by Frank Wilczek
We usually think of the human brain as a single organ, but it is a complex assembly of modules that process different kinds of information in quite different ways. Somehow, we construct a rich world of objects out of the two-dimensional images projected onto our retinas through two tiny irises effortlessly, and in real time. Human abilities here still far outstrip even the most powerful computers. Analytical processing of more abstract symbolic information, such as mathematical formulas or logical schemas (like family relationships, recipes or computer programs), occurs elsewhere. Visualization is the art of getting those two systems to speak a common language, so they can pool their strengths. Family trees are a humble but eloquent example.
Historically, innovations in visualization have powered scientific advances. Take the memorable story of August Kekulé, the 19th-century German scientist and creative dreamer who was one of the great visionaries of theoretical chemistry.
In the 1850s, Kekulé developed the familiar chain-like representation of molecules using letters—indicating the constituent atoms—joined by lines representing “chemical bonds.” In 1865, he proposed the ring structure of benzene. That involved taking his abstract representation of molecules seriously, as a model of their geometry—a crucial step toward modern organic chemistry. By suggesting the possibility of new compounds and reactions, Kekulé’s visionary molecular hoops led almost immediately to important practical applications.
At a meeting of the German Chemical Society to celebrate the 25th anniversary of that discovery, Kekulé reminisced about the two crucial breakthroughs in his career. He associated both with unusual states of consciousness. The chaining of atoms, he said, occurred to him as he fell into a daydream while riding a horse-drawn London omnibus: “Lo, the atoms were gamboling before my eyes! I saw how, frequently, two smaller atoms united to form a pair…I saw how the larger combinations formed a chain, dragging the smaller ones after them but only at the ends of the chain.’’
As for the benzene ring, Kekulé recalled nodding off by a fire to find atoms again “gamboling before my eyes. This time, the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together, all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes.”
Kekulé’s snake-dream has become an iconic story of science, psychology and the sources of creativity. Carl Jung connected its power to the archetype of Ouroboros, the self-eating snake, which figures in metaphorical representations of rebirth and eternal return across several cultures.
Several other huge scientific breakthroughs were also breakthroughs in visualization. Descartes’s invention of analytic geometry, which translates between equations and geometric shapes, is a brilliant example. Through it, algebra bends, loops and generally comes to life while, conversely, shapes get boiled down to symbols that our minds can easily juggle.
Einstein’s 1905 special theory of relativity became more popular and far easier to use after Hermann Minkowski’s 1908 address “Space and Time,” in which Minkowski showed that the theory is best pictured by regarding time as a new, fourth dimension. In modern physics, Richard Feynman’s versatile visualizations of elementary processes—Feynman diagrams—are an essential mind-tool. They map the mathematics of space-time processes in quantum theory to simple, flexible wiring patterns. (They’ve changed my life more than once.) None of these breakthrough visualizations, unfortunately for Jung, involves snakes.
Today, at the frontiers of quantum theory, we routinely work in spaces and space-times of high dimension. Modern “big data” collections, depending on many variables, also define structure in high-dimensional spaces. They aren’t what our brain’s visual processors evolved to cope with. Yet in coping with vast and unfamiliar complexity, more than ever, we need to tap vision’s power—and to expand the intersection of art and science.
Dr. Wilczek, winner of the 2004 Nobel Prize in Physics, is a professor of physics at the Massachusetts Institute of Technology. His most recent book is “A Beautiful Question: Finding Nature’s Deep Design.”
This article appeared in The Wall Street Journal