slight modifications, my theory would absolutely break down. But I can find out no such case" (Darwin 1859, 158)
Darwin was emphasizing that his was a gradual theory. Natural selection had to improve systems by tiny steps, over a long period of time, because if things improved too rapidly, or in large steps, then it would begin to look as if something other than natural selection were driving the process.
It is hard to see how something like a mousetrap could arise gradually by something akin to a Darwinian process.
A spring by itself, or a platform by itself, would not catch mice, and adding a piece to the first nonfunctioning piece wouldn't make a trap either.
There are many biochemical systems that are examples of irreducible complexity: the eukaryotic cilium, the intracellular transport system, and more.
However, let's discuss the bacterial flagellum.
The flagellum can be thought of as an outboard motor that bacteria use to swim. It was the first truly rotary structure discovered in nature. It consists of a long filamentous tail that acts as a propeller; when it is spun, it pushes against the liquid medium and can propel the bacterium forward. The propeller is attached to the drive shaft indirectly through something called the hook region, which acts as a universal joint. The drive shaft is attached to the motor, which uses a flow of acid or sodium ions from the outside to the inside of the cell to power rotation.
Just as an ouboard motor has to be kept stationary on a motorboat while the propellor turns, there are proteins that act as a stator structure to keep the flagellum in place. Other proteins act as bushings to permit the drive shaft to pass through the bacterial membrane.
Studies have shown that thirty or forty proteins are required to produce a functioning flagellum in the cell. About half of the proteins are components of the finished structure, whil the others are necessary for the construction of the parts that act as the propeller, drive shaft, hook, and so forth- no functioning flagellum is built (Derosier 1998; Shapiro 1995).
A hook by itself, or a driveshaft by itself, will not act as a propulsive device.
Also, there is associated with the functioning of the flagellum an intricate control system, which tells the flagellum when to rotate, when to stop, and sometimes when to reverse itself and rotate in the opposite direction. This allows the bacterium to swim forward or away from an appropriate signal, rather than in a random direction that could much more easily take it the wrong way.
Thus the problem of accounting for the origin of the flagellum is not limited to the flagellum itself but extends to associated control systems as well.
Second of all, a more subtle problem is how the parts assemble themselves into a whole.
The information for assembling a bacterial flagellum resides in the component proteins of the structure itself.
Recent work shows that the assembly process for a flagellum is exceedingly elegant and intricate (Yonekura et al. 2000).
If that assembly information is absent from the proteins, then no flagellum is produced. Thus, even if we had a hypothetical cell in which proteins homologous to all of the parts of the flagellum were present (perhaps performing jobs other than propulsion) but were missing the information on how to assemble themselves into a flagellum, we could still not get the structure (Dembski and Ruse 2004).
The problem of irreducibility would remain.