upworthy
Heroes

It’s the Hubble Telescope's most famous image. Here’s how it almost didn’t happen.

Every part of the sky deserves a closer look.

In 1995, astronomer Robert Williams had the opportunity of a lifetime: a chance to use the freshly repaired and ready for action Hubble Space Telescope.

Every astronomer in the world was desperate to get time on the Hubble to photograph galaxies, nebulae, and deep space objects with humanity's most powerful telescope. Williams wasn't interested in that. He knew there was something remarkable out in space that regular earthbound telescopes couldn't see. Normally, his colleagues would be excited for such an opportunity. This time, they told him he was crazy to even consider it.

The Hubble Space Telescope: humanity's eye above the sky. Image via NASA.

When the Hubble Space Telescope was placed into orbit 340 miles above the Earth in 1990, it was one of the most ambitious — and expensive — scientific projects in history.

NASA promised an eager public that the Hubble would take better images than any telescope on Earth. But for the first few years of its life it couldn't focus properly, leaving it unable to deliver the awe-inspiring images of space it was meant to provide.

The Hubble's repairs made a huge difference: at left, a galaxy photographed by Hubble before its repairs; at right, the same galaxy after. Image via Space Telescope Science Institute/NASA.

Most people in NASA felt that the first images to come from the Hubble after its billion-dollar repairs needed to help them regain the public's trust. They had to be a sure thing, and Williams’ project was anything but.

“It was very risky. I had a team of young, bright astronomers who were fresh out of school. Plus, there was a real chance we might not see anything,” Williams said. “I felt it had to be tried anyway. I told administrators that I would take full responsibility if it was a flop. It took me promising to turn in my resignation to convince them.”

Williams picked a tiny square of space near the Big Dipper constellation. It was one with very few visible stars — to be fair, very few visible anything. It was as close to an empty speck of sky as one might find looking upward, as tiny as a single grain of sand held out at arm's length.

Then he pointed the Hubble Telescope at it for 10 full days.

The image that resulted is one of the most important photographs of space ever taken. Astronomers called it the Hubble Deep Field.

From a distance, it looks like any average image of space — a smattering of stars shining in inky blackness.

Image via Robert Williams (STScI), the Hubble Deep Field Team/NASA.

But only about 20 of those bright lights are individual stars. The rest are distant galaxies. More than 3,000 of them.

Aside from the one bright star-shaped spot in the front, every object in this image is a galaxy. Image via Robert Williams (STScI), the Hubble Deep Field Team/NASA.

For Williams and his team, the realization that they had taken a truly remarkable image didn’t come right away. It took months of research for them to confirm what they’d suspected — that they’d captured evidence of some of the oldest objects in the universe.

Here's where it gets mind-bendy.

Because of the time it has taken their light to reach us, the Hubble Deep Field shows us galaxies as they were a few billion years after the Big Bang. As Williams explains:

"If you want to study anything — people, agriculture, etc. — it’s always good to understand the past to see how you got there. Astronomy is the only profession where you can actually do that. At the time, the Hubble Deep Field was the closest we’ve come to seeing the moment where our universe came into being 13.7 billion years ago. I like to call it 'Humanity’s Baby Picture.'"

For many astronomers, this image made them question everything they thought they understood about the size and age of the universe.

At the time, astronomers believed there were about 10 billion galaxies in the known universe spaced out so widely they could hardly be photographed together. The Hubble Deep Field showed that wasn’t nearly enough. Now they estimate there are trillions of galaxies, at least. Maybe more.

They also learned that young galaxies formed closer to the Big Bang looked a lot different from older ones. Our home galaxy the Milky Way is a beautiful majestic spiral galaxy with four graceful swirling arms. The adolescent galaxies captured in the Hubble Deep Field were oddly-shaped and awkwardly bumping together. Taking this image and others based on it allowed astronomers to view space in a brand new way: during its teenage years.

By far, the most important legacy of the Hubble Deep Field project is the data it created.

Before the Hubble Deep Field project, astronomers would retain exclusive rights to their data for at least one year, giving them the best chance of making a big discovery on their own. Williams and his team opted to make their research available as soon as they finished collecting it. “Having unique access to this data would have been a great thing for all our careers. But data needs to be free and shared,” recalled Williams. “This was an important community service project that might change the culture of science to be more collaborative than competitive.”

Robert Williams. Image used with permission.

Once again, Williams was right. In 2004, astronomers built off the work of the Hubble Deep Field team to take another snapshot of empty sky, this time near the Fornac constellation. The resulting image — the Hubble Ultra Deep Field — showed 10,000 galaxies, the most that can be seen in the visible light spectrum.

In 2012, they took it even further. Astronomers viewed the same space with an infrared telescope to capture galaxies so far away their light can't be seen by the human eye. The Hubble eXtreme Deep Field reveals the faintest and most distant galaxies ever seen, up to 13.2 billion years back in time.

The Hubble eXtreme Deep Field is the furthest back in time humanity has ever looked. Image via NASA, ESA, H. Teplitz and M. Rafelski (IPAC/Caltech), A. Koekemoer (STScI), R. Windhorst (Arizona State University), and Z. Levay (STScI).

Williams had no way of knowing for sure what the Hubble would see when he pointed it at that patch of empty sky in December 1996. All he had was a theory he wanted to test.

His gambit paid off, but even if it hadn’t, Williams would have no regrets. “If you’re going to make a discovery, you’re going to have to be a risk-taker.”

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Democracy

Here’s a paycheck for a McDonald’s employee. And here's my jaw hitting the ground.

The federal minimum wage is still less than this.

via JustFrugalMe/YouTube

How can anyone get by on this?

I've written extensively about minimum wage, supported by fact-checkers, economists, and scholarly studies. All of them support raising the minimum wage as a solution to lifting people out of poverty and getting them off public assistance. It's slowly happening, and there's much more to be done.

But when it comes right down to it, where the rubber meets the road is what it means for everyday workers who have to live with those wages. I honestly don't know how they do it. Ask yourself: Could I live on this small of an hourly wage? I know what my answer is.

(And note that the minimum wage in many parts of the county is STILL $7.25, so it could be even less than this).

paychecks, McDonalds, corporate power, broken systemOne year of work at McDonalds grossed this worker $13,811.18.via JustFrugalMe/YouTube

The YouTube channel Just Frugal Me discussed the viral paycheck and noted there's absolutely nothing wrong with working at McDonald's. More than 2 million people in the U.S. alone work for the fast food giant. The worker's paycheck shows they put in 72 hours over the pay period, making $8.75 per hour. Before taxes, that's $631 for the week. Just Frugal Me's breakdown is even more eye-opening, breaking down this person's pay after taxes and weighing across average rent and utility costs. Spoiler Alert: the total costs for basic necessities far outweigh what this person is making even while working 12 hours per day. But they do make too much to qualify for Medicaid, meaning they will have to go out and buy their own health insurance.

mcdonald's, minimum wage, restaurants, fast food, burgers, big macA photo of a McDonald's in Hartford, CT. via Mike Mozart/Flickr

Even in states like California, where the state's $20 minimum wage ensures that people earn nearly three times as much as the federal minimum wage, which remains as low as when this paycheck first made the rounds nearly 10 years ago.

Still, even for a worker that maxed out at 40 hours per week and took zero vacation or sick time, that's only a little over $41,000 per year. That's barely half the median wage in the state of $78,000 and far below a sustainable living wage in cities like Los Angeles.

- YouTubewww.youtube.com

The U.S. federal minimum wage is just $7.25 and hasn't been raised since 2009. In April 2025, the Raise the Wage Act of 2025 was introduced in the House of Representatives and U.S. Senate. The bill would increase the federal minimum wage to $17 an hour by 2030 and eliminate the subminimum wage for tipped workers and those with disabilities. But supporters should be cautious that it's unlikely to pass the Republican-controlled Congress.

If the Wage Act of 2025 were to pass, over $22 million workers would get a raise, which is 15% of the U.S. workforce. It would raise $70 billion for low-wage Americans, an increase of $3,200 per worker.

“No person working full-time in America should be living in poverty," Virginia Congressman Bobby Scott said in a statement. "The Raise the Wage Act will increase the pay and standard of living for nearly 22 million workers across this country. Raising the minimum wage is good for workers, good for business, and good for the economy. When we put money in the pockets of American workers, they will spend that money in their communities,”

This story originally appeared ten years ago. It has been updated to reflect new information.

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Fatherhood

Daughter of Clemon's president 'sacks' him during graduation ceremony. And it was perfect.

"Apparently I need to get back in the gym and start lifting weights more!"

TODAY/Youtube

Clemson University president Jim Clements receives hug of a lifetime from daughter Grace at graduation.

College graduation is a milestone moment for graduates and parents alike. For Clemson University president Jim Clements and his daughter Grace, it was an experience that they will remember for a lifetime thanks to a genuine moment of joy shared on the graduation stage.

President Clements got to present Grace with her diploma during the ClemsonLIFE graduation ceremony on May 8, 2025. ClemsonLIFE is a program for students with intellectual disabilities that counts Tanner Smith from Netflix'sLove on the Spectrum as an alum.

After Grace's name was called during the ceremony, she joyfully ran and jumped into her father's arms–sacking him to the ground as smiles and cheers went up from the crowd. "ClemsonLIFE teaches independence, job skills…and apparently, how to sack a university president. #DadDown #BestGraduationEver #AmazingGrace," President Clements captioned the video.

On the ground, Clements smiles and helps Grace up as they embrace. The two quickly recover and stand up, and Clements gives Grace a kiss on the forehead and turns her toward the crowd to take in the applause. He then gives her a big bear hug and pats her on the back before she continues to walk the stage.

During the commencement speech, President Clements said, "Grace, I'm so incredibly proud of you and all the other ClemsonLIFE graduates. And apparently I need to get back in the gym and start lifting weights more!"

- YouTubewww.youtube.com

In an interview with TODAY, President Clements shared, "It was pure joy, total and complete happiness, to see this girl, our beautiful daughter, run across the stage and literally leap into my arms. It was magical."

However, Grace quipped during the interview, "You missed me!" President Clements replied while laughing, "I did miss you, I missed you, but then when we fell, we helped each other up. And I wanted to turn her to the audience and let everyone see how beautiful and amazing she is. Then, I wanted to give her a big huge hug to let her know how much I love her,."

In another touching Instagram post, he shared, "Amazing Grace walked the stage and I hit the turf! And I wouldn’t change a thing. Watching all that Grace has accomplished during her time with ClemsonLIFE is one of the greatest joys of my life. I can’t wait to see what she achieves next."

The emotional video and photos from the graduation ceremony captured hearts and made tears flow for viewers.

"This is why I love my school. This was a daddy/daughter moment not her and the president. Such a sweet moment. I love how he went with it and how proud he is! 🧡💜," one wrote.

"Such a genuine moment!! Love everything about this and all the work that Clemson Life does!! Amazing!! 💜🧡" said another.

And one touched viewer shared, "Is there a limit on how many times you can watch a video?! This is the most amazing Grace/Daddy (aka Pres Clements) moment I’ve ever seen! It will go down in Clemson history. Congratulations, Grace! God bless you, Mom and Dad! God is good. 😭🧡💜"

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Art

In 125 years, millions of people have looked at this painting. No one really saw it until recently.

Van Gogh saw something it took scientists another 100 years to see.

Image from Wikimedia Commons.

Van Gogh's Starry Night, 1889.

Vincent van Gogh never got to enjoy his own historic success as an artist (even though we've been able to imagine what that moment might have looked like). Van Gogh died in 1890 at the age of 37 in Auvers-sur-Oise, France after shooting himself in the chest with a revolver. It was a tragic end to a turbulent life marked by mental instability and severe self-doubt.

According to the Van Gogh Museum, in a letter to his brother Theo in 1890, just a couple of weeks before his death, Van Gogh wrote, "...my life, is attacked at the very root, my step also is faltering." The man was struggling and exhausted. The high standards he had set for himself and his art were taking a toll. He was unsure about his future and, up to this point, had not received much recognition for his work and thought himself a failure "as a man and as an artist."

His most well-known work, Starry Night, was famously painted while Van Gogh was staying in an asylum in France 1889 after he mutilated his ear during a psychotic episode. According to the Van Gogh Museum, though, this may not be the full story. While it is widely agreed that Van Gogh did in fact cut off his own ear, the museum notes that it was because of a fight between Van Gogh and Paul Gaugin, the artist he had been working for in Aries, that led to the violent explosion that highlighted his deteriorating mental state.

Vincent Van Gogh, artist, 19th century, famous artist, Starry NightVincent Van Gogh's Self-Portrait, 1889Image via Canva.

As one of the best known and most studied artists of the 19th century, Van Gogh's madness and how it influenced his work is not new information. But it turns out that those of us who have appreciated his work have been missing out on some critical details for more than 100 years—revealed in the 2010s thanks to the Hubble Space Telescope.

A video at the bottom of the page will explain everything, but before we get there, let's do some backstory:

We known Van Gogh was an artist—and a genius artist at that—but, it turns out, he was also scientist. Kind of.

Whether intentionally or not, fresh eyes have found that Van Gogh's art—aside from being breathtaking—also captures one of science and nature's most elusive concepts: Turbulence.

The concept of turbulence is hard to understand with math, but it turns out art makes it fairly easy to comprehend through depiction. So, what is turbulence?

According to Britannica, turbulence, or turbulent flow, is a concept of fluid dynamics in which a type of fluid flow (liquid or gas like air or water or air) undergoes an irregular fluctuation or energy cascade. In other words, the air or water swirls and eddies as it moves: big eddies make smaller eddies, and those make even smaller ones, and so on. Common examples of turbulent flow include blood flow in arteries, lava flow, atmosphere and ocean currents, and the flow in boat wakes or surrounding the tips of aircraft wings.

It looks like this:

figures, flow, turbulence, turbulent flow, science, movementTurbulent flow illustrated and animated.All Van Gogh GIFs via TED-Ed.

The thing is, scientists only started figuring this out pretty recently.

turbulence, turbulent flow, science, nature, researchAnimation of art referencing science.All Van Gogh GIFs via TED-Ed.

And yet, there was Mr. Vincent van Gogh, 100 years earlier in his asylum with a mutilated ear and able to accurately capture this turbulent flow in what would become his most famous work, Starry Night.

Starry Night, Van Gogh, turbulence, art, art captures scienceAnimated Starry NightAll Van Gogh GIFs via TED-Ed.

The folks who noticed Van Gogh's ability to capture turbulence checked to see whether other artists did the same. Most of the Impressionists achieved "luminance" with their art—a striking and lifelike depiction of light's effect on color. While impressive, they did not capture or depict turbulence the way Van Gogh did.

The Scream, Edvard Munch, art, popular art, history, painting An animated depiction of The Scream.All Van Gogh GIFs via TED-Ed.

Not even Edvard Munch's The Scream, with it's swirling color and movement, could recreate what Van Gogh had accomplished.

Even in his darkest time, Van Gogh was able to capture—with eerie accuracy—one of nature's most complex and confusing concepts 100 years before scientists had the technology to do so.

Who would have thought that the beauty Van Gogh captured was foreshadowing what scientists would observe in the real, natural world in a century's time? To learn even more, watch the TED-Ed video below:

- YouTubeyoutu.be

This article originally appeared twelve years ago. It has been updated.

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Education

Frugal people share 15 silly money-saving tips guaranteed to save you a few bucks

Simple changes can really bring down your electric bill.

via Unsplash

Hand holding an unplugged electric cord and hand holding rolled up money.

Most adults periodically examine their lives to try to figure out where they can save money. It might be cutting one of the streaming services we're not using or dialing back the Starbucks PSLs. However, the people on the subreddit r/frugal take saving money to a whole new level.

A recent thread posted by u/Jskyesthelimit was chock-full of solid gold advice for anyone looking to trim the budget but who doesn't want to put in a lot of work. (Yeah, yeah — we all know meal-prepping is effective, but who's got the time? We're looking for easy wins, here.)

The prompt, "What's the little effortless, stupid thing you do that TECHNICALLY saves you money?", got some responses and tips you've probably never thought of.

They're small, they're silly — but they do add up.

1. Spend more time outside

"if i go outside and play all day, i don't have consumerist urges to buy stupid shit." - looney417

Can't spend money if you don't go into a store!

It's a good idea to get away from your phone or laptop for a while, too. If you're not careful, you can buy a hundred dollars worth of junk on Amazon before you even realize what's happening.

2. Time your dishwasher runs

"When our dishwasher is full and ready to be started, I set an alarm on my watch for 9pm. I start the dishwasher when the alarm goes off since the electricity rate goes down after 9pm." - misterfuss

dishes, dishwasher, clean dishes, unload dish, money hacks, kitchen hacksA half loaded dishwashervia Nathan Dumloa/Unsplash

Did you know that electricity costs more during "peak hours"? Where I live, power can cost up to 4x as much from 2-7pm versus off-peak hours.

Most people run the dishwasher at night anyway, but you should look up your own local peak hours. Starting the nightly load at 9 instead of 8 every night could actually save you a couple of bucks a month.

I like that you can program a Google Nest to do this for you. It knows how expensive electricity is at different times, and will manage your supercooling for you.3. Fill a large water bottle at work before you leave.

u/MrPerfectionisback swears by this one.

Getting a gigantic, high-quality water bottle could be a great investment if you're able to top it off at the office every day and bring your water bill down a smidge.

4. Use less laundry detergent

Most of us approach laundry detergent with a "fill 'er up" attitude. But, usually, you can get away with even just one tablespoon if your clothes aren't that dirty. and using less will help your clothes last longer.

u/jbblue48089 also recommends using solid bar shampoo and dish soap, which have a longer lifespan than liquid soaps.

5. Re-wear clothes (other than socks and underwear)

Another option from u/ztreHdrahciR — don't wash your clothes at all! At least not right away.

Chances are you can get a few wears out of jeans or even t-shirts and save on laundry costs, to the tune of a few dollars per year.

6. Make your own doggie poo bags

"Use used food bags to pick up the dogs poop." - bezere

Poop bags are expensive! You could easily spend $20-50 per year, depending on what brand you use.

Next time you pack a sandwich for lunch, save that plastic baggie and use it for pick-up duty later on.

7. Charge your phone at work (or wherever there's an outlet)

A good one from u/runmemymo.

Never pass up a chance for free electric!

If you don't work in an office, just carry your phone charger with you. Lots of restaurants and even public spaces have outlets so you can get a little free juice.

8. Poo at work (or wherever there's a bathroom)

u/larkfor says they save a ton of money each year on water and toilet paper by doing their business at work or the office.

Never pass up a chance for free water and toilet paper!

9. Cut sponges in half


sponge, cleaning, money hacks, house keeping, soap, domestic laborA yellow soapy sponge.via Pille R. Priske/Unsplash

u/plaincheeseburger recommends turning one sponge into two.

It will still work exactly the same and last twice as long.

10. Repair old dog toys

I love this one from u/pdxarchitecht!

My dogs love immediately ripping the stuffing out of new toys, which doesn't feel like a great value for my money.

The hack? Put the stuffing back in and add a stitch or two to close it up and save yourself $10 or more.

11. Twist the stems off of peppers if paying by weight

This ingenious and petty tip comes from u/casterix75.

Not all supermarkets charge by weight for bell peppers (or similar produce), but if they do, why pay for the stem? Twist it off and save yourself a few cents at the checkout.

12. Save the cold water when running a shower or bath

An old science teacher taught me this one in high school, recommended in this thread by u/smartquokka.

Put a bucket in the shower or bath to collect the cold water while it's heating up. Use that to water plants, fill the dog bowls, or flush the toilet.

13. Unplug everything at night

via Canva/Photos


Many people recommended this — it's an r/frugal staple.

Appliances on standby still use power, so unplug as many things as possible before going to bed. u/Larkfor estimates this saves them $10 a month or so on power.

14. Library card

Yes. And take advantage of audiobooks, ebooks, and even streaming. My library has many great movies, shows, and lecture series (I love The Great Courses).

15. Credit card points

[I] Use my CC that gets rewards points for all purchases and bills that I can.

My entire family is going in a trip in a few months, and we booked all our flights together, 4.5k of airfare. I very generously offered to put all the airfare on my (2% cash back) card. My entire family paid me back their portion that week, and now I get the $90 in cash back!

These tips are so small they're almost microscopic, but you know what? Most of them are so easy you'd barely notice a difference in your lifestyle and routine. And all together, you could save yourself a decent chunk of money every year by making a few simple changes.

Thanks to the thrifty people of Reddit for sharing their hacks with the rest of us!

This article originally appeared last year.

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Planet

45 years ago, Carl Sagan beautifully explained the fourth dimension with just an apple

Sagan was the Mister Rogers of complex scientific concepts.

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.

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