A category-theoretic approach to modeling John Cage's Silent piece

TL;DR

This paper models John Cage's Silent piece using category theory, deriving a formal schema from his compositions to analyze its structure and semantics.

Contribution

It introduces a novel category-theoretic framework to represent and reason about Cage's Silent piece and its related compositions.

Findings

Derived a category schema for the Silent piece from multiple compositions.

Used functors and pushouts to formalize the meta-work within category theory.

Provided a semantics for analyzing the spatio-temporal structures of the piece.

Abstract

We derive a schema of John Cage's meta-work the Silent piece from his compositions 4'33'', 0'00''(4'33'' No. 2), and One3, using the mathematics of category theory within Spivak and Kent's (2012) framework of ontological logs for knowledge representation. A category presentation A of a database that describes an instance of 4'33'' from its premiere in 1952 is translated via two functors into the category presentations B (0'00'') and C (One3). A pushout of B and C along A allows for the presentation of the category S (the meta-work the Silent piece), and a discussion of the category's S-specification and fiber order. Finally, we derive a semantics from the fiber in order to reason on persistent spatio-temporal structures of Cage's Silent piece.