Book contents
- Frontmatter
- Contents
- Mathematics: user's manual
- Appetizers
- 1 Space and geometry
- 2 Motions on the plane
- 3 The many symmetries of planar objects
- 4 The many objects with planar symmetries
- 5 Reflections on the mirror
- 6 A raw material
- 7 Stretching the plane
- 8 Aural wallpaper
- 9 The dawn of perspective
- 10 A repertoire of drawing systems
- 11 The vicissitudes of perspective
- 12 The vicissitudes of geometry
- 13 Symmetries in non-Euclidean geometries
- 14 The shape of the universe
- Appendix: Rule-driven creation
- References
- Acknowledgements
- Index of symbols
- Index of names
- Index of concepts
6 - A raw material
Published online by Cambridge University Press: 05 May 2013
- Frontmatter
- Contents
- Mathematics: user's manual
- Appetizers
- 1 Space and geometry
- 2 Motions on the plane
- 3 The many symmetries of planar objects
- 4 The many objects with planar symmetries
- 5 Reflections on the mirror
- 6 A raw material
- 7 Stretching the plane
- 8 Aural wallpaper
- 9 The dawn of perspective
- 10 A repertoire of drawing systems
- 11 The vicissitudes of perspective
- 12 The vicissitudes of geometry
- 13 Symmetries in non-Euclidean geometries
- 14 The shape of the universe
- Appendix: Rule-driven creation
- References
- Acknowledgements
- Index of symbols
- Index of names
- Index of concepts
Summary
That is, of you, who are a firmament
Of virtues, where no one is grown, nor spent;
They are your materials, not your ornament.
J. Donne (Carey, 2000: 232)Birkhoff, Gombrich and Lorand purport different, and at times antithetical, views on art and beauty. The three coincide, however, in taking for granted a basic dichotomy in its analysis.
On the one hand, the formal aspects of an artwork (which roughly coincide with the formal associations in Birkhoff, the sense of order in Gombrich and the discursive order in Lorand) and, on the other hand, the semantic aspects (connotational associations, sense of meaning and aesthetic order respectively). Not that these are watertight compartments. On the contrary, the interplay between them is a defining feature of many artforms (poetry being a notable example).
Unlike Lorand, but in agreement with Birkhoff and Gombrich, I see symmetry – in the various forms we have seen in Chapter 3 and in other forms we will meet – as a formal aspect, and a notable one for that matter. Furthermore, I see discursive and aesthetic orders as possible raw materials for each other (see the end of Section 5.1). In particular, I see symmetry as a raw material in the interplay mentioned above. This view is the theme of the present chapter and a starting point to develop it is the realization that, as a raw material, symmetry does not need to be exact.
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- Manifold MirrorsThe Crossing Paths of the Arts and Mathematics, pp. 128 - 157Publisher: Cambridge University PressPrint publication year: 2013