Statistical arguments and life don't mix very well. This can be effectively parodied by considering an extreme example: the spontaneous generation of a bacterium.

Given a soup of components, what is the probability a bacterial cell will form? Well, say it has to have 100 proteins and 100 genes to code for them. Let each protein be 100 amino acids long and full frameshifting in effect1. This means a genome of 10,000 bases1 and 10,000 amino acids of protein sequence. Since both have to occur in the same soup simultaneously (one to package the other which in turn codes for more of the same) the probability of forming each must be multiplied together : 410,000.2010,000.

So a chance of 1 in 10 to 20,000 (or therabouts). Even if you have difficulty imagining 106 or 109 (million/billion), this is clearly a laughably huge number. Not just one in a trillion, lucky old earth type of thing - but actually wrong. Yes, that's right : incorrect. Clearly the whole approach is in error.

In fact, even this ridiculous number is an underestimate. For real reactions to take place the components must be in the right orientation and be travelling at the right speed. So this soup has to have amino acids and bases arranged so that they join together all at the same time. It's a little like expecting thousands of passengers in a crowded railway station to happen to form (against their will, probably) a giant line dance. In a particular order.

It seems clear that any such argument that produces such impossible numbers is a parody of itself. In the first place, it is an abuse of statistical mathematics - starting with a particular goal and calculating its probability is simply a waste of paper. Secondly it ignores the importance of intermediate stages.

These models of reality are let down by the built in assumptions that are the very truths the argument tries to prove. The improbability of life's spontaneous generation is easy to explain - it is impossible. Fortunately only those who wish to prove life was generated in an instant by a divine creator start with this strange assumption.

1Although it's normally 3 bases for each amino acid, frameshifting means that you can reduce the bases needed by 1/3. As an interesting sidenote, this does not change the probability. Even though this might seem more improbable - because of the hidden assumtion of particular sequences it makes no difference. If you understand this, you undestand the whole problem.

Update: Re-reading this, I find (as usual) that I have been unclear, vague and wooly (I was Reader in Wooly Logic for a while...).Even I'm not sure what I was trying to say (who IS this "The Alchemist" anyway?).

So, to clear up some of the confusion:

1. In an infinite universe everything occurs. (although see here for an alternative veiwpoint. Involving beans.
2. Eric-the-half-a-bacterium is just the 'problem' attacked by these types of arguments. The bootstrap problem.
3. I have no idea what themusic is going on about.
4. The Custodian raises some important points, which should be addressed more fully here.
5. None of the above are relevant, since I am arguing that life was created neither randomly or by divine will. I believe (yes, yes, science and faith etc etc) that it's misleading to look at modern life and claim it improbable when you cannot see the intermediary steps. There are few (recognisable) 'cellular fossils' to show a progression - an expanding web of complexity. Irreducible Complexity is relevent here.