Lindley, if a molecule can't self-reproduce, it cannot 'spread' its 'advantages'. Other molecules disappearing from the environment also doesn't help it, if it can't self-reproduce. AKA NO Darwinian evolution.
Feel free to post a scenario for Darwinian selection where the actors are not self-replicating - if you have one.
I'm not referring to Darwinian selection per se (that requires reproduction). More that if certain environments favor a particular molecular intermediate heavily, then that form may dominate in that environment; and the probability of any other outcome *prior* to that point in the chain becomes of little importance. Hence, the decision tree could be heavily pruned in places.
This works on the theory that many reactions are reversible, so even if a molecule undergoes the "wrong" reaction at some point it may eventually end up in the "right" state due to conditions. Also, there can be more than one way to synthesize a given molecule, so that needs to be considered as well.
The difference between Darwinian selection and life appearing by chance is probability:
It is very probable that a molecule that can self-replicate better will replicate more - Darwinian selection.
It is not probable that just the right environment will come to help along a not-yet-self-replicating molecule.
If the outcomes prior to one point in the chain are not relevant, then the chain effectively starts there; if you need certain non-common compounds in the 'warm pond', though, it doesn't start there.
And yes, there could be more than one road to life (for example, you mentioned a variant of 101 steps where the molecule goes wrong and then an environment comes that redresses it).
But the number of roads to life is limited - that is pretty certain after the failures of artificial abiogenesis.
You're the one arguing the number of possibilities is immense. I'm not convinced "science" gives us enough of an advantage to claim we could find in a few years when nature took billions of years to figure out. Heuristics only improve state space search if you pick the right one.
Our inability to design a self-replicating molecule is highly relevant, showing us we're talking about a highly complex construct - that is not easily achievable by putting some environments one after the other. You need some very, very specific environments - so subtle, we didn't figure out which despite a lot of searching (not blindly, but guided by science).
Yes, but of this immense number of possibilities, the overwhelming majority are gibbeish. Nature didn't eliminate those; we did.
Nature advanced blindly; we don't.
I'm not sure how it affects the math, but I'd also point out that even though the number of possible molecules increases incredibly fast, the number of possible *reactions* at each step does not. There are a (comparatively) restricted number of ways functional groups can interact. This *might* indicate your assumption of 100! possible outcomes is overly pessimistic.
100! gives such a small chance not because of the number of possible reactions at each point, but because the 100 environments must be independent from each other (environment 1 must not create environment 2, etc) and they must come in a specific order and no other.
I took these environments as independent of each other.
That's why I took the number of environments as small as 100; if environment A creates B creates C, for example, I took them all as a single environment 1 in the 100 chain (due to the high probability of B, C).
Let's say that there are 1.000.000 roads to life (and shame on our biologists for not discovering even one) - this increases the chance of life emerging, but not enough.