Honestly I just struggle with the overall statistical likelihood of life evolving. I've tried to get folks to engage on my thinking here but it never happens. I don't know where I'm off.
One example. The number of interactions per second in water is roughly the mean molecular velocity divided by the mean free path times the number of molecules. For a mole of water (~18g) that's approximately 590 m/s * 1/3.1e-10m * 6.02e23 or ~1.15e36 interactions per second. Per kg of water that's ~1.15e36 * (1000/18) = ~6.4e37. Given that most chemical reactions related to the formation of life are going to happen in solution in water, this seems like a reasonable place to start on this journey.
Expanded across all of the water and entire biomass of the earth (in kg) for 5 billion years, this is 1.15e36/kgs * (1.4e18kg + 6e14kg) * (360024365*5e9)s = 2.5e71 potentially life-forming molecular interactions in water on planet earth's history. We're just spitballing here so let's square that to account for any bullshit that I missed.
6.25e142 'interesting' molecular interactions on earth since it was a sphere of magma.
I know this is broken but just roll with the idea for a second.
Given 6.25e142 molecular interactions total, let's assume that's the upper bound of base pairs of DNA stacking on each other (reality is obviously many many many order of magnitudes less). A+C+A+G, then A+C+A+T, then A+C+T+A, etc etc. Let's further assume that the absolute minimum number of base pairs required for a critter to reproduce is 1/10 the smallest observed genome. The smallest i can find is Carsonella ruddi with 160k base pairs. Let's split that down to 16k base pairs just for shits and giggles and assume that most of it can be random and still result in a living reproducing organism. The only constraint i'm going to ask for is that there are one or more critical sections that need to be reasonably correct for the DNA to be viable.
The question is what is the likelyhood that all of these interactions are going to create one of those critical sections?
There are four nucleotides that make up dna, commonly labled as A, C, G and T. The possible combinations of these nucleotides grow exponentially with the length of the sequence. 4 base pairs have 4^4 combinations, 10 base pairs have 4^10 combinations. etc etc. What if we assume perfectly uniform distribution of random variations (obviously broken), what's the maximum length of 'critical section' that we can guarantee will get at least one shot at life.
log₄(6.25e140)=237
237 nucleotides is the limit to where our mythical mix master could explore all possible combinations and any one of those has a 100% chance of being realized. (Keep in mind that this is individual nucleotides, not genes. A single gene typically starts at 1000 nucleotides, our 'most simple organism' Carsonella ruddi has 160,000 base pairs, and the human genome has ~3 billion base pairs.)
What this tells me is that you cannot have a 'critical section' in ANY gene or DNA sequence that is more than 237 nucleotides long and attribute the source of that sequence as some kind of statistical certainty...from there it starts to become a function of chance. The degree to which it is chance depends on what kind of sequence you need to find to get life moving. (ANd this is completely ignoring the fact that DNA is not living, it needs all sorts of mechanisms around it to actually function) This is all true also if you limit the scope of your investigation to the planet earth.
If you expand it to all of the atoms across the entire universe assuming it's one giant blob of water, just expand the middle term from ~1.5e18kg to 1.5e53kg and the length to 15 billion years. You wind up with max critical section length of 355 nucleotides.
Again i'm sure something is wrong with my thinking. But my mental model is that we are operating somewhere along an infinite stream of events of trillions of universes and we are unbelievably special/unique. OR the universe is much more bizarre than we even remotely understand.
¯\_(ツ)_/¯