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The thing about questions like this is that the complexity of mathematical explanations is highly dependent on what each reader considers "simple." Consider two different approaches to understanding a concept, expressed in information-theoretic terms:

  H(concept) + H(existing explanation|concept) 
vs

  H(concept) + H(existing explanation|concept) + H(categorical explanation|existing explanation, concept)
This additional complexity layer of categorical framing has a nonzero cognitive cost, which varies based on the learner's intuitions and background. The investment in learning categorical thinking only becomes worthwhile when the learner can amortize its cost by envisioning its broad applicability - when they can see how categorical frameworks enable systematic problem decomposition and generalization. This implies they've already recognized the limitations and redundancies of non-categorical approaches, understanding intuitively how many concepts would need to be reinvented as the problem evolves within its conceptual framework (gestell).

However, there exists a middle path that often goes unrecognized as categorical thinking, despite embodying its essence. This approach involves incrementally discovering generalizations -- "oh, this can be generalized with this type" or "oh, if I wrap this in another type I can do something else later on" or "oh this syntactic sugar for this particular operator overload feels quite nice"



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