What Is Infinity?

iStock
iStock

Albert Einstein famously said: “Two things are infinite: the universe and human stupidity. And I'm not sure about the universe.”

The notion of infinity has been pondered by the greatest minds over the ages, from Aristotle to German mathematician Georg Cantor. To most people today, it is something that is never-ending or has no limit. But if you really start to think about what that means, it might blow your mind. Is infinity just an abstract concept? Or can it exist in the real world?

THERE'S MORE THAN ONE KIND

Infinity is firmly rooted in mathematics. But according to Justin Moore, a math researcher at Cornell University in Ithaca, New York, even within the field there are slightly different uses of the word. “It's often referred to as a sort of virtual number at the end of the real number line,” he tells Mental Floss. “Or it can mean something too big to be counted by a whole number.”

There isn't just one type of infinity, either. Counting, for example, represents a type of infinity that is unbounded—what's known as a potential infinity. In theory, you can go on counting forever without ever reaching a largest number. However, infinity can be bounded, too, like the infinity symbol, for example. You can loop around it an unlimited number of times, but you must follow its contour—or boundary.

All infinities may not be equal, either. At the end of the 19th century, Cantor controversially proved that some collections of counting numbers are bigger than the counting numbers themselves. Since the counting numbers are already infinite, it means that some infinities are larger than others. He also showed that some types of infinities may be uncountable, as opposed to collections like the counting numbers.

"At the time, it was shocking—a real surprise," Oystein Linnebo, who researches philosophies of logic and mathematics at the University of Oslo, tells Mental Floss. "But over the course of a few decades, it got absorbed into mathematics."

Without infinity, many mathematical concepts would fall apart. The famous mathematical constant pi, for example, which is essential to many formulas involving the geometry of circles, spheres, and ellipses, is intrinsically linked to infinity. As an irrational number—a number that can't simply be expressed by a fraction—it's made up of an endless string of decimals.

And if infinity didn't exist, it would mean that there is a biggest number. "That would be a complete no-no," says Linnebo. Any number can be used to find an even bigger number, so it just wouldn't work, he says.

CAN YOU MEASURE THE IMMEASURABLE?

In the real world, though, infinity has yet to be pinned down. Perhaps you've seen infinite reflections in a pair of parallel mirrors on opposite sides of a room. But that's an optical effect—the objects themselves are not infinite, of course. "It's highly controversial and dubious whether you have infinities in the real world," says Linnebo. "Infinity has never been measured."

Trying to measure infinity to prove it exists might in itself be a futile task. Measurement implies a finite quantity, so the result would be the absence of a concrete amount. "The reading would be off the scale, and that's all you would be able to tell," says Linnebo.

The hunt for infinity in the real world has often turned to the universe—the biggest real thing that we know of. Yet there is no proof as to whether it is infinite or just very large. Einstein proposed that the universe is finite but unbounded—some sort of cross between the two. He described it as a variation of a sphere that is impossible to imagine.

We tend to think of infinity as being large, but some mathematicians have tried to seek out the infinitely small. In theory, if you take a segment between two points on a line, you should be able to divide it in two over and over again indefinitely. (This is the Xeno paradox known as dichotomy.) But if you try to apply the same logic to matter, you hit a roadblock. You can break down real-world objects into smaller and smaller pieces until you reach atoms and their elementary particles, such as electrons and the components of protons and neutrons. According to current knowledge, subatomic particles can't be broken down any further.

THE INFINITIES OF THE SINGULARITY

Black holes may be the closest we've come to detecting infinity in the real world. In the center of a black hole, a point called a singularity is a one-dimensional dot that is thought to contain a huge mass. Physicists theorize that at this bizarre location, some of the singularity's properties are infinite, such as density and curvature.

At the singularity, most of the laws of physics no longer work because these infinite quantities "break" many equations. Space and time, for example, are no longer two separate entities, and seem to merge.

According to Linnebo, though, black holes are far from being an example of a tangible infinity. "My impression is that the majority of physicists would say that is where our theory breaks down," he says. "When you get infinite curvature or density, you are beyond the area where the theory applies."

New theories may therefore be needed to describe this location, which seems to transcend what is possible in the physical world.

For now, infinity remains in the realm of the abstract. The human mind seems to have created the concept, yet can we even really picture what it looks like? Perhaps to truly envision it, our minds would need to be infinite as well.

10 Products for a Better Night's Sleep

Amazon/Comfort Spaces
Amazon/Comfort Spaces

Getting a full eight hours of sleep can be tough these days. If you’re having trouble catching enough Zzzs, consider giving these highly rated and recommended products a try.

1. Everlasting Comfort Pure Memory Foam Knee Pillow; $25

Everlasting Comfort Knee Pillow
Everlasting Comfort/Amazon

For side sleepers, keeping the spine, hips, and legs aligned is key to a good night’s rest—and a pain-free morning after. Everlasting Comfort’s memory foam knee pillow is ergonomically designed to fit between the knees or thighs to ensure proper alignment. One simple but game-changing feature is the removable strap, which you can fasten around one leg; this keeps the pillow in place even as you roll at night, meaning you don’t have to wake up to adjust it (or pick it up from your floor). Reviewers call the pillow “life-changing” and “the best knee pillow I’ve found.” Plus, it comes with two pairs of ear plugs.

Buy it: Amazon

2. Letsfit White Noise Machine; $21

Letsfit White Noise Machine
Letsfit/Amazon

White noise machines: They’re not just for babies! This Letsfit model—which is rated 4.7 out of five with nearly 3500 reviews—has 14 potential sleep soundtracks, including three white noise tracks, to better block out everything from sirens to birds that chirp enthusiastically at dawn (although there’s also a birds track, if that’s your thing). It also has a timer function and a night light.

Buy it: Amazon

3. ECLIPSE Blackout Curtains; $16

Eclipse Black Out Curtains
Eclipse/Amazon

According to the National Sleep Foundation, too much light in a room when you’re trying to snooze is a recipe for sleep disaster. These understated polyester curtains from ECLIPSE block 99 percent of light and reduce noise—plus, they’ll help you save on energy costs. "Our neighbor leaves their backyard light on all night with what I can only guess is the same kind of bulb they use on a train headlight. It shines across their yard, through ours, straight at our bedroom window," one Amazon reviewer who purchased the curtains in black wrote. "These drapes block the light completely."

Buy it: Amazon

4. JALL Wake Up Light Sunrise Alarm Clock; $38

JALL Wake Up Light Sunrise Alarm Clock
JALL/Amazon

Being jarred awake by a blaring alarm clock can set the wrong mood for the rest of your day. Wake up in a more pleasant way with this clock, which gradually lights up between 10 percent and 100 percent in the 30 minutes before your alarm. You can choose between seven different colors and several natural sounds as well as a regular alarm beep, but why would you ever use that? “Since getting this clock my sleep has been much better,” one reviewer reported. “I wake up not feeling tired but refreshed.”

Buy it: Amazon

5. Philips SmartSleep Wake-Up Light; $200

Philips SmartSleep Wake-Up Light
Philips/Amazon

If you’re looking for an alarm clock with even more features, Philips’s SmartSleep Wake-Up Light is smartphone-enabled and equipped with an AmbiTrack sensor, which tracks things like bedroom temperature, humidity, and light levels, then gives recommendations for how you can get a better night’s rest.

Buy it: Amazon

6. Slumber Cloud Stratus Sheet Set; $159

Stratus sheets from Slumber Cloud.
Slumber Cloud

Being too hot or too cold can kill a good night’s sleep. The Good Housekeeping Institute rated these sheets—which are made with Outlast fibers engineered by NASA—as 2020’s best temperature-regulating sheets.

Buy it: SlumberCloud

7. Comfort Space Coolmax Sheet Set; $29-$40

Comfort Spaces Coolmax Sheets
Comfort Spaces/Amazon

If $159 sheets are out of your price range, the GHI recommends these sheets from Comfort Spaces, which are made with moisture-wicking Coolmax microfiber. Depending on the size you need, they range in price from $29 to $40.

Buy it: Amazon

8. Coop Home Goods Eden Memory Foam Pillow; $80

Coop Eden Pillow
Coop Home Goods/Amazon

This pillow—which has a 4.5-star rating on Amazon—is filled with memory foam scraps and microfiber, and comes with an extra half-pound of fill so you can add, or subtract, the amount in the pillow for ultimate comfort. As a bonus, the pillows are hypoallergenic, mite-resistant, and washable.

Buy it: Amazon

9. Baloo Weighted Blanket; $149-$169

Baloo Weighted Blanket
Baloo/Amazon

Though the science is still out on weighted blankets, some people swear by them. Wirecutter named this Baloo blanket the best, not in small part because, unlike many weighted blankets, it’s machine-washable and -dryable. It’s currently available in 12-pound ($149) twin size and 20-pound ($169) queen size. It’s rated 4.7 out of five stars on Amazon, with one reviewer reporting that “when it's spread out over you it just feels like a comfy, snuggly hug for your whole body … I've found it super relaxing for falling asleep the last few nights, and it looks nice on the end of the bed, too.” 

Buy it: Amazon 

10. Philips Smartsleep Snoring Relief Band; $200

Philips SmartSleep Snoring Relief Band
Philips/Amazon

Few things can disturb your slumber—and that of the ones you love—like loudly sawing logs. Philips’s Smartsleep Snoring Relief Band is designed for people who snore when they’re sleeping on their backs, and according to the company, 86 percent of people who used the band reported reduced snoring after a month. The device wraps around the torso and is equipped with a sensor that delivers vibrations if it detects you moving to sleep on your back; those vibrations stop when you roll onto your side. The next day, you can see how many hours you spent in bed, how many of those hours you spent on your back, and your response rate to the vibrations. The sensor has an algorithm that notes your response rate and tweaks the intensity of vibrations based on that. “This device works exactly as advertised,” one Amazon reviewer wrote. “I’d say it’s perfect.”

Buy it: Amazon

This article contains affiliate links to products selected by our editors. Mental Floss may receive a commission for purchases made through these links.

It's Black Birders Week—Here's Why Celebrating Black Scientists and Naturalists Matters

Rawpixel/iStock via Getty Images
Rawpixel/iStock via Getty Images

BlackAFInSTEM, a community of Black scientists, kicked off the inaugural Black Birders Week from May 31 through June 5. What started as a group chat organized by birder Jason Ward evolved, in a matter of mere days, into a week-long celebration of Black naturalists. “It is a movement that was started out of pain, and its goal is not necessarily pleasure, but uplifting,” Alexander Grousis-Henderson, a zookeeper and member of BlackAFInSTEM, tells Mental Floss. “We want people, especially our community, to come out of this stronger and better.”

The movement started after a video of a white woman harassing and threatening Christian Cooper, a Black birder, went viral. As part of Black Birders Week, you can follow along as professional and amateur Black naturalists, scientists, and outdoor enthusiasts share their expertise and experiences and celebrate diversity in the outdoors. Throughout the week, members of BlackAFInSTEM are facilitating online events and conversations like #AskABlackBirder and #BlackWomenWhoBird.

Though Black Birders Week was created for Black nature enthusiasts, everyone is welcome to participate. Follow along the #BlackBirdersWeek hashtag, or check out the @BlackAFInSTEM Twitter account. Ask questions, engage with their posts, or simply retweet the scientists to help amplify their voices.

Scroll through the hashtags on Twitter and Instagram, and you’ll find a stream of Black naturalists honoring their love of the outdoors. “We want kids to see our faces and attach them to the outdoors, and we want our peers to recognize that we belong here too,” Grousis-Henderson tells Mental Floss.

Not only does Black Birders Week make space for Black birders to share their passion, it’s also a way for the community to raise awareness of their unique experiences and address systemic racism in nature and STEM (science, technology, engineering, and math). According to Grousis-Henderson, it’s an opportunity to foster a dialogue within the birding community; to prompt conversations about diversity within the outdoors.

“We wanted to draw on what we know about the diversity of biological systems and bring that perspective to social systems,” Grousis-Henderson says. “A diverse ecosystem can stand up to a lot of change, but a non-diverse ecosystem, one lacking biodiversity, is easy to topple.”

The movement goes beyond birding. Alongside Black Birders Week, Black outdoorspeople are sharing their experiences of what it’s like to be a Black person in nature—a space where they’re far too often made to feel unwelcome and unsafe. Organizations like Backyard Basecamp, Melanin Base Camp, and Outdoor Afro continue to foster the Black community's connection to nature.

"Black Birders Week is an opportunity to highlight joy and belonging, to showcase expertise, and to remind people that Black people have been inextricably connected to nature for generations," Yanira Castro, communications director for Outdoor Afro, tells Mental Floss in an email. "It is a celebration of that relationship."