Victoria Kalinina / Shutterstock

The Formula That's Supposed to 'Prove Beauty' Is Fundamentally Wrong

Back to the drawing board.

8 JAN 2016

Back in 1855, German psychologist Adolf Zeising published a book with a ridiculously long title called: A New Theory of the proportions of the human body, developed from a basic morphological law which stayed hitherto unknown, and which permeates the whole nature and art, accompanied by a complete summary of the prevailing systems.

The title is wordy and superfluous - enough to elicit a few chuckles - but silly or not, the book effectively launched a craze that has captivated mathematicians, philosophers, artists, filmmakers, and the general public for nearly two centuries. But there's one problem: "He was just some sort of a crank," Keith Devlin, mathematician and executive director of Stanford's Human Sciences and Technologies Advanced Research Institute told Tech Insider. "People make money by writing these things, and he made money and it took off."


Zeising's claim was that the proportions of the human body are based on the golden ratio - also referred to as the Fibonacci sequence - which Zeising says appears the most scientifically "pleasing".

Zeising went on to say that the golden ratio informs ancient Greek and Renaissance architecture, stating that these exact proportions make such structures the most balanced and easy on the eyes.

But Devlin says that the belief that the golden ratio exists outside of the garden is simply that - a belief. "It's like Creationism. You can believe it if you want, but there's no evidence," Devlin says. "If you believe it, you're not being scientific."

Proponents have been trying to prove that the golden ratio is a fundamental characteristic of the universe ever since. And while the golden ratio has been mathematically proven to exist in nature, the allegation that it exists in the human body has little to no scientific validation.

"Many of the people that make these claims actually have businesses," Devlin says. "You can go down to Beverly Hills and you'll find people who will sell you dentistry based on people who will make your teeth the Golden ratio."

So what is the Fibonacci sequence and the Golden ratio anyways? The Fibonacci sequence is a series of numbers where each number is a sum of the two numbers before it.

For example, with the string 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, if you add 0 + 1, you get 1. If you add 1 + 1, you get 2. If you add 1 + 2, you get 3, and so on forever down the sequence.

Another way to describe this is by looking at the ratio the two numbers make. Say you have a line that is divided into two parts, where "a" represents the length of the longer section of the line, and "b" represents the length of the shorter section.

Golden Ratio DiagramWikimedia Commons

A given set of numbers is said to be in a golden ratio if the following occurs: If the two ratios a/b and (a + b)/a both equal 1.618.

For example, Zeising claimed that if you calculate the distance between your bellybutton and your toes, and then divide that by your total height, you get the golden ratio, or 1.6. Zeising also asserted that you could get this same ratio by dividing the height of your face by its width. The claim is that the closer these measurements are to the golden ratio, the more beautiful someone is.

But, as Devlin says, mathematicians haven't found evidence that the golden ratio proves anything, let alone beauty, in the human body.

"Let's put it this way, if someone comes along tomorrow with a scientific explanation for why the golden ratio would play a role in aesthetics and whatever else, then we'd all revise our opinion," Devlin said. "But on the science side, there's no evidence." No evidence, Devlin says, that things conforming to this ratio are more beautiful, or that the ratio exists in the human body at all.

We've known for about twenty-five years, Devlin says, that the golden ratio exists all over the place in the natural world - in things like plant growth (such as the spiral pattern in sunflowers), seed heads, and pine cones. Years of extremely complex mathematical calculations have shown this.

And the reason for its existence comes down to utility. Because plants survive by optimising the amount of sunlight and nutrients they receive, many grow in this perfect pattern. The petals of some flowers, for instance, fan out in a Fibonacci sequence to get the most sunlight. Seeds on flower heads spiral from the center outwards to fill every possible space in proportion to the golden ratio. The sets of pine cone spirals are in accordance with Fibonacci numbers. The examples in nature are aplenty.

If you look at what it takes for the shapes of these things to be optimal in terms of survival and natural selection," Devlin says, "you find that the golden ratio plays a huge role, and that means also that the Fibonacci numbers play a role."

But when you try to apply it to humans, Devlin says, the theory falls flat because there's simply no evidence that we are optimised in the same way that plants are. Humans come in all different shapes and sizes after all.

Not only that, but the ratio appears in pretty much anything you look at.

Golden ratio cactusLaughlin Elkind / Wikimedia Commons

"The golden ratio is 1.6. That's such a common ratio that you can find it everywhere," Devlin says. "Finding the golden ratio [in the human body] tells you nothing. In order to have something meaningful, you need a scientific explanation" for why it's there.

In addition to using this ratio to prove beauty, musicians have tried to claim the golden ratio's significance in the scales of a piano keyboard, artists have argued its foundations in composition and design, and analysts have touted its implications in playing the stock market.

"Unfortunately all of this fun stuff about the art gallery and music and things is just spurious, it's a fairy tale," Devlin said. "You can believe in fairies, you can believe in Santa Claus, and millions of people do, but it doesn't make them true."

While we can find the golden ratio in a ton of places in nature, mathematically proving that it exists anywhere in the universe is extremely hard and involves a ton of complicated calculations. Devlin says that he gets messages from people all the time saying that they have found the golden ratio in the human body, but in his 25 years of studying the golden ratio and the Fibonacci numbers, he has yet to receive a piece of scientific evidence or a mathematical calculation backing up any of these claims.

"It's not that we haven't disproved that the golden ratio explains the human body, it's that we haven't proved it," Devlin says. "I'm not saying any of these things are false, I'm saying that as a scientist, the way they argue it is bullshit. There's just no substantiation for it."

This article was originally published by Business Insider.

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