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 : 4^10,000.20^10,000.

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.

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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.

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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.

Sure, maybe it has a ridiculously small probability of occurring, but it would only have to happen once. And how large would you say the universe is? How many planets are there out there that might meet these conditions? And how long have they had for these conditions to meet and occur in exactly the right way? Sure, it's a laughably large unprobability, but it's entirely possible for it to happen, if I have ANY clue as to what I'm talking about.

I read about a theory of Erwin Schroedinger (I believe it was actually in the appendix of the Riven strategy guide) about how the universe is, to us, infinite. Infinity is such a large number, that is the universe is indeed infinite, then every single possible scenario of outcomes has been played out. Every wild fantasy of a science fiction writer, every daydream or idea that anyone has ever had - it has occured somewhere, sometime, in the vastness of infinity.

So perhaps there are 10^20,000 worlds identical to earth where the spark of life never hit the flint. Still, though, all it would have taken was that one freak chance where the right proteins were in the right place at the time and lighting happened to strike and fuse them and the cell happened to suddenly find itself with a new purpose - propagation. Perhaps we are indeed living on that one world out of 10^20,000

In reality though, the chances were probably not as dramatically infinitesimal as you make them out to be. Even as a half-alive organism, the half-bacterium still had the urge to propagate at its core, and it no doubt wandered around bumping into amino acids and proteins until it found the right ones, and eventually it had enough to commence life as we define it.

However, even if the chances are still as minute as 1 in 10^20,000, occam's razor says that the easier answer - that it really was just "lucky old earth" - is probably correct. If you think about just how many times each hour life could theoretically arise, and just how many billions of hours the process had as its' disposal, it isn't that far out of the realm of possibility that it just happened to get lucky and hit on the right combination. After all, there's always a chance, however microscopic it is.

So often we hear about the improbability, which seems to slide into impossibility, when we talk about accidents in nuclear power plants, air traffic control systems, genetically modified organisms, and the whole panoply of low probably, high consequence occurrences.

And they happen; we suffer the consequences.

So why not this low probably, high consequence occurrence?

I can't help but chime in here. What seems to be missing from the original w/u is the notion of sample size. We've all heard the phrase 'large N.' If these unlikely conditions only have to occur once, what if the soup is the size of a planet? Take Earth's oceans. If you divide up their volume into spaces the size of these potential proteins, then what happens?

There's also the notion of time. If we assume that a 'snapshot' of the soup state (God I miss my Newton) lasts for as long as it takes these potential protein spaces to completely slide past each other, then you have even more chances. If it takes a minute, even, for the soup to mix, how many minutes has the Earth been around?

The problem with these arguments, as The Alchemist has properly noted, is that they can be reduced or extended ad absurdum. It's all in the assumptions, baby.