What Is Infinity?

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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 Rad Gifts for Hikers

Greg Rosenke/Unsplash
Greg Rosenke/Unsplash

The popularity of bird-watching, camping, and hiking has skyrocketed this year. Whether your gift recipients are weekend warriors or seasoned dirtbags, they'll appreciate these tools and gear for getting most out of their hiking experience.

1. Stanley Nesting Two-Cup Cookset; $14

Amazon

Stanley’s compact and lightweight cookset includes a 20-ounce stainless steel pot with a locking handle, a vented lid, and two insulated 10-ounce tumblers. It’s the perfect size for brewing hot coffee, rehydrating soup, or boiling water while out on the trail with a buddy. And as some hardcore backpackers note in their Amazon reviews, your favorite hiker can take the tumblers out and stuff the pot with a camp stove, matches, and other necessities to make good use of space in their pack.

Buy it: Amazon

2. Osprey Sirrus and Stratos 24-Liter Hiking Packs; $140

Amazon

Osprey’s packs are designed with trail-tested details to maximize comfort and ease of use. The Sirrus pack (pictured) is sized for women, while the Stratos fits men’s proportions. Both include an internal sleeve for a hydration reservoir, exterior mesh and hipbelt pockets, an attachment for carrying trekking poles, and a built-in rain cover.

Buy them: Amazon, Amazon

3. Yeti Rambler 18-Ounce Bottle; $48

Amazon

Nothing beats ice-cold water after a summer hike or a sip of hot tea during a winter walk. The Yeti Rambler can serve up both: Beverages can stay hot or cold for hours thanks to its insulated construction, and its steel body (in a variety of colors) is basically indestructible. It will add weight to your hiker's pack, though—for a lighter-weight, non-insulated option, the tried-and-true Camelbak Chute water bottle is incredibly sturdy and leakproof.

Buy it: Amazon

4. Mappinners Greatest 100 Hikes of the National Parks Scratch-Off Poster; $30

Amazon

The perfect gift for park baggers in your life (or yourself), this 16-inch-by-20-inch poster features epic hikes like Angel’s Landing in Zion National Park and Half Dome in Yosemite National Park. Once the hike is complete, you can scratch off the gold foil to reveal an illustration of the park.

Buy it: Amazon

5. National Geographic Adventure Edition Road Atlas; $19

Amazon

Hikers can use this brand-new, updated road atlas to plan their next adventure. In addition to comprehensive maps of all 50 states, Puerto Rico, Canada, and Mexico, they'll get National Geographic’s top 100 outdoor destinations, useful details about the most popular national parks, and points on the maps noting off-the-beaten-path places to explore.  

Buy it: Amazon

6. Adventure Medical Kits Hiker First-Aid Kit; $25

Amazon

This handy 67-piece kit is stuffed with all the things you hope your hiker will never need in the wilderness. Not only does it contain supplies for pain, cuts and scrapes, burns, and blisters (every hiker’s nemesis!), the items are organized clearly in the bag to make it easy to find tweezers or an alcohol wipe in an emergency.

Buy it: Amazon

7. Hiker Hunger Ultralight Trekking Poles; $70

Amazon

Trekking poles will help increase your hiker's balance and stability and reduce strain on their lower body by distributing it to their arms and shoulders. This pair is made of carbon fiber, a super-strong and lightweight material. From the sweat-absorbing cork handles to the selection of pole tips for different terrain, these poles answer every need on the trail. 

Buy it: Amazon

8. Leatherman Signal Camping Multitool; $120

Amazon

What can’t this multitool do? This gadget contains 19 hiking-friendly tools in a 4.5-inch package, including pliers, screwdrivers, bottle opener, saw, knife, hammer, wire cutter, and even an emergency whistle.

Buy it: Amazon

9. RAVPower Power Bank; $24

Amazon

Don’t let your hiker get caught off the grid with a dead phone. They can charge RAVPower’s compact power bank before they head out on the trail, and then use it to quickly juice up a phone or tablet when the batteries get low. Its 3-inch-by-5-inch profile won’t take up much room in a pack or purse.

Buy it: Amazon

10. Pack of Four Indestructible Field Books; $14

Amazon

Neither rain, nor snow, nor hail will be a match for these waterproof, tearproof 3.5-inch-by-5.5-inch notebooks. Your hiker can stick one in their pocket along with a regular pen or pencil to record details of their hike or brainstorm their next viral Tweet.

Buy it: Amazon

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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."