thinker:takashi-ibaTakashi Iba
Primary author of this paper; researcher at Keio University studying visualization and analysis of Alexander's Fifteen Properties.
Authored papers (1)
Correspondence analysis applied to Alexander's own dependency table (from *The Nature of Order, Book One*, p. 238) reveals that the 15 fundamental properties of wholeness cluster into 4 or 5 coherent groups rather than operating as a flat, undifferentiated list. Using SPSS version 21.0 with symmetric normalization on a binary contingency matrix encoding Alexander's asterisk-marked inter-property dependencies, the analysis projects χ² distances onto a two-dimensional map and yields a stable 4-cluster solution: {CONTRAST, NOT-SEPARATENESS, ROUGHNESS, ALTERNATING REPETITION, GOOD SHAPE}; {LOCAL SYMMETRIES, THE VOID, LEVELS OF SCALE, GOOD SHAPE, POSITIVE SPACE}; {BOUNDARIES, STRONG CENTERS, DEEP INTERLOCK AND AMBIGUITY}; and {SIMPLICITY AND INNER CALM, ECHOES, GRADIENTS, POSITIVE SPACE}. GOOD SHAPE and POSITIVE SPACE function as bridging properties spanning multiple clusters, signaling higher structural centrality than Alexander's prose treatment implies. The paper introduces illustration-mapping — the superimposition of purpose-built schematic diagrams of each property directly onto the correspondence analysis plot — as a dual-mode representation tool for the properties. This implies that the 15 properties are not cognitively or structurally equivalent: three tightly coupled foundational properties (BOUNDARIES, STRONG CENTERS, DEEP INTERLOCK AND AMBIGUITY) may constitute a structural core, while properties like SIMPLICITY AND INNER CALM and ECHOES occupy a more peripheral, dependent role, a structural hierarchy that Alexander's original presentation obscures.
More papers — OpenAlex / S2
Studies (1)
Affiliations (1)
- Keio University(institute)
Co-authors (1)
- Shingo Sakai1 shared