Brucken … Asthetik und Gestaltung (Bridges … Aesthetics and Design) by Fritz Leonhardt (review)

60 Book Reviews design is still evolving in the cartographic community. This manificent effort by Howard Fisher consolidates many accumulated results and extends important areas of consideration in useful forms. The text is logically organized for so vast a resource, with comparative discussions for guidance in selection of the most appropriate representations. I. E. Raisz, Principles ofCartography (New York: McGraw-Hill, 1962). 2. A. H. Robinson and R. D. Sale, Elements 0/ Cartography, 4th ed. (New York: John Wiley, 1976). 3. J. P. Cole and C. A. M. King, Quantitative Geography (New York: John Wiley, 1968). 4. J. Bertin, Semiologie Graphique (Paris: Gauthier-Villars, 1967). The Fourth Dimension and Non-Euclidian Geometry in Modem Art. Linda Dalrymple Henderson. Princeton University Press, Princeton, 1983.457 pp., iIlus. Cloth, $60.00; paper, $18.50. ISBN: 0-691-04008-7. Reviewed by Roger F. Malina* This comprehensive and scholarly account details the influence of the concepts of four-dimensional space on visual artists. Selected portions of this thesis have been published before, in particular the challenge to the claimed historical connection between Cubism and Relativity. Most of the material is new, however, and will be of interest to readers of Leonardo. The author presents a lucid account of the historical evolution of the mathematical and scientific ideas involved in non-Euclidian geometry, multi-dimensional hyperspaces and Einsteinian Special and General Relativity. Henderson tracks the transmutation of these ideas as they were incorporated and popularized by philosophers, science-fiction writers, and Theosophists. The bulk of this book is the study of the work of artists influenced by the concept of four-dimensional space. Clearly the concepts took on lives of their own, and diverged from their original sources. Henderson notes that the "fourth dimension" may become an influential concept once again-although ideas of space-time have evolved significantly since Riemann and Lobachevsky. Contemporary scientists involved in the empirical verification of General Relativity, observational confirmation of the existence of black holes, and cosmology are seriously proposing island worlds embedded in an inflationary universe. Ironically some of these ideas appear even more fantastic than those advocated by the mystics and Theosophists. Brucken ... Asthetik und Gestaltung (Bridges ... Aesthetics and Design). Fritz Leonhardt. Deutsche Verlags-Anstalt, G.m.b.h., Stuttgart, 1982, 308 pp., iIlus. Cloth. Reviewed by S. K. Ghaswala** This large volume with colour photographs seeks to bring the complex subject of bridge design and engineering into the realms of aesthetic analysis. As a doyen of the engineering profession, Dr Leonhardt has succeeded in this attempt to bring to structural and bridge designers concrete concepts for building bridges which are not only strong, durable and economical, but also architecturally pleasing and appealing to the senses. The book is unique in that the author has given his own interpretive rules and guidelines on bridge aesthetics in the first 70 pages and then analysed bridges of all varieties from stone to concrete and from small elevated structures to mighty arches in concrete to suspension structures in steel. In questioning whether objects have aesthetic qualities, the author discusses the concepts of I. Kant, Jean Paul, H. Schmitz and H. P. Bahrdt and draws his own conclusion that aesthetic characteristics are expressed not only by form, colour, light and shadows, but also by the objects' immediate surroundings and environment. The scientific bases of aesthetic perception are explained in terms of the wavelength of visible light and its effect on the human eye, including the concept of monotonous waves. In dealing with proportions of structures, the author covers the 'Golden Mean' and the Fibonacci series, as well as concepts of Vitruvius, Corbusier's Modulor, etc. The guidelines presented for the use of aesthetics in bridge structures are worth a close study by all designers. The basic tenet is that the most *Space Sciences Laboratory, University of California, Berkeley, CA 94720, U.S.A. **Consulting engineer, Bombay, India. aesthetic design is one in which we can neither remove nor add any element without disturbing the harmony of the whole structure. With examples and drawings the author explains his rules, indicating their practical feasibility and limitations, while taking into account two other parameters, alignment of the bridge and the materials used in...