Yeah, you're right. Degenerate cases would violate the intuition. But that happens everywhere we're forced to develop coherent and complete definitions. The empty set is a good example. A set with nothing in it? Pffft. So, I'd be OK with the extreme case where the generators were expressive and the phenomena could express only the empty proposition. But in order to talk about the complexity of such a map, we'd have to have a *constructive* definition of that map. (Reminds me of this: https://www.youtube.com/watch?v=wn8XFiAwLkM)
As for removing the ordering at all (allowing the phenomena to be more or less expressive than the generators), without allowing that, I'm hard pressed to handle cases like Russell mentioned, where sets of explicit primitives are represented by an algorithmic compression, especially if we allow evolutionary algorithms (or eg swarm optimization or ANNs) to "discover" those compressions ... and especially as Marcus points out if some of those compressions are inscrutably opaque. I mean, it's reasonable to allow that maps like AxAxA → BxB can be complex maps, right? On 5/8/19 5:21 AM, [email protected] wrote:
Surely not *simply* "different"? If the post-map language has strictly less expressibility than the pre-map language, does "emergence exist"? Well, maybe. What if (the extreme case) it has NO expressibility? Either of those would fit under that other proposed description, "phase transition", but (to me) the informal notion of "emergence" just can't include the extreme case, and probably shouldn't include the "strictly less" case (but maybe I could be argued out of that "shouldn't").
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