What's the chance?

Often we talk about the probability of things in evolution, of life forming by natural processes, for example. Murray Eden put the nail in this with a paper he gave at the Wistar Institute many decades ago on the mathematical challenges to evolution.

But, what does it mean to have a probability of a 'one-off' event?

Some quotes from the very much  pro-evolutionist book A Beautiful Math by Tom Siegfried (pp. 206-7). Emphasis mine.

So here's a clue about what to do when you know nothing about the probabilities in the system you want to study. Choose a probability distribution that maximizes the entropy! Maximum entropy means maximum ignroance, and if you know nothing, ignorance is by definition at a maximum. Assuming maximum entropy/ignorance then is not just an assumption; it's a factual statement about your situation.
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But what, exactly, does it mean to 'maximize the entropy'? It simply means choosing the probability distribution that would result from adding up all the possibilities permited by the laws of nature (since you know nothing you cannot leave out anything that's possible).

And, there's the rub. When we talk about the 'probability' of life evolving by chance, it must be a type of 'blunt instrument' probability because it remains to be established that there is anything possible in the story of life evolving by known processes. Life is a very low entropy phenomenon and needs a mechanism to overcome the comparitively high entropy equilibrium of the environment and then to keep it there as it 'evolves' the components, inter-dependent sub-systems and dependent machinery to do the job.

Paley's watch

Paley's watch remains one of the most famous arguments for design being produced by a designer. Of course the world and creationist discourse has moved on, but there are those who keep running the arguments of previous centuries and thinking they are cool in so doing.

The typical pro discussion runs this way.

But there's more:

I wonder if a watch is truly complex. It is ordered, no doubt, but it is fairly simple even as machines go: cogs and springs, essentially. Although the dependency chains from any component would be staggering, let alone the interactions between the chains to produce a watch.

However, I think the issue is that coming across a watch in a field we come across something that is not in equilibrium with its environment and that could not be produced by any local equilibrating process. It has very low entropy and very high specified information producing a radical disequilibrium in an artifact with strongly specified function. A mechanism/s is required to achieve this state in the absence of disequilibrating process.

The heart of Paley's argument is that this state is typically and reasonably achieved by a designer; that is, one who applies intelligence to the organisation of materials and processes, rather than the stochastic interplay of 'natural' factors which produce equilibrium even in the short run.