Question from Nick:
How do you refute the argument that it is mathematically impossible for “good” mutations to occur and that evolution is mathematically impossible, and thus not a real theory, but a pseudoscience?
Short answer by SmartLX:
With evidence.
Okay, longer answer by SmartLX:
The idea that beneficial mutations are “mathematically” impossible is based on easily addressed misunderstandings of the process. The fact that the idea is so widely held by creationists despite being so easily addressed speaks to a common reluctance among their number to accept simple facts, if those facts are inconvenient.
A very simple counter to the claim is the fact that most individual mutations can potentially be reversed in subsequent generations. This is an observed and well-known phenomenon straightforwardly called reverse mutation. The list of reversible mutations includes many that would be regarded as “bad” or detrimental to survival and procreation. The reverse of these mutations would by definition be “good”, so there’s no barrier to this whatsoever.
The other effective counter is the set of beneficial mutations that have been observed. You can look them up on Google, or follow up on the short list given here. Most famously, the Lenski E.coli experiment tightly controlled an isolated population of E.coli and documented its acquisition, via repeatable mutation, of the ability to metabolise (eat) the citrate in its environment. The bacteria couldn’t do it, then they could. Creationists did everything they could to discredit this and failed pretty badly. We had our own little argument over it in the comments here (search the page for keyword “Lenski”).