John Cage's Silent Piece and the Japanese gardening technique of shakkei: Formalizing Whittington's conjecture through conceptual graphs. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Fowler, Michael D.
• Is Part Of: Journal of mathematics and music. Volume 13:Issue 1(2019)
• Page Start: 4
• Page End: 26
• Publication Date: 2019-01-02
• Subjects: indeterminacy -- conceptual graphs -- 4′33′′ -- first-order logic -- John Cage; 00A65; applied computing; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2019.1605412
• Languages: English
• ISSNs: 1745-9737

Abstract

Abstract : This article examines John Cage's Silent Piece (commonly known as 4 ′ 33 ′ ′ ). I analyze the work through formalizing the frame conjecture of Stephen Whittington [2013. "Digging In John Cage's Garden: Cage and Ryōanji." Malaysian Music Journal 2 (2): 12–21], which suggests that the work's spatial conditions are akin to those found in the Japanese gardening technique of shakkei, or borrowed scenery. By firstly expressing core axioms in natural language that describe the spatial conditions of Cage's Silent Piece, its' 1952 premiere as 4 ′ 33 ′ ′, the technique of shakkei, and an exemplar manifestation of shakkei at the garden Adachi Teien (Japan), I construct an ontology that enables the fundamental assumptions of Whittington's conjecture to be explicated through conceptual graphs John Sowa [1984. Conceptual Structures: Information Processing in Mind and Machine . Reading, MA: Addison-Wesley]. From the ontology, I create a number of graphs and derive first-order logic formulas that are then used for inference and further reasoning. I conclude by providing a formalism of Whittington's conjecture via a conceptual graph rule that accounts for both auditory and visual conditions that generate shakkei in the cited examples of the premiere of the Silent Piece as 4 ′ 33 ′ ′ and the garden of Adachi Teien.