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Traditionally physical science operates under two fundamental assumptions: one, that the universe may be reduced to a set of consistent parts and fundamental laws that govern their behavior; two, that the universe and its phenomena may then be reconstructed from this set of fundamental laws. And yet many natural phenomena possess emergent properties that are difficult or even mathematically impossible to deduce even from a complete microscopic description [1, 2].The existence of irreducibly complex systems presents a challenge: to build a science of model discovery beyond the traditional reductionist-constructionist paradigm. 

There are important questions: what is the meaning of structure, divorced from a domain-specific physical context? Can we mathematically define it and detect it? How does one build a consistent mathematical language to describe things as disparate as bird flocking behavior and the formation of galaxies...