The belief that randomness produces information (central to Darwinism) is obviously false. It’s never been demonstrated because it can’t be. It is assumed.
No, it's not "assumed". It's proved. It's one of the most basic results in Kolmogorov information theory, demonstrated every year in the classes I teach. With high probability, a randomly-generated list of symbols will contain a lot of information. To understand this you can use one of Dembski's own metaphors: the combination lock. Which will be harder for someone to deduce, a combination that is your birthday in the form mmdd, or the first four digits of pi, or a randomly-generated 4-digit code?
This does not seem to penetrate the skull of the rather dense Ms. O'Leary, who then tries to weasel out of her claim by saying
by "information," one means here complex, specified information, produced in vast interlocking patterns on a regular basis.
Oh, so she's not talking about "information" in the way it is used by mathematicians and computer scientists. She's talking about creationist information, that vague, incoherent, and self-contradictory mess invented by Dembski and used by basically no one except creationists.
That mess was debunked years ago.
Here's an example: take any English text T, like the first 10 lines of a Shakespearean sonnet. Now apply any decent encryption function f to it that is not known to an adversary, getting U. To the adversary, U will look like random noise and hence be "unspecified", so it will not constitute creationist information. Now I come along and apply f-1 to U, getting T back again. Voilà! I have now magically created information deterministically, something Dembski claims is impossible.
No matter how many times you explain this, creationists offer nothing but lies in response.