The Mysterious Mathematical Principle That Links Bus Systems and Chicken Eyes

iStock
iStock

Math is everywhere—if you know where to look. Elegant equations can be observed in everything from flower petals to swirling galaxies. Universality, a phenomenon that strikes a balance between order and randomness, is one of these ubiquitous mathematical patterns that repeats itself again and again in the natural world. As Quanta Magazine lays out in the new episode of its In Theory video series, examples of universality can be seen in biology, quantum physics, and even public transportation.

In math, universality is what determines the spacing between solutions in a large matrix of random numbers. The numbers that go into the matrices may themselves be random, but when they interact, they produce a predictable outcome.

You can see the same principle at work in the world around us. Take bus routes, for instance. In 1999, a Czech physicist named Petr Šeba found the pattern in Cuernavaca, Mexico after observing how the city's bus system operated. Paid "spies" were positioned along the bus routes, and whenever a bus came, they'd let the driver know how long it had been since the last one passed through. Based on this intel, the bus driver would either slow down or speed up to maximize his passengers at the next stop. On paper, this method creates a barcode pattern of lines that appear to be placed at random but actually follow a set pattern.

That same random-looking pattern appears elsewhere, too, like in chicken eyes. While the color-sensitive cone cells in the eyes of some animals, like fish, are laid out uniformly across the retina, the cells in chickens' eyes look different. The cone cells are different sizes and look like they're scattered at random. But these cells are actually distributed according to the universality pattern—the first-ever instance of the pattern recorded in biology.

You can also see universality when you map out the energy spectrum of the uranium nucleus, the spectral measurements of sea ice, and elsewhere. To learn more about the math behind universality and how to spot it in the real world, check out the video below.

[h/t Quanta Magazine]

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

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Common Misconceptions About Dreams

If your nightmares look like Henry Fuseli's The Nightmare (1781), we're so sorry.
If your nightmares look like Henry Fuseli's The Nightmare (1781), we're so sorry.
Henry Fuseli, Detroit Institute of Arts, Wikimedia Commons // Public Domain

Contrary to what Ebenezer Scrooge initially thought in Charles Dickens's A Christmas Carol, nightmares aren’t merely a side effect of eating cheese before bed. In fact, studies have shown that pre-sleep snacks—dairy or otherwise—probably don’t influence your dreams at all. But even if you can’t blame your latest wacky snooze vision on last night’s midnight helping of chicken nuggets, you can try to trace it back to some stressor from your daily life.

Since dream interpretation isn’t an exact science—and sleep in general is one of science’s murkier territories—quite a few myths have arisen about what, why, and how we dream. In this episode of Misconceptions, Mental Floss's own Justin Dodd walks us through some of the more common fallacies about dreams. (And if you’re convinced you never dream, well, he has some news for you on that front, too.)

For more videos like this one, subscribe to the Mental Floss YouTube channel here.