The original version ofthis storyappeared in Quanta Magazine.
In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate it so that it points in every direction in turn. What’s the smallest area the needle can sweep out?
If you simply spin it around its center, you’ll get a circle. But it’s possible to move the needle in inventive ways, so that you carve out a much smaller amount of space. Mathematicians have since posed a related version of this question, called the Kakeya conjecture. In their attempts to solve it, they have uncovered surprising connections to harmonic analysis, number theory, and even physics.
“Somehow, this geometry of lines pointing in many different directions is ubiquitous in a large portion of mathematics,” said Jonathan Hickman of the University of Edinburgh.
But it’s also something that mathematicians still don’t fully understand. In the past few years, they’ve proved variations of the Kakeya conjecture in easier settings, but the question remains unsolved in normal, three-dimensional space. For some time, it seemed as if all progress had stalled on that version of the conjecture, even though it has numerous mathematical consequences.
Now, two mathematicians have moved the needle, so to speak. Their new proof strikes down a major obstacle that has stood for decades—rekindling hope that a solution might finally be in sight.
What’s the Small Deal?
Kakeya was interested in sets in the plane that contain a line segment of length 1 in every direction. There are many examples of such sets, the simplest being a disk with a diameter of 1. Kakeya wanted to know what the smallest such set would look like.
He proposed a triangle with slightly caved-in sides, called a deltoid, which has half the area of the disk. It turned out, however, that it’s possible to do much, much better.
The deltoid to the right is half the size of the circle, though both needles rotate through every direction.Video: Merrill Sherman/Quanta Magazine
In 1919, just a couple of years after Kakeya posed his problem, the Russian mathematician Abram Besicovitch showed that if you arrange your needles in a very particular way, you can construct a thorny-looking set that has an arbitrarily small area. (Due to World War I and the Russian Revolution, his result wouldn’t reach the rest of the mathematical world for a number of years.)
To see how this might work, take a triangle and split it along its base into thinner triangular pieces. Then slide those pieces around so that they overlap as much as possible but protrude in slightly different directions. By repeating the process over and over again—subdividing your triangle into thinner and thinner fragments and carefully rearranging them in space—you can make your set as small as you want. In the infinite limit, you can obtain a set that mathematically has no area but can still, paradoxically, accommodate a needle pointing in any direction.
“That’s kind of surprising and counterintuitive,” said Ruixiang Zhang of the University of California, Berkeley. “It’s a set that’s very pathological.”
When the history of Burning Man 2023 is written, it’s likely Diplo and Chris Rock deciding to trudge for five miles out of the festival site will be recorded as the point the fun stopped.
The musician and actor were forced to abandon their campsite by foot as torrential rains turned the Nevada desert, which hosts the annual hedonists’ festival, into a mud bath. The temporary roads throughout the vast festival site turned into rivers, and people who signed up for eight days of partying and dancing—Burning Man began on August 27—have instead been forced to plod through thick dirt. Many have resorted to rationing food and water as toilets fail and new supplies can’t reach the site because of treacherous conditions.
This year, rain, and plenty of it, has reduced Burning Man and Black Rock City, the festival’s 70,000-strong temporary settlement, to a quagmire. All routes in and out of Black Rock City have been closed to traffic to avoid the ground being torn up by repeated tyre tracks. Attendees are being asked to choose between sheltering in place or trekking on foot through mud to escape.
The cause? Extreme weather wrought by climate change, which is resulting in increasing amounts of rain being dumped on the southwestern US states at this time of year. “These sorts of heavy summer rainfall events in the region are expected, as the well-known southwestern summer monsoon is expected to yield larger amounts of rainfall in a warming climate,” says Michael Mann, presidential distinguished professor in the University of Pennsylvania’s department of earth and environmental science.
This year’s summer has been particularly hot in the southwest: NASA Earth Observatory called this year’s heatwave “relentless.” That has a knock-on effect on potential rainfall. For every one degree Celsius temperature increase there is, there’s a 7 percent increase in moisture in the atmosphere. “A warmer atmosphere holds more moisture. So when conditions are favorable for rainfall to occur, as they are during the monsoon season, we expect more of it,” says Mann. And when that rainfall lands on the 4,000-acre dry lake bed that hosts Burning Man, it causes problems. The ground underfoot “consists of the sort of soil that easily creates a layer of mud when you add enough water,” says Mann. Campers know that: The launch of the event was delayed in late August because of rainfall from Hurricane Hilary. And research shows that the Black Rock playa, where Burning Man is based, turns into a mud bath in winter months when rain traditionally falls, “making the central portions almost entirely inaccessible for recreation.”
What Is Burning Man?
Burning Man is a weeklong festival held in the Nevada desert that attracts hedonists and the rich to party in a “utopian” community where commerce is banned and bartering is the main method of economics. Of course, you have to pay for some things—like entry, which starts at $575, but excludes camp fees, which can run into thousands of dollars, and supplies, which cost a similar amount.
Because Burning Man chooses to situate its event in the Nevada desert, resources, including food and generators, need to be trucked to the site—a challenge given heavy rain has made roads impassable. It’s this, in part, that explains why Chris Rock decided to abandon the event: In an Instagram Story, he posted that he understood portable toilets couldn’t be emptied, supplies delivered, and extra generators sent because of flooding.
But others haven’t given up. For Anya Kamenetz, who attended her first Burning Man in 2003, the rainfall hasn’t fazed her—or her fellow campmates. “We’re really prepared,” she says, though she admits that the weather’s impact means “you can’t get around the city at all.” Vehicles are banned from traveling around for fear of making the ground worse or getting stuck and blocking routes earmarked as exit routes for when it’s safe to leave. Those who choose to walk around the site can still party as always, but some have decided against doing so. Kamenetz and her campmates are continuing as normal, with some significant alterations. “We don’t know when we’re going to get drinking water—or if—or portapotty services, or fuel, or gray water services,” she says. As a result, they’re conserving as much water as possible. They’re not urinating in the portapotties, but on the ground. “We’re not rationing food, but we’re just trying to make [sure] everyone is as thoughtful as possible,” she says. Showers are out—as is dishwashing.
Not long after the deadliest wildfire in modern American history swept through Lahaina, Maui, on August 8, speculation began swirling about a notorious igniter of out-of-control blazes: electrical equipment.
Although investigators have yet to officially determine the cause of the wildfire, witnesses reported power poles snapping in the 60-mile-an-hour winds that were pouring down the nearby mountains, showering dried vegetation in sparks. And last week, the County of Maui hit Hawaiian Electric with a lawsuit, accusing the utility of neglecting its duty to power down its infrastructure, given the known risk of such high winds sparking wildfires.
On Sunday, the utility responded with a press release, saying that at 6:30 am, a morning fire “appears to have been caused by power lines that fell in high winds.” Firefighters extinguished that blaze, the press release continues, but another fire popped up in the same area at about 3 pm, when the utility says its lines had been de-energized for more than six hours. That fire then spread into Lahaina.
“Hawaiian Electric has now admitted to starting the Lahaina Fire on August 8th,” said John Fiske, the counsel representing the County of Maui, in a statement provided to WIRED. “In its recent release, issued Sunday night before the markets opened, Hawaiian Electric appears to have suggested there could be a possible second ignition source in the afternoon of August 8th without providing any supporting information.”
Investigators have yet to determine if there were two separate ignitions, or if the afternoon fire was a flare-up of the one earlier in the morning. Hawaiian Electric declined to answer questions for this story, referring WIRED to its press release.
If investigators ultimately conclude that the fire’s cause was electrical equipment, the Maui fire will join other recent city-razing blazes in the American West that were started—and then powered—by fierce winds rattling the power infrastructure. But even if utilities are able to prevent their equipment from sparking blazes—like by “undergrounding” lines, meaning enclosing them in piping and burying them in trenches—there are lots of other ways to start an epic conflagration on a warming planet.
Wind is essential to whipping up the biggest, fastest, deadliest wildfires. And electricity can be a dangerous add-on: If gusts down trees into power lines, or utility poles snap or fall over, all that jostling can send sparks into the vegetation below. Winds fan the growing flames, driving the blaze across the landscape with such speed that people in the way don’t have time to evacuate. (Strong winds also loft embers into the air, and can carry them perhaps 2 miles ahead of the main fire, creating new fires and making it harder for firefighters to manage.) Towns like Lahaina in the “wildland-urban interface,” where unkempt vegetation butts up against structures or intermingles with them, are especially vulnerable to such fast-moving fires.
America’s aging grid wasn’t designed for today’s climate, with its warmer atmosphere, intense, longer-lasting droughts, and increasingly dry landscapes. So electrical-sparked, wind-driven fires are growing more destructive and deadly. In 2017 the Tubbs Fire destroyed over 5,600 structures and killed 22, and in 2018 the Camp Fire destroyed the town of Paradise and killed 85. In 2019, the California utility Pacific Gas and Electric, or PG&E, reached a $13.5 billion settlement for wildfires linked to its equipment, including both of these fires. Both have now been eclipsed by the Lahaina fire in terms of the human cost: At least 115 people have been confirmed dead, with hundreds still missing.
Nearly one year ago, NASA flung the DART spacecraft into the asteroid Dimorphos at 14,000 miles per hour. It was the first test to see whether they could slightly deflect a space rock’s trajectory using a high-speed collision, a technique that could be used to protect Earth from future killer asteroids. It worked. But now they’re trying to figure out the details of the crash. And if people have to defend earthly life from a potential asteroid impact, those details will surely matter.
Scientists are starting by studying the ejecta, boulders, and numerous smaller bits the strike cast off. They predicted there would be debris, but they didn’t know exactly what to expect. After all, compared to stars and galaxies, asteroids are tiny and dim, so it’s hard to ascertain their density and composition from afar. When you strike one, will it simply bounce? Will the probe thud into it and create a crater? Or if the asteroid is brittle, will slamming a craft into it risk creating space shrapnel that is still big enough to threaten Earth?
“This is exactly why we needed to do an in-space test of this technology. People had done laboratory experiments and models. But how would an actual asteroid, of the size we’re concerned about for planetary defense, react to a kinetic impactor?” says Nancy Chabot, the DART coordination lead and a planetary scientist at Johns Hopkins University’s Applied Physics Laboratory, which developed the craft in partnership with NASA.
Many asteroids appear to be “rubble piles,” dirt, rocks, and ice loosely held together, rather than something hard and dense like a billiard ball. The asteroid Ryugu, visited by the Japanese space agency’s Hayabusa2 in June 2018, and the asteroid Bennu, which NASA’s OSIRIS-REx took samples from in 2020, both count as rubble piles. A new study published in July in Astrophysical Journal Letters shows that Dimorphos appears to be built like that too, which means that an impact is likely to create a crater and to fling off debris on or near the asteroid’s surface.
To figure out what happened after the crash, David Jewitt, a University of California, Los Angeles astronomer, and his colleagues used the Hubble Space Telescope to zoom in repeatedly on Dimorphos. The combined deep observations allowed them to discern objects that are otherwise too faint to see. A few months after the DART probe’s impact, they found a swarm of about three dozen boulders not seen before—the largest of which is 7 meters in diameter—slowly drifting away from the asteroid. “It’s a slow-speed cloud of shrapnel from the impact that’s carrying away a significant amount of mass: about 5,000 tons in boulders. That’s quite a lot, considering the impactor itself was only half a ton. So it blew out a tremendous mass in boulders,” Jewitt says.
Other researchers, including the DART team, have also been investigating the cloud of rocks thrown off by the spacecraft’s swift punch. Chabot and her colleagues published a study in Nature earlier this year, also using Hubble photos, imaging the ejecta. They showed that at first the pieces flew off in a cone-shaped cloud, but over time, that cone turned into a tail, not so different from a comet’s tail. That finding also means that models of the behavior of comets could be applied to impactors like DART, Chabot says.
Dimorphos was never a threat to Earth, but details like these would matter in a real asteroid deflection scenario. Boulders and smaller ejecta would have to be knocked out of the way, along with the rest of the asteroid, in order to spare the planet. Or let’s say the asteroid wasn’t spotted until it was very close to Earth, and its trajectory couldn’t be altered enough to avoid a crash. Could it at least be pulverized into boulders small enough to burn up in Earth’s atmosphere? “Is it better to be shot by a high-velocity rifle bullet or a bunch of pellets from a shotgun?” asks Jewitt. “The answer is: The shotgun is better, because the smaller boulders are more likely to be cushioned or dissipated by the impact with the atmosphere.”
And nations should avoid cluttering those spots with mechanical detritus, which could complicate future missions. Like campers heading into the backcountry, it’s important to think carefully about what you pack with you and what you take out, Birk says.
India’s success doesn’t mean the end of the race toward the moon’s south pole, but it does boost India’s standing. “This will certainly contribute to its status as a rising power with technological prowess. What’s happening in space is a reflection of what’s happening geopolitically on Earth,” says Cassandra Steer, an expert on space law and space security at the Australian National University in Canberra. And while Roscosmos suffered a setback, this isn’t the end of their moon program either, or their role in the new lunar competition. The Soviets beat the US at every stage of the 20th-century space race, Steer says, except for the landing of astronauts on the moon. Next, Russia intends to collaborate with China on a lunar research station.
Over the past decade, only China’s space program has achieved considerable success landing spacecraft on the moon, including its Chang’e 3, 4, and 5 missions in 2013, 2019, and 2020. India’s Chandrayaan-2 and Israel’s Beresheet lander failed in 2019, and Japan’s Ispace lander failed this April.
In fact, until China made its first landing, the moon had arguably been neglected for decades. NASA ended its Apollo mission in 1972, and the USSR’s Luna-24 mission in 1976 was the last successful lunar landing. That could mean limited institutional memory, especially for Russia, making it tough to develop and deploy new moon missions, Metzger says.
Over the past few decades, Russia has been trying to resuscitate its program, but with little success. Roscosmos has Luna-26 and Luna-27 planned for 2027 and 2029, as the agency aims to bring an orbiter and a larger lander to the moon. But their limited funding, thanks to sanctions following the Ukraine invasion, means these followup missions will likely be delayed, Zak says. And if the space agency decides to overhaul their propulsion system design after investigating the failure of Luna-25, that could be another reason for delays, he adds.
NASA has fared better with its Artemis program, which last year sent the uncrewed Artemis 1 to orbit the moon and is aiming for a crewed landing in 2026. But the program has faced its own challenges: NASA plans on using a SpaceX Starship lander, though, as its abortive test flight in April shows, Starship clearly has a long way to go. More than half of the 10 cubesat satellites deployed by Artemis 1 experienced technical glitches or lost contact with Earth, including the Japanese Omotenashi probe, which was unable to land on the moon as planned.
NASA has increasingly relied on commercial partners in a bid to boost the speed and lower the price of moon exploration—moving some of the costs onto businesses, rather than taxpayers. But these companies, too, are new players in the space race. In late 2024, NASA plans to send its Viper rover on an Astrobotic lander, though that company’s first moon lander, meant to demonstrate the technology, hasn’t even launched yet. NASA has also charged Firefly Aerospace, Intuitive Machines, and Draper with delivering a variety of payloads to the lunar surface over the next couple years.
In the meantime, nations like India, Japan, and Israel have begun moon programs from scratch. India next plans to collaborate with Japan on the Lunar Polar Exploration rover, which would launch no sooner than 2026.
“We have set the bar now so high. Nothing less spectacular than this is going to be inspiring for any of us in the future,” said Shri M. Sankaran, director of ISRO’s U R Rao Satellite Centre, speaking on today’s telecast. “We will now be looking at putting a man in space, putting a spacecraft on Venus, and landing on Mars. Those efforts have been ongoing for years. This success today will inspire us and spur us to take those efforts even more strongly to make our country proud again and again and again.”
Updated 8/23/2023 12:00 pm ET: This story was updated to correct the ISRO chief’s name.
