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A New Puzzle Turns Earth Into a Rubik’s Cube, But More Complex

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A New Puzzle Turns Earth Into a Rubik’s Cube, But More Complex

One other orbit across the solar and right here we’re once more: again the place we began however spun about — modified, maybe deranged.

Henry Segerman, a British American mathematician and mathematical artist at Oklahoma State College, has invented simply the puzzle for this disorienting annual occasion: Continental Drift, a 3-D sliding puzzle that made its debut earlier this 12 months. The underlying geometric idea is holonomy: While you journey a loop on a curved floor and return to the place to begin, you arrive considerably rotated, rotated, maybe by 180 levels.

“Take a mathematical thought, are you able to make it actual?” — this query, Dr. Segerman mentioned, is what motivates his innovations.

He’s eager on visualizing arithmetic, whether or not with 3-D printing (he has written a e-book on the topic) or via non-Euclidean digital actuality experiences. However Dr. Segerman has aphantasia, an lack of ability to assemble psychological photos, or “visually hallucinate photographs at will,” as he places it. This may clarify his ardour for making concrete photos, particularly the spectacular assortment he produced in 2022.

Continental Drift is Earth in miniature, mapped onto a truncated icosahedron — a soccer ball — with its common patchwork of 12 pentagonal faces and 20 hexagonal faces.

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The conceptual inspiration was a Victorian craze: the basic 15 Puzzle, whereby sq. tiles numbered 1 to fifteen are scrambled on a 4-by-4 grid, with one sq. left empty; you resolve the puzzle by sliding tiles round into numerical order.

In Continental Drift, a spherical model of the 15 Puzzle, it’s the hexagonal tiles which are scrambled. (The pentagons are recessed and stay stationary.) “One of many hexagons, this one within the South Pacific, comes out,” Dr. Segerman explains on his YouTube channel. “We are able to then activate the San Andreas fault and slide California south into the ocean. And we will maintain going, mixing up the entire continents.”

Holonomy occurs when a tile travels a full loop alongside the curved floor of the puzzle: Slide the tile that includes, say, Greenland all the way in which across the perimeter of a single pentagonal tile — maybe the tile that includes the North Atlantic. After a whole loop, the Greenlanders return to their beginning place rotated by 60 levels. If the loop encompasses two adjoining pentagons, then the tile returns to the place to begin rotated 120 levels. And so forth.

Dr. Segerman’s extra formal investigations are in topology, the research of geometric objects with out regard for lengths or angles. “All you may have left is how issues are linked collectively — what number of holes a factor ha, and so forth,” he mentioned. As an previous topology joke goes: “A topologist is any person who can’t inform the distinction between a espresso mug and a doughnut.”

“Henry is a mathematician who additionally likes making,” mentioned his youthful brother and someday collaborator, Will Segerman. Mr. Segerman, who lives in Manchester, England, is a maker who likes mathematical shapes; he studied nice artwork and now designs and manufactures escape-room puzzles. Collectively, the brothers’ artistic course of is to ask of every thing, “However what if…?” Every time Dr. Segerman mentions a brand new undertaking, it’s invariably “very, very intelligent,” mentioned Mr. Segerman, who nonetheless appears to be like to poke holes.

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A couple of years in the past, Dr. Segerman demonstrated Extensors: a development equipment for making extending mechanisms from scissor-like hinged elements. “Not silly sufficient,” mentioned his brother, who wished extra silliness. They added an activator deal with on one finish and a four-pronged claw on the opposite. The outcome, which made its debut in April, was the Grabber Mechanism — the patent is pending.

Sabetta Matsumoto, an utilized mathematician on the Georgia Institute of Expertise and Dr. Segerman’s associate, gave enter into the contraption’s improvement and got here up with the title Extensor. Between them, math is “a fairly frequent dialog,” Dr. Matsumoto mentioned.

In a variation on the scissor theme, Dr. Segerman and Kyle VanDeventer, a former scholar, offered Kinetic Cyclic Scissors this summer time.

This invention was the reply to an issue: Given a tile sample of “self-similar” quadrilaterals — the identical form however rotated, translated, scaled — can the tiles get replaced with scissor linkages (like a scissor elevate), and might the construction then be made to maneuver?

Two courses of shapes work, they proved: “boring parallelograms” and “shocking cyclic quadrilaterals,” cyclic which means that each one vertexes of a quadrilateral lie on a circle. Mr. VanDeventer, now an aerospace engineer at Aurora Flight Sciences in Manassas, Va., sees potential purposes within the aerospace business; for proprietary causes, he declined to elaborate. Scissor programs have been utilized in structure, house applied sciences and satellite tv for pc panels. In a YouTube remark, a viewer steered that this mechanism would function “one hell of a back-scratcher.”

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Additionally contemplate the Countdown d24, a 24-sided die that’s the newest invention to emerge from the Cube Lab, a enterprise partnership with Robert Fathauer, a mathematical artist and puzzle designer in Apache Junction, Ariz. The Countdown d24 is used to maintain observe of factors, corresponding to within the card sport Magic: The Gathering.

One downside with some countdown cube, which regularly are the form of an icosahedron with 20 triangular sides, is that the numerical path across the form doesn’t observe a constant sample, which leaves you fumbling round to search out the quantity you need.

The Countdown d24 overcomes this downside by as an alternative being a sphericon, long-established from a triple-cone form, like an awkwardly formed soccer, which is then lower up, twisted about and glued again collectively.

This invention resulted from a “collision of concepts,” as do lots of Dr. Segerman’s creations. He had beforehand collaborated on making a rolling circus acrobatics equipment based mostly on a two-cone sphericon.

For the countdown die, two cones didn’t resolve that fumbling downside, however three cones did. The outcome shows a transparent path, zigzagging up and down across the die, counting down from 24 to 1, making it a cinch to rotate the die to the quantity you need.

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And because it turned out, the die can “roll alongside its path,” Dr. Segerman famous. Given the precise slope, gravity and a nudge, the die wiggles alongside an ideal chronological countdown. “That was a shock,” Dr. Segerman mentioned. “Actuality does are inclined to chew again.”

Continental Drift isn’t Dr. Segerman’s first time across the holonomy block. Final 12 months, he made the dodecahedral holonomy maze and extra not too long ago the Helix Dice Puzzle. His holonomy craze began with riffs on the 15 Puzzle that predated Continental Drift. He added hinges so the tiles can rotate as they slide, producing the 15+4 Puzzle after which the Hyperbolic 29 Puzzle.

“Simply taking a look at this puzzle prompts my fight-or-flight response,” a YouTube commenter wrote of the Hyperbolic 29 Puzzle. Dr. Segerman’s good friend Rick Rubenstein, a former skilled juggler and a semiretired software program engineer in Sunnyvale, Calif., adopted with: “Henry Segerman, Mad Genius.”

Mr. Rubenstein bought to know Dr. Segerman as a fellow leisure juggler at Stanford. Dr. Segerman can stably juggle 5 balls, and he usually takes 100-catch work breaks.

“He’s truly a really wise man with a barely non-Euclidean humorousness,” Mr. Rubenstein mentioned.

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Certainly, whereas Dr. Segerman is aware of that his puzzles are solvable, he doesn’t bother himself with the duty of discovering the options.

Nonetheless, for a tough measure of Continental Drift’s complexity, he calculated that it has 7 × 10³¹ states, or attainable configurations. (The Rubik’s Dice, with roughly as many shifting elements, has solely round 4 × 10¹⁹ states.) A YouTube viewer calculated that precisely half of Continental Drift’s states are attainable.

To Dr. Segerman’s information, just one individual has solved Continental Drift up to now. “I resolve it by unscrewing the detachable a part of the body that permits you to take the tiles out,” he mentioned. Then he reorients himself and the tiles, and screws the puzzle again collectively.

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Opinion: Most older Americans who need hearing aids don't use them. Here's how to change that

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Opinion: Most older Americans who need hearing aids don't use them. Here's how to change that

Having depended on hearing aids for nearly three decades, I’m astounded by the lack of Medicare coverage for devices that can solve a problem afflicting tens of millions of older Americans.

Nearly two-thirds of Americans over age 70 have some degree of hearing loss, and over half of those 75 and older experience impairment serious enough to be considered disabling. But most don’t wear hearing aids.

Because the legislation that created Medicare nearly 60 years ago specifically excluded hearing aids, those who rely on the program’s traditional coverage must pay for them out of pocket. That expense is among the chief barriers to wider use of the devices.

Age-related hearing loss impedes basic communication and the relationships that depend on it. Expanded access to hearing aids could therefore do no less than enable more older Americans to establish and maintain the social connections that are essential to a meaningful life.

Hearing loss is like an invisible, muffling curtain that falls in front of anyone speaking. Asking people to repeat themselves can yield irritated and hurtful responses. And it’s hopeless to ask a soft-spoken person to speak up. Sometimes it’s easier just to nod and smile.

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Many older people I know choose to avoid social gatherings altogether because they can’t hear well. Without hearing aids, I’d stay home too.

Hearing loss can harm one’s health in other ways. For example, I’ve written about the need for a comprehensive approach to reducing cancer risk at older ages, including preventive services such as colorectal cancer screening. But these services rely on conversations between patients and their healthcare providers. An older patient’s ability to hear and understand such conversations shouldn’t be taken for granted or ignored.

The Food and Drug Administration did improve access to hearing aids by making some of them available without a prescription in 2022, but the over-the-counter devices are inadequate for serious hearing loss like mine. My private health insurance, meanwhile, started covering hearing aids a few years ago, providing up to $2,500 for them every five years. One hearing aid alone can cost that much or more, however.

Despite its limitations, my private coverage for hearing aids is better than nothing, which is what traditional Medicare provides.

Hearing loss is more common among lower-income people and those without advanced education. The toll from noisy workplaces compounds age-related hearing loss for some. One analysis found that most Americans with a serious hearing disability can’t afford the typical price of hearing aids.

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Many of the older adults who can’t come up with these significant out-of-pocket expenses spent their working years in low-wage jobs that our country depends on. Denying them treatment for their hearing loss is a lousy way to treat people who gave years of service to our society.

Although some older adults with hearing loss won’t benefit from hearing aids, Medicare coverage for the devices might encourage more beneficiaries to get their hearing tested so they can get the treatment that’s right for them. And while Medicare coverage alone won’t address the stigma some people associate with hearing aids, the availability of newer, more comfortable and less obvious technology might win over some refuseniks.

Legislation reintroduced with bipartisan support last year would finally correct this glaring gap in Medicare coverage by removing the hearing aid exclusion from the law. There’s no reason to delay action on this any longer. Are our representatives listening?

Mary C. White is an adjunct professor of environmental health at Emory University’s Rollins School of Public Health, a Public Voices fellow at AcademyHealth in partnership with the OpEd Project and a former federal epidemiologist.

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Second human case of bird flu detected in Michigan dairy worker

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Second human case of bird flu detected in Michigan dairy worker

A second human case of bird flu in a diary worker has been confirmed in Michigan, state and federal health officials announced Wednesday.

The symptoms were mild, consisting of conjunctivitis. The Texas dairy worker who contracted the virus in March also came down with pink eye.

At a press call on Wednesday, Nirav Shah, principal deputy director of the U.S. Centers for Disease Control and Prevention, said the finding was “not unexpected” and that it was a scenario “that we had been preparing for.”

He said that since the discovery of H5N1 in dairy cattle, state and federal health officials have been closely monitoring farmworkers and slaughterhouse workers and urging farmers and farmworker organizations to “be alert, not alarmed.”

Federal officials say they still believe the human health risk of bird flu is low; however, it underscores the need for people who are interacting with infected or potentially infected farm animals or birds to take precautions, including avoiding dead animals and wearing personal protective equipment (PPE) if there’s a need to be in close contact.

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Though a nasal swab from the person in Michigan tested negative for influenza, an eye swab from the patient was shipped to the CDC and tested positive for influenza A(H5N1) virus.

This is the third case of H5N1 reported in the United States. A poultry worker in Colorado was identified in 2022.

Although the symptoms in the three farmworkers in the U.S. have been mild, people elsewhere in the world have suffered more severe illness, including death. According to the World Health Organization, between Jan. 1, 2003, and March 28, 2024, there have been 888 cases of human infection from 23 countries; 463 were fatal.

In preparation for a more widespread outbreak, the CDC updated its guidance for PPE in dairies and issued a nationwide order for healthcare providers to be on the lookout for novel influenza.

On Tuesday, the CDC asked clinical laboratories and health departments to increase the number of influenza samples being analyzed “to maximize the likelihood of catching a case of H5N1 in the community,” Shah said.

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The US Department of Agriculture is also expanding its surveillance and support by providing $1500 to non-infected farms to beef up biosecurity, and $100 to producers who want to buy inline samplers to test their milk. The agency will also provide $2000 per farm to cover veterinary fees for testing, as well as shipping costs to send those tests to laboratories for analysis.

There have been no cases of H5N1 detected in California’s dairy herds.

Officials said ongoing analysis of the nation’s dairy supply suggests it is safe to consume, Despite the risk to human health being low, an official with the Administration for Strategic Preparedness and Response said it will make Tamiflu available upon request “to jurisdictions that do not have their own stockpile and are responding to pre-symptomatic persons with exposure to confirmed or suspected infected birds, cattle or other animal exposures.”

Dawn O’Connell, assistant secretary of the preparedness agency, said it started the “fill and finish” process for approximately 4.8 million doses of vaccine “that is well matched to the currently circulating strain of H5N1 through the national pre-pandemic influenza vaccine stockpile program.”

She said the decision to get started on H5N1 vaccines was not a response to any heightened concern, but since it takes several months to fill and finish vaccine doses, the agency “thought it made sense given what we were seeing.”

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Gas stoves may contribute to early deaths and childhood asthma, new Stanford study finds

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Gas stoves may contribute to early deaths and childhood asthma, new Stanford study finds

Lung-irritating pollution created by cooking with gas stoves may be contributing to tens of thousands of premature deaths and cases of childhood asthma in the United States, according to a new study published in the journal Science Advances.

For decades, scientists have known the flames from a gas stovetop produce nitrogen dioxide, a pungent gas that can inflame a person’s lungs when inhaled. But for the first time, a team of researchers from Stanford University and Oakland-based research institute PSE Healthy Energy published a nationwide estimate of the long-term health consequences associated with cooking with natural gas and propane stoves.

Researchers concluded that exposure to nitrogen dioxide emissions alone may contribute to nearly 19,000 premature deaths in the United States each year. It has also resulted in as many as 200,000 current cases of pediatric asthma compared with cooking with electric stoves, which do not produce nitrogen dioxide.

Aggressive and impactful reporting on climate change, the environment, health and science.

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Stanford researcher Yannai Kashtan noted higher levels of pollution were correlated with the amount of gas that was burned. But pollution also accumulated at higher levels inside smaller homes.

“If you live in a smaller house, you’re exposed to more pollution, and that can lead to income and racial disparities in exposure,” Kashtan said. “In general, folks living in neighborhoods with higher levels of outdoor pollution also tend to have higher indoor pollution. So this environmental injustice extends indoors as well.”

The American Gas Assn., a trade organization representing more than 200 local energy companies nationwide, dismissed the findings as “misleading and unsupported.”

“Despite the impressive names on this study, the data presented here clearly does not support any linkages between gas stoves and childhood asthma or adult mortality,” the association’s president and CEO, Karen Harbert said in a statement earlier this month.

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The study is the latest examining the serious health effects associated with breathing fumes from gas stoves, which release planet-warming carbon emissions and a variety of air pollutants. In recent years, the popular household appliance has become a political hot-button issue as policymakers and regulators have weighed environmental impacts against consumer choice.

Many large cities in California, including Los Angeles, have moved toward phasing out gas stoves in newly constructed residences. Earlier this month, the California Assembly advanced a bill to the Senate that would require gas stoves to come with warning labels detailing the pollution and health effects that can arise from cooking with gas.

Gas stoves emit a variety of pollutants, including asphyxiating carbon monoxide, cancer-causing formaldehyde and benzene. The flame also creates nitrogen dioxide, a precursor to smog and a pollutant that can cause difficulty breathing.

Environmental groups say consumers should be notified about these pollutants and the potential harm they can cause.

“Gas stoves create pollution in our homes, increasing the risk of childhood asthma and other respiratory problems for our families,” said Jenn Engstrom, state director for California Public Interest Research Group. “However, this risk has largely been hidden from the public. Consumers deserve the truth when it comes to the danger of cooking with gas. Warning labels will give consumers what they need to make informed decisions when they purchase appliances for their homes.”

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Kashtan and other researchers had previously discovered cooking with gas stoves presented a similar cancer risk as inhaling second-hand cigarette smoke. They also found some gas stoves leaked contaminants even when the burners were off.

The effects are especially devastating to children, whose smaller and still-developing lungs need to take more breaths than adults, Kashtan said. Older adults, especially those with cardiovascular or respiratory illness, are also more vulnerable to pollution from gas stoves.

To alleviate indoor air pollution, experts recommend using ventilation hoods and opening windows while cooking,

Starting in 2008, California required new and redeveloped homes to have ventilation that could prevent pollution from building up indoors. But during their research, measuring emissions in more than 100 households across the country, Yannai said they found many kitchens didn’t have ventilation hoods at all.

Although the health effects of breathing these pollutants are clear, researchers still wonder to what degree these conditions could be reversible. As communities take steps to mitigate their exposure or transition away, he said we could soon see the results.

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“It’s never too late to stop breathing in pollution,” he said.

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