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]

Looking to Downsize? You Can Buy a 5-Room DIY Cabin on Amazon for Less Than $33,000

Five rooms of one's own.
Five rooms of one's own.
Allwood/Amazon

If you’ve already mastered DIY houses for birds and dogs, maybe it’s time you built one for yourself.

As Simplemost reports, there are a number of house kits that you can order on Amazon, and the Allwood Avalon Cabin Kit is one of the quaintest—and, at $32,990, most affordable—options. The 540-square-foot structure has enough space for a kitchen, a bathroom, a bedroom, and a sitting room—and there’s an additional 218-square-foot loft with the potential to be the coziest reading nook of all time.

You can opt for three larger rooms if you're willing to skip the kitchen and bathroom.Allwood/Amazon

The construction process might not be a great idea for someone who’s never picked up a hammer, but you don’t need an architectural degree to tackle it. Step-by-step instructions and all materials are included, so it’s a little like a high-level IKEA project. According to the Amazon listing, it takes two adults about a week to complete. Since the Nordic wood walls are reinforced with steel rods, the house can withstand winds up to 120 mph, and you can pay an extra $1000 to upgrade from double-glass windows and doors to triple-glass for added fortification.

Sadly, the cool ceiling lamp is not included.Allwood/Amazon

Though everything you need for the shell of the house comes in the kit, you will need to purchase whatever goes inside it: toilet, shower, sink, stove, insulation, and all other furnishings. You can also customize the blueprint to fit your own plans for the space; maybe, for example, you’re going to use the house as a small event venue, and you’d rather have two or three large, airy rooms and no kitchen or bedroom.

Intrigued? Find out more here.

[h/t Simplemost]

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13 Inventors Killed By Their Own Inventions

Would you fly in this?
Would you fly in this?

As it turns out, being destroyed by the very thing you create is not only applicable to the sentient machines and laboratory monsters of science fiction.

In this episode of The List Show, Mental Floss editor-in-chief Erin McCarthy takes us on a sometimes tragic, always fascinating journey through the history of invention, highlighting 13 unfortunate innovators whose brilliant schemes brought about their own demise. Along the way, you’ll meet Henry Winstanley, who constructed a lighthouse in the English Channel that was swept out to sea during a storm … with its maker inside. You’ll also hear about stuntman Karel Soucek, who was pushed from the roof of the Houston Astrodome in a custom-designed barrel that landed off-target, fatally injuring its occupant.

And by the end of the episode, you just might be second-guessing your secret plan to quit your day job and become the world’s most daredevilish inventor.

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