DUBAI: A 3,700-year-old clay tablet analyzed by researchers in Australia has proven that Babylonians, not Greeks, developed trigonometry.
The tablet, known as Plimpton 332, was found in the early 1900s in modern-day southern Iraq but experts at the University of New South Wales, Australia, have only just discovered what the etchings on the tablet mean.
It is the world’s oldest and most accurate trigonometric table and proves that Babylonians developed the mathematic technique some 1,500 years before the Greeks, whose version is still in use today.
However, unlike the modern form of trigonometry, Babylonian mathematics used a sexagesimal system.
“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Dr. Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science, according to The Telegraph.
“It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.
“This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics and education.
“This is a rare example of the ancient world teaching us something new.”
Until now, Greek astronomer Hipparchus, who lived around 120BC, was regarded as the father of trigonometry.
“Plimpton 322 predates Hipparchus by more than 1000 years,” says Wildberger.
The tablet is thought to have come from the ancient Sumerian city of Larsa and has been dated between 1822 and 1762 BC.
Tablet found in modern-day Iraq shows Babylonians, not Greeks, developed trigonometry
Tablet found in modern-day Iraq shows Babylonians, not Greeks, developed trigonometry
‘No more fear’: Stand-up comedy returns to post-Assad Syria
DAMASCUS: In post-Assad Syria, stand-up comedians are re-emerging to challenge taboos, mocking the former president and his regime and even testing the waters with Damascus’s new rulers.
Melki Mardini, a performer in the Syrian capital’s stand-up scene, is among those embracing newfound freedoms.
“The regime has fallen,” he declares from the stage, referring to Bashar Assad’s abrupt departure earlier this month, ending more than half a century of his family’s rule.
The audience at an art gallery hosting the show remains silent.
“What’s the matter? Are you still scared?” Mardini says, triggering a mix of awkward laughter and applause.
“We’ve been doing stand-up for two years,” says the 29-year-old. “We never imagined a day would come when we could speak so freely.”
Now, his performances are “safe spaces,” he says.
“We can express our views without bothering anyone, except Bashar.”
Under the old regime, jokes about elections, the dollar or even mentioning the president’s name could mean arrest or worse.
Chatting with the audience during his set, Mardini learns one man is a psychiatrist.
“A lord in the new Syria!” he exclaims, imagining crowds rushing into therapy after five decades of dictatorship.
For two hours, 13 comedians — including one woman — from the collective Styria (a play on the words Syria and hysteria) take the stage, sharing personal stories: an arrest, how they dodged compulsory military service, how they sourced dollars on the black market.
“Syria wants freedom!” declares Rami Jabr as he takes the stage.
“This is our first show without the mukhabarat in the room,” he quips, referring to the feared intelligence agents.
He reflects on his experience in Homs, dubbed the “capital of the revolution” in March of 2011 when anti-government protests broke out in the wake of the Arab Spring, followed by brutal repression.
A commercial representative for a foreign company, Jabr recalls being detained for a month by various security services, beaten, and tortured with a taser, under the accusation that he was an “infiltrator” sent to sow chaos in Syria.
Like him, comedians from across the country share their journeys, united by the same fear that has suffocated Syrians for decades living under an iron fist.
Hussein Al-Rawi tells the audience how he never gives out his address, a vestige of the paranoia of the past.
“I’m always afraid he’ll come back,” he says, referring to Assad. “But I hope for a better Syria, one that belongs to all of us.”
Said Al-Yakhchi, attending the show, notes that free speech is flourishing.
“During the last performance before the regime fell, there were restrictions,” says the 32-year-old shopkeeper.
“Now, there are no restrictions, no one has to answer to anyone. There’s no fear of anyone.”
Not even Syria’s new rulers — a diverse mix of rebel groups, including Islamists and former jihadists, who quickly marched on Damascus and toppled Assad’s government.
“We didn’t live through a revolution for 13 or 14 years... just to have a new power tell us, ‘You can’t speak,’” Mardini says.
When not performing on stage, Mary Obaid, 23, is a dentist.
“We unload everything we’ve been holding inside — we do it for all Syrians,” she says.
“Each person shares their own experience. The audience reacts as if each story has happened to them too.”
Of the country’s new leaders, Obaid says she will wait to see “what they will do, then we’ll judge.”
“Right now, we feel freedom,” she says. “We hope we won’t be targets of harassment.”
“We’re at a pivotal moment, transitioning from one era to another,” she adds.
“Now we are the country of freedom, and we can put forward all our demands. From now on, never again fear.”
Zelensky hails Usyk victory over Fury
RIYADH: Ukrainian President Volodymyr Zelensky hailed Oleksandr Usyk’s victory over Tyson Fury in their heavyweight world championship rematch on Saturday, calling it proof that Ukraine “will not give up what’s ours.”
“Victory!” Zelensky said in a post on Telegram. “So important and so necessary for all of us now.”
Ukraine remains locked in war nearly three years after Russia invaded, but Zelensky said Usyk’s triumph was a mark of Ukrainian resiliency and determination.
“Having retained the championship belts, Oleksandr proves: we are Ukrainians and we will not give up what’s ours. And no matter how difficult it is — we will win.
“Be it the ring, battlefield or diplomatic arena — we fight and we will not give up what’s ours.
“Congrats on the victory, Cossack! Congrats on the victory Ukraine! Glory to Ukraine.”
Usyk’s victory — seven months after his first triumph over Britain’s Fury to become the first undisputed heavyweight world champion of the four-belt era — took his record to 23-0 with 14 knockouts.
Weightlifting Taiwan granny, 90, garners cheers, health benefits at gym
TAIPEI: Cheng Chen Chin-Mei beamed broadly as she hoisted a 35-kg weightlifting bar to her waist, dropped it and waved confidently to the enthusiastic crowd in a competition in Taipei. Cheng Chen, 90, has been pumping iron since last year, encouraged by her granddaughter to take up the sport after she was diagnosed with Parkinson’s disease. She credits the regimen with helping to fix her posture.
Three generations of her family were among a couple of hundred people watching Cheng Chen and 44 others aged 70 or over in a weightlifting competition on Saturday. In the three-round competition, Cheng Chen lifted as much as 45kg using a hexagonal-shaped bar that is said to allow the lifter more stability and options for gripping.
“I want to tell all the old people to join the workout,” Cheng Chen told Reuters after the competition. “You don’t need to work extremely hard, but this is to stay healthy.”
Cheng Chen was not the only nonagenarian in the competition. The oldest participant is 92.
Taiwan is projected to become a “super-aged society” next year, with 20 percent or more of its 23 million people aged 65 or older, according to National Development Council data.
The government has set up fitness centers across the island with equipment suitable for older people, to encourage them to train, according to the Health Promotion Administration, which encourages healthy lifestyles.
Santa and Mrs. Claus use military transports to bring Christmas to an Alaska Native village
- Operation Santa started in 1956 when flooding severely curtailed subsistence hunting for residents of St. Mary’s, in western Alaska
YAKUTAT, Alaska: Forget the open-air sleigh overloaded with gifts and powered by flying reindeer.
Santa and Mrs. Claus this week took supersized rides to southeast Alaska in a C-17 military cargo plane and a camouflaged Humvee, as they delivered toys to the Tlingit village of Yakutat, northwest of Juneau.
The visit was part of this year’s Operation Santa Claus, an outreach program of the Alaska National Guard to largely Indigenous communities in the nation’s largest state. Each year, the Guard picks a village that has suffered recent hardship — in Yakutat’s case, a massive snowfall that threatened to buckle buildings in 2022.
“This is one of the funnest things we get to do, and this is a proud moment for the National Guard,” Maj. Gen. Torrence Saxe, adjutant general of the Alaska National Guard, said Wednesday.
Saxe wore a Guard uniform and a Santa hat that stretched his unit’s dress regulations.
The Humvee caused a stir when it entered the school parking lot, and a buzz of “It’s Santa! It’s Santa!” pierced the cold air as dozens of elementary school children gathered outside.
In the school, Mrs. Claus read a Christmas story about the reindeer Dasher. The couple in red then sat for photos with nearly all of the 75 or so students and handed out new backpacks filled with gifts, books, snacks and school supplies donated by the Salvation Army. The school provided lunch, and a local restaurant provided the ice cream and toppings for a sundae bar.
Student Thomas Henry, 10, said while the contents of the backpack were “pretty good,” his favorite item was a plastic dinosaur.
Another, 9-year-old Mackenzie Ross, held her new plush seal toy as she walked around the school gym.
“I think it’s special that I have this opportunity to be here today because I’ve never experienced this before,” she said.
Yakutat, a Tlingit village of about 600 residents, is in the lowlands of the Gulf of Alaska, at the top of Alaska’s panhandle. Nearby is the Hubbard Glacier, a frequent stop for cruise ships.
Some of the National Guard members who visited Yakutat on Wednesday were also there in January 2022, when storms dumped about 6 feet (1.8 meters) of snow in a matter of days, damaging buildings.
Operation Santa started in 1956 when flooding severely curtailed subsistence hunting for residents of St. Mary’s, in western Alaska. Having to spend their money on food, they had little left for Christmas presents, so the military stepped in.
This year, visits were planned to two other communities hit by flooding. Santa’s visit to Circle, in northeastern Alaska, went off without a hitch. Severe weather prevented a visit to Crooked Creek, in the southwestern part of the state, but Christmas was saved when the gifts were delivered there Nov. 16.
“We tend to visit rural communities where it is very isolated,” said Jenni Ragland, service extension director with the Salvation Army Alaska Division. “A lot of kids haven’t traveled to big cities where we typically have Santa and big stores with Christmas gifts and Christmas trees, so we kind of bring the Christmas program on the road.”
After the C-17 Globemaster III landed in Yakutat, it quickly returned to Joint Base Elmendorf-Richardson in Anchorage, an hour away, because there was nowhere to park it at the village’s tiny airport. Later it returned to pick up the Christmas crew.
Santa and Mrs. Claus, along with their tuckered elves, were seen nodding off on the flight back.
Scientists observe ‘negative time’ in quantum experiments
- The researchers emphasize that these perplexing results highlight a peculiar quirk of quantum mechanics rather than a radical shift in our understanding of time
TORONTO, Canada: Scientists have long known that light can sometimes appear to exit a material before entering it — an effect dismissed as an illusion caused by how waves are distorted by matter.
Now, researchers at the University of Toronto, through innovative quantum experiments, say they have demonstrated that “negative time” isn’t just a theoretical idea — it exists in a tangible, physical sense, deserving closer scrutiny.
The findings, yet to be published in a peer-reviewed journal, have attracted both global attention and skepticism.
The researchers emphasize that these perplexing results highlight a peculiar quirk of quantum mechanics rather than a radical shift in our understanding of time.
“This is tough stuff, even for us to talk about with other physicists. We get misunderstood all the time,” said Aephraim Steinberg, a University of Toronto professor specializing in experimental quantum physics.
While the term “negative time” might sound like a concept lifted from science fiction, Steinberg defends its use, hoping it will spark deeper discussions about the mysteries of quantum physics.
Years ago, the team began exploring interactions between light and matter.
When light particles, or photons, pass through atoms, some are absorbed by the atoms and later re-emitted. This interaction changes the atoms, temporarily putting them in a higher-energy or “excited” state before they return to normal.
In research led by Daniela Angulo, the team set out to measure how long these atoms stayed in their excited state. “That time turned out to be negative,” Steinberg explained — meaning a duration less than zero.
To visualize this concept, imagine cars entering a tunnel: before the experiment, physicists recognized that while the average entry time for a thousand cars might be, for example, noon, the first cars could exit a little sooner, say 11:59 am. This result was previously dismissed as meaningless.
What Angulo and colleagues demonstrated was akin to measuring carbon monoxide levels in the tunnel after the first few cars emerged and finding that the readings had a minus sign in front of them.
The experiments, conducted in a cluttered basement laboratory bristling with wires and aluminum-wrapped devices, took over two years to optimize. The lasers used had to be carefully calibrated to avoid distorting the results.
Still, Steinberg and Angulo are quick to clarify: no one is claiming time travel is a possibility. “We don’t want to say anything traveled backward in time,” Steinberg said. “That’s a misinterpretation.”
The explanation lies in quantum mechanics, where particles like photons behave in fuzzy, probabilistic ways rather than following strict rules.
Instead of adhering to a fixed timeline for absorption and re-emission, these interactions occur across a spectrum of possible durations — some of which defy everyday intuition.
Critically, the researchers say, this doesn’t violate Einstein’s theory of special relativity, which dictates that nothing can travel faster than light. These photons carried no information, sidestepping any cosmic speed limits.
The concept of “negative time” has drawn both fascination and skepticism, particularly from prominent voices in the scientific community.
German theoretical physicist Sabine Hossenfelder, for one, criticized the work in a YouTube video viewed by over 250,000 people, noting, “The negative time in this experiment has nothing to do with the passage of time — it’s just a way to describe how photons travel through a medium and how their phases shift.”
Angulo and Steinberg pushed back, arguing that their research addresses crucial gaps in understanding why light doesn’t always travel at a constant speed.
Steinberg acknowledged the controversy surrounding their paper’s provocative headline but pointed out that no serious scientist has challenged the experimental results.
“We’ve made our choice about what we think is a fruitful way to describe the results,” he said, adding that while practical applications remain elusive, the findings open new avenues for exploring quantum phenomena.
“I’ll be honest, I don’t currently have a path from what we’ve been looking at toward applications,” he admitted. “We’re going to keep thinking about it, but I don’t want to get people’s hopes up.”
