  Complex hierarchical structures composed of simple nanoscale building blocks
form the basis of most biological materials. Here we demonstrate how analogies
between seemingly different fields enable the understanding of general
principles by which functional properties in hierarchical systems emerge,
similar to an analogy learning process. Specifically, natural hierarchical
materials like spider silk exhibit properties comparable to classical music in
terms of their hierarchical structure and function. As a comparative tool here
we apply hierarchical ontology logs (olog) that follow a rigorous mathematical
formulation based on category theory to provide an insightful system
representation by expressing knowledge in a conceptual map. We explain the
process of analogy creation, draw connections at several levels of hierarchy
and identify similar patterns that govern the structure of the hierarchical
systems silk and music and discuss the impact of the derived analogy for
nanotechnology.
