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If you're freaking out about the election, these 7 things might give you hope.

The conventions are over, and I'm still worried. I suspect I'm not alone.

Photo via iStock.


I'm a pretty simple guy. My needs are basic. I like walking in the park and taking naps. I like being able to say whatever I want and practice my religion without fear of harassment or prosecution. I appreciate when my black, brown, female, and LGBTQ friends and family members have basic civil rights. I want my country to be safe and respected in the world.

Unfortunately, that's all in jeopardy. Because this guy...

Photo by Gustavo Caballero/Getty Images.

...who has a well-documented history of bigotry against Mexicans and Muslims, who wants to transform NATO into a mafia protection racket, who plays footsie with white supremacists, who deploys anti-Semitic dog whistles, who publicly dehumanizes women, who voices hostility toward the First Amendment's protections of freedom of speech and religion, and who calls on a foreign government to hack his opponent's emails, could be our next president.

And the polls have gotten closer. Too close for comfort. Trump could actually win this thing.

But hope springs eternal! Hope never dies!

Hope, believe it or not, floats.

If you're as appalled as I am that Donald (freaking) Trump could be the leader of the free world come November, there are a few things that still make me optimistic that he never, ever will be:

I'm hanging on to these things for dear life. I hope they help.

1. The current polling — which shows Trump pulling into a tie — isn't necessarily how things are going to shake out in November.

Despite Trump's recent gains, as of July 29, FiveThirtyEight's "Polls Plus" forecast, which takes into account current polling and adjusts for historical trends, finds a 60% chance of the former "Apprentice" host going down in November.


Dear God, please be right, Nate Silver. Please be right. Photo by Andrew Toth/Getty Images.

According to Josh Katz and Kevin Quealy of the New York Times, the period surrounding the party conventions is one of "high polling volatility," and averages taken around this time tend to miss final result by nearly 8 percentage points. Trump, just off his vice presidential rollout and convention, is likely enjoying a similar bump to what both Mitt Romney and John McCain experienced four and eight years ago, respectively.

Still, even a 40% chance of Trump becoming president is way too high...

2. Which is why we should be grateful that Michelle Obama is such a boss that not even Trump will step to her.

You know that scene in a movie where the good guys are getting their asses kicked, and they're all huddled together in a room, and one of them says: "We're outnumbered. We don't have a chance." But then Samuel L. Jackson says, "Yes, we do." And he opens a closet door to reveal a huge, futuristic bazooka as warm, celestial light spills out from behind it?

That's basically what happened when Michelle Obama spoke at the first night of the 2016 DNC.

Image via CNN/YouTube.

You've already seen the highlights. You know how good she was.

She was so good that Trump, not one to shrink from a third-grade Twitter insult — who, indeed, tweeted attacks against nearly every other speaker on the stage that night — didn't dare deploy a comeback against the first lady.

For the next three and a half months, we have that bazooka in our arsenal.

I feel pretty good about that.

3. Karla Ortiz bravely took the stage at the DNC with her undocumented mother and challenged us all to do something about immigration reform.

What was the bravest thing you did recently? For me, it was yesterday when the deli I stopped at for lunch was out of regular Diet Coke, so I drank the caffeine-free kind instead.

For Karla Ortiz, an 11-year-old from Florida who likes doing science experiments and searching for rare rocks, it was risking her family's safety and security to call out Donald Trump's racist immigration policy in front of millions of people.

Karla Ortiz and her mother. Photo by Alex Wong/Getty Images.

"I don't feel brave every day. On most days, I'm scared," Ortiz said, proudly making everyone in the audience feel ashamed for complaining about the lack of detachable hangers in their hotel rooms just a few hours earlier.

"I'm scared that, at any moment, my mom and my dad will be forced to leave. And I wonder, 'What if I come home and find it empty?'" she said, ironically revealing that her guts are made of goddamn iron.

She said these things on TV, in full view of thousands of political foes of immigration reform, violent racists, and immigration authorities. The risk she took is scarily real, especially if Trump becomes president.

But she did it anyway. Because it's just that important.

If she can do that, the least we can do is tell our bosses we need to take a long lunch on Nov. 8 to go vote him the hell out of all our lives forever.

4. Non-Democrat Michael Bloomberg made the clarifying, simple, devastating case against Trump to independent voters.

Bloomberg is not a typical person. Like Trump, he's a billionaire. Unlike Trump, he definitely, actually is a billionaire.

He's also no one's idea of a left-wing fire-breather. He was a Republican mayor of New York City and is now a zealous independent.

In his speech at the 2016 DNC, he criticized both parties. But ultimately, he really stuck it to Trump, delivering, perhaps, the best one-liner of the week:

Ultimately, to defeat Trump, there just needs to be a constituency for sanity and competence. That's a low bar.

And I believe we can leap it with room to spare.

5. Ted Cruz pointedly refused to endorse Trump at his own convention, an inspiring move in its own right.

If there's one politician who I hope stays nearly as far away from the White House as Donald Trump, it's Ted Cruz. Pick 10 issues at random and Ted Cruz and I probably disagree on 11 of them. I think his program for America would make pretty much everything worse. Profoundly worse.

Thing is, Ted Cruz, for all his many faults, actually respects the Constitution. And in his speech at the RNC, Cruz refused, over a chorus of jeers, to endorse Trump.

"Vote your conscience," he said.

Yay? Photo by Chip Somodevilla/Getty Images.

Whether it was revenge for Trump spending the last days of the GOP primary attacking Cruz's wife's mental health and suggesting with absolutely no evidence that Cruz's father might have helped assassinate John F. Kennedy, or simply an attempt to stand up for Cruz's (admittedly pretty messed-up) principles, it was invigorating and, yes, even inspiring.

Self-serving or not, if someone I disagree so intensely and so completely with can refuse to get behind Trump, it gives me hope that thousands (millions?) more like him are out there.

6. The stage at the DNC looked like the real America, not the "real America."

For years, politicians have sold us a story of a "real America." There are good things about this America — small businesses have a steady stream of customers there, the bunting is festive, and the desserts are really, ridiculously sweet. But ultimately, it seems to be an America that's pretty exclusively white, pretty exclusively Christian, and pretty exclusively rural — and occasionally suburban.

At the DNC, we saw a different — but just as real — America. That America includes:

Dozens of black, Latino, LGBTQ, and female officeholders from big cities and small towns across the country.

Photo by Alex Wong/Getty Images.

A Muslim-American father, who spoke eloquently and emotionally about the death of his U.S. soldier son — and defended the Constitution against Trump's call to place an immigration ban on an entire religion.

Photo by Alex Wong/Getty Images.

The first out trans woman to speak at a party convention.

Photo by Saul Loeb/Getty Images.

And, of course, the first woman ever nominated to run on a major party ticket for president, which — whether or not you agree with her politics or like her as a person — is still a pretty huge deal.

Photo by Win McNamee/Getty Images.

That America isn't a story. It's real.

If it can hang together, then this thing should be in the bag.

7. Even though democracy can be scary — OK, terrifying — at times, it's still pretty great.

As bad as things seem, as horrifyingly close Donald Trump might be to the White House, the fact that we get to watch passionate people spend two weeks in July arguing via speeches, original songs, and funny hats about who would be a better president — and then actually getting to choose which one we like best — is pretty inspiring.

Photo by Drew Angerer/Getty Images.

Just ask this guy:

Photo by Robyn Beck/AFP/Getty Images.

...who on the third night of the DNC showed up to deliver a rousing defense of democracy.

He shouldn't even have to say it, but he's right.

You can disagree with this person's thoughts on the Second Amendment:

Photo by Spencer Platt/Getty Images.

Or with these people's feelings about Citizens United:

Photo by Ralph Freso/Getty Images.

But that doesn't matter even a little bit if you don't vote.

We don't have to sit around biting our nails. We don't have to worry about others making decisions about who's going to lead us without our consent. We don't have a king or a generalissimo or whatever. This is America, dammit.

And in America, we still have the right to choose.

Photo by Michael Owen Baker/Getty Images.

This November, let's make sure we use it to fire Donald Trump.

Click here to register to vote.

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.

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. 😭🧡💜"

Golden Years

7 'old people' sayings that are actually solid life advice at every age

"Make all your words sweet because tomorrow you may have to eat them."

Elder wisdom can come in handy.

With age comes wisdom, or at least we hope it does. As we get older, we collect life lessons that we can pass along to younger generations, sometimes with lengthy stories, sometimes with quippy sayings.

Adages like "A penny saved is a penny earned," or "Early to bed, early to rise makes a man healthy, wealthy, and wise," have been part of our collective treasure chest of life advice for generations, but the aphorisms that spring from the experience of our loved ones and mentors are often the most meaningful.

Someone shared that they'd read and appreciated this old man's advice: “My grandpa once told me 'if you get on the wrong train, get off at the nearest station, the longer it takes you to get off, the more expensive the return trip will be.' He wasn’t talking about trains.” The person asked for more tidbits of wisdom from old folks and people started sharing sayings they heard from their elders growing up.

Here are some of the best "old man advice" sayings and how they can be applied in a person's life.

"You might miss what’s ahead of you if you keep concentrating on what’s in the rear view mirror."

Another commenter put it another way: "Don't look behind you, you aren't going that way." This adage is about not dwelling on the past. Many of us have a tendency to spend more time mentally in the past, rehashing old memories or being nostalgic for what once was, than we do in the present or looking forward to the future. There's nothing wrong with a little reflection, but if most of our focus is in the past, we miss out on the present. Rear view mirrors are for quick glances, not where our focus should be.

"Do the right thing, even if nobody is watching."

This saying is about good character and true integrity. If you notice someone drop a $20 bill and no one is around to see but you, do you give it back to them or do you pick it up and keep it? If you realize that a store didn't charge you for an item, do you point it out and make it right or do you allow the mistake to remain? There are opportunities each day for us to choose between right and wrong, and those choices really speak to who we are if they are made without anyone else knowing.

bart simpson episode 21 GIFGiphy


"Be nice to everybody you meet on the way up the ladder. You'll see the same faces on the way down "

Don't get cocky and don't burn bridges you think you won't need to return to. There's value in being kind for its own sake, but there's also the reality that being kind also makes people like you. When people like you, they're more likely to lend you a helping hand, and you never know when you're going to be in a position to need one. It's also a good reminder that you're not inherently better than anyone else just because of where you are in life. We're all constantly in flux, so it's important to stay humble and kind.

In other words, "Make all your words sweet because tomorrow you may have to eat them."

"One of the most powerful negotiating tools is silence."

The power of silence in general is often underrated, but it can be an especially useful tool in a negotiation. Some people are so uncomfortable with silence that they will make concessions simply to avoid it. And sometimes the best response to an unreasonable demand is to just say nothing and stare, letting the other party come to the realization themselves. It takes calm confidence to simply be quiet and let the silence fill the room, which can feel surprisingly intimidating.

Eddie Murphy Shut Up GIF by BounceGiphy

"Always listen to your gut, even if you can’t explain it."

Ah, the strange and mysterious sense of intuition that we can't really describe but know when we feel it. Whether it's getting a creepy vibe about a person or a little voice telling you to do or not do something, those "gut instincts" can serve us well. Of course, if we are prone to anxiety, our instincts can sometimes be confused with anxious thoughts, but "go with your gut" is solid advice anyway.

“It doesn’t matter what path you’re on if it’s the wrong mountain.”

Sometimes people trying to find their way end up hitting roadblock after roadblock, which may mean they just haven't found the right path yet or might mean they need an entire overhaul of their life. That might look like switching career paths entirely, rather than trying to find a job in your field that fits. It might mean changing majors in the middle of your studies when you find yourself not enjoying any of your classes. It might mean finding a new community or reevaluating your relationships.

"The harder I work, the luckier I get."

Several sayings line up with this one, like "Luck is the intersection of preparation and opportunity," and "Luck favors the prepared mind." There's a lot to be said for fortune and hard work going hand in hand. If we expect good things to just land in our lap, we will likely be disappointed, but if we move in the direction of things we want to happen and do the work of preparing for good things to come our way, "luck" frequently seems to follow.

Finding a saying that resonates can be really helpful when we're facing a specific challenge in life, especially when we commit it to memory and repeat it often.

This article originally appeared in March.

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.

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.