A while ago @swamidass commented on a blog post I wrote back in 2013 (https://standard-deviations.com/2013/10/07/the-semiotic-argument-against-naturalism/) to help me make sense of John Lennox’s argument in his book God’s Undertaker. He asked me if we could continue the conversation here.
I’ll give a short summary of the blog post below. Lennox’s book is a much better version of it, which I would recommend. It’s interesting to me because it uses mathematics and algorithmic theory to critique evolutionary theory (I’m an engineer, not a biologist). Although I have no vested interest in it being valid, I think it is fun and have yet to see a strong refutation.
I’ve called it the semiotic argument against naturalism, since it uses information theory (semiotics) to argue against evolution as a plausible mechanism for abiogenesis (the origin of life), but probably also for increasingly complex organisms. The short version goes like this:
1. Genetic systems are information systems
This is widely acknowledged by most biologists, so I’ll leave it at that.
2. The information contained in a DNA molecule is algorithmically incompressible.
Some information can be compressed by algorithms. For example, a string saying ‘ILOVEYOUILOVEYOU’ can be compressed since there is repetition. There may still be information in there, but the more you can compress it, the less information it contains (see https://pudding.cool/2017/05/song-repetition/ for a fun illustration of this). Then there are other strings can’t be compressed. For our purposes, there are two kinds of incompressible strings: ones with random letters, and ones with information, for example this post. The random string is as complex, in the sense that it is one of many different combinations of letters and getting that specific combination is unlikely/difficult to repeat with an algorithm. But it doesn’t convey meaning the way this English does. There are many ways to spill ink on a page: few of them turn out to be letters in meaningful sentences. Also, there is nothing in the physics and chemistry of ink and paper that makes ink molecules self-assemble to write English sentences, so the underlying building blocks are independent of the meaning their combination conveys.
There are 10320 sequence alternatives for the genome to code the simplest biologically significant amino acids, and only a few of them work.
3. Such information-producing algorithms aren’t present in nature
Again, no-one has been able to come up with a counter-example as far as I know, so I’ll leave it there.
4. Algorithms that produce incompressible pieces of information have to themselves be more complex, or receive a more complex input of information, than that which they produce, and therefore do not produce new information.
There is some serious mathematical firepower behind the much of this premise, but from personal experience writing such algorithms, this is self-evident.
5. Therefore the algorithm of evolution by natural selection (or any other unguided process) cannot produce any new information, including that contained in the DNA molecule.
This implies that the information contained in DNA had to be present before evolution took over, and that it had to come from somewhere outside such natural processes.
@swamidass thinks that some of these premises are problematic, but I’ll leave it to him to critique them