Today in Science: Math's "hairy ball theorem" is everywhere

Daily discovery, science that inspires. February 27, 2025: Math's "hairiest" problem. Plus, time may flow in two directions in a quantum system, and a private lunar lander launches. —Andrea Gawrylewski, Chief Newsletter Editor TODAY'S NEWS A SpaceX Falcon 9 rocket launches from NASA's Kennedy Space Center. Manuel Mazzanti/NurPhoto via Getty Images • A SpaceX Falcon 9 rocket lifted off last night, carrying the private Athena lunar lander and NASA's Lunar Trailblazer. Both missions will be looking for signs of water ice on the moon. | 5 min read • Rats have tested positive for bird flu. Plus, a report on the disease in cats and more egg shortages. | 4 min read • We humans experience time in one direction. But in the quantum world, the arrow of time may travel forward AND backward. | 5 min read More News TOP STORIES A Hairy Math Problem You can't comb down the hairs on a coconut without creating a cowlick. Mathematicians have proved this with the (appropriately named) "hairy ball theorem." No matter where you put the hairs (or vectors, as mathematicians call them) along the surface of the coconut (the sphere), a discontinuity will arise–in no arrangement could all hairs lie flat along the surface. Tufts on either side demonstrate the hairy ball theorem. This sphere is covered in small lines resembling hairs that are all combed in the same direction.Buckyball Design Why this matters: This idea applies to spheres of all kinds. The theory predicts that at any given moment, there will always be a point on Earth's surface where the wind (the vector) isn't blowing. Nuclear physicists used the hairy ball theorem to solve the problem of containing plasma in fusion reactors. Knowing that a container the shape of a perfect sphere would be subject to hairy math, they opted for a doughnut-shaped container. The solution: A doughnut shape allows for continuous vectors all running in the same direction, with no resulting discontinuities (tufts). Consider a spinning basketball. At any moment on the basketball, one point will be still (the hairy ball theorem at work). If you remove the still points by cutting them out, say, then all points on the basketball would be spinning, but you've just created a doughnut! This doughnut shape is covered in small lines resembling hairs that are all combed in the same direction, with no tufts resulting. Buckyball Design Are you enjoying this newsletter? Consider supporting the vital science journalism we do with a subscription to Scientific American. Special discounts are available for Today in Science readers! EXPERT PERSPECTIVES • A meme exploded in 2019 that "everything will eventually evolve into a crab" or "crab is the ideal form," referring to the evolution of body forms that look like a crab, which appeared at least five times within crustaceans (a concept called carcinization). As fun a shorthand for "some things happen multiple times" as it is, the meme misleads about the true processes of evolution, writes Joanna Wolfe, an evolutionary biologist at Harvard University. "Some carcinization memes explicitly state that evolution has a goal of turning other species into crabs. That's wrong," she says. "When we use words that imply some organisms are 'ultimate forms,' it implies they are genetically better than others. Not so, because there are millions of species already well adapted to their own environments that haven't turned into crabs." | 4 min read More Opinion QUOTE OF THE DAY "It can be very valuable for people to pay attention to their dreams — not necessarily to overanalyze their meaning, but to understand how dreaming is a sign your brain is doing important emotional and cognitive work." Cognitive neuroscientist Jing Zhang has some tips if you want to remember more of your dreams. (Popular Science | 7 min read) Mathematics deals with numbers, yes. Prime numbers, irrational numbers, infinite series, and of course, Pi. But math is a powerful tool for understanding not only the shape of our world, but how to optimize all aspects of life, from matchmaking to cookie-baking (and, of extreme importance, the best beer glass shape). An invisible equation seems to undergird every facet of reality.  Do you have a love or hate relationship with math? Send me your thoughts and any other feedback to: newsletters@sciam.com. Until tomorrow! —Andrea Gawrylewski, Chief Newsletter Editor Subscribe to this and all of our newsletters here. Scientific American One New York Plaza, New York, NY, 10004   Support our mission, subscribe to Scientific American here   Unsubscribe Email Preferences View in browser