A Bird’s-Eye View of Nature’s Hidden Order
Fascinating article by Natalie Wolchover in Quanta:
Seven years ago, Joe Corbo stared into the eye of a chicken and saw something astonishing. The color-sensitive cone cells that carpeted the retina (detached from the fowl, and mounted under a microscope) appeared as polka dots of five different colors and sizes. But Corbo observed that, unlike the randomly dispersed cones in human eyes, or the neat rows of cones in the eyes of many fish, the chicken’s cones had a haphazard and yet remarkably uniform distribution. The dots’ locations followed no discernible rule, and yet dots never appeared too close together or too far apart. Each of the five interspersed sets of cones, and all of them together, exhibited this same arresting mix of randomness and regularity. Corbo, who runs a biology lab at Washington University in St. Louis, was hooked.
“It’s extremely beautiful just to look at these patterns,” he said. “We were kind of captured by the beauty, and had, purely out of curiosity, the desire to understand the patterns better.” He and his collaborators also hoped to figure out the patterns’ function, and how they were generated. He didn’t know then that these same questions were being asked in numerous other contexts, or that he had found the first biological manifestation of a type of hidden order that has also turned up all over mathematics and physics.
Corbo did know that whatever bird retinas are doing is probably the thing to do. Avian vision works spectacularly well (enabling eagles, for instance, to spot mice from a mile high), and his lab studies the evolutionary adaptations that make this so. Many of these attributes are believed to have been passed down to birds from a lizardlike creature that, 300 million years ago, gave rise to both dinosaurs and proto-mammals. While birds’ ancestors, the dinos, ruled the planetary roost, our mammalian kin scurried around in the dark, fearfully nocturnal and gradually losing color discrimination. Mammals’ cone types dropped to two — a nadir from which we are still clambering back. About 30 million years ago, one of our primate ancestors’ cones split into two — red- and green-detecting — which, together with the existing blue-detecting cone, give us trichromatic vision. But our cones, particularly the newer red and green ones, have a clumpy, scattershot distribution and sample light unevenly.
Bird eyes have had eons longer to optimize. Along with their higher cone count, they achieve a far more regular spacing of the cells. But why, Corbo and colleagues wondered, had evolution not opted for the perfect regularity of a grid or “lattice” distribution of cones? The strange, uncategorizable pattern they observed in the retinas was, in all likelihood, optimizing some unknown set of constraints. What these were, what the pattern was, and how the avian visual system achieved it remained unclear. The biologists did their best to quantify the regularity in the retinas, but this was unfamiliar terrain, and they needed help. In 2012, Corbo contacted Salvatore Torquato, a professor of theoretical chemistry at Princeton University and a renowned expert in a discipline known as “packing.” Packing problems ask about the densest way to pack objects (such as cone cells of five different sizes) in a given number of dimensions (in the case of a retina, two). “I wanted to get at this question of whether such a system was optimally packed,” Corbo said. Intrigued, Torquato ran some algorithms on digital images of the retinal patterns and “was astounded,” Corbo recalled, “to see the same phenomenon occurring in these systems as they’d seen in a lot of inorganic or physical systems.”
Torquato had been studying this hidden order since the early 2000s, when he dubbed it “hyperuniformity.” (This term has largely won out over “superhomogeneity,” coined around the same time by Joel Lebowitz of Rutgers University.) Since then, it has turned up in a rapidly expanding family of systems. Beyond bird eyes, hyperuniformity is found in materials called quasicrystals, as well as in mathematical matrices full of random numbers, the large-scale structure of the universe, quantum ensembles, and soft-matter systems like emulsions and colloids.
Scientists are nearly always taken by surprise when it pops up in new places, as if playing whack-a-mole with the universe. They are still searching for a unifying concept underlying these occurrences. In the process, they’ve uncovered novel properties of hyperuniform materials that could prove technologically useful.
From a mathematical standpoint, “the more you study it, the more elegant and conceptually compelling it seems,” said Henry Cohn, a mathematician and packing expert at Microsoft Research New England, referring to hyperuniformity. “On the other hand, what surprises me about it is the potential breadth of its applications.”
A Secret Order
Torquato and a colleague launched the study of hyperuniformity 13 years ago, describing it theoretically and identifying a simple yet surprising example: “You take marbles, you put them in a container, you shake them up until they jam,” Torquato said in his Princeton office this spring. “That system is hyperuniform.” . . .