Montag, 26. September 2011

Probablility of life on earth, calculated

So I wanted to estimate the probability of life on earth, VERY VERY roughly, just to see if it seems at all likely, within any reasonable order of magnitude, that life could have just by chance popped into existence on the Earth. I'm going to ignore the laws of chemistry for now, which would increase the likelihood significantly, and just see how likely would be for all the right atoms to randomly fall into all the right places to accidentally form a bacteria.

So i started with an average single celled organism, which has about (200x10^10) atoms. Individual pieces of elements. Atoms, not molecules, Atoms. And the number of different types of elements necessary for life, about 10. So some math, giving us the statistical likelihood of all the right atoms falling into all the right places by chance...10^(200x10^10) or 10^20,000,000,000,000.

Thats a one with twenty trillion zeros, the number of shakes it would statistically take to accidentally construct one specific living bacteria, atom by atom, by putting some primordial soup in a glass jar and shakin'.

Really we can stop right there, cuz aint nothin gonna touch that number. But we'll continue, just to see what happens.

We still need to divide that figure by all possible bacterias. At any one time, there are 5x10^30 bacterias alive on the earth. With an average lifespan of 50 minutes, thats 3,650,000 lifespans per year times 4 billion years is about 10,000,000,000,000,000,000 lifespans, times 5x10^30 bacterias giving us 5x10^50 different possible bacterias, cuz yknow, every one is just a little different. So we can nix 50 of those twenty trillion zeros.

So then I took an average size bacteria, 1000nm, which gives us enough space in 1 cubic meter of primordial ooze for 10^27 bacterias. Or, in our case, attempts at bacteria. And multiply that over 1/10 of the earths surface (5x10^10 meters) and we get ...(5x10^10)x(10^27)= (5x10^37) spaces for attempts at bacteria... assuming the primordial ooze us just 1 meter thick.

Then if we say that the primordial ooze gets mixed up 10x per second, that gives us (3x10^8) mixes per year, and with (5x10^37) spaces we get (15x10^48) chances at accidentally creating a bacteria per year. I figure primordial ooze was probably around for about 1 billion years, giving us a total of...(15x10^57) chances for life to form spontaneously. So we can nix another 60 zeros from our twenty trillion.

That leaves us with a 10^-19,999,999,999,89% chance of life just randomly happening to fall into place, atom by atom.

Dang, we should feel lucky!

This calculation is, of course, complete nonsense. But it shows, with some simple math, that even EXTREMELY unlikely things are still possible.

1 Kommentar:

Krakonos hat gesagt…

Nah, sorry to tell you, but I don't really like that, Dan :-( This kind of estimation of magnitude of something is called a Fermi problem. The trouble in your case is that you want to calculate the chance of something, but you don't know of what, because your approach doesn't take into account the existing hypotheses about how life could have started. Bacteria as we see them now are also the product of 3.5 billion years of evolution just like us. (Although admittedly they changed far less.) You also didn't take into account the rarity of some of the involved elements and the chemical reactions necessary to form the required molecules like a many cm long DNA strand that is coiled into a bacteria! This decreases the chance you "calculated" by several magnitudes instead of increasing it, because many of those reactions need complex catalyzers to happen at all or at least need energy. So life definitely didn't start with a bacterium popping up by chance. On the other hand there are many self organizing effects that come into play once you have the right molecules.
You might want to start reading about the very basic Miller experiment. Which is quite old but still a classic, when talking about the formation of the basic molecules that are necessary to form the much more complex ones that form bacteria for example. There you can see, just how much energy is necessary! And from there on there's for example the RNA world hypothesis and one that involves clay as the starting point. You can read that up in the Blind Watchmaker by Richard Dawkins, I think. But it was proposed by someone else. And there are many others. Math only works when you know what to calculate and know at least which variables are involved and how they interplay.
Cheers, Georg