AE: "In short, perhaps, science operates competently at each level, but has no competence in grasping the relationships between levels. It works horizontally, not vertically."
As ChrisW says, there need be nothing very mysterious about emergence (after all, this message is merely dots on a screen). And I think science does try to stretch vertically, and does try to study action in that dimension.
In Complexity Theory they say "More is Different" - a slogan confirmed by AI simulations and termites. It's not always easy to "explain" the observed emergent behaviour, but progress is being made. However especially if the different layers share a common code one risks Hofstadter's strange loops, tangled hierarchies, and hierarchy violation.
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