Is there some link between the concept of emergence and Turing Completeness? The ideas feel intuitively like they might be linked, but I can find nothing online.

The idea came to me because I was exploring Conway's Game of Life, and it was hard not to suppose a link between these two properties.

Edit: In response to Raphael's point, I have a clarification to the question (which I thought was implied, but in hindsight, it really wasn't)

Must it be the case that systems that exhibit weak emergent complexity are also Turing Complete?

  • $\begingroup$ The question in itself is very interesting, but I'm not sure how to frame it. Turing completeness is a property of computational models, mathematical, "ideal" objects with a formal definition. On the other hand, natural phenomena exist in the real world, and we can at most model them with our mathematical tools. Whether or not a model is suitable for a given phenomenon depends on what kind of questions you want to ask to the model, and there are often multiple valid models, used depending on context. $\endgroup$ – quicksort Nov 4 '17 at 18:14
  • $\begingroup$ Conway's Game of Life is just a special case of a cellular automaton, a computational model that in some variants is indeed universal. $\endgroup$ – quicksort Nov 4 '17 at 18:15
  • $\begingroup$ This seems like a prompt for philosophical discussion, not a question for scientific or mathematical facts. Too broad? Primarily opinion-based? Community votes, please! $\endgroup$ – Raphael Nov 4 '17 at 20:29

I suggest you to give a look to S. Wolfram's book "A New Kind Of Science" (that is also available online).

The centeral ideas are:

Though these ideas are probably not new, they are exposed in a fascinating way (to be honest, a rather informal and non-mathematical "way").

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