Science is not a ‘body of knowledge’ – it’s a dynamic, ongoing reconfiguration of knowledge and must be free to change ... each scientific discipline is governed by an accepted set of theories and metaphysical assumptions, within which normal science operates. Periodically, when this rather humdrum ‘puzzle solving’ leads to results that are inconsistent with the regnant perspective, there follows a disruptive, exciting period of ‘scientific revolution’, after which a new paradigm is instituted and normal science can operate once more. ... When Newton said: ‘If I have seen farther, it is by standing on the shoulders of giants’, he wasn’t merely being modest; rather he was emphasising the extent to which science is cumulative, mostly building on past achievements rather than making quantum leaps. ... the accumulation process generates not just something more, but often something altogether new. Sometimes the new involves the literal discovery of something which hadn’t previously been known (electrons, general relativity, Homo naledi). At least as important, however, are conceptual novelties, changes in the ways that people understand – and often misunderstand – the material world: their operating paradigms. ... The world’s factual details are in continual Heraclitean flux, but the basic rules and patterns underlying these changes in the physical and biological world are themselves constant. ... Our insights, however, are always ‘evolving’. ... Science is a process, which, unlike ideology, is distinguished by intellectual flexibility, by a graceful, grateful (albeit sometimes grudging) acceptance of the need to change our minds, as our understanding of the world evolves. Most people aren’t revolutionaries, scientific or otherwise. But anyone aspiring to be well-informed needs to understand not only the most important scientific findings, but also their provisional nature, and the need to avoid hardening of the categories: to know when it is time to lose an existing paradigm and replace it with a new one. ... Holding still is exactly what science won’t do.
In the 1980s, two ecologists, Jim Brown at the University of New Mexico and Brian Maurer at Brigham Young University, coined the term macroecology, which gave a name and intellectual home to researchers searching for emergent patterns in nature. Frustrated by the small scale of many ecological studies, macroecologists were looking for patterns and theories that could allow them to describe nature broadly in time and space. ... Brown and Maurer had been influenced heavily by regularities in many ecological phenomena. One of these, called the species-area curve, was discovered back in the 19th century, and formalized in 1921. That curve emerged when naturalists counted the number of species (of plants, insects, mammals, and so on) found in plots laid out in backyards, savannahs, and forests. They discovered that the number of species increased with the area of the plot, as expected. But as the plot size kept increasing, the rate of increase in the number of species began to plateau. Even more remarkable, the same basic species-area curve was found regardless of the species or habitat. To put it mathematically, the curve followed a power law, in which the change in species number increased proportionally to the square root of the square root of the area. ... Power laws are common in science, and are the defining feature of universality in physics. They describe the strength of magnets as temperature increases, earthquake frequency versus size, and city productivity as a function of population.
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. ... Determining whether a system is hyperuniform requires algorithms that work rather like a game of ring toss. ... Hyperuniformity is clearly a state to which diverse systems converge, but the explanation for its universality is a work in progress.
Consider the most familiar random shape, the random walk, which shows up everywhere from the movement of financial asset prices to the path of particles in quantum physics. These walks are described as random because no knowledge of the path up to a given point can allow you to predict where it will go next. ... Beyond the one-dimensional random walk, there are many other kinds of random shapes. There are varieties of random paths, random two-dimensional surfaces, random growth models that approximate, for example, the way a lichen spreads on a rock. All of these shapes emerge naturally in the physical world, yet until recently they’ve existed beyond the boundaries of rigorous mathematical thought. Given a large collection of random paths or random two-dimensional shapes, mathematicians would have been at a loss to say much about what these random objects shared in common. ... have shown that these random shapes can be categorized into various classes, that these classes have distinct properties of their own, and that some kinds of random objects have surprisingly clear connections with other kinds of random objects. Their work forms the beginning of a unified theory of geometric randomness. ... “You take the most natural objects — trees, paths, surfaces — and you show they’re all related to each other,” Sheffield said. “And once you have these relationships, you can prove all sorts of new theorems you couldn’t prove before.” ... incoherent is not the same as incomprehensible. ... In practical terms, the results by Sheffield and Miller can be used to describe the random growth of real phenomena like snowflakes, mineral deposits, and dendrites in caves, but only when that growth takes place in the imagined world of random surfaces.
He was, she remembered, preoccupied with the math problems he worked over in the evenings, and he was prone to writing down stray equations on napkins at restaurants in the middle of meals. He had few strong opinions about the war or politics, but many about this or that jazz musician. ... Oliver, Pierce, and Shannon—a genius clique, each secure enough in his own intellect to find comfort in the company of the others. They shared a fascination with the emerging field of digital communication and co-wrote a key paper explaining its advantages in accuracy and reliability. ... Partly, it seems, the distance between Shannon and his colleagues was a matter of sheer processing speed. ... Shannon’s response to colleagues who could not keep pace was simply to forget about them. ... George Henry Lewes once observed that “genius is rarely able to give an account of its own processes.” This seems to have been true of Shannon, who could neither explain himself to others, nor cared to. In his work life, he preferred solitude and kept his professional associations to a minimum. ... Shannon wouldn’t have been the first genius with an inward-looking temperament, but even among the brains of Bell Labs, he was a man apart. ... It was Shannon who made the final synthesis, who defined the concept of information and effectively solved the problem of noise. It was Shannon who was credited with gathering the threads into a new science. But he had important predecessors at Bell Labs, two engineers who had shaped his thinking since he discovered their work as an undergraduate at the University of Michigan, who were the first to consider how information might be put on a scientific footing, and whom Shannon’s landmark paper singled out as pioneers.