, Volume 1, Issue 4, pp 153–161

Reoccurring Patterns in Hierarchical Protein Materials and Music: The Power of Analogies

  • Tristan Giesa
  • David I. Spivak
  • Markus J. Buehler

DOI: 10.1007/s12668-011-0022-5

Cite this article as:
Giesa, T., Spivak, D.I. & Buehler, M.J. BioNanoSci. (2011) 1: 153. doi:10.1007/s12668-011-0022-5


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 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.


Hierarchical materialsNanostructureCategory theoryMusicCompositionAnalogyPatternNatural materialsBiomaterials

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Tristan Giesa
    • 1
    • 2
  • David I. Spivak
    • 3
  • Markus J. Buehler
    • 1
    • 4
  1. 1.Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Mechanical EngineeringRWTH Aachen UniversityAachenGermany
  3. 3.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  4. 4.Center for Computational EngineeringMassachusetts Institute of TechnologyCambridgeUSA