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]

Take Advantage of Amazon's Early Black Friday Deals on Tech, Kitchen Appliances, and More

Amazon
Amazon

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

Even though Black Friday is still a few days away, Amazon is offering early deals on kitchen appliances, tech, video games, and plenty more. We will keep updating this page as sales come in, but for now, here are the best Amazon Black Friday sales to check out.

Kitchen

Instant Pot/Amazon

- Instant Pot Duo Plus 9-in-115 Quart Electric Pressure Cooker; $90 (save $40) 

- Le Creuset Enameled Cast Iron Signature Sauteuse 3.5 Quarts; $180 (save $120)

- KitchenAid KSMSFTA Sifter with Scale Attachment; $95 (save $75) 

- Keurig K-Mini Coffee Maker; $60 (save $20)

- Cuisinart Bread Maker; $88 (save $97)

- Anova Culinary Sous Vide Precision Cooker; $139 (save $60)

- Aicook Juicer Machine; $35 (save $15)

- JoyJolt Double Wall Insulated Espresso Mugs - Set of Two; $14 (save $10) 

- Longzon Silicone Stretch Lids - Set of 14; $13 (save $14)

HadinEEon Milk Frother; $37 (save $33)

Home Appliances

Roomba/Amazon

- iRobot Roomba 675 Robot Vacuum with Wi-Fi Connectivity; $179 (save $101)

- Fairywill Electric Toothbrush with Four Brush Heads; $19 (save $9)

- ASAKUKI 500ml Premium Essential Oil Diffuser; $22 (save $4)

- Facebook Portal Smart Video Calling 10 inch Touch Screen Display with Alexa; $129 (save $50)

- Bissell air320 Smart Air Purifier with HEPA and Carbon Filters; $280 (save $50)

Oscillating Quiet Cooling Fan Tower; $59 (save $31) 

TaoTronics PTC 1500W Fast Quiet Heating Ceramic Tower; $55 (save $10)

Vitamix 068051 FoodCycler 2 Liter Capacity; $300 (save $100)

AmazonBasics 8-Sheet Home Office Shredder; $33 (save $7)

Ring Video Doorbell; $70 (save $30) 

Video games

Nintendo

- Legend of Zelda Link's Awakening for Nintendo Switch; $40 (save $20)

- Marvel's Spider-Man: Game of The Year Edition for PlayStation 4; $20 (save $20)

- Marvel's Avengers; $27 (save $33)

- Minecraft Dungeons Hero Edition for Nintendo Switch; $20 (save $10)

- The Last of Us Part II for PlayStation 4; $30 (save $30)

- LEGO Harry Potter: Collection; $15 (save $15)

- Ghost of Tsushima; $40 (save $20)

BioShock: The Collection; $20 (save $30)

The Sims 4; $20 (save $20)

God of War for PlayStation 4; $10 (save $10)

Days Gone for PlayStation 4; $20 (save $6)

Luigi's Mansion 3 for Nintendo Switch; $40 (save $20)

Computers and tablets

Microsoft/Amazon

- Apple MacBook Air 13 inches with 256 GB; $899 (save $100)

- New Apple MacBook Pro 16 inches with 512 GB; $2149 (save $250) 

- Samsung Chromebook 4 Chrome OS 11.6 inches with 32 GB; $210 (save $20) 

- Microsoft Surface Laptop 3 with 13.5 inch Touch-Screen; $1200 (save $400)

- Lenovo ThinkPad T490 Laptop; $889 (save $111)

- Amazon Fire HD 10 Tablet (64GB); $120 (save $70)

- Amazon Fire HD 10 Kids Edition Tablet (32 GB); $130 (save $70)

- Samsung Galaxy Tab A 8 inches with 32 GB; $100 (save $50)

Apple iPad Mini (64 GB); $379 (save $20)

- Apple iMac 27 inches with 256 GB; $1649 (save $150)

- Vankyo MatrixPad S2 Tablet; $120 (save $10)

Tech, gadgets, and TVs

Apple/Amazon

- Apple Watch Series 3 with GPS; $179 (save $20) 

- SAMSUNG 75-inch Class Crystal 4K Smart TV; $998 (save $200)

- Apple AirPods Pro; $199 (save $50)

- Nixplay 2K Smart Digital Picture Frame 9.7 Inch Silver; $238 (save $92)

- All-New Amazon Echo Dot with Clock and Alexa (4th Gen); $39 (save $21)

- MACTREM LED Ring Light 6" with Tripod Stand; $16 (save $3)

- Anker Soundcore Upgraded Bluetooth Speaker; $22 (save $8)

- Amazon Fire TV Stick with Alexa Voice Remote; $28 (save $12)

Canon EOS M50 Mirrorless Camera with EF-M 15-45mm Lens; $549 (save $100)

DR. J Professional HI-04 Mini Projector; $93 (save $37)

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Miss Blockbuster Video? New Kiosks With Free Movies Are Popping Up Around the Country

Got a VCR? You still might be able to make it a Blockbuster night.
Got a VCR? You still might be able to make it a Blockbuster night.
Pete, Flickr // Public Domain

With just one remaining Blockbuster Video store in the world located in Bend, Oregon, the venerable video rental chain has largely disappeared from sight. Streaming services can queue up thousands of movies, making the ritual of wandering through store aisles virtually obsolete.

For residents in and around Los Angeles, Philadelphia, and other locations, however, grabbing a tangible DVD from a Blockbuster is still an option. Stephanie Farr of The Philadelphia Inquirer reports that a number of small, newspaper-type kiosks (also called newsracks or boxes) have popped up in areas bearing the familiar Blockbuster logo and sporting several movies that people can “borrow” for free.

The kiosks, which are dubbed Free Blockbuster Video, are the work of Brian Morrison, a Los Angeles resident who noticed the empty newspaper kiosks and decided to repurpose them by branding them with the Blockbuster logo and supplying a small inventory of DVDs or VHS cassettes. Others have followed his lead in Oklahoma, Virginia, and elsewhere, using not only movies but books and even popcorn.

People are encouraged to take an item and leave an item. In Richmond, a kiosk recently sported a library containing VHS copies of 1993’s Demolition Man, 1984’s The Terminator, and a box of Skittles.

“There are a lot of abandoned newspaper boxes around L.A.,” Morrison told the Inquirer. “We’re a city that loves movies, and free movie boxes seemed like a great way to rehabilitate commercial blight.”

Morrison’s site, FreeBlockbuster.org, provides artwork for those looking to repurpose the kiosks, which have often been abandoned by area newspapers. Those that are no longer being stocked with papers may be marked for removal by the city, though that depends on local laws.

[h/t The Philadelphia Inquirer]