A common argument by Intelligent Design theoreticians (Dembski, Meyer, Behe) and forum participants (you know who you are! ) is that the astronomically large DNA search space makes the probability of finding functionality by evolutionary mechanisms so vanishingly small as to be effectively impossible.
A very, very strong rebuttal is that evolution has an array of algorithms that allow it to search the space extremely efficiently. Dead ends can be cut off quickly and optima can be approached because existing functionality gradients can be traversed by purifying and positive selection, respectively.
A highly relevant example is the GPT-3 language model, which has 175B 16-bit parameters. The parameter search space is therefore 175,000,000,00016, which can be approximately expressed in binary as 10180. Importantly, this far exceeds Dembski’s universal probability bound of 1 in 10150 – by 30 orders of magnitude.
So the standard ID logic would seem to predict that a search algorithm starting from randomized initial conditions in the GPT-3 search space in which useful, functional peaks are extremely rare – (and they are, I have examined the output of language models in their initialized state!) – would be unable to do anything useful in geological time, much less in human lifetimes.
The success of the OpenAI GPT-3 project proves this ID logic to be unviable. The reason is that the search algorithm, as previously mentioned, can perform hill-climbing in order to find a highly effective functional optimum. It may or may not reach the functional optimum in the search space, but the local optimum it finds is good enough to make it an extremely effective NLP language model.
Similarly, natural selection provides an optimization function that facilitates hill-climbing in biology’s search for optima. This optimization of efficient search strategies (copy-and-modify, reverse transcription, open reading frames, transpositions, etc.) provides a robust explanation of how and why evolution works, and how it is that biologists have been able to accumulate such strong evidence for evolution.
EDIT: Removed an erroneous comparison of search space sizes. HT @Rumraket