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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.
There was a time when every other girl was named Ashley. That time has ended.
As we know, baby name trends are constantly changing. One generation’s Barbara is another generation’s Bethany. But it doesn’t make it any less odd when you suddenly realize that your very own name has suddenly made it into the “old and unhip” pile. And for many of us 80s babies…that time is now.
In a now-viral TikTok post, baby name consultant Colleen Slagen went through the top 100 girl names from 1986 to find which ones “did not age well” and were no longer ranked top 1,000 today. Such a descent from popularity would mark them as what she calls “timestamp names.” Spoiler alert: what might be even more surprising than the names now considered old school are the names that are still going strong.
The first name that Slagen says is “officially out” is Heather. That’s right, not even cult movie fame could help it keep its ranking.
Winona Ryder in Heathers.media3.giphy.com
Other extinct names include Erica, Courtney, Lindsay, Tara, Crystal, Shannon, Brandy and Dana. Tiffany, Brittany and Casey are also heading very much in that direction.
“My name is Brandy. The Gen Z hostess at Olive Garden told me that she’d never heard my name before and it was so unique,” one viewer wrote.
However, Andrea ranks “surprisingly high,” and Jessica, Ashley and Stephanie have survived…so far.
Gobsmacked, one person asked “How is Stephanie still in there? I don’t think I’ve met a Stephanie younger than myself at 34.”
But the biggest holdout still belongs to Jennifer. “She was a top 100 name all the way up until 2008. Round of applause for Jennifer,” Slagen says in the clip.
@namingbebe Sorry Lindsay, Heather, and Courtney. #babynames #nametok #nameconsultant #girlnames #80skid #1986 #nametrend
If your name has found its way into relic of a bygone era status, fret not. Slagen, whose name also ranks out of the top 1000, assures it just means “we are creatures of the 80's.”Of course, while we still have baby names that become incredibly common for extended periods of time (looking at you, little Liam and Olivia), the real contemporary trend is going for uniqueness. As an article in The Atlantic notes, for most of American history families tended to name their children after a previous family member, with the goal of blending in, rather than standing out. But now, things have changed.
Recently, Kelley Cole went viral on TikTok for a video in which she shared the names that Gen Z teens think are now officially for "old ladies," which they read right out of a classroom from 1985. “I was told my name was an old lady's name by the teenagers on the adolescent unit I was working on,” she begins her video. “I was surprised, so the subject came up of what names are old lady names versus young names.”
@kelleykelleykelley #oldladynames #names #girlnames #babynames #popularnames #trendynames #genx #millennial #genxnames
Laura Wattenberg, the founder of Namerology, told the outlet that “Parents are thinking about naming kids more like how companies think about naming products, which is a kind of competitive marketplace where you need to be able to get attention to succeed.”
But again, even with a keen eye on individualism, patterns pop up. “The same thing we see in fashion trend cycles, we see in names,” Jessie Paquette, another professional baby namer, told Vox. “We’re seeing Eleanor, Maude, Edith—cool-girl grandma names.”
So who knows…give it time (or maybe just a pop song) and one of these 80s names could make a comeback.
This article originally appeared last year.
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.
Katie's had a rough life, but hope has arrived.
When Rocky Kanaka first met Katie, a scruffy beige Australian Shepherd mix, he thought she was a senior dog. As it turned out, the shelter pup was only about a year old. She had just been found by a good samaritan as a stray, her fur and skin in terrible shape, her paws swollen and her spirit muted. She didn't even want to look at Kanaka when he first entered the kennel to sit with her.
That all changed as he took the time to sit with her and earn her trust. Kanaka has gained a huge following on YouTube with his videos sitting with shelter dogs, and his way with them is truly inspiring. He brings his own home-baked treats and a huge amount of patience and compassion, helping abandoned animals learn that humans can be kind and caring companions.
Katie hasn't had a chance to learn to be a dog.rockykanaka.com
Katie is one of many dogs Kanaka has visited, and her behavior in the kennel showed him that she hadn't had much of a chance in her short life to learn how to be a dog.
"Introducing toys to Katie was its own adventure," Kanaka wrote. "I mean, you’d think a toy is just a toy, but for Katie, it was like I’d brought a puzzle from another planet. First up was the unicorn toy, all colorful and plush. To me, it screamed fun, but to Katie, it was a head-scratcher. She eyed it like it was going to come alive any second. Honestly, watching her try to figure it out was both heartwarming and a bit funny. It was a reminder that she hadn’t had the chance to just be a dog, to play without a care in the world."
He tried a squeaky toy, which she also didn't know what to do with and found overwhelming after a few squeaks. She took Kanaka's treats, but not immediately and not in the way a dog who understands the concept of treats would.
But throughout the video, the stray pup responded to Kanaka's affection and love by melting right into it. She even wanted to sit in his lap toward the end, but didn't seem to know how. Kanaka scooped her up, despite the foul smell her skin condition created, and it's clear that this pupper just loves being loved.
Watch:
- YouTubeyoutu.be
It's hard for animals with obvious health issues, especially something as visible as a skin condition that makes them look and smell bad, to attract people looking to adopt. But by taking half an hour to get to know her, Kanaka helped us all look past all that and see Katie's sweet spirit shine through.
So many people fell in head over heels for Katie through this video:
"OMG, The person who gets her will have the best dog as she is so obviously starved for affection and so willing to give it back ten fold."
"That dog doesn't have an aggressive bone in her body. she was instantly ready for you to pet her."
Katie loved getting pets from Rocky.rockykanaka.com
"Her little tail wag broke my heart for what’s she’s been through but also lifted my spirits that she has a strength to survive and become a loved family member."
"It's shocking how neglected she looks but her desire to be loved is so strong. She's going to bring such joy to her forever home."
"I consider myself somewhat of a tough guy.... I'm from the streets, had a crazy hard life, i did 9 yrs in prison, seen it all, done it all and ain't scared of nothing... I'm telling you that because in spite all that, when i see videos like this, i start crying like a 5 yr old girl...Goes to show you that what life has done to them, we can relate, and we see it in animals that have been hurt by others and part if me wants to knock out someone that would hurt a dog or kitty like that. Animals bring out the love and compassion we've forgotten because we know they're teaching us what we definitely need to learn. What is truly considered, unconditional love...."
Not long after this video aired, Katie was rescued and will hopefully continue to get the tender care and kindness she deserves. Rocky Kanaka's work with dogs is both inspiring and informative, and he's succeeded in helping so many dogs find forever homes instead of languishing in shelters because they don't make the best first impression.
Kanaka has also started a dog rescue coffee farm in Southern California because, as he says, "Nothing's better than dogs and coffee." Isn't that the truth?
- YouTubewww.youtube.com
You can read Katie's full story on Kanaka's website here. You can also follow Rocky Kanaka's channels on YouTube, TikTok and Instagram.
This article originally appeared last year.
Mel Robbins making a TED Talk.
Towards the end of The Beatles’ illustrious but brief career, Paul McCartney wrote “Let it Be,” a song about finding peace by letting events take their natural course. It was a sentiment that seemed to mirror the feeling of resignation the band had with its imminent demise.
The bittersweet song has had an appeal that has lasted generations, and that may be because it reflects an essential psychological concept: the locus of control. “It’s about understanding where our influence ends and accepting that some things are beyond our control,” Jennifer Chappell Marsh, a marriage and family therapist, told The Huffington Post. “We can’t control others, so instead, we should focus on our own actions and responses.”
This idea of giving up control (or the illusion of it) when it does us no good was perfectly distilled into two words that everyone can understand: "Let Them." This is officially known as the “Let Them” theory. Podcast host, author, motivational speaker and former lawyer Mel Robbins explained this theory perfectly in a vial Instagram video posted in May 2023.
“I just heard about this thing called the ‘Let Them Theory,’ I freaking love this,” Robbins starts the video.
“If your friends are not inviting you out to brunch this weekend, let them. If the person that you're really attracted to is not interested in a commitment, let them. If your kids do not want to get up and go to that thing with you this week, let them.” Robbins says in the clip. “So much time and energy is wasted on forcing other people to match our expectations.”
“If they’re not showing up how you want them to show up, do not try to force them to change; let them be themselves because they are revealing who they are to you. Just let them – and then you get to choose what you do next,” she continued.
The phrase is a great one to keep in your mental health tool kit because it’s a reminder that, for the most part, we can’t control other people. And if we can, is it worth wasting the emotional energy? Especially when we can allow people to behave as they wish and then we can react to them however we choose?
@melrobbins Stop wasting energy on trying to get other people to meet YOUR expectations. Instead, try using the “Let Them Theory.” 💥 Listen now on the #melrobbinspodcast!! “The “Let Them Theory”: A Life Changing Mindset Hack That 15 Million People Can’t Stop Talking About” 🔗 in bio #melrobbins #letthemtheory #letgo #lettinggo #podcast #podcastepisode
How you respond to their behavior can significantly impact how they treat you in the future.
It’s also incredibly freeing to relieve yourself of the responsibility of changing people or feeling responsible for their actions. As the old Polish proverb goes, “Not my circus, not my monkeys.”
“Yes! It’s much like a concept propelled by the book ‘The Subtle Art of Not Giving a F**k.’ Save your energy and set your boundaries accordingly. It’s realizing that we only have “control” over ourselves and it’s so freeing,” one viewer wrote.
“Let It Be” brought Paul McCartney solace as he dealt with losing his band in a very public breakup. The same state of mind can help all of us, whether it’s dealing with parents living in the past, friends who change and you don’t feel like you know them anymore, or someone who cuts you off in traffic because they’re in a huge rush to go who knows where.
The moment someone gets on your nerves and you feel a jolt of anxiety run up your back, take a big breath and say, “Let them.”
the beatles wave GIFGiphy
This article originally appeared last year.