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To this non-specialist’s understanding, the only thing that could be called truly statistically random as far as biological evolution’s concerned would be point-mutations (i.e., in nucleic acid materials) that are caused by covalent bond-breaking radiations (e.g., cosmic rays);  am not certain that mutations wrought by mutagenic chemicals could be called completely random, given the interactions between molecules’ surrounding fields on their approaching one another.

The premature claims of ‘irreducibility’ will eventually have to yield before a rational prebiotic chemical theory for an origin of life.