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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:

Michael-Pawlyn-Biomimicry-A-new-paradigm-1

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.

Some sci fi novels you might find inspiring:

Bernal Sphere

Bernal Sphere; source:wikipedia.org

John Desmond Bernal – The World, the Flesh and the Devil (1929)

A space habitat intended for permanent residence; radical changes to human bodies and perception and the implications for society;

Brave New World

Brave New World – Impressions on Reading Aldous Huxley (Album Cover); source: discogs.com

Aldous HuxleyBrave New World (1931)

Radical social changes due to technological advances. Huxley’s other work is worth checking as well.

Stapledon

Star Maker; source:jonathanrosenbaum.net

Olaf Stapledon – Star Maker (1937)

It is a masterpiece that AC Clarke, F Herbert, OS Card and other great sci fi writers have quoted as a major influence. Virginia Wolf was a fan as well. I would say architectural references in this book are not very direct, but it is nothing but pure inspiration. A conventional guy has a disembodied visionary experience that takes him across time and space and slowly allows him to merge his consciousness with the Universe. There is a mystical beauty about the way the cosmos is described, sci fi and philosophy at the same time. It has some interesting relevant concepts as well, such as the Dyson sphere – an artificial mega structure entirely surrounding a star in 3D to capture the entire power output.

Equilibrium

Scene from Equilibrium directed by Kurt Wimmer; source: lettherebemovies.com

George OrwellNineteen Eighty-Four (1949)

Relevant for the issue of surveillance and how it reflects on social life and implicitly, architecture. The descriptions of the ministry buildings are memorable.

Trantor

Hari Seldon on Trantor; source: theincrediblog.com

Isaac AsimovFoundation series (1951)

A sci fi classic novel in which Asimov anticipates big data and open source encyclopedias and envisages a science which can use information to predict the future on a large scale. It is interesting from an architectural point of view as Trantor, the capital of the Galactic Empire, is a completely built up planet, covered in its entirety by a continuous mass of metal high-rise buildings and subterranean structures.

scene from Stalker directed by Andrey Tarkovsky; source: .verdensteatret.no

Stanislaw Lem  – Solaris (1961)

Questions alien nature and the issue of communication between alien species. The Russian film by Andrey Tarkovsky is also a masterpiece.

Dick; source: sfreviews.com

Philip K Dick  – all his work

Man in the High Castle (1963); Ubik; A Scanner Darkly (1978); Do Androids Dream of Electric Sheep (1968); The Three Stigmata of Palmer Eldritch (1965) – all have subtle architectural references and address contemporary issues like immigration, mass-media, politics, drugs. Dark paranoid atmosphere throughout.

Dune

Dune-inspired render at http://newsite.markmolnar.com/

Frank Herbert Dune (1965)

Not so much about architecture, but it is a realistic depiction of the layered complexities of a planet: politics, religion, sociology, economy, ecology, technology, etc.

RingWorld

Larry Niven – Ringworld; source: sci-fi-o-rama.com

Larry NivenRingworld (1970)

Larry Niven, in 1970 theorized the Niven Ring – a continuous ring-shaped mega structure that rotates around a star to create artificial gravity force; Architecture at a star-system scale.

Rama; source:imageshack.us/

Arthur C. Clarke – Rendezvous with Rama (1972)

One of Arthur C. Clarke’s most well-known works, the main architectural interest is on th 50 Km cylindrical alien star ship which has its own geography and cities. Clarke comes from a scientific background and this is reflected in the rigor of his novels. Also check 2001:A Space Odyssey and his work on fractals.

Gheorghe Sasarman

Squaring the Circle; source: scifiportal.eu

Gheorghe SasarmanSquaring the Circle – A Pseudotreatise of Urbogony (1975)

Written in the style of Calvino’s Invisible Cities.  it is a collection of short stories full of mythical and symbolic references about utopias, politics, geometry and of course, urban design. <Spoiler> Babylon is an egalitarian society where everyone is allowed access to the top of the ziggurat but the steep ramps are greased every day. Rome is a fractal city made by recursively placing forums at the intersection of the cardo and decumanum; tunnel cities, underground, or moving, or towering ones, Atlantis, all linked to a poetic idea about their creation.

Magrathea

Magrathea; by microbot23

Douglas AdamsThe Hitchhiker’s Guide to the Galaxy (1979)

This is a comic series, but it has some unique ideas. My favourite is that Earth and some other planets are artificial mega structures manufactured on Magrathea for some wealthy clients. A planet-building factory! <Spoiler> Earth was originally commissioned as a mega human driven computer to compute the ultimate question about life, the universe and everything. One of the characters, Slartibartfast is a coastal designer and won a prestigious award for the design of the Norwegian fjords.

A picture of the Moon before it was fully constructed; Source: uncyclopedia.wikia.com

Brussolo

Serge Brussolo – Territoire de Fievre; source: p.gr-assets.com

 Serge BrussoloTerritoire de Fievre (1983)

Brussolo has an intimidating imagination. Short novels, easy to read, you can also check Les mangeurs de murailles (about a cube-shaped dystopian city), Portrait du diable en chapeau melon (about a labyrinthine prison city), <Spoiler> In Territoire de Fievre people live on a breathing planet and their planet gets ill.

Ring

Stephen Baxter – Ring; source:wikipedia.org

Stephen Baxter – Ring (1994)

A mega structure formed of cosmic strings;

Stephen Baxter

Time Ships; source: amazon.com

Stephen BaxterThe Time Ships (1995)

A sequel to HG Wells’ The Time Machine; It has a few architectural references, but the main one is the Dyson Sphere at the centre of the Solar System built by an advanced civilization;

Vernor Vinge

Rainbows End; source:wikipedia.org

Vernor VingeRainbows End (2006)

It is a critical insight into plausible extensions of technologies available today, seen through the eyes of a man who just recovered from Alzheimers.

Helix Fractal; source: deviantart

Eric BrownHelix (2007)

Galactic-scale mega structure; Depending on the complex relationship between the geometry of the Helix and the stars, various ecosystems form;