The Crystalline Law & the Organic Accident

A BEYOND BORDERS column by David Krakauer, President of the Santa Fe Institute.

Plate xxxi from James Bell Pettigrew’s Design in Nature, published in 1908, illustrates lines of force, motion, and light as seen in electric sparks.

Glittering below her in the sunlight was what appeared to be an immense crystalline orchid carved from some quartzlike mineral. The entire structure of the flower had been reproduced and then embedded within the crystal base, almost as if a living specimen had been conjured into the center of a huge cut-glass pendant.

“The Crystal World” by J.G. Ballard

In Thomas Mann’s final novel, Doctor Faustus — the biography of a musical prodigy, Adrian Leverkühn — there is a formative scene in which Adrian’s father, Jonathan, becomes entranced by ice crystals on a windowpane:

“Were these phantasmagorias an imitation of plant life, or were they the pattern for it? — that was his question.”

Jonathan pursues this question through a series of experiments that cause Adrian to wonder at the boundary of the purely physical and living world:

“The crystallization vessel in which this transpired was filled to three-quarters with a slightly mucilaginous liquid, diluted sodium silicate to be precise, and from the sandy bottom up rose a grotesque miniature landscape of different colored growths — a muddle of vegetation, sprouting blue, green, and brown and reminiscent of algae, fungi, rooted polyps, of mosses, too, but also of mussels, fleshy flower spikes, tiny trees or twigs, and here and there even of human limbs.”

Doctor Faustus was published in 1947, a period when Mann was living in California’s Pacific Palisades, in exile from Nazi Germany. The novel is a long meditation on the pattern and structure of music, the sacrifice of a personal life to beauty, and the symbological relation of musical form to the vacuousness of a perfectly ordered society.

The experiment with the crystal ultimately refers back to the idea of crystalline beauty in the writings of the philosopher Georg Wilhelm Friedrich Hegel, but their use in Mann’s novel derives from their development as a typology in art history. In his book Historical Grammar of the Visual Arts, the Austrian art historian Alois Riegl suggests that the world divides into inorganic crystalline forms and amorphous organic forms. Riegl asserts that “[b]ecause the crystalline motif obeys natural laws most perfectly, it is the only intrinsically appropriate and justifiable motif for human artistic creation.” The composer Adrian Leverkühn sees in the crystalline form the ideal of order that he wishes to realize in his music and that the National Socialists sought in parallel to realize in society.

The work of Charles Darwin is firmly rooted in the description of amorphous organic forms. Darwin’s metaphor for life, the “entangled bank,” is about as far from the crystalline as matter could diverge, and his mechanism for order is not based on regularity but irregularity — the contingent fit of form to function. In a period described as the “eclipse of Darwinism,” around 1880 to 1920, a new desire for symmetry reasserted itself in the work of two Scottish naturalists, James Bell Pettigrew and D’Arcy Wentworth Thompson, both faculty members at the University of St. Andrews. Pettigrew and Thompson showed extraordinary promise in their early careers. As an undergraduate, Thompson translated Hermann Joseph Muller’s work on the fertilization of flowers, accompanied by an introduction by Darwin. Pettigrew’s undergraduate drawings of cardiac muscle were so precise that he became the youngest scientist to deliver the Royal Society’s Croonian Lectures.

In 1908, Pettigrew published his monumental monograph, Design in Nature: Illustrated by Spiral and Other Arrangements in the Inorganic and Organic Kingdoms as Exemplified in Matter, Force, Life, Growth, Rhythms, &c., Especially in Crystals, Plants, and Animals, etc. The book is in three volumes, accompanied by around 2000 figures. Throughout, what is clearly an analog of Riegl’s “crystalline form” is adduced as evidence of parsimonious design and geometric wisdom. The closing section of the work sealed Pettigrew’s fate in the tomb of obscurity:

“He [man] is the highest of all living forms. The world was made for him and he for it…Everything was made to fit and dovetail into every other thing. There was moreover no accident or chance. On the contrary, there was forethought, prescience, and design.”

Pettigrew’s colleague, Thompson (whom Pettigrew hired at St Andrews), wrote an only slightly briefer, yet equally monumental, treatise on the crystalline principles inherent in the natural world, On Growth and Form. And like Pettigrew, Thompson was dismissive of the ideas of Darwin, whose case studies abound in what Thompson describes as the unnecessary teleological hypothesis. Unlike Pettigrew, Thompson pursued the Leverkühn question (“Were these phantasmagorias an imitation of plant life, or were they the pattern for it?”) through physics, not theology. For Thompson, the world, like artwork, was founded on a principle of perfect order — in his case, the order of Aristotle, Isaac Newton, and Pierre Louis Maupertuis.

We look back on these arguments, with their binary oppositions, and see that they have in no way abated, either in science or in art. The history of complexity science was to a considerable degree founded on the crystalline concept of self-organization, despoiled by the organic concept of selection. Complex reality is that which fascinated Riegl — it is a Frankenstein of organic asymmetry animated by a spark of symmetry.

— David Krakauer
President, Santa Fe Institute

From the Autumn 2025 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.