Hierarchical Analysis of Music and Spider Silk using Category Theory

Complex hierarchical structures composed of simple basic building blocks form the basis of most biological materials. The comprehension of these materials (i.e. how functionality emerges) is mostly done by understanding its structure in a top-down approach. Here we show that with a simple analogy between seemingly different fields it is possible to gain insights in general principles and properties. Specifically, we showcase that material science exhibits comparable properties as classical music in terms of hierarchical structures, functionality and mutability. As a comparative tool we utilize an application of mathematical category theory called onthology logs (olog). Ologs provide an illuminative system representation by expressing knowledge in a conceptual map that follows a rigorous mathematical formulation based on category theory. We exemplify these similarities with a case study of classical music and spider silk which intrigued scientists for a long time. We will draw connections on several levels of hierarchy and indentify similar patterns that govern the structure of these two hierarchical systems. The analogy developed in our work will enable further understanding of natural and novel protein based materials and show that seemingly disparate fields such as material science and classical music are closely related.