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via Carl Sagan Planetary Society/Wikimedia Commons and John Finkelstein/Pexels

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.


carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einsteinA 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.

carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einsteinSagan 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.

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“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.

carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einsteinA 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.

Funny on purpose or by default?

Imagine this: You're at Target when a guy in his early 30s awkwardly approaches and asks if he can "try to make you laugh with a physical comedy-type thing." He then proceeds to attempt to sneeze confetti, fumble his keys and, of course, fall down for no reason. He's open to notes. In fact, he always asks for them, and in this particular case, his extremely polite one-person audience suggests "lifting a box that's clearly too heavy?"


That's Dax Flame, and he has been creating content since he was a kid back in Dallas. The thing is, he's actually quite famous, having become one of the first YouTube stars to receive a million clicks. To say he was ahead of his time would be an understatement, as he slowly built a following by dressing up as an "angry Superman" and venting on camera, among other strange and hilarious videos. He'll stop at nothing to make people feel simultaneously happy and uncomfortable. It's so layered and mysterious that even a good portion of his longtime fans can't figure out if he's Andy Kaufman-level genius or just plain awkward.

@ttfeo

Dax Flame’s villian origin story. #daxflame #daxflameprojectx #daxflameedit #redrex #editaudio #villian #orginstory #evil #whereitallbegan #vsp #capcut #ttfeo #edits

If you Google Dax Flame, the suggested queries include: Is Dax Flame for real? Does Dax Flame have anxiety? Was Dax Flame in the movie 21 Jump Street? The answer to the latter is yes. But the other two questions remain unclear.

The truth is—it might just not matter. With 2.3 million followers on TikTok and over a million on Instagram, Dax's star continues to rise. He appeared in the films Project X, 21 Jump Street, and 22 Jump Street and often asks random people if they've seen those films. And yet, fans still wonder—is he in on the joke? Did he create the joke? Is there even a joke at all?

An entire documentary called Ice Cream Man was posted on YouTube, which explores Dax's enigmatic personality and his dreams of hosting an online game show about making smoothies. If he breaks character, it's tough to tell. One of the commenters shares, "Dax radiates charisma. It doesn't matter how you look at him; he is so genuine that you will feel drawn to him and appreciate his approach to things in life. His speech is very gentle, and he didn't put pressure on either of the contestants during the show. It was awesome."

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Five years ago, the BBC did a story on him and wrote, "Dax Flame was huge on YouTube. But that was more than a decade ago. What happens as he tries to revive his career—and why does a mystery about his channel persist to this day?"

Now, a handful of years later, Dax IS reviving his career. Sort of. In the last year or so, he has started trying his hand at stand-up comedy by doing open-mics. Hard to tell if it's cringe on purpose or just a level of anti-comedy brilliance done with such an adorably deadpan delivery you'll feel gaslit. That said, he might just make you laugh harder than any working headliner today.



He also enjoys ordering pizzas and giving gifts to delivery drivers when they arrive.


That's why this week, when Will Smith appeared in one of his videos, his fans went wild. On what appears to be a basketball court, Dax asks Will, "If you check out my new song, I'll check out your new song." Will agrees, "That's a deal." And in keeping with Dax's brand of (in his words) "making people feel awesome," Dax then asks, "Do you feel good?" Will emphatically replies, "I feel great!"

One Instagram follower wrote, "It must have been such a honor for Will Smith to meet Dax Flame."

After watching these videos, we still might not have a clear answer as to "Is Dax Flame for real?" But many of us will feel awesome, either way.

Elmo got real on his Chicken Shop Date.

For some, little is more daunting than the question: "What's your 5-year plan?" No matter the generation, it can be anxiety-inducing at best. Sesame Street's Elmo was asked this very question by English comedian Amelia Dimoldenberg on her popular web series Chicken Shop Date.

On the show, Amelia has various "dates" where she peppers celebrities with awkward and often endearing interview questions. Obviously, Elmo was the perfect guest, though it's specifically noted on YouTube that Elmo is having a "play date" since he's only three and a half years old, of course. But when she bluntly asks him, "What's your five-year plan?" Elmo is confused. "What's that mean, five-year plan? Elmo is me." She restates, "Yeah, you need to have a plan. You need to have a five-year plan."

gif of Amelia DimoldenbergDisappointed Amelia Dimoldenberg GIF by Chicken Shop DateGiphy

On the show, Amelia has various "dates" where she peppers celebrities with awkward and often endearing interview questions. Obviously, Elmo was the perfect guest, though it's specifically noted on YouTube that Elmo is having a "play date" since he's only three and a half years old, of course. But when she bluntly asks him, "What's your five-year plan?" Elmo is confused. "What's that mean, five-year plan? Elmo is me." She restates, "Yeah, you need to have a plan. You need to have a five-year plan."

And then Elmo becomes all of us. "Elmo doesn't really know what he's gonna do in the next five hours!"

@emil1yc

😭 #chickenshopdate

When this clip was posted on TikTok, the followers definitely saw themselves in Elmo. "Me, in a job interview," says the top commenter, with over 25,000 likes. Another writes, "I just panicked, like am I supposed to have a 5-year plan? Marriage? Do some people have a five-year plan?!?"

This person asks, "Also, isn't Elmo like 5 or 6 or something? She's basically asking him what he's gonna be doing after another lifetime." (Repliers rightfully point out that Elmo is three and a half years old in perpetuity.)

Since that clip went viral three months ago, people have been having a field day on TikTok answering the question for themselves. Many simply lip-sync with Elmo, expressing how much they relate. But TikTok user @GenX_Michelle took it a little further. In their video, we see a woman at the grocery store with a giant raven perched on her arm. The chyron reads: "When someone asks me where I see myself in 5 years."

The comments are not only supportive of the OP, but they're impressed by the grocery-shopping woman, as well. "This woman is a goddess, because you don't choose a raven, a raven chooses you."

@genx_michelle

Raven Lady of Vegas has a nice ring to it... 😉 #raven #5yearplan #ravenladyofvegas #genx_michelle #besties_chosenfamily


Many therapists and career counselors nowadays actually believe you don't need a 5-year plan, and that the very idea of them is obsolete. In Lily Zhung's article "Why You Really Don't Have to Have a 5-Year Plan" for The Muse, she cites John D. Krumboltz’s Happenstance Learning Theory, where she reports, "He posits that unplanned events are to be expected because they’re inevitable and, in fact, necessary to every career."

person in an office saying, "New plan."Plan Change Of Plans GIFGiphy

She then asks, "How many successful people actually followed a plan to get to where they were? Maybe a handful. Most were (and continue to be) superbly hardworking and just really good at recognizing and acting on opportunities that come their way."

Success, she says, comes from grabbing opportunities when they arise and being as prepared as possible for the moment. "Ultimately, the goal of career planning is not to have a step-by-step plan, but to maximize the opportunities for you to learn and to be in the right mindset to take advantage of opportunities as they come."

Zhung quotes Shonda Rhimes from a commencement speech she gave at Dartmouth in 2014: "Maybe you know exactly what it is you dream of being, or maybe you're paralyzed because you have no idea what your passion is. The truth is, it doesn't matter. You don't have to know. You just have to keep moving forward. You just have to keep doing something, seizing the next opportunity, staying open to trying something new. It doesn't have to fit your vision of the perfect job or the perfect life. Perfect is boring and dreams are not real. Just do."

Pets

Terrified, emaciated dog comes to life as volunteer sits with him for human connection

"Just a few kind words and a little attention. That’s all animals need."

Terrified dog transforms after human sits with him.

There's something about dogs that makes people just want to cuddle them. They have some of the sweetest faces with big curious eyes that make them almost look cartoonish at times. But not all dogs get humans that want to snuggle up with them on cold nights; some dogs are neglected or abandoned. That's where animal shelters come in, and they work diligently to take care of any medical needs and find these animals loving homes.

Volunteers are essential to animal shelters running effectively to fill in the gaps employees may not have time for. Rocky Kanaka has been volunteering to sit with dogs to provide comfort. Recently he uploaded a video of an extremely emaciated Vizsla mix that was doing his best to make himself as small as possible in the corner of the kennel.

Kanaka immediately wanted to help him adjust so he would feel comfortable enough to eat and eventually get adopted. The dog appeared scared of his new location and had actually rubbed his nose raw from anxiety, but everything changed when Kanaka came along.

Vizsla, dog rescue, animal shelter, animal rescue brown short coated dog in tilt shift lens Photo by John Spence on Unsplash

The volunteer slowly entered the kennel with the terrified dog, crouching on his knees for an easy escape if needed. But the dog attempted to essentially become invisible by avoiding eye contact and staying curled in a tiny ball. It seemed like it was going to take a long time for this nervous pup to warm up.

Before long, he's offered a treat. Success! The brown dog takes the treat, and as minutes pass you can see his body slowly relax, eventually coming to sit directly next to Kanaka for pets. In the few minutes of the video, you see such an amazing transformation that proves this little guy just needed some love.


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"It was so cute when he started wagging his tail. You could tell his whole demeanor just changed, and he was happy. Just a few kind words and a little attention. That’s all animals need. Well, besides food. Lol," one commenter says.

"That moment when he starts to realize he's actually safe. That gradual tail wag, and the ears perking, the eyes lighting up. You don't have to be an expert to show an animal love and respect," another writes.

dog rescue, dogs, animal rescue, animal sheltera dog wrapped in a blanket on a rocky beach Photo by Jessica Bulling on Unsplash

"After that first treat his entire demeanor changed. He went from not trusting you to thinking you may be kind and he could feel less stressed. That was really amazing to see," someone gushes.

This sweet scared dog just needed human connection by someone taking the time to sit with him to know he was safe. Once he was sure the shelter was a safe place, the dog even welcomed those who came to visit him after seeing the video.

"I went to the shelter today to visit 'Bear'! Everyone would be thrilled to hear that he seems very happy and energetic! He has a little red squeaky bone toy that he loves. He licked my hand immediately and rubbed his head on my legs and arms, eager for affection. What a sweetheart," a commenter writes.

Thanks to Kanaka's sweet gesture, the dog, now named Shadow Moon, was adopted and is now living his best life with his new human dad and husky brother. You can follow Shadow Moon's journey on his Instagram page.

This article originally appeared three years ago.