Using a new mathematical methodology, scientists have created a scientifically rigorous analogy that shows the similarities between the physical structure of spider silk and the sonic structure of a melody.
According to researchers at MIT, the new way proves that the structure of each relates to its function in an equivalent way.
David Spivak, Markus Buehler of the Department of Civil and Environmental Engineering (CEE) and CEE graduate student Tristan Giesa created the analogy using ontology logs, or “ologs”, a concept introduced about a year ago by Spivak, who specializes in a branch of mathematics called category theory.
Ologs provide an abstract means for categorizing the general properties of a system, be it a material, mathematical concept or phenomenon, and showing inherent relationships between function and structure.
To build the ologs, the researchers used information from Buehler’s previous studies of the nanostructure of spider silk and other biological materials.
“There is mounting evidence that similar patterns of material features at the nanoscale, such as clusters of hydrogen bonds or hierarchical structures, govern the behaviour of materials in the natural environment, yet we couldn’t mathematically show the analogy between different materials,” Buehler said.
‘The olog lets us compile information about how materials function in a mathematically rigorous way and identify those patterns that are universal to a very broad class of materials. Its potential for engineering the built environment — in the design of new materials, structures or infrastructure — is immense,” he said.
At first glance, an olog may look deceptively simple, much like a corporate organizational chart that shows reporting relationships using directional arrows.
However, ologs demand scientific rigor to break a system down into its most basic structural building blocks, define the functional properties of the building blocks themselves with respect to one another, show how function emerges through the building blocks’ interactions, and do this in a self-consistent manner. With this structure, two or more systems can be formally compared.
“The fact that a spider’s thread is robust enough to avoid catastrophic failure even when a defect is present can be explained by the very distinct material makeup of spider silk fibers,” Giesa said.
“It’s exciting to see that music theoreticians observed the same phenomenon in their field, probably without any knowledge of the concept of damage tolerance in materials. Deleting single chords from a harmonic sequence often has only a minor effect on the harmonic quality of the whole sequence,” Giesa added.
The study has been published in BioNanoScience.