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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.

- 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.

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.

Health

Why time seems to accelerate as we get older and what we can do to slow it down

How time works is totally trippy, but there are some "tricks" to change how our brains process it.

Jordan Benton/Canva

Time is weird.

You're going along, minding your own business on the internet, when suddenly this little gem comes across your timeline:

screenshot that reads "1980 and 2023 are as far apart as 1937 and 1980 were. Sleep tight, odl fogies"1980 to 2023 = 1937 to 1980. How can that math be right? Kevin Smith/GenX Only Facebook Group

Your first reaction is, "Nuh-uh, no way," so you pull out the calculator to do the math yourself—several times because you're sure you must've missed a number somewhere. You remember how long ago 1937 seemed in 1980, and there's no possible way that much time has passed between 1980 and now. Then, as the warped reality of time washes over you, you sit and stare in stunned silence, contemplating the existential crisis.

Why does time work this way? Why does it seem to get faster and faster and condense to make decades seem shorter and shorter as we age? And perhaps more importantly, how the heck do we stop time from feeling like a runaway freight train?

Here are a few theories about what creates the freight train phenomenon.

Time perception is relative—and kids perceive it differently

"Time flies when you're having fun" is a saying for a reason. Time also drags when you're doing drudgery work and feels like it stands still in moments of significance. And yet the ticking of seconds as they go by doesn't change tempo. We measure it with steady, unchanging beats, but how it feels changes constantly.

This relativity exists in every passing moment, but it also exists in the bigger picture as well. The years felt like they passed by much more slowly when we were children, and by middle age, they feel like they pass in the blink of an eye. The pandemic gave us an even greater sense of this relativity as disruptions to our normal routines and the stress associated with the COVID-19 years messed with our sense of time. (On an odd side note, surveys show that our time perception during the pandemic varied a lot from place to place—people in some parts of the world felt that time moved more slowly, while others felt time moved more quickly.)

According to a 2023 Hungarian study published in Nature Scientific Reports, very young children perceive time differently than older children and adults. Researchers split 138 people into three age groups—pre-kindergarten, school-age and adults 18 and over—and showed them two videos of the same duration, one that was "eventful" and one that was "uneventful." Interestingly, the pre-K group perceived the eventful video to be longer, while the older children and adults saw the uneventful video as longer.

The way the study participants described the length of the videos in gestures was also telling. Young children were much more likely to use vertical hand gestures, connoting volume or magnitude, to indicate a length of time than the other two age groups. School-aged kids and adults tended to use horizontal gestures, indicating time as linear, increasing with age.

Our neural processing slows down as we age

Professor Adrian Bejan has a theory based on how neurons process signals. As we age, our neural networks increase in size and complexity, and as a result, process visual information at a slower rate. That slower processing means we create fewer mental images each second than we did when we were younger, thereby making time seem to slow down.

“People are often amazed at how much they remember from days that seemed to last forever in their youth, Bejan shared with Harvard University. "It’s not that their experiences were much deeper or more meaningful; it’s just that they were being processed in rapid fire.”

In other words, processing the same number of mental images we did in our youth takes longer now, somewhat counterintuitively making time seem to pass more quickly. So goes the theory, anyway.

It might simply be about time-to-life ratios

Another popular theory about why time feels different as a child than it does as an adult is the ratio of any given day, week or year to the amount of time we've been alive. To a 5-year-old, a year is 20% of their entire life. For a 50-year-old, a year only is 0.2% of their life, so it feels like it went by much more quickly.

It's also a matter of how much change has happened in that year. A year in the life of a 5-year-old is full of rapid growth and change and learning and development. A year in the life of a 50-year-old probably isn't a whole lot different than when they were 48 or 49. Even if there are major life changes, the middle-aged brain isn't evolving at nearly the same rate as a child. A 50-year-old looking back at the past year will have a lot fewer changes to process than a 5-year-old, therefore the year will seems like it went by a lot faster.

“Our perception of days, weeks, years and that kind of time seems to be especially influenced by our perspective: Are we in the moment experiencing it, or are we looking backward on time?” psychology professor Cindy Lustig told the University of Michigan.

The key to slowing it all down? Be mindful of the present moment.

Lustig has a point. When we are in the moment, our perception of time is much different than when we look back. So, being fully conscious in the present moment can help us rein in the freight train effect.

One way to do that is to be mindful of your physical existence in this moment. Feel your heart beating. Feel your breath going in and out. Cornell University psychology professor Adam Anderson, Ph.D., conducted a study that found our perception of time may be linked with the length of our heartbeats. (Study participants were fitted with electrocardiograms and asked to listen to a brief audio tone. They perceived the tone as longer after a longer heartbeat and shorter after a shorter one.) He suggests starting a stopwatch, closing your eyes and focusing on your breathing for what you think feels like a minute. Then, check your time to see how accurate your estimation was.

“This can give you a sense of how much your experience of your body is related to your experience of time,” Anderson told WebMD. “It will help teach you to enjoy the pure experience of time.”

You can also use focused breathing to purposely slow down your heart rate, and thus slow down your time perception. “We show that slow heart rates—that is, a longer duration between heartbeats—dilates time, slowing it down," Anderson said.

Finally, try to take in the world the way you did as a small child. Take note of life's wonders. Engage fully in whatever you're doing. Notice details and take mental pictures as much as you can. Time goes by fast when we're distracted, so training our attention on the here and now can help. Ultimately, we can strive to perceive time more like we did when we were little, in its full depth and magnitude instead of a narrow, straight line.


This article originally appeared last year.

Science

MIT’s trillion-frames-per-second camera can capture light as it travels

"There's nothing in the universe that looks fast to this camera."

Photographing the path of light.

A new camera developed at MIT can photograph a trillion frames per second (fps).

Compare that with a traditional movie camera which takes a mere 24fps. This new advancement in photographic technology has given scientists the ability to photograph the movement of the fastest thing in the Universe: light.


The actual event occurred in a nano second—that is one billionth of a second—but the camera has the ability to slow it down to twenty seconds.

time, science, frames per second, bounced light

The amazing camera.

Photo from YouTube|Nova50

For some perspective, according to New York Times writer John Markoff, "If a bullet were tracked in the same fashion moving through the same fluid, the resulting movie would last three years."


In the video below, you'll see experimental footage of light photons traveling 600-million-miles-per-hour through water.

It's impossible to directly record light, so the camera takes millions of scans to recreate each image. The process has been called "femto-photography" and according to Andreas Velten, a researcher involved with the project, "There's nothing in the universe that looks fast to this camera."


This article originally appeared seven years ago.

Joy

There are over 30 years between these amazing before-and-after photos.

"It's important for me for my photography to make people smile."

All photos by Chris Porsz/REX/Shutterstock.

Before and after photos separated by 30 years.


Chris Porsz was tired of studying sociology.

As a university student in the 1970s, he found the talk of economics and statistics completely mind-numbing. So instead, he says, he roamed the streets of his hometown of Peterborough, England, with a camera in hand, snapping pictures of the people he met and listening to their stories. To him, it was a far better way to understand the world.

He always looked for the most eccentric people he could find, anyone who stood out from the crowd. Sometimes he'd snap a single picture of that person and walk away. Other times he'd have lengthy conversations with these strangers.


But eventually, life moved on and so did he. He fell out of love with photography. "Those pictures collected dust for 25 years," he says.

Then, a few years ago, Porsz found those 30- to 40-year-old photos and sent them to be printed in his local newspaper.

Peterborough, reunions, Chris Porsz

Chris Porsz and his camera.

All photos by Chris Porsz/REX/Shutterstock.

And remarkably, people started recognizing much younger versions of themselves in his shots. "There was this lightbulb moment," he says of the first time someone wrote to him about one of his photos.

Eventually, he became curious about the people he'd photographed all those years ago, and he decided he'd try to find some of them. It wouldn't be easy — the photos were taken a long time ago, and Porsz didn't have names or contact information for many of the people in them.

But he did find some of them, sometimes in extraordinary ways. "Some were absolute million-to-one coincidences," he says.

Like the time he went out on a call (he's a parademic these days) at 3 a.m., and the man he was there to treat recognized him as the photographer who'd snapped his picture all those years ago. On another call, he asked a local shopkeeper if he recognized any of the subjects in the photos. He did.

Once Porsz began posting about the project online — he calls it "Reunions" — it became easier and easier to reconnect with his former subjects.

Many were eager to recreate the old shots as best they could, like Layla Gordon, who Porsz originally photographed drinking milk in 1983.

time, memories, photos

The child version drinking milk.

All photos by Chris Porsz/REX/Shutterstock.

milk, history, project

The adult enjoys milk too.

All photos by Chris Porsz/REX/Shutterstock.

Others groups, like these schoolgirls, had fallen out of touch. "Reunions," fittingly enough, brought them back together.

schoolgirls, pose, soul mate

Schoolgirls pose for a photo.

All photos by Chris Porsz/REX/Shutterstock.

best friends, intimate, confidant

The adult versions find time for a group photo.

All photos by Chris Porsz/REX/Shutterstock.

Porsz says that his subjects, like this wild-haired couple, were strangers to him 30 years ago. Now he considers many of them friends.

punk rock, narrative, archive

Pink colored hair and mohawks.

All photos by Chris Porsz/REX/Shutterstock.

record, story, account

The color has moved to the sleeves.

All photos by Chris Porsz/REX/Shutterstock.

In all, Porsz has collected over 130 before-and-afters in his new book.

The response to Porsz's work has been more than he ever imagined.

He's personally heard from people all over the world who've been inspired by his project and want to try to recreate it themselves. But beyond that, he just hopes it brings a little warmth and happiness to the people who see it.

"It's important for me for my photography to make people smile," he says. "Because there is so much sadness in the world."

And while the project is finished for now, don't count out the possibility of "Reunions Part 2" somewhere down the line.

"I'd love to meet these guys in 2046 when I'm 94 years old," Porsz says.


This article originally appeared on 11.30.16