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Carl Sagan used a sliced apple to perfectly explain the fourth dimension.
The concept of the fourth dimension seems beyond human comprehension. As three-dimensional beings, we are unable to see beyond a physical object's height, width and depth. What else could there be? Even if you understand the concept, it is almost impossible to picture it in your mind, which is bound by the limits and realities of the physical world around us.
Enter Carl Sagan, revered as one of the greatest science communicators of his time. Perhaps best known for his research into extraterrestrial life, he was one of the first people to demonstrate that life could have existed on Mars. Sagan possessed a unique gift for demystifying complex scientific concepts, making them accessible and thrilling for the general public. If you never had the pleasure of watching him on television, you could imagine him as something of a Scientific Mister Rogers. Friendly, a wonderful storyteller, and always able to distill difficult lessons into their simplest form.
In 1980, on Episode 10 of the groundbreaking PBS show “Cosmos,” Sagan embarked on a mission to explain the seemingly impossible fourth dimension.
A great communicator and handsome, to boot.Giphy
Many of us have commonly heard of time being considered the fourth dimension. That's not so hard to understand — in order to locate an object in the universe, you'd need to know three dimensions of its spatial location and also the time during which it exists.
But there is also a more theoretical and harder to understand place, where all four dimensions are spatial. It is nearly impossible for any of us to comprehend... without the help of a gifted teacher.
What’s excellent about Sagan’s explanation is that he uses simple and relatable objects: an apple and a Tesseract, or a hypercube.
Sagan explains that if an apple existed in a 2-dimensional space, anyone living in this "flatland" would only see a cross-section of it at a time.Giphy
"In discussing the large scale structure of the cosmos, astronomers sometimes say that space is curved. Or that the universe is finite but unbound," Sagan begins. "Whatever are they talking about?"
Yeah, this guy gets it.
Sagan then goes on to explain how a two-dimensional being living in a flat world would perceive a three-dimensional object like an apple.
Watch his full explanation here. It's hypnotic and entertaining and incredibly enlightening.
- YouTubewww.youtube.com
“Imagine we live in this ‘Fllatland’/2-D plane with no concept of ‘up’ or ‘down.’ Then along comes a 3-D object like an apple. We do not even notice it until it crosses our plane of existence — and even then, we have no idea what the apple is,” Sagan explains. “We see only a fragment as it passes through our plane. There is no way we can comprehend the 3-D quality/dimension of the apple, because it is more than we can understand. We only have the evidence of what has passed through our plane.”
To further demonstrate, Sagan stamps the apple into an inkpad and then onto the surface in front of him, which represents Flatland and all of its inhabitants. Inside Flatland, the apple exists only as its points of contact on the paper; or four small dots. He adds that as the apple passes through the 2-dimensional Flatland, its cross-section changes. So someone living in that plane of existence would experience the apple as an ever-shifting and rearranging set of shapes or objects. Wild!
Sagan then related this two-dimensional experience of the third dimension to how we might try to understand the fourth. To do so, he used the Tesseract, a four-dimensional cube, to demonstrate how difficult it is for us to perceive or visualize dimensions beyond our own three.
A tesseract can not exist in 3-dimensional space, but it can be approximated the same way a cube can be drawn on paper.Giphy
Sagan explains that the tesseract is a cube expanded into a 4th dimension, but "I cannot show you a tesseract because I, and you, are trapped in three dimensions." But what he can do is show us a 3-dimensional rendering of one. Just like a cube can be drawn and approximated (or cast a shadow) onto a piece of paper, a 4-dimensional tesseract can be imperfectly represented in 3-dimensional space. Still following?
At this point, Sagan is asking the viewer to expand their minds to understand the fourth dimension metaphorically. Though we cannot see it or even properly visualize it, that doesn't mean that the things we can see can't offer clues and lessons about the fourth dimension.
Studying 4-dimensional space can help in our understanding of the universe around us. Just because we see and experience only three dimensions doesn't mean that's all that exists. It's critical for physicists and mathematicians to be able to understand and map these theoretical spaces to better comprehend things we otherwise can not explain. Remember the ever-changing, rearranging set of shapes as the apple passes through Flatland?
Sagan’s demonstration of the fourth dimension isn’t just a wonderful explanation of a scientific idea that many of us find difficult to comprehend; it’s also a great example of how to teach complex ideas by combining clear explanations, everyday concepts everyone can understand, and brilliant storytelling.
This article originally appeared last year. It has been updated.
A nurse explains how 'visioning' 3-4 weeks before death works.
Death is the final mystery that we all must face and it’s natural to be scared about going through the process. Experts say a few things can help, including using our fear to live a purposeful life and even making jokes, or using 'gallows humor'. One bit of good news is that we tend to get a little bit less afraid of death as we age. But in general, it helps to not shy away from death completely. Learning and talking about it is actually a good thing.
A new video by a hospice nurse shows an excellent reason for people to feel comfortable facing the unknown. Julie McFadden posts videos helping to demystify the dying process and bring comfort to people with a loved one in hospice care, or who may be dying themselves. Her profile reads, "Helping understand death to live better and die better." McFadden is also the author of the bestselling book, “Nothing to Fear.”
Hospice Nurse Julie has earned over half a million subscribers and has witnessed over a hundred deaths. In a recent video, she reveals that people are often comforted by friends and relatives who have passed away in their final days.
She says that when people begin experiencing these visions, it’s a sign that they will be passing away within a few weeks.
"Here's one sign that someone is close to death that most people don't believe happens,” Julie begins the video.
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"Usually a few weeks to a month before someone dies, if they're on hospice, they will start seeing dead loved ones, dead relatives, dead pets. This happens so often that we actually put it in our educational packets that we give to patients and their families when they come on hospice so they aren't surprised or scared when it happens,” she continues.
The experience is called visioning; although no one knows how or why it happens, it’s common among all her patients.
"We don't know why it happens, but we see it in definitely more than half of our patients," she continues.
People often believe that the visions are caused by a lack of oxygen to the brain. However, Julie says that isn’t true. “Because when it does happen, most people are alert and oriented and are at least a month from death, so they don't have low oxygen," she said.
The good news is that the visioning experience is almost always comforting for those who are nearing the end.
Dying patients may be visited 3-4 weeks before death by loved ones, deceased spouses, or even dead pets.
Photo by Anirudh on Unsplash
It often involves relatives who 'come from the other side' to let them know everything will be okay and encourage them to let go and pass away. People also experience being taken on journeys with loved ones or having sensory experiences from the past, such as smelling their grandmother's perfume or father’s cigar.
These visitors can also appear several at a time. Patients might report the room feeling 'crowded' like they are being joined by many people at once. It's possible they may be visited by 'spirits' or people they don't know, though that's less common.
Christopher Kerr, a CEO of Hospice & Palliative Care, an organization that provides palliative care in Buffalo, New York, says that the relatives that often appear in these visions are people who protected and comforted the dying parent when they were alive. So, they may see a parent who nurtured them but not one they feared.
Kerr has extensively studied the mysterious phenomena that happen when people die but has no real explanation for why the visioning experience happens. “I have witnessed cases where what I was seeing was so profound, and the meaning for the patient was so clear and precise, that I almost felt like an intruder,” he told BBC Brazil. “And trying to decipher the etiology, the cause, seemed futile. I concluded that it was simply important to have reverence, that the fact that I could not explain the origin and process did not invalidate the experience for the patient.”
In a more in-depth video, Hospice Nurse Julie shares a real video of a dying woman experience visioning. It's extremely powerful:
- YouTubewww.youtube.com
Again, experts agree that once your loved one begins experiencing these visions, it's likely that they will pass on in the next 3-4 weeks. Remember that they are not a symptom to be treated or a concern to be addressed, as long as they aren't causing distress. They are simply a comforting sign of things to come.
It's comforting to know that for many, the final days of life may not be filled with pain and fear but instead with a sense of peace and joy. While we may never fully understand the reasons behind these mysterious visions, if they bring calm during such a daunting time, we can simply be grateful for their presence. They’re kind of like life, in general. In the end, we may not really know what it was all about, but we can be happy that it happened.
This article originally appeared last year. It has been updated.
Many middle class families are sharing that they have nothing in savings right now.
According to an April 2024 Gallup poll, 54% of Americans identify as part of the middle class, with 39% identifying as "middle class" and 15% identifying as "upper-middle class." That percentage has held fairly steady for years, but what it feels like to be a middle-class American has shifted for many.
Notably, inflation caused by the pandemic has hit middle-class families hard, with incomes not keeping up with cost-of-living increases. Housing costs have skyrocketed in many areas of the country, mortgage interest rates have risen to levels not seen since the pre-Obama era, and grocery bills have increased significantly. One government study found that the cost of living has increased between around $800 and $1,300 a month, depending on the state, since 2021, putting a squeeze on everyone, including the middle class.
One woman shared that her family is just getting by and asked other middle-class people to "chime in" with what they have in their savings accounts.
@abbyy..rosee somethings gotta give #savings #middleclass #relatable
"I swear, every paycheck I am putting money into my savings, but needing to transfer it back within a few days," shared @abbyy..rosee on TikTok. "My registration is due. My husband's registration is due. He needed two new tires, even though they had a warranty. That's $300. My oldest needs braces, he needs a palate expander, that's $120 a month. Not to mention groceries are $200 more a week. Forget about feeding your family great ingredients because who has $500 a week to spend on perfect ingredients to feed your family?"
A depressed couple doing their bills.via Canva/Photos
She explained that her husband makes enough money that they should be able to live comfortably, and that she quit her job because the cost of daycare was more than she was making.
"At some point, something has to give," she said. "What is going on? How do I save money?"
People in the comments chimed in with their savings account totals and it was quite eye-opening. Many people shared that they have $0 saved.
"We make the most money we ever have and have zero savings. We live paycheck to paycheck and every month I don’t know how we get by."
"I think the middle class is 1 personal disaster away from bankruptcy."
"Y’all got savings accounts?!?! 😂"
"I used to freak out if I had under $10k in savings, now I’m happy when I have over $150. 😫"
"We make almost 100,000 a year with no savings!!!! It's always something!!"
"I'm lucky if we have $500-$1K for an emergency. Every single time we start saving, something happens: the vet, the cars, the kids... something."
"Savings account? I transfer money each paycheck but always end up needing to transfer it back. My husband makes great money too but we are scraping by."
"$803 but we have to pay a $750 deductible this week b/c my Husband hit a deer soooo… back at it 😭 It’s exhausting. Constantly draining it, refilling it, transferring."
An upset couple doing their bills.via Canva/Photos
Some people shared that they do have some savings, but several said it was because they'd had an inheritance or other chunk of money come their way. Many people shared that their savings has dwindled as increased costs have taken their toll. Some people gave lifestyle advice to save money, but most agreed that just the basics have gotten so expensive it's harder to make ends meet much less put extra into savings.
Thankfully, the inflation issue appears to be waning, but even just plateauing at their current financial reality isn't ideal for many American families. Middle class is supposed to be a comfortable place to be—not rich, but well enough off to feel secure. That's not how many middle class folks feel, though. Most Americans don't have anything close to the amount of money saved that is recommended across the age spectrum, but at least hearing that others are in the same boat is somewhat comforting.
An upset couple doing their bills.via Canva/Photos
Further, a 2024 study found that 37% of Americans can't afford an unexpected expense over $400, and nearly a quarter of them don't have any emergency savings at all. “Not all surprises are good, and people know it. The study suggests financial precarity at a time when household finances may be stretched due to rising prices and inflation,” says Rebecca Rickert, head of communications at Empower. “Life happens, and people are stressed about the surprise expenses that could tip them off-balance.”
It can be vulnerable to share your financial reality, but it's helpful to hear what other people are doing and dealing with so we all feel less alone when we're struggling. Perhaps if people were more open about money, we'd all be able to help one another find ways to improve our financial situations rather than lamenting our empty savings accounts and wondering how to change them.
This article originally appeared last year.
Confidence can be a powerful tool if you know how to show it.
If there's one "trick" to achieving success regardless of skill, ability, or talent, it's confidence. And the good news is it doesn't necessarily have to be actual confidence—merely the appearance of confidence is often enough to influence people and change outcomes.
Confidence is how con men are able to rope people in, but confidence can also be used for good. If you learn how to exude confidence, it can be one of the most powerful tools for creating the life you want and effecting positive change in the world.
So what does that look like, especially when you're not really feeling it? We all wish we could walk boldly through the world without any worry or self-doubt, but most of us don't feel 100% confident 100% of the time. That doesn't mean we can't appear confident, though. Former FBI agent and body language expert Joe Navarro shares six elements we need to understand in order to project confidence with WIRED.
- YouTubewww.youtube.com
There are certain traits confident people have that help them appear comfortable when they walk into a room and command whatever space they are in.
"When we talk about confidence, it's so many things," says Navarro. "It has to do with our posture, the way we present, how we look. Where's our chin? Where are the eyes looking and gazing? Our gestures are loose, but they're smoother. As we walk about, we walk as though we are on a mission."
Even how we move our eyeballs makes a difference. "The less confident we are, the less eye contact we make," Navarro says. "The less confident we are, the more reluctant we are to look about."
People who are confident make more eye contact and look around more.Photo credit: Canva
Confident people don't show their confidence in the way many people assume. "I think sometimes people mistake machismo or theatrical displays of power as confidence," Navarro adds. "Confidence can be very quiet."
Jane Goodall, for example, is not a loud-speaking person bursting with bravado. She's rather meek and mild, and yet she commands every room. "One of the things you notice is they sort of have this command of themselves, and in doing so, that command transmits outward," Navarro explains.
You can also use time to convey confidence. Don't rush, go at your own pace. "If you're in charge, you're in charge of time," says Navarro. "I'm gonna take my time to walk out. I'm gonna take my time to answer your question. I will answer it in the pace, manner, and tone that I choose. And in doing that, we are demonstrating that we are confident and in control."
One of the most effective ways of exuding confidence is to choose someone who is confident in a way that you admire and model yourself after them. What traits do they have that you could emulate? How do they move? How do they speak?
How do people who are confident behave?Photo credit: Canva
This doesn't mean changing who you are on a fundamental level, but rather observing the people who have an ability you're struggling with and behaving your way toward gaining that ability.
"You know, we're not born this way," says Navarro. "These are things that we have to develop, and say, 'How do I want to be perceived? And what can I do to achieve that?'"
Navarro shares that little things can make a difference. For instance, indicating a direction by pointing with your finger is an undesirable behavior almost universally, but pointing with an open hand is not.
He gave an example of something he had to learn when he first joined the police force and had to make an arrest. The first time he had to say, "Stop, you're under arrest!" he said it in a high-pitched voice and said it sounded terrible.
"You have to work at having that command presence, where you say [in a deeper voice], 'Stop right there, don't move.' That's almost theatrical, but it's what is needed."
Under Arrest GIF by ABC NetworkGiphy
He gave another example of saying "No, stop," with confidence, using a lower voice and an outstretched hand. The more confident you are in saying it, the more your fingers will spread apart. Those little behaviors convey confidence more than people realize.
We all have certain vocal habits that include how we use tone in our speaking. Navarro describes a phenomenon known as "uptalk," which is when you raise your intonation at the end of phrases or sentences, almost as if you're asking a question even when you're not.
He shared that speaking with confidence involves bringing your voice down in a more declarative way when you speak rather than sounding as if you're questioning.
Slowing down and using powerful pauses can make you appear confident.Photo credit: Canva
Many of us, especially when we're not feeling comfortable or confident, talk too fast. But when you talk too fast, people stop listening. Pacing your speech and using the power of pauses can be a powerful way to convey confidence.
"If you want people to listen to you, use cadence to get their attention, hold their attention, but then look forward to what that next set of words will be," says Navarro. "It lets them know, at a subconscious level, this is the person in charge. And we know that they're in charge because they have temporal control over this. They're not in a hurry."
People often think that confidence looks like holding your shoulders back, puffing up your chest, and keeping your chin up. It can look like that, says Navarro, but it doesn't have to.
Confidence can be conveyed in lots of non-verbal ways.Photo credit: Canva
"You know, a lot of times confidence is just sitting comfortably in a chair. And that may have more to do with how much space you control. It may have to do with the gestures that you use."
When people look confident, their gestures are smooth. There's no hesitation, quick movements, or jitteriness. They appear calm and in charge. When people are less confident, they feel like they have to hurry and answer right away.
"Let's face it: people are not born confident," says Navarro. "They're just not. We can become confident with the assistance of our parents who encourage us. We can become confident through our own achievements. We can become confident by going beyond our boundaries. But confidence is something that we can grow, we can nurture."
Of course, we all want to feel truly confident and not just act like we are, but sometimes the behavior helps to create the feeling.
"If you want to be confident, know your material, know the information, hone that skill, work at it, have that mastery of things, and of self," says Navarro. "And that's how you will come across as confident, no matter what your station in life is."
A French woman, a cheerleader, and a garbage disposal.
As the leader of the free world, many people outside of the U.S. have strong opinions about America and its residents. Not all of them are accurate, of course, which can lead to some misunderstandings with non-Americans. However, it also opens the door for plenty of humor.
Americans are admired by many across the world for our creativity, entrepreneurial spirit, and can-do attitude. But they also draw some side-eye for their love of huge portions, guns, and patriotism. Non-Americans are also skeptical about why they have garbage disposals and love putting ranch dressing on just about everything.
A Reddit user asked Americans for “the funniest thing a foreigner has said to you about America.” The answers were a great mix of cultural misunderstandings, myth-busting, and much-needed geography lessons. Here are 15 of the funniest things non-Americans have told Americans about the U.S.
A man laughing.via Canva/Photos
"While being transported from the airport to the hotel in Morocco, the cab driver said, 'American?' I responded, 'Yes.' His response: 'Ahhh yes. Bill Clinton.'"
"Buddy was in Eastern Europe in the 90s, and a little old lady who spoke no English found out he was American and just said 'Monica Lewinsky' and then laughed."
"An International Student (from Malta) and I were hanging out at the 'Smoker's Lounge,' aka the place in front of the dorms where people smoked. A raccoon popped out of one of the trash cans, and he freaked out and said that the animals in North America were the size of monsters."
"A Japanese person once told me that the US is 'enviably wide.'"
"Because Japan is similarly tall, but lamentably skinny."
A map of the United States.via Canva/Photos
"A guy from the UK I know loves to refer to Americans as melon farmers. Melon farming imbeciles. Doesn't know what some object I refer to is? Must be some kind of weird melon farming contraption. Where have I been the last few days? Must have been tending to my melon farm. I wish I had a backyard instead of a dumb asphalt apartment parking lot? Ah, I must be missing life back on my melon farm."
"This man I knew in college was from rural Kenya. Apparently, your temporary house was constructed of wood. Folks that had gained enough wealth no longer had a wooden house."
"We had a guy from Kenya bring pumpkin spice muffins to a potluck. He said something like 'I see how you keep pumpkins on your porches, so I figured you must really love them.'"
"A French guy asked me if we really put ranch on everything. I said, 'Yes, even salad,' and he stared at me like I’d just admitted to living in a dumpster."
"A Persian man that I worked with did a redneck impression. He said 'I'm an American and I like guns and Jesus' in a perfect southern accent."
"When I lived in Italy, one of the first questions my neighbors asked was 'How many guns do you have and where do you keep them all?' They were absolutely floored that I didn’t own any guns."
"A waiter in Prague asked where I was from. I told him Boston. He said, 'Oh, I have a friend named Tomas Dvorak in Wyoming. Do you know him?'"
"When I studied abroad in Germany, my host family told me 'We bought lots of peanut butter for you. We know Americans need peanut butter.' I do love peanut butter, but I had definitely never heard that stereotype before!"
"I did once startle a lovely Australian couple with my PBJ. Apparently, PB and J are only considered compatible here in North America. They looked at the sandwich I made with the same kind of horror I might’ve used on something with, IDK, tuna and marshmallow fluff."
"'Are cheerleaders real?' Cheerleaders were in movies, but a teenager in London had no idea if that was a real thing. It was a charming conversation as a teenager."
"I like how foreigners will believe that everyone in America is dodging gunfights and car chases on their morning commute, but then think we made up cheerleaders and yellow busses for the movies."
Cheerleaders with their pom-poms up.via Canva/Photos
"A British friend of mine called southern sweet tea 'the most vile, disturbing, horrific swill ever created. Please bring another pitcher.'"
"If they don't have to amputate a foot after your first glass it needs more sugar."
"Saying I had an angry sink because it had a garbage disposal in it."
"My fiancé from the Netherlands asked what the 'zing' road sign meant that he kept seeing everywhere. I couldn’t figure out what the heck he was talking about at first. It was the X-ing (crossing) sign."
"My international colleague thought it was a word in Chinese (Xing) and was very confused by this lol."
People crossing the street.via Canva/Photos
"My wife's Swedish cousins thought they could go explore both New York City and Los Angeles in a single weekend."
"Also had Swedish visitors, and we live in New England. They wanted to take a drive to California during the 5 days they were going to be here, and they wanted to stop and see the Grand Canyon along the way, then be back in time to catch their flight home out of Boston."
"Was at a pub in Italy with a friend, and some of the guys found out we were American. Proceeded to take shots with them toasting ‘to the Ohios!’… we’re not from Ohio lol."
"Which Ohio are you not from, North Ohio, or South Ohio?"