杏吧原创

鈥淭HERE is no evidence that scientists do or ever did think visually,鈥� said an anonymous reviewer of an earlier version of my book Seen/Unseen, when it was being considered by a major American university press.

That such a stance could be seriously maintained testifies to the astonishing ignorance even in educated circles about the nature of science and the mental tools available to innovative researchers. Many leading scientists would join me in being aghast or astonished at being told that visual thinking plays no role in their work. Harry Kroto, for example, who played a leading role in the discovery of the carbon molecules known as fullerenes, of which 鈥渂uckyballs鈥� (C₆₀) became the most famous, would definitely demur. And the type of 3D visualisation that Kroto exploited in the 鈥渄esigning鈥� of his buckyballs can, I believe, be shown to be part of a distinguished historical tradition and to play a continued role in cutting-edge thinking across diverse scientific fields.

In the history of western science, there is a chronological succession of scientists who used astonishingly high levels of skill in plastic visualisation to build mental and graphic models of complex structures in space. The great astronomer Johannes Kepler yields to no one in this respect. When he was drawing triangles inscribed in circles for his students, he hit on the idea that the ratio of the orbits of the planets might be represented by the successive nesting of the five regular, Platonic solids (tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron) within spheres. The great folding plate in his Mysterium Cosmographicum of 1596 displays the configuration like a great piece of high Renaissance Mannerist metalwork 鈥� just how he hoped it would be realised for his patron.

With the advent of the microscope, it was possible to show objectively that natural engineering exploited geometrical structures on a tiny scale at least as remarkably as those in the macroscopic world, such as bees鈥� cells and spiders鈥� webs. A classic example is Robert Hooke鈥檚 exploration of the perceptual delights presented by a fly鈥檚 eye in his Micrographia of 1665. There he discusses how varied the eye looks in different lights and from various orientations. Hooke is honest about how difficult it is to make sense of a complex visual configuration in an entirely new visual realm, and how analogies with known structures inform our viewing. He allies his knowledge of geometry to his sensibility as an instrument-maker and architect to make a visually literate choice of the true nature of the array he is studying.

The way modern scientists use comparable means to model structural engineering in nature is exemplified by two very contrasting but related acts of visualisation: the spatial configuration of C₆₀, and a new model for the cosmos suggested by astrophysicist Jean-Pierre Luminet and his colleagues at the French national research agency CNRS in Paris. The story of the discovery of C₆₀ began in 1985 with radical new evidence for a form of carbon consisting of 60 atoms which demanded an array very different from the tetrahedral patterns of diamond or the sheets of hexagons that characterise graphite. How could the 60 units be arranged stably? Kroto, who led the team working on the structure at Rice University, had earlier been to the Expo 67 show in Montreal, Canada, where he had been fascinated by the American Pavilion constructed as a geodesic dome by designer Buckminster Fuller.

Fuller鈥檚 pavilion used a double skin of lattices of triangles and hexagons, and had emerged from his exploration of geometrical engineering solutions centred on the five Platonic solids. He followed D鈥橝rcy Wentworth Thompson, the first of the bio-mathematicians and author of the seminal 1917 book On Growth and Form, in seeing solutions as rooted in fundamental structures in the natural world. If Fuller did not know Hooke鈥檚 eye of a fly, he should have done, but he certainly did know biologist and philosopher Ernst Haeckel鈥檚 beguiling illustrations of the geometrical intricacies of radiolarians (amoeboid protozoa that produce intricate mineral skeletons). The dome, the eye and the radiolaria are among nature鈥檚 optimum design solutions, and have that sense of perfect inevitability that characterises the most resolved acts of engineering. Their shared properties relate to enduring aspects in our human perception and creation of structures, transcending time and place.

The continued vitality of this kind of design in architecture and engineering is also apparent in the lattice structure of the roof of the Great Court at the British Museum, designed by Norman Foster and made reality by engineering firm Buro Happold. The creative role of the engineer is crucial in determining the complex geometry of the doughnut-like form of the roof, which bridges the space between the rectangular courtyard and the circular reading room in its centre. It is no coincidence that much of the design philosophy of the engineering firm was forged by the late Edmund Happold, a huge fan of D鈥橝rcy Thompson. Throughout his work, Happold conducted a keen and fruitful dialogue between natural and human design 鈥� an enthusiasm fully shared by Norman Foster 鈥� and the roof of the Great Court accordingly resonates creatively with a series of structural skeletons in natural organisms.

鈥淣ature鈥檚 optimum design solutions have that feeling of perfect inevitability鈥�

Returning to the 鈥渄esigning鈥� of C₆₀, it is worth noting that Kroto had once been interested in training as a designer, and retains a natural flair for working with complex graphics. Kroto proposed the array of hexagons and pentagons in the structure that the Rice team aptly named buckminsterfullerene.

From the tiny scale of buckyballs to the mighty scale of the cosmos, Luminet currently argues that the recent measurements of the cosmic microwave background radiation can be best understood via a dodecahedral model of the cosmos. It is, however, a model that exploits dimensions unknown to Kepler: the pentagonal faces are arranged around a multi-dimensional hypersphere. Although the mathematics lie far beyond those available to the earlier devotees of Platonic solids, Luminet openly acknowledges that his modes of visualisation are locked into a tradition that involves Leonardo da Vinci and Fuller. It is satisfying to discover that he also practises as an artist and is deeply involved in music.

In this essay, I am not so much talking about a chain of influence, but about how diverse artists, architects, engineers and scientists have shared insights into structural arrays because they exhibit an inherent stability and even a 鈥渂eauty鈥� that makes them feel right. I call these kinds of insights 鈥渟tructural intuitions鈥� 鈥� and I believe that they have played major roles in visual thinking over the ages and across the disciplines.