- Title
- The mathematics of architectural beauty: an analysis of Christopher Alexander's second theory of architecture
- Creator
- Dawes, Michael J.
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2019
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- The oldest architectural treatise to survive from antiquity identifies beauty as one of the central concerns in architectural theory, yet over 2000 years later there is little consensus among practitioners and academics about how this property can be created in buildings. Christopher Alexander devoted his career to developing a theory of architecture that was intended to enable the creation of buildings that epitomised the beauty of traditional design. This theory is comprised of three distinct stages that are conceptually differentiated enough to be considered independent theories. The focus of this dissertation is Alexander’s second theory of architecture, which was presented in three canonical texts, including A Pattern Language, which is believed to be the most widely-read architectural treatise ever published. However, despite this notoriety, Alexander’s second theory received relatively little serious engagement from academics and practitioners, and several major aspects of its structure and logic remain completely untested. This dissertation identifies three gaps in our knowledge of Alexander’s second theory and develops three research aims to address these unknowns. Each research aim is framed as a series of directional hypotheses that are paired with evaluation metrics and associated methodologies for mathematical analysis. The first knowledge gap is concerned with the underlying structure of A Pattern Language and the role of invariant patterns (the ones Alexander was most confident in) within this structure. This knowledge gap is investigated by computationally modelling the complete structure of the pattern language for the first time and includes all 253 patterns and more than 2200 connections between them. Then, using the mathematics of graph theory, the structure of the language is analysed and the prominence of each pattern is measured. This analysis yields three significant findings. The first is that, due to ambiguities in Alexander’s canonical texts, it is possible to construct several different but equally valid models of A Pattern Language. This has never been revealed before, and it leads to the testing of each hypothesis in two ways in the remainder of the dissertation, in order to accommodate the two models that most closely resemble Alexander’s descriptions of designing with patterns. The second finding is that, on average, invariant patterns are the most prominent in the language, but when patterns are considered individually, significant numbers of poorly refined patterns are more prominent than invariant ones. The third finding is that patterns with high and medium invariance ratings form a central structure within the language, and that many low invariance patterns require connections to better refined patterns for integration into the language. The second knowledge gap centres on Alexander’s assertion that organic architecture possesses greater wholeness and is therefore inherently superior to mechanistic architecture. This knowledge gap is addressed by developing four measures of wholeness from Alexander’s theory and using them to quantify the degree of wholeness in seven houses by Frank Lloyd Wright and seven villas by Le Corbusier. The first finding of this process is that Wright’s organic architecture achieves significantly greater wholeness than Le Corbusier’s mechanistic villas, so much so that in many cases Le Corbusier’s most whole design is inferior to Wright least whole design. Thus, within the boundaries of Alexander’s theory, this potentially indicates that some of the fundamental principles of Alexander’s second theory are valid. The next finding is that eight of the considered patterns appear in every analysed design and seventeen patterns are absent from every design. This suggests that certain patterns in Alexander’s language are critical to the design of contemporary residences, and that certain other patterns require adaptation or refinement in order to become useful. The final knowledge gap is associated with the relationship between patterns in Alexander’s language and patterns in architectural works. This knowledge gap is addressed through a statistical comparison of the data that is generated by investigating the previous two research aims. This data documents the accessibility of every pattern in the language and the extent to which each pattern appears in the residential design of Wright and Le Corbusier, and it might be expected that there are significant correlations between these data sets. However, the results of this analysis reveal that virtually no correlation exists between the accessibility of patterns in the language and appearance of patterns in the selected residences. While the interpretation of this result is complex, one reading is that the structure of A Pattern Language does not prioritise the same patterns that these two famous architects prioritised in their designs. By creating the first complete computational mapping and mathematical analysis of A Pattern Language, this dissertation addresses three substantial gaps in the research pertaining to Alexander’s work, and provides new knowledge about its limits and applications.
- Subject
- architecture; Christopher Alexander; A Pattern Language; graph analysis; Frank Lloyd Wright; Le Corbusier
- Identifier
- http://hdl.handle.net/1959.13/1397839
- Identifier
- uon:34363
- Rights
- Copyright 2019 Michael J. Dawes
- Language
- eng
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 9 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 45 KB | Adobe Acrobat PDF | View Details Download |