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“This is the classic reference on how the golden ratio applies to spirals and helices in nature.” – Martin Gardner

The Curves Of Life

What makes this book particularly enjoyable to flip through is an abundance of beautiful hand drawings and diagrams. Sir Theodore Andrea Cook explores, in great detail, the nature of spirals in the structure of plants, animals, physiology, the periodic table, galaxies etc. – from tusks, to rare seashells, to exquisite architecture.

He writes, “a staircase whose form and construction so vividly recalled a natural growth would, it appeared to me, be more probably the work of a man to whom biology and architecture were equally familiar than that of a builder of less wide attainments. It would, in fact, be likely that the design had come from some great artist and architect who had studied Nature for the sake of his art, and had deeply investigated the secrets of the one in order to employ them as the principles of the other.

Cook especially believes in a hands-on approach, as oppose to mathematic nation or scientific nomenclature – seeing and drawing curves is far more revealing than formulas.

252264because I believe very strongly that if a man can make a thing and see what he has made, he will understand it much better than if he read a score of books about it or studied a hundred diagrams and formulae. And I have pursued this method here, in defiance of all modern mathematical technicalities, because my main object is not mathematics, but the growth of natural objects and the beauty (either in Nature or in art) which is inherent in vitality.

Despite this, it is clear that Theodore Cook has a deep love of mathematics. He describes it at the beautifully precise instrument that allows humans to satisfy their need to catalog, label and define the innumerable facts of life. This ultimately leads him into profoundly fascinating investigations into the geometry of the natural world.

 

Relevant Material

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“An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be an unlikely and an unusual circumstance. Rates vary, proportions change, and the whole configuration alters accordingly.” – D’Arcy Wentworth Thompson

D’Arcy Wentworth Thompson wrote, on an extensive level, why living things and physical phenomena take the form that they do. By analysing mathematical and physical aspects of biological processes, he expresses correlations between biological forms and mechanical phenomena.

He puts emphasis on the roles of physical laws and mechanics as the fundamental determinants of form and structure of living organisms. D’Arcy describes how certain patterns of growth conform to the golden ratio, the Fibonacci sequence, as well as mathematics principles described by Vitruvius, Da Vinci, Dürer, Plato, Pythagoras, Archimedes, and more.

While his work does not reject natural selection, it holds ‘survival of the fittest’ as secondary to the origin of biological form. The shape of any structure is, to a large degree, imposed by what materials are used, and how. A simple analogy would be looking at it in terms of architects and engineers. They cannot create any shape building they want, they are confined by physical limits of the properties of the materials they use. The same is true to any living organism; the limits of what is possible are set by the laws of physics, and there can be no exception.

 

Further Reading:

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Biomimicry in Architecture by Michael Pawlyn

“You could look at nature as being like a catalogue of products, and all of those have benefited from a 3.8 billion year research and development period. And given that level of investment, it makes sense to use it.” – Michael Pawlyn

Michael Pawlyn, one of the leading advocates of biomimicry, describes nature as being a kind of source-book that will help facilitate our transition from the industrial age to the ecological age of mankind. He distinguishes three major aspects of the built environment that benefit from studying biological organisms:

The first being the quantity on resources that use, the second being the type of energy we consume and the third being how effectively we are using the energy that we are consuming.

Exemplary use of materials could often be seen in plants, as they use a minimal amount of material to create relatively large structures with high surface to material ratios. As observed by Julian Vincent, a professor in Biomimetics, “materials are expensive and shape is cheap” as opposed to technology where the inverse is often true.

Plants, and other organisms, are well know to use double curves, ribs, folding, vaulting, inflation, as well as a plethora of other techniques to create forms that demonstrate incredible efficiency.

SpiritualPathSacredPlace

This is a very good book that thoroughly relates to our Brief 3.

“This book is a comparative study of how sacred space if formed and entered, documented by architectural examples from many different religions, locations, and historical settings. Moreover, it intends to establish correspondences between the religious and cultural setting and the architecture, arguing that sacred architecture often symbolizes the spiritual path and its goal. […] The book argues that sacred architecture often provided a detailed “symbol posted” way to spiritual transformation”.

The writer Thomas Barrie points out that “the Way, the spiritual path, the sacred journey” describe not only a spiritual and psychological setting but a physical one as well. Thus he attempts to show that “sacred architecture often provided a detailed ‘symbol posted’ way to spiritual transformation,” and he tries to illustrate this with specific examples in chapter 6. The first chapter provides an introductory overview. The second is about “symbols, structures, and rituals,” and includes archetypes, the hero’s journey, and pilgrimage. The third chapter is on “elements and experience” in architectural theory. In chapter 4 he discusses “the Sacred Path and Place,” including meaning and place, the place of creation, axis mundi etc., the celestial city, sacred geometry, and ritual settings. The fifth chapter describes the sacred use that can be made. Six types of paths: the axial, split, radial, grid, circumambulating, and segmented. The selected sites in chapter 6 are the Temple of Amun-Re; the Temple of Apollo; Koto-in Xen Temple, Daitoku-ji Monastery; the Cathedral of Sainte-Madeleine; and the Brion-Vega Cemetery. The final chapter, Arrival, is a kind of archetypal description of the elements common to many forms of sacred architecture. He criticizes modern architecture for its failure to provide “a meaningful sense of place and an articulated path to attain it—paths and places that perhaps lead us to a better understanding of who we are”.

In relation to our Brief 3, I recently found this book written by Vincent Mosco, The Digital Sublime: Myth, Power, and Cyberspace.
In the book, Vincent Mosco goes beyond the usual stories of technological break through and economic meltdown to explore the myths constructed around the new digital technology and why we feel compelled to believe in them. He tells us that what kept enthusiastic investors in the dotcom era bidding up stocks even after the crash had begun was not willful ignorance of the laws of economics but belief in the myth that cyberspace was opening up a new world.Myths are not just falsehoods that can be disproved, Mosco points out, but stories that lift us out of the banality of everyday life into the possibility of the sublime. He argues that if we take what we know about cyberspace and situate it within what we know about culture — specifically the central post-Cold War myths of the end of history, geography, and politics — we will add to our knowledge about the digital world; we need to see it “with both eyes” — that is, to understand it both culturally and materially. After examining the myths of cyberspace and going back in history to look at the similar mythic pronouncements prompted by past technological advances — the telephone, the radio, and television, among others — Mosco takes us to Ground Zero. In the final chapter he considers the twin towers of the World Trade Center — our icons of communication, information, and trade — and their part in the politics, economics, and myths of cyberspace.

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You can find a short book review here: http://www.law.ed.ac.uk/ahrc/script-ed/vol2-2/sublime_review.pdf

Homo Ludens: A study of the Play Element in Culture.

The seminal sociological work by the Dutch Cultural theorist Johan Huizinga  (December 7, 1872 – February 1, 1945) describes and analyses the nature and significance of the play element in culture, a phenomenom hugely relevant to the nature of the individual experience at Burning Man festival.

“In play there is something ‘at play’ which transcends the immediate needs of life and imparts meaning to the action”

Huizinga describes the detachment and unreality of playing and the way in which it provides release from the reality of the everyday, embodied in the idea of constructing a temporary city (or playground) in the desert, in which fun, interaction and play are fundamental facets of the experience .

“The feeling of being ‘apart together’ in an exceptional situation, of sharing something important, of mutually withdrawing from the rest of the world and rejecting the usual norms, retains its magic beyond the duration of the individual game.”