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"Mathematicians solve decades-old geometry problem."

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Russ Roberts (https://hawaiisciencejournal.blogspot.com.

 

August 12, 2024: Shapes that roll but aren't round, fight-or-flight needs an update, and it takes a lot to stress out a Joro spider. —Andrea Gawrylewski, Chief Newsletter Editor

TOP STORIES

Predictive Brain The idea that human brains react to stress with either a fight, flight or freeze response may be outdated. New research shows that the brain region called the periaqueductal gray (PAG), long thought to control the fight-or-flight response, regulates elements of the limbic system (like the heart and lungs) at all times, when emotions are high or in deep sleep.  What this means: Decades of research point to the brain being far more predictive than reactive. The brain is constantly at work evaluating uncertainty in the world (where will my next meal come from? Do these people accept me in the in-group?) and crafting automatic responses that kick in when required.  What the experts say: Too much uncertainty in a person’s daily experience (whether the stress of world events, or striving to meet basic needs) strains the brain’s prediction circuits and can be metabolically draining, writes Lisa Feldman Barrett, a professor of psychology at Northeastern University. “These feelings don’t emerge from mythical, overtaxed fight-or-flight circuits. They may just mean, in an ever changing and only partly predictable world, that you’re doing something really hard.”

Shapes That Roll Mathematicians have created a new shape that can roll, but it’s not a circle or sphere. They devised a multi-dimensional "guitar pick" shape that rolls in ways beyond our three-dimensional comprehension. This breakthrough solves a decades-old geometry problem. How it works: Circles and spheres have so-called "constant width," which means there’s always the same distance between the edge of the shape and two parallel planes, such as the ground, as it rolls along. The researchers figured out how to create new shapes in any dimension by examining the intersection of an infinite number of n-dimensional balls–shapes where all edge points are the same distance from the center in n-dimensions. The result is the shape of a guitar pick in three dimensions that can “roll” by maintaining a constant width between two parallel planes in any dimension. What the experts say: “It’s really difficult to estimate volume in high dimensions, yet this whole proof is fairly simple and so elegant,” says Gil Kalai, a professor at the Einstein Institute of Mathematics. He suggests this could mark the beginning of a new era in studying constant-width shapes from a new perspective, and that in the future mathematicians might construct even smaller ones. --Max Springer, news intern

The infinite intersection of n-dimensional balls in two dimensions Credit: Amanda Montañez

TODAY'S NEWS

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• The United Nations approved its first international cybercrime treaty last week. But tech companies and human rights groups say the measure will infringe on freedom of speech and expression. | 4 min read

• It's peak season for West Nile virus. Here's how to protect yourself. | 3 min read

• This is the forgotten story of Helen Edwards, a particle physicist who oversaw the design and construction of the Tevatron particle accelerator. | 30 min listen

More News

EXPERT PERSPECTIVES

• A study in July found that members of Generation X and Millennials face a higher risk than older generations of 17 types of cancer. Several types of cancer are preventable with early detection tools, as long as young people use them, write Karen E. Knudsen and Othman Laraki, chief executive officer and partner of the American Cancer Society, respectively. "If you are under 50, you need to realize that you are not too young to develop cancer," they say. "Too often people with symptoms of cancer below the recommended screening age are reassured that they are too young to have cancer and that their symptoms must be linked to something less troublesome." | 5 min read

More Opinion

As I write above, the brain is always evaluating uncertainty and predicting what might happen next. Extended stretches of uncertainty--stressful news cycles, personal strife--can amp up anxiety and vigilance. Chronic stress and anxiety can shut down the function of higher "executive" areas of the brain that help us manage our lives, control impulses and make plans for the future. Read more about the science of stress (and how to bust it) in this collection of articles.

De-stress with games! Here's the latest Spellements, math puzzle and science jigsaw. Thank you for being part of our circle of science-curious readers. Email me anytime: newsletters@sciam.com. See you tomorrow.

—Andrea Gawrylewski, Chief Newsletter Editor

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