Javascript的數學難題
首先先考大家幾個數學題，如果這幾題的答案你都能順利的回答，那恭喜你！你可以安心地閱讀這篇文章，你一定能看懂！
題目ㄧ. 0.1 + 0.2 = ？
題目二. 1 – 0.9 = ？
題目三. 0.69 x 10 = ？
相信上面三個簡單的十進位數學運算，你的答案應該會跟我一樣吧？
第一題. 0.3
第二題. 0.1
第三題. 6.9
上面應該是無庸置疑的答案，但是如果我們把這三個題目丟給Javascript去運算之後，得到的結果會變成這樣：
第一題. 0.1 + 0.2 = 0.30000000000000004
第二題. 1 – 0.9 = 0.09999999999999998
第三題. 0.69 x 10 = 6.8999999999999995
什麼！？Javascript連這種小學生的算術都會算錯嗎？其實是有原因的，Javascript所有數字都是以64位浮點數形式儲存，也就是所有的數字都會變轉換成二進位。
上面題目中特別有提到這是3個十進位的數學運算，這也就是這個題目的重點，如果今天的題目改成：10 / 3 = 3.3333333333333334 也許你就能比較明白了，也就是說在十進位中要表達 1 / 3 和二進位中表達 1 / 10 一樣困難。
但其實在我們設計網頁的過程中，使用者是沒有二進位觀念的，只在乎運算出來的數值是否符合十進位的結果，這個時候我們可以利用一些技巧來達成正確的結果。
方法1 . 將小數變成整數後再進行運算
第一題. ((0.1 x 10) + (0.2 x 10)) / 10 = 0.3
第二題. ((1 x 10) – (0.9 x 10)) / 10 = 0.1
第三題. ((0.69 x 100) x 10 / 100) = 6.9
雖說以上的方法能夠順利完成任務，但若運算的數值是動態（Dynamic）的，乘數的部分就比較難下，所以我們可以採用第二種方法。
方法2. Math.js（https://mathjs.org/）
透過網站上提供的js，或是透過CDN（https://cdnjs.com/libraries/mathjs）來引入後，透過以下的方法，就可以正確計算出上面三個題目的結果，其中14指的是精準度，通常已經很夠用了。
第一題. math.format(0.1 + 0.2 , 14) = 0.3
第一題. math.format(1 – 0.9 , 14) = 0.1
第一題. math.format(0.69 x 10 , 14) = 6.9
其實Math.js還有很多好用的功能，可以到它官方的網站閱讀一些文章，基本上所有的數學運算應該都可以透過它來玩完成。
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Scientists redid an experiment that showed how life on Earth could have started. They found a new possibility
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In the 1931 movie “Frankenstein,” Dr. Henry Frankenstein howling his triumph was an electrifying moment in more ways than one. As massive bolts of lightning and energy crackled, Frankenstein’s monster stirred on a laboratory table, its corpse brought to life by the power of electricity.
Electrical energy may also have sparked the beginnings of life on Earth billions of years ago, though with a bit less scenery-chewing than that classic film scene.
Earth is around 4.5 billion years old, and the oldest direct fossil evidence of ancient life — stromatolites, or microscopic organisms preserved in layers known as microbial mats — is about 3.5 billion years old. However, some scientists suspect life originated even earlier, emerging from accumulated organic molecules in primitive bodies of water, a mixture sometimes referred to as primordial soup.
But where did that organic material come from in the first place? Researchers decades ago proposed that lightning caused chemical reactions in ancient Earth’s oceans and spontaneously produced the organic molecules.
Now, new research published March 14 in the journal Science Advances suggests that fizzes of barely visible “microlightning,” generated between charged droplets of water mist, could have been potent enough to cook up amino acids from inorganic material. Amino acids — organic molecules that combine to form proteins — are life’s most basic building blocks and would have been the first step toward the evolution of life.
Mindful wellness challenges
If you’re the type of person who thrives on challenges and pushing your limits, this doesn’t mean you need to shy away from wellness challenges altogether. But before diving in, take a step back and ask yourself if you’re pursuing the challenge for the right reasons, McGregor said.
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Some people want to try these challenges because they believe something is missing from their life, and they’re looking to attain “worth” or receive validation, McGregor noted.
A good way to assess your motivation is by considering whether the challenge will benefit your health or if it’s about showcasing your accomplishments on social media or some other reason.
Before trying any new trend, make sure you have the foundation to handle it and be aware of any potential risks, McGregor said.
For casual runners, this might mean signing up for a 5K but building your endurance gradually while incorporating other strength training exercises into your routine. For more intense challenges, such as a marathon, McGregor encourages people to consult with professionals or a coach who can monitor your progress and condition along the way.
Focusing on sustainable habits
Both McGregor and Curran emphasize the importance of fostering sustainable health habits before embarking on more extreme challenges.
Rather than chasing the idea of being “healthy,” McGregor suggests focusing on actual healthful behaviors and starting small.
If you’re a highly sedentary person and want to add more movement to your day, try doing lunges while brushing your teeth or taking short walks throughout your typical routine.
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Family affair
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Americans Brittany and Blake Bowen had never even been to Ecuador when in 2021 they decided to move to the South American country with their four children.
Tired of “long commutes and never enough money” in the US, the Bowens say they love their new Ecuadorian life. “We hope that maybe we’ll have grandkids here one day.”
Erik and Erin Eagleman moved to Switzerland from Wisconsin with their three children in 2023.
“It feels safe here,” they tell CNN of their new outdoorsy lifestyle in Basel, close to the borders with France and Germany. Their youngest daughter even walks to elementary school by herself.
For adventures with your own family, be it weekend breaks or something longer-term, our partners at CNN Underscored, a product review and recommendations guide owned by CNN, have this roundup of the best kids’ luggage sets and bags.
Starry, starry nights
For close to 100 years, Michelin stars have been a sign of culinary excellence, awarded only to the great and good.
Georges Blanc, the world’s longest-standing Michelin-starred restaurant, has boasted a three-star rating since 1981, but this month the Michelin guide announced that the restaurant in eastern France was losing a star.
More culinary reputations were enhanced this week, when Asia’s 50 best restaurants for 2025 were revealed. The winner was a Bangkok restaurant which is no stranger to garlands, while second and third place went to two Hong Kong eateries.
You don’t need to go to a heaving metropolis for excellent food, however. A 200-year-old cottage on a remote stretch of Ireland’s Atlantic coast has been given a Michelin star. At the time of awarding, Michelin called it “surely the most rural” of its newest winners.
Challenging our perceptions of ‘perfection’
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With health influencers raising the bar for success, the wellness space now often feels like a performative space where people strive to showcase peak physical and mental strength.
While seeing others’ achievements can be motivating, it can also be discouraging if your progress doesn’t match theirs.
Each person is chasing the perfect version of themselves — whether it’s a body or a lifestyle — which is dangerous because this is typically an impossible or dangerous version to achieve, Curran said. He added that this type of comparison creates a dangerous cycle in which people constantly feel dissatisfied with their own progress.
“It’s a fantasy in many ways, and once you start chasing after it, you constantly find yourself embroiled in a sense of doubt and deficit,” he said.
Curran also noted that wellness challenges can be particularly damaging for women who struggle with perfectionism, as they tend to be bombarded with impossible beauty standards and societal expectations.
Renee McGregor, a UK-based dietitian who specializes in eating disorders and athlete performance, encourages people to approach wellness trends with curiosity and skepticism. That’s because some influencers and celebrities could be promoting products because there’s a financial benefit for them.
“The thing to ask yourself about the person you’re taking advice from is what do they gain from it?” McGregor said. “If they are going to gain financially, then you know that they (could be willing) to sell you a lie.”
Whether you want to try a new challenge or product that promises amazing results, McGregor suggests doing your research and seeking diverse perspectives, including consulting with doctors when possible.
New design revealed for Airbus hydrogen plane
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In travel news this week: Bhutan’s spectacular new airport, the world’s first 3D-printed train station has been built in Japan, plus new designs for Airbus’ zero-emission aircraft and France’s next-generation high-speed trains.
Grand designs
European aerospace giant Airbus has revealed a new design for its upcoming fully electric, hydrogen-powered ZEROe aircraft. powered by hydrogen fuel cells.
The single-aisle plane now has four engines, rather than six, each powered by their own fuel cell stack.
The reworked design comes after the news that the ZEROe will be in our skies later than Airbus hoped.
The plan was to launch a zero-emission aircraft by 2035, but now the next-generation single-aisle aircraft is slated to enter service in the second half of the 2030s.
Over in Asia, the Himalayan country of Bhutan is building a gloriously Zen-like new airport befitting a nation with its very own happiness index.
Gelephu International is designed to serve a brand new “mindfulness city,” planned for southern Bhutan, near its border with India.
In rail travel, Japan has just built the world’s first 3D-printed train station, which took just two and a half hours to construct, according to The Japan Times. That’s even shorter than the whizzy six hours it was projected to take.
France’s high-speed TGV rail service has revealed its next generation of trains, which will be capable of reaching speeds of up to 320 kilometers an hour (nearly 200 mph).
The stylish interiors have been causing a stir online, as has the double-decker dining car.
Finally, work is underway in London on turning a mile-long series of secret World War II tunnels under a tube station into a major new tourist attraction. CNN took a look inside.
Greenland’s leader says US officials’ visit is ‘highly aggressive.’ Trump says it’s ‘friendliness, not provocation’
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Greenland’s prime minister said a planned visit to the island by US officials, including second lady Usha Vance, is “highly aggressive,” plunging relations to a new low after President Donald Trump vowed to annex the autonomous Danish territory.
But despite the backlash, Trump has insisted the visit is about “friendliness, not provocation” – and claims the US team was “invited.”
Vance, the wife of US Vice President JD Vance, will travel to Greenland this week to watch the island’s national dogsled race and “celebrate Greenlandic culture and unity,” according to a statement from the White House. National security adviser Mike Waltz is also expected to visit the territory this week, according to a source familiar with the trip.
Greenland Prime Minister Mute B. Egede called the US delegation’s trip to the island “highly aggressive” in an interview with Greenlandic newspaper Sermitsiaq on Sunday, and raised particular objection to Waltz’s visit.
“What is the national security adviser doing in Greenland? The only purpose is to demonstrate power over us,” Egede said. “His mere presence in Greenland will no doubt fuel American belief in Trump’s mission — and the pressure will increase.”
Trump claimed on Monday that people in Greenland have responded warmly to the US’s recent interest in the territory. “They’re calling us. We’re not calling them. And we were invited over there,” he said.
“We’re dealing with a lot of people from Greenland that would like to see something happen with respect to them being properly protected and properly taken care of,” Trump told reporters following a meeting with his Cabinet.
“I think Greenland is going to be something that maybe is in our future,” Trump added.
The president said he believes Secretary of State Marco Rubio would be traveling to Greenland too.
Trump’s idea to annex Greenland has thrown an international spotlight on the territory, which holds vast stores of rare earth minerals critical for high-tech industries, and has raised questions about the island’s future security as the US, Russia and China vie for influence in the Arctic. Trump has repeatedly expressed interest in the US taking the island by force or economic coercion, even as Denmark and Greenland have firmly rejected the idea.
Some scientists believe that fatty acids such as decanoic acid and dodecanoic acid formed the membranes of the first simple cell-like structures on Earth, Pearce said.
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“(This is) the closest we’ve come to detecting a major biomolecule-related signal — something potentially tied to membrane structure, which is a key feature of life,” Pearce said via email. “Organics on their own are intriguing, but not evidence of life. In contrast, biomolecules like membranes, amino acids, nucleotides, and sugars are central components of biology as we know it, and finding any of them would be groundbreaking (we haven’t yet).”
Returning samples from Mars
The European Space Agency plans to launch its ExoMars Rosalind Franklin rover to the red planet in 2028, and the robotic explorer will carry a complementary instrument to SAM. The rover LS6 will have the capability to drill up to 6.5 feet (2 meters) beneath the Martian surface — and perhaps find larger and better-preserved organic molecules.
While Curiosity’s samples can’t be studied on Earth, the Perseverance rover has actively been collecting samples from Jezero Crater, the site of an ancient lake and river delta, all with the intention of returning them to Earth in the 2030s via a complicated symphony of missions called Mars Sample Return.
Both rovers have detected a variety of organic carbon molecules in different regions on Mars, suggesting that organic carbon is common on the red planet, Williams said.
While Curiosity and Perseverance have proven they can detect organic matter, their instruments can’t definitively determine all the answers about their origins, said Dr. Ashley Murphy, postdoctoral research scientist at the Planetary Science Institute. Murphy, who along with Williams previously studied organics identified by Perseverance, was not involved in the new research.
“To appropriately probe the biosignature question, these samples require high-resolution and high-sensitivity analyses in terrestrial labs, which can be facilitated by the return of these samples to Earth,” Murphy said.
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Wellness perfectionism doesn’t exist. Focus on these sustainable habits
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ou’re scrolling through your phone when you stumble upon the next viral trend: an influencer claiming that following their incredibly strict diet will help you achieve their jaw-dropping physique. Or you see a fresh-faced runner swearing you can run a marathon without any training — just like they did.
Whether or not you’re actively searching for wellness advice, it’s nearly impossible to avoid hearing about the latest health craze making bold guarantees of transformation.
As you wonder if these claims hold any truth, you might also question why people often feel motivated to dive into intense challenges — when seemingly simple habits, such as getting enough sleep or eating more vegetables, often feel much harder to tackle.
Many of us are drawn to these extreme challenges because we’re craving radical change, hoping it will help prove something to ourselves or to others, experts say.
“We always see these kinds of challenges as opportunities for growth, particularly if we’re in a phase of our life where we’ve let ourselves go,” said Dr. Thomas Curran, associate professor of psychology at the London School of Economics and Political Science and an expert on perfectionism. “Maybe we feel that we need to be healthier, or we just had a breakup or (major) life event.”
With social media amplifying these movements, it’s easy to see why people are increasingly drawn to the idea of achieving the “perfect” version of themselves. But before jumping into a new wellness challenge, it’s important to take a moment, reflect on your goals, and consider where you’re starting from.
New design revealed for Airbus hydrogen plane
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In travel news this week: Bhutan’s spectacular new airport, the world’s first 3D-printed train station has been built in Japan, plus new designs for Airbus’ zero-emission aircraft and France’s next-generation high-speed trains.
Grand designs
European aerospace giant Airbus has revealed a new design for its upcoming fully electric, hydrogen-powered ZEROe aircraft. powered by hydrogen fuel cells.
The single-aisle plane now has four engines, rather than six, each powered by their own fuel cell stack.
The reworked design comes after the news that the ZEROe will be in our skies later than Airbus hoped.
The plan was to launch a zero-emission aircraft by 2035, but now the next-generation single-aisle aircraft is slated to enter service in the second half of the 2030s.
Over in Asia, the Himalayan country of Bhutan is building a gloriously Zen-like new airport befitting a nation with its very own happiness index.
Gelephu International is designed to serve a brand new “mindfulness city,” planned for southern Bhutan, near its border with India.
In rail travel, Japan has just built the world’s first 3D-printed train station, which took just two and a half hours to construct, according to The Japan Times. That’s even shorter than the whizzy six hours it was projected to take.
France’s high-speed TGV rail service has revealed its next generation of trains, which will be capable of reaching speeds of up to 320 kilometers an hour (nearly 200 mph).
The stylish interiors have been causing a stir online, as has the double-decker dining car.
Finally, work is underway in London on turning a mile-long series of secret World War II tunnels under a tube station into a major new tourist attraction. CNN took a look inside.
Tesla is bringing its electric cars to oil-rich Saudi Arabia amid falling global sales
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Tesla will start selling its electric vehicles in Saudi Arabia, entering the Gulf region’s largest economy as the company’s global sales are sliding and CEO Elon Musk courts controversy with his role in the US government.
The carmaker announced Wednesday that it would host a launch event in the kingdom on April 10, where it will showcase its EVs. Attendees will also have the chance to “experience the future of autonomous driving with Cybercab and meet Optimus, our humanoid robot, as we showcase what’s next in AI and robotics,” Tesla (TSLA) said.
Tesla may struggle to gain market share in oil-rich Saudi Arabia as EVs make up a little over 1% of all car sales in the country, according to a report by consultancy PwC published in September.
Tesla’s entry into the new market comes as the company fights battles on several fronts.
Last year, it recorded the first annual decline in sales in its history as a public company, posting a drop of 1%.
The company is facing intensifying competition in China, the world’s largest auto market. On Tuesday, BYD, a Chinese maker of electric and hybrid cars, reported $107 billion in annual sales for 2024, beating the near-$98 billion notched by Tesla.
And last week, BYD unveiled an ultra-fast charging system, which it said was capable of adding 250 miles (402 km) of range in just five minutes, easily outdoing Tesla’s charging technology. Tesla’s Superchargers take 15 minutes to charge an EV, providing a range of 200 miles.
Tesla has also suffered slumping sales in Europe. In February, the carmaker sold around 40% fewer vehicles on the continent compared with the same month in 2024, according to the European Automobile Manufacturers’ Association.
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While the Cumberland sample may contain longer chains of fatty acids, SAM is not designed to detect them. But SAM’s ability to spot these larger molecules suggests it could detect similar chemical signatures of past life on Mars if they’re present, Williams said.
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“Curiosity is not a life detection mission,” Freissinet said. “Curiosity is a habitability detection mission to know if all the conditions were right … for life to evolve. Having these results, it’s really at the edge of the capabilities of Curiosity, and it’s even maybe better than what we had expected from this mission.”
Before sending missions to Mars, scientists didn’t think organic molecules would be found on the red planet because of the intensity of radiation Mars has long endured, Glavin said.
Curiosity won’t return to Yellowknife Bay during its mission, but there are still pristine pieces of the Cumberland sample aboard. Next, the team wants to design a new experiment to see what it can detect. If the team can identify similar long-chain molecules, it would mark another step forward that might help researchers determine their origins, Freissinet said.
“That’s the most precious sample we have on board … waiting for us to run the perfect experiment on it,” she said. “It holds secrets, and we need to decipher the secrets.”
Briony Horgan, coinvestigator on the Perseverance rover mission and professor of planetary science at Purdue University in West Lafayette, Indiana, called the detection “a big win for the whole team.” Horgan was not involved the study.
“This detection really confirms our hopes that sediments laid down in ancient watery environments on Mars could preserve a treasure trove of organic molecules that can tell us about everything from prebiotic processes and pathways for the origin of life, to potential biosignatures from ancient organisms,” Horgan said.
Dr. Ben K.D. Pearce, assistant professor in Purdue’s department of Earth, atmospheric, and planetary sciences and leader of the Laboratory for Origins and Astrobiology Research, called the findings “arguably the most exciting organic detection to date on Mars.” Pearce did not participate in the research.
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Arctic auroras
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For getting around during winter, the Inuit here nowadays prefer snowmobiles, although they still keep their sled dogs. During winter they’ll offer intrepid visitors, wrapped up warm against the deep-freeze temperatures, dog-sledding jaunts. These can last either an hour or be part of expeditions over several days, sometimes with the added experience of learning how to build an igloo. Sisimiut on the west coast and Tasilaq in the southeast are active winter centers for dog sledding.
Winter’s most stellar attraction, though, is northern lights watching. With little urban light pollution, Greenland is a dark canvas for spectacular displays, and aurora borealis-watching vacations are becoming more popular.
Staying outdoors, Greenland is developing a reputation among adventure enthusiasts: from long-distance skiing expeditions and heliskiing on the icecap to hiking the 100-mile-long Arctic Circle Trail from Kangerslussuaq, where firearms need to be carried for warning shots in case of polar bear encounters.
Life is definitely changing here. The climate crisis is eating away at its icecap and Greenland may well end up as a pawn in a game of geopolitical chess. But for now, the bright glare of international attention should shine a favorable light on one of the wildest travel destinations on Earth.
Travel writer Mark Stratton is an Arctic specialist who has traveled to Greenland six times and counting. He’s marveled at the aurora borealis, sailed to Disko Island, dog-sledded with the Inuit, and once got stuck in an icefloe.
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Josh Giddey hits halfcourt buzzer-beater over LeBron James to cap wild finale as the Bulls stun the Lakers
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Josh Giddey hit a game-winning, halfcourt buzzer-beater over LeBron James as the Chicago Bulls stunned the Los Angeles Lakers in one of the wildest endings to an NBA game you are ever likely to see.
Trailing 115-110 with 12.6 seconds remaining, Giddey’s inbound pass found Nikola Vucevic, who pushed the ball to a wide-open Patrick Williams for a corner three-pointer.
James then fluffed the Lakers inbound pass from the baseline, allowing Giddey to steal the ball and find Coby White for a second Bulls triple in quick succession to put Chicago up 116-115 with 6.1 seconds remaining.
Austin Reaves then made a driving layup to put the Lakers ahead 117-116 with 3.3 seconds left, but the game wasn’t done yet.
With no timeouts remaining, Giddey inbounded the ball to Williams from the baseline, got the pass back, took one dribble and launched a shot from beyond halfcourt.
Supporters in the stands seemed frozen in anticipation as the ball sailed through the air, and the United Center then erupted as it fell through the net. After the dramatic win, Giddey found himself being swarmed by his teammates.
“Special moment to do it with these guys, this team,” Giddey said, per ESPN. “We’ve shown over the last month to six weeks that we can beat anybody. The way we play the game, I think it wears people down.
“We get up and down. We run. We put heat on them to get back. A lot of veteran teams don’t particularly want to get back and play in transition.”
Giddey later told the Bulls broadcast that he’d “never made a game-winner before.”
The ending capped an incredible couple of games for the Lakers, who had themselves won their last game against the Indiana Pacers on Wednesday with a buzzer-beating tip-in from James.
Water and life
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Lightning is a dramatic display of electrical power, but it is also sporadic and unpredictable. Even on a volatile Earth billions of years ago, lightning may have been too infrequent to produce amino acids in quantities sufficient for life — a fact that has cast doubt on such theories in the past, Zare said.
Water spray, however, would have been more common than lightning. A more likely scenario is that mist-generated microlightning constantly zapped amino acids into existence from pools and puddles, where the molecules could accumulate and form more complex molecules, eventually leading to the evolution of life.
“Microdischarges between obviously charged water microdroplets make all the organic molecules observed previously in the Miller-Urey experiment,” Zare said. “We propose that this is a new mechanism for the prebiotic synthesis of molecules that constitute the building blocks of life.”
However, even with the new findings about microlightning, questions remain about life’s origins, he added. While some scientists support the notion of electrically charged beginnings for life’s earliest building blocks, an alternative abiogenesis hypothesis proposes that Earth’s first amino acids were cooked up around hydrothermal vents on the seafloor, produced by a combination of seawater, hydrogen-rich fluids and extreme pressure.
Researchers identified salt minerals in the Bennu samples that were deposited as a result of brine evaporation from the asteroid’s parent body. In particular, they found a number of sodium salts, such as the needles of hydrated sodium carbonate highlighted in purple in this false-colored image – salts that could easily have been compromised if the samples had been exposed to water in Earth’s atmosphere.
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Yet another hypothesis suggests that organic molecules didn’t originate on Earth at all. Rather, they formed in space and were carried here by comets or fragments of asteroids, a process known as panspermia.
“We still don’t know the answer to this question,” Zare said. “But I think we’re closer to understanding something more about what could have happened.”
Though the details of life’s origins on Earth may never be fully explained, “this study provides another avenue for the formation of molecules crucial to the origin of life,” Williams said. “Water is a ubiquitous aspect of our world, giving rise to the moniker ‘Blue Marble’ to describe the Earth from space. Perhaps the falling of water, the most crucial element that sustains us, also played a greater role in the origin of life on Earth than we previously recognized.”