# Issues of scale in the emergence of life

Given environment has probability p of developing life per cubic metre per billion years, and it has n cubic metres. Assume that the bits are all independent.

Probability of developing life at all is p * n.

More exactly, it's 1 - [(1-p)]^n, which is approx. p * n provided p is small enough.

If p is big enough that p * n doesn't work, life is sufficiently certain that it doesn't matter.

There might be scale problems tho, especially in an inhomogenous environment, as (for example) if there are intermediate forms (e.g. one arising in an organic medium, and one in an aqueous medium), the size can be a problem if those two things need to meet, as while these intermediate steps might be very likely to arise individually, they might have a low chance of meeting and so the joining stage might be very unlikely. But that's hard to model and getting very speculative.

The point of all this is that we happened to evolve in a TINY environment. So if we start with our intuition, which is about how likely things are to happen on the earth, the calculation above is always going to tell us to scale it up. Sometimes by a lot.