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In the 1995 Pixar film Toy Story, the gung ho space action figure Buzz Lightyear tirelessly incants his catchphrase: “To infinity … and beyond!” The joke, of course, is rooted in the perfectly reasonable assumption that infinity is the unsurpassable absolute—that there is no beyond. That assumption, however, is not entirely sound. As German mathematician Georg Cantor demonstrated in the late 19th century, there exists a variety of infinities—and some are simply larger than others....

Editor’s Note: This is a supplement to “The Evolution of Future Wealth” At first, the insight that predicting future innovations in goods and services is fundamentally impossible might sound deceptively obvious. It is after all the common experience of mankind that we do not know exactly what tomorrow holds. But what our work reveals is that the depth of our ignorance about certain types of future developments is far more impenetrable even in principle than one commonly supposes, and the larger significance of that finding for sciences such as biology and economics, if true, is profound....

Two years and counting into the COVID pandemic, we’ve all seen plenty of misinformation and junk science, whether online, on cable news or even in person by those eager to share their (sigh) “alternative views.” Meanwhile, trust in public health experts and institutions is at a discouraging low. It’s easy for sensible folks to feel exhausted by trying to do the right thing for public health, or for their kids’ education, in the face of so much negativity directed toward science....

At first the computer game looks awfully easy for an eight-year-old–like something out of the Stone Age of arcades in the 1980s. A red triangle “arrow” appears on the monitor’s blue screen, and then the nose of a cartoon airplane glides into view from the left. If the arrow points upward, Ben must make the plane climb. When he succeeds, a spiky yellow sun beams. A second glance shows that all is not as it seems....

It can be tricky to resolve different tales that are told about which U.S. energy sources are growing or fading. But now we have hard numbers. Annual flowcharts from Lawrence Livermore National Laboratory show that over the past decade, wind power has increased 396 percent and solar power is up 956 percent. Of course, a very small share can rise by many percentage points and still be small, but that traditional narrative about wind and solar is nearly over: together they now provide 3....

AT THE HEART OF SCIENCE are judicious observations and measurements. This reality presupposes that something can be measured. But how can consciousness—the notorious ineffable and ethereal stuff that can’t even be rigorously defined—be measured? Recent progress makes me optimistic. Consider a problem of great clinical, ethical and legal relevance, that of inferring the presence of consciousness in severely brain-damaged patients. Often the victims of traffic accidents, cardiac arrests or drug overdoses, such patients have periods when they are awake, and they may spontaneously open their eyes....

A mother’s milk is a comestible marvel. It’s packed with nutrients and other benefits for babies’ health. A steady stream of research has linked breastfeeding to lower risk of infection, obesity, diabetes and respiratory disease in infants. Scientists are busy investigating how exactly breast milk provides these protective effects. Researchers have a good grasp of how many of the nutrients it contains, such as fats and vitamins, affect infant health, says Steven Hicks, a paediatrician at Pennsylvania State University College of Medicine in Hershey....

Three-quarters of U.S. teens and adults are deficient in vitamin D, the so-called “sunshine vitamin” whose deficits are increasingly blamed for everything from cancer and heart disease to diabetes, according to new research. The trend marks a dramatic increase in the amount of vitamin D deficiency in the U.S., according to findings set to be published tomorrow in the Archives of Internal Medicine. Between 1988 and 1994, 45 percent of 18,883 people (who were examined as part of the federal government’s National Health and Nutrition Examination Survey) had 30 nanograms per milliliter or more of vitamin D, the blood level a growing number of doctors consider sufficient for overall health; a decade later, just 23 percent of 13,369 of those surveyed had at least that amount....

Eugenia Cheng’s passion for theoretical mathematics is rivaled only by her love of food. In talks and in her book, How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics, the mathematician and pianist uses baking and cooking to explore the concepts behind pure math. Pure mathematics deals with its underlying structures and concepts. It is sometimes referred to as math for math’s sake and has a philosophical bent, in contrast to the more familiar applied mathematics used for problem-solving....

Researchers have used a three-dimensional printer to create polymer structures that change color when stretched (ACS Appl. Mater. Interfaces 2014, DOI: 10.1021/am506745m). The 3-D printing approach can be used to build easy-to-read mechanical force sensors that would be difficult, if not impossible, to make with standard methods, the team says. Functional polymers change shape or composition in response to stimuli such as light, heat, and mechanical force, and hold promise as sensors or in drug delivery devices....

As storms go, the one that struck northwest Alaska in mid-November was not remarkable. Its pressure was not particularly low, nor its 30-mile-per-hour winds particularly strong. Still, it sent several feet of rough seas surging into the beleaguered coastal communities that dot Alaska’s northern and western shores. In Deering, a village of 126 people perched on a sandy spit on the northern coast of the Seward Peninsula, the tempestuous waters eroded some 10 to 20 feet of beach, according to local news reports....

Compared with other animals, human babies take much longer to learn to walk. Does this have something to do with our big brains? —Mahmoud Dhaouadi, via e-mail John Bock, an anthropologist at California State University, Fullerton, provides a reply: A HORSE can walk within an hour after birth. A newborn baboon baby can cling to its mother’s hair while she jumps through the trees. Even among our closest evolutionary relatives—chimpanzees and bonobos—babies are far more agile than their human counterparts....

A squishy octopus-shaped machine less than 2 centimetres tall is making waves in the field of soft robotics. The ‘octobot’ described today in Nature is the first self-contained robot made exclusively of soft, flexible parts. Interest in soft robots has taken off in recent years, as engineers look beyond rigid Terminator-type machines to designs that can squeeze into tight spaces, mould to their surroundings, or handle delicate objects safely. But engineering soft versions of key parts has challenged researchers....

A stroke happens when blood flow to the brain is interrupted and brain cells starve of oxygen. Aftereffects include muscle weakness and altered senses. In many cases, strokes also affect the way a patient thinks or processes information. Quickly identifying the effects of a stroke helps doctors to tailor rehabilitation programs to the needs of a patient. Currently, structural neuroimaging and neuropsychological tests assess cognitive damage, but these take time and require the patient to be involved and compliant....

SHANGHAI – China will soon begin its grand experiment to rein in climate change, using the nation’s regionwide carbon markets as the building blocks for what could become the world’s second-largest emissions trading market. Four out of seven Chinese pilot regions – Shanghai, Guangdong, Tianjin and Hubei – have issued their versions of cap-and-trade plans for greenhouse gas emissions. While Beijing and Shenzhen have yet to unveil their final plans, major parts of them were drafted and discussed in news conferences last year....

Key concepts Chemistry Surface tension Surfactant Molecules Chemical bonds Introduction If you’ve ever washed dishes, you know the right dish soap can make a dirty job a lot easier. Have you ever wondered how dish soap is able to clean dishes so much more effectively than water alone? Like many household cleaners, dish soap is a surfactant—it helps break up leftover food on plates by making it easier for food particles to dissolve in water....

Hundreds of chemicals likely to be identified by the European Union (E.U.) as “substances of very high concern” are produced throughout the U.S., sometimes in large quantities. In fact, chemicals such as varieties of plastic-softening phthalates—linked to developmental and reproductive problems because they mimic hormones—are produced in excess of hundreds of million of pounds per year, according to a new report from Environmental Defense Fund (EDF) that is based on U....

In 1891, William B. Coley—the head of the bone tumor service at Memorial Hospital in New York City—noticed an interesting phenomenon. Among certain cancer patients, the disease seemed to regress with the acquisition of a bacterial infection—not an uncommon occurrence in 19th century hospitals. Curious, Coley began injecting patients with bacteria, and indeed, certain among them got better. Presumably, the injections set off an immune response that battled the bacteria and, subsequently, the cancer....

Amphibious fish that feed on land use water held in their mouths to help them grab and manipulate their prey. The unusual feeding behavior of mudskippers (Periophthalmus barbarus), captured in high-speed and X-ray video by biologist Krijn Michel and his colleagues at the University of Antwerp, could shed light on the evolution of sea-dwelling animals into terrestrial ones. Michel’s colleagues showed in 2006 that eel catfish (Channallabes apus) can successfully feed on land....

Most people can stand comfortably under the jawline of a mounted Tyrannosaurus rex or walk under the rib cage of a Brachiosaurus without bumping their heads. T. rex is as big as the largest known African elephant, and Brachiosaurus, like other great sauropods, was much larger than any land animal alive today. We are so used to the enormous size of dinosaurs that we almost forget to think about how they grew to be so large....