All circles, from onion rings to Saturn’s rings, share a magnificent property: their circumferences stretch about three times longer than their diameters. To be more precise (though still not exact), the circumferences are 3.14159, or pi, times longer. Circles are such fundamental shapes that pi, the number that governs them, stamps its signature across the… Continue reading Does Pi Contain All of Shakespeare?
Category: Quantum Stuff
My Fantastic Voyage at Quanta Magazine
In 2016, I joined Natalie, Siobhan Roberts and Emily Singer in profiling four master science and math teachers as part of an education series that included video vignettes produced by my former New York Times colleague Lisa Iaboni, an interactive survey of readers’ experiences with math and science built by Emily Fuhrman, my interview with… Continue reading My Fantastic Voyage at Quanta Magazine
How Do Machines ‘Grok’ Data?
As a network trains, it tends to learn more complex functions, and the discrepancy between the expected output and the actual one starts falling for training data. Even better, this discrepancy, known as loss, also starts going down for test data, which is new data not used in training. But at some point, the model… Continue reading How Do Machines ‘Grok’ Data?
Geometers Engineer New Tools to Wrangle Spacecraft Orbits
You can create a graph with the angle as the x-axis and the speed as the y-axis. But since traveling 360 degrees brings you back to the start, you can sew together the vertical lines where x is zero degrees and where x is 360 degrees. This makes a cylinder. The cylinder doesn’t directly reflect… Continue reading Geometers Engineer New Tools to Wrangle Spacecraft Orbits
Pleasure or Pain? He Maps the Neural Circuits That Decide.
Does finding this skin-to-brain pathway have any medical implications? Yes, the skin is a good therapeutic target. It’s accessible and presents a direct highway to the part of the brain that makes us feel good. What if we could turn on these neurons with a skin cream to improve mental health — say, to offset… Continue reading Pleasure or Pain? He Maps the Neural Circuits That Decide.
Hopes of Big Bang Discoveries Ride on a Future Spacecraft
The theory has its flaws. For instance, the mass of the Higgs boson — the component of the Standard Model that determines the masses of other particles — is frustratingly “unnatural.” It appears arbitrary, and puzzlingly small compared to the far greater energy scales of the universe. Moreover, the Standard Model offers no explanation for… Continue reading Hopes of Big Bang Discoveries Ride on a Future Spacecraft
NASA’s Voyager 1 Is Bound for the Great Beyond
In the fall of last year, one of NASA’s most venerable spacecraft started beaming home nonsense. Its usual string of 1’s and 0’s—binary code that collectively told of its journey into the unknown—became suddenly unintelligible. Some 15 billion miles from Earth, beyond the protective bubble blown by the sun and in interstellar space, Voyager 1… Continue reading NASA’s Voyager 1 Is Bound for the Great Beyond
Math Can’t Solve Gerrymandering
Math Can’t Solve Gerrymandering Researchers use powerful geometrical methods to try fixing unfair districts. That alone isn’t enough; we need to fight the values behind gerrymandering By Matthew R. Francis Voters cast their ballots at a polling station inside the Adamsville Baptist Church in Goldsboro, North Carolina, US, on Tuesday, March 5, 2024. This year’s… Continue reading Math Can’t Solve Gerrymandering
Overexposure Distorted the Science of Mirror Neurons
In the summer of 1991, the neuroscientist Vittorio Gallese was studying how movement is represented in the brain when he noticed something odd. He and his research adviser, Giacomo Rizzolatti, at the University of Parma were tracking which neurons became active when monkeys interacted with certain objects. As the scientists had observed before, the same… Continue reading Overexposure Distorted the Science of Mirror Neurons
Dark Energy May Be Weakening, Major Astrophysics Study Finds
While researchers find these numbers tantalizing, they also warn against reading too much into the higher values. The universe is a lot more complicated than a coin, and the statistical significances depend on subtle assumptions in the data analysis. A stronger reason for enthusiasm is the fact that all three supernova catalogs — which span… Continue reading Dark Energy May Be Weakening, Major Astrophysics Study Finds