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.

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 1020,000 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 1020,000

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 1020,000, 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.

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.

It is important to avoid the critical mistake of conflating our modern notions of complex life (even the most basic single-celled life being relatively complex so far as molecular machinery goes) with the sort of 'life' which is invoked by this question. Indeed, the question to be asked first is, what is 'life' at all? It seems upon examination that we ought to count as a living thing any entity which, having come into existence, is capable of making a reproduction of itself prior to the end of its existence, so long as such reproduction is capable of in turn making another generation of reproduction, with no inherent end to this process incumbent in the composition of the original thing or its progeny. And so we then must ask, what is the simplest possible arrangement of atoms into a molecule capable of either self-replication, or of replication of other molecules?

The reason the 'either/or' must be asked is that there are two possible paths to answering the self replication question. If, in nature, a molecule can be formed which is capable of replicating itself -- that is, of attracting atoms of the same kind of which it is composed in such a way that they order themselves along the same alignment as the atoms of the original -- then no second molecule is needed at all. But if there is a molecule capable by its structure of copying molecules around it, and it bumps into a second molecule, the same as itself or different from it, but equally capable of copying molecules around it, then each could make copies of the other ad infinitum; and if these copies stay essentially paired up, then you've got your standard two-molecule self-replicating machine. So forget the unnecessary notion of hundreds of molecules comprising chains of hundreds of atoms each, what is needed is either one self-replicating molecule, or two molecules capable of replicating something else around them.

Now, these sorts of molecules are hardly as hard to come by as one might imagine. The simplest self-replicating molecule is, naturally, a crystal; and the simplest crystal is that of frozen water. With water, the amazing complexity of the crystalization process is displayed in the formation of snowflakes, which take on any of a seemingly infinite array of tri-symmetrical hexagonal patterns. But though water must freeze to crystalize, a great many crystals of somewhat (though not too much) greater molecular complexity can be observed to form and grow through the same molecular self-replication process at higher temperatures in rocks and caves, under the ground, sometimes right out there in the open, some even at quite high temperatures.

But, naturally, we don't consider snowflakes and other crystals of that nature to be alive. Snowflakes form from circumstances, and are not borne from other snowflakes. Crystals do not reproduce beyond the environment of their initial formation and growth; there are no new generations to consume the remains of the old and adapt to the conditions around them. But, in truth, it is quite likely that there is at the basest level no sharp division between what we can consider to be alive and what we can not. After all, a sufficiently complex self-replicating molecule which quite fortuitously is in a position to find materials with which to replicate itself indefinitely could be considered alive. Or perhaps life could require a slight step up in complexity even above that -- perhaps a central molecule which not only replicates itself, but replicates (or causes to be replicated) some other structure. Indeed, what we seek, then, would be something much like this example of biologists creating a self-replicating RNA molecule, which not only replicates itself, but additionally generates an enzyme, a separate molecule capable of assisting in the replication process.

And, really, that's all it takes, for once such a thing as this exists in an environment sufficiently soupy with raw materials, it not only will replicate itself, but some copies can and will generate copying errors (perhaps even reduplication of entire strings) which can with surprising quickness lead to better and better reproduction models. And that's a process powerful enough to bring about limitless variation, just as we experience in the most complex of molecular machines, ourselves.

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locke baron says re spontaneous creation of life on Earth: Things like viroids and prions really muddy up this mess, don't they? Prions are pretty much just rather complex crystals, and viroids aren't a heck of a lot more than that....

DTal says re spontaneous creation of life on Earth: .... I think your closing paragraph is overdrawn, however - a molecule that copies itself need not copy itself in such a way that copying errors leading to increased complexity, or that the mutated molecule will *pass on* its deformity. Obviously this did in fact happen, but the interesting part of abiogenesis is it's not at all easy to see how....

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