Category: Quantum Stuff

The next step up in that hierarchy is the “restriction” conjecture. If it is true, so is the Kakeya conjecture. (This also means that if the Kakeya conjecture turns out to be false, the restriction conjecture can’t be true.) The restriction conjecture, in turn, is implied by the so-called Bochner-Riesz conjecture. And at the very… Continue reading A Tower of Conjectures That Rests Upon a Needle

For ecologists, tropical rainforests hold many enigmas. A single hectare can contain hundreds of tree species, far more than in forests closer to the poles. Somehow these species coexist in such dizzying abundance that, as naturalists and ecologists have sometimes noted, tropical forests can feel like botanical gardens, where every plant is something new. For… Continue reading ‘Species Repulsion’ Enables High Biodiversity in Tropical Trees

Understanding the quantum universe is not an easy thing. Intuitive notions of space and time break down in the tiny realm of subatomic physics, allowing for behavior that seems, to our macro sensibilities, downright weird. Quantum computers should allow us to harness this strangeness. Such machines could theoretically explore molecular interactions to create new drugs… Continue reading Machine Learning Aids Classical Modeling of Quantum Systems

The sun looks immutable, a boring celestial lightbulb that’s always turned on. But this fusion-powered ball of plasma is in constant flux. Every 11 years or so, it swings between slumber and an active, unruly epoch marked by sunspots and solar eruptions, such as flares and plasma outbursts. The sun is now approaching its maximum level of activity in… Continue reading How Scientists Are Tackling the Tricky Task of Solar Cycle Prediction

Consider a square with a bunch of points inside. Take three of those points, and you can make a triangle. Four points define four different triangles. Ten points define 120 triangles. The numbers grow quickly from there — 100 points define 161,700 different triangles. Each of those triangles, of course, has a particular area. Hans… Continue reading The Biggest Smallest Triangle Just Got Smaller

In 2019, Noel and her colleagues began collaborating with two theorists who had come up with an easier way of doing the experiment. They had worked out a way of setting aside one qubit that, like a canary in a coal mine, could serve as a bellwether for the state of the entire chain. The… Continue reading Physicists Observe ‘Unobservable’ Quantum Phase Transition

Scientists have recognized that memory formation is a multistage process since at least the early 1950s, in part from their studies of a patient named Henry Molaison — known for decades in the scientific literature only as H.M. Because he suffered from uncontrollable seizures that originated in his hippocampus, surgeons treated him by removing most… Continue reading The Usefulness of a Memory Guides Where the Brain Saves It

Now, with the use of not just computers but even AI, how is the notion of proof changing? We’ve moved to a different place, where computers can do some wild things. Now people say, oh, we’ve got this computer, it can do things people can’t. But can it? Can it actually do things people can’t?… Continue reading Why Mathematical Proof Is a Social Compact