As to your experiment, similar things have been done. An experiment showed that as the length of a program grows, the space that holds functional programs tends towards 0. Stephen Wolfram has done several characterizations of automatons which were very interesting, and are referenced in my paper.

Of course, this is all rather speculative, since the structure of sequence space is unknown (plus the fact that it changes shape continuously and in response to things travelling through it makes it difficult to analyse).

An interesting experiment might be to take a model organism like a cellular automaton and mutate one bit of it at a time, to generate a fitness space.

Very good thoughts. The issue is for _open-ended evolution_. It is true that the entire search space is not chaotic. However, in order to get open-ended evolution , it MUST traverse the parts that are chaotic. If it didn’t, it could be implemented with a non-universal computer, and therefore, it would not be open-ended. It might be powerful, but it would only be powerful along the lines for which the system was already built.

So, for non-novel systems (i.e. parameterized evolution), yes, they don’t need to navigate chaotic search spaces. But, to get open-ended evolution, it requires such navigation.

The cell can also have parts which limit the effects of catastrophic error. However, those same systems would also limit truly novel developments.

As the paper pointed out, it’s not that such evolutions can’t happen at all, it’s just that if they do happen, it means that there was an information source guiding the change – either externally or through a parameterized space.

I think you’re right when we’re talking about, say, machine code. If I have a few thousand bits which make up a program, then changing a bit randomly will sometimes produce wildly unpredictable effects. But I’m not sure that just because universal systems CAN be chaotic doesn’t mean they always are. Isn’t life more robust than that?

Take for example a virtual replicator like the von Neumann universal constructor (or perhaps the Hutton replicator, if you don’t want to be waiting all year for results ). As you probably know they’re so fragile that a mutation in one cell will likely make them cease functioning completely. This is obviously not true of DNA (or we wouldn’t survive the mutations we’re born with), which implies that on some level, the system is not completely chaotic.

Am I confusing myself here?