 In the Aristotelian/Porphyrian worldview, to be able to distinguish (via strict proof) which qualities of a thing represent its essence vs. property vs. accident vs. definition, and by virtue of this formal description to segregate that entity into its proper place in the taxonomy of nature — this was to achieve the very height of wisdom.In natural or artificial systems that require components to be integrated in some fashion, but where the number of components exceeds what could reasonably be fully interconnected (due to square wise growth in number of connections (= n over two or = n * (n - 1) / 2)), one often finds that some degree of hierarchicality must be employed in the solution.The general advantages of sparse hierarchical systems over densely connected systems—and quantitative estimates of these advantage—are presented by .