The original version of this story appeared in Quanta Magazine. David Bessis was drawn to mathematics for the same reason that many people are driven away: He didn’t understand how it worked. Unlike other creative processes, like making music, which can be heard, or painting pictures, which can be seen, math is for the most […]
Read MoreIf you double the radius of a balloon, you increase the volume by a factor of eight (since volume is proportional to the radius cubed). But what about the material on the outside of the balloon? Let’s say I want to make everything fair and I increase the thickness of the material by a factor […]
Read MoreTheir result shows the importance of not taking anything for granted, said Noga Alon, a mathematician at Princeton. “We have to be suspicious, even about things that intuitively look very likely to be true.” Gladkov, Pak, and Zimin found many small-graph examples that satisfied the conjecture, but in the end, those did not reflect the […]
Read MoreIs that really true? Yup. Look, I can prove it. Here’s a plot of the trajectories of the Earth and moon as they orbit the sun over the course of half a month. The blue curve is the path of the Earth going from left to right, and the red represents the moon. Graph: Rhett […]
Read More“It’s a great algorithm,” said Erik Demaine, a computer scientist at the Massachusetts Institute of Technology. “It’s very fast, simple, and easy to implement.” To put this procedure into practice, you’d need to decide on a system for organizing your notes—a data structure, in the lingo of computer science. That may sound like a minor […]
Read MoreI get a minimum height of 2.5R. So if the loop is 4 meters high (with a radius of 2 meters), the car would have to start 5 meters above the ground to just make the loop. Of course, this assumes there’s no energy loss due to friction; you’d probably want to start a bit […]
Read MoreIn the world of quantum physics, another record appears to have just been broken. In a paper listed on the preprint site ArXiv, researchers at the University of Science and Technology of China claim to have observed atoms in a state of quantum superposition for 23 minutes. Being able to keep quantum states stable for […]
Read MoreThe original version of this story appeared in Quanta Magazine. It’s not easy to study quantum systems—collections of particles that follow the counterintuitive rules of quantum mechanics. Heisenberg’s uncertainty principle, a cornerstone of quantum theory, says it’s impossible to simultaneously measure a particle’s exact position and its speed—pretty important information for understanding what’s going on. […]
Read More“It provides a natural framework, or a bookkeeping mechanism, to assemble very large numbers of Feynman diagrams,” said Marcus Spradlin, a physicist at Brown University who has been picking up the new tools of surfaceology. “There’s an exponential compactification in information.” Carolina Figueiredo, a graduate student at Princeton University, noticed a striking coincidence where three […]
Read MoreThis developing field, known as aerial electroreception, opens up a new dimension of the natural world. “I find it absolutely fascinating,” said Anna Dornhaus, a behavioral ecologist at the University of Arizona who was not involved with the work. “This whole field, studying electrostatic interactions between living animals, has the potential to uncover things that […]
Read MoreYou can see that it’s limited by the materials in the tires and track (captured by the frictional coefficent) and the gravitational field (so, what planet you’re on). Notice that the mass has canceled out. It doesn’t matter if you have a more massive vehicle. Yes, you get more friction, but it’s also harder to […]
Read MoreJust before Hurricane Milton slammed into Florida as a Category 3 storm on Wednesday, many people reported that the sky above them turned a sinister purple hue. A sign of the apocalypse? Well, yes, actually—the climate catastrophe we’ve made for ourselves. But it’s still a natural phenomenon with a scientific explanation. Light and Color Visible […]
Read MoreYet Hodgkinson worries that researchers in the field will pay attention to the technique, rather than the science, when trying to reverse engineer why the trio won the prize this year. “What I hope this doesn’t do is make researchers inappropriately use chatbots, by wrongly thinking that all AI tools are equivalent,” he says. The […]
Read MoreYet Hodgkinson worries that researchers in the field will pay attention to the technique, rather than the science, when trying to reverse engineer why the trio won the prize this year. “What I hope this doesn’t do is make researchers inappropriately use chatbots, by wrongly thinking that all AI tools are equivalent,” he says. The […]
Read MoreFiguring out what subgroups a group contains is one way to understand its structure. For example, the subgroups of Z6 are {0}, {0, 2, 4} and {0, 3}—the trivial subgroup, the multiples of 2, and the multiples of 3. In the group D6, rotations form a subgroup, but reflections don’t. That’s because two reflections performed […]
Read MoreDuring the Age of Sail, ships circled the globe on voyages of discovery and trade. That era ended in the 1800s, when coal-fired steam engines began to replace wind power. Now we may be entering a new age of sail—but this time in space. Reversing history, engines and fuel could be replaced by sails on […]
Read MoreBut not all questions about quantum systems are easier to answer using quantum algorithms. Some are equally easy for classical algorithms, which run on ordinary computers, while others are hard for both classical and quantum ones. To understand where quantum algorithms and the computers that can run them might offer an advantage, researchers often analyze […]
Read MoreWe can break that diagonal motion down into horizontal and vertical portions; for now let’s just focus on the former. Say you start with a horizontal velocity (v1) of –1 meter per second and rebound with a horizontal velocity (v2) of +1 m/s. The change of sign indicates the reversal of direction. Think of it […]
Read MoreNow two mathematicians have proved Hawking and his colleagues wrong. The new work—contained in a pair of recent papers by Christoph Kehle of the Massachusetts Institute of Technology and Ryan Unger of Stanford University and the University of California, Berkeley—demonstrates that there is nothing in our known laws of physics to prevent the formation of an extremal black hole. Their mathematical proof […]
Read MoreYou could say that this is exactly what Isaac Newton’s picture of gravity does—giving a relation between an object’s mass and the gravitational force it exerts. And you would be right. But the concept of space-time curvature gives rise to a much richer range of phenomena than a simple force. It allows a kind of […]
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