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The Golden Ratio: Design’s Biggest Myth

21 Thursday May 2015

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architecture, arts, Barcelona Museum of Contemporary Art, ChatresCathedral, DeDivinaProportione, Euclid's, Fuseproject, GoldenRatio, iPad, LeCorbusier, LucaPacioli, Michelangelo, Modulorsystem, MonaLisa, Mozart, RichardMeier, SalvadorDalí, Seurat, StanfordUniversity, Stonehenge, The Parthenon, TheSacramentoftheLastSupper, UniversityofArkansas

THE GOLDEN RATIO IS TOTAL NONSENSE IN DESIGN. HERE’S WHY.

In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Greats like Le Corbusier and Salvador Dalí have used the number in their work. The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple logo are all said to incorporate it.

The golden ratio’s aesthetic bona fides are an urban legend, a myth, a design unicorn. Many designers don’t use it, and if they do, they vastly discount its importance. There’s also no science to really back it up. Those who believe the golden ratio is the hidden math behind beauty are falling for a 150-year-old scam.

Flickr user Sébastien Bertrand

What is the Golden Ratio?

First described in Euclid’s Elements 2,300 years ago, the established definition is this: two objects are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The value this works out to is usually written as 1.6180. The most famous application of the golden ratio is the so-called golden rectangle, which can be split into a perfect square, and a smaller rectangle that has the same aspect ratio as the rectangle it was cut away from. You can apply this theory to a larger number of objects by similarly splitting them down.

THE GOLDEN RATIO IS ALWAYS GOING TO BE A LITTLE OFF.

In plain English: if you have two objects (or a single object that can be split into two objects, like the golden rectangle), and if, after you do the math above, you get the number 1.6180, it’s usually accepted that those two objects fall within the golden ratio. Except there’s a problem. When you do the math, the golden ratio doesn’t come out to 1.6180. It comes out to 1.6180339887… And the decimal points go on forever.

“Strictly speaking, it’s impossible for anything in the real-world to fall into the golden ratio, because it’s an irrational number,” says Keith Devlin, a professor of mathematics at Stanford University. You can get close with more standard aspect ratios. The iPad’s 3:2 display, or the 16:9 display on your HDTV all “float around it,” Devlin says. But the golden ratio is like pi. Just as it’s impossible to find a perfect circle in the real world, the golden ratio cannot strictly be applied to any real world object. It’s always going to be a little off.

The Golden Ratio As Mozart Effect

It’s pedantic, sure. Isn’t 1.6180 close enough? Yes, it probably would be, if there were anything to scientifically support the notion that the golden ratio had any bearing on why we find certain objects like the Parthenon or the Mona Lisa aesthetically pleasing.

But there isn’t. Devlin says the idea that the golden ratio has any relationship to aesthetics at all comes primarily from two people, one of whom was misquoted, and the other of whom was just making shit up.

The first guy was Luca Pacioli, a Franciscan friar who wrote a book called De Divina Proportione back in 1509, which was named after the golden ratio. Weirdly, in his book, Pacioli didn’t argue for a golden ratio-based theory of aesthetics as it should be applied to art, architecture, and design: he instead espoused the Vitruvian system of rational proportions, after the first-century Roman architect, Vitruvius. The golden ratio view was misattributed to Pacioli in 1799, according to Mario Livio, the guy who literally wrote the book on the golden ratio. But Pacioli was close friends with Leonardo da Vinci, whose works enjoyed a huge resurgence in popularity in the 19th century. Since Da Vinci illustrated De Divina Proportione, it was soon being said that Da Vinci himself used the golden ratio as the secret math behind his exquisitely beautiful paintings.

One guy who believed this was Adolf Zeising. “He’s the guy you really want to burn at the stake for the reputation of the golden ratio,” Devlin laughs. Zeising was a German psychologist who argued that the golden ratio was a universal law that described “beauty and completeness in the realms of both nature and art… which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical.”

He was a long-winded guy. The only problem with Zeising was he saw patterns where none exist. For example, Zeising argued that the golden ratio could be applied to the human body by taking the height from a person’s navel to his toes, then dividing it by the person’s total height. These are just arbitrary body parts, crammed into a formula, Devlin says: “When measuring anything as complex as the human body, it’s easy to come up with examples of ratios that are very near to 1.6.”

IN MY OWN WORK, I CAN’T EVER RECALL USING THE GOLDEN RATIO.

But it didn’t matter if it was made up or not. Zeising’s theories became extremely popular, “the 19th-century equivalent of the Mozart Effect,” according to Devlin, referring to the belief that listening to classical music improves your intelligence. And it never really went away. In the 20th century, the famous Swiss-French architect Le Corbusier based his Modulor system of anthropometric proportions on the golden ratio. Dalí painted his masterpiece The Sacrament of the Last Supper on a canvas shaped like a golden rectangle. Meanwhile, art historians started combing back through the great designs of history, trying to retroactively apply the golden ratio to Stonehenge, Rembrandt, the Chatres Cathedral, and Seurat. The link between the golden ratio and beauty has been a canard of the world of art, architecture, and design ever since.

Ian Yen via Yanko Design

You Don’t Really Prefer The Golden Ratio

In the real world, people don’t necessarily prefer the golden ratio.

Devlin tells me that, as part of an ongoing, unpublished exercise at Stanford, he has worked with the university’s psychology department to ask hundreds of students over the years what their favorite rectangle is. He shows the students collections of rectangles, then asks them pick out their favorite one. If there were any truth behind the idea that the golden ratio is key to beautiful aesthetics, the students would pick out the rectangle closest to a golden rectangle. But they don’t. They pick seemingly at random. And if you ask them to repeat the exercise, they pick different rectangles. “It’s a very useful way to show new psychology students the complexity of human perception,” Devlin says. And it doesn’t show that the golden ratio is more aesthetically pleasing to people at all.

Devlin’s experiments aren’t the only ones to show people don’t prefer the golden ratio. A study from the Haas School of Business at Berkeleyfound that, on average, consumers prefer rectangles that are in the range of 1.414 and 1.732. The range contains the golden rectangle, but its exact dimensions are not the clear favourite.

Many of Today’s Designers Don’t Think It’s Useful

The designers we spoke to about the golden ratio don’t actually find it to be very useful, anyway.

Richard Meier, the legendary architect behind the Getty Center and the Barcelona Museum of Contemporary Art, admits that when he first started his career, he had an architect’s triangle made that matched the golden ratio, but he had never once designed his buildings keeping the golden ratio in mind. “There are so many other numbers and formulas that are more important when designing a building,” he tells me by phone, referring to formulas that can calculate the maximum size certain spaces can be, or ones that can determine structural load.

THERE ARE SO MANY OTHER NUMBERS AND FORMULAS THAT ARE MORE IMPORTANT WHEN DESIGNING A BUILDING.

Alisa Andrasek, the designer behind Biothing, an online repository of computational designs, agrees. “In my own work, I can’t ever recall using the golden ratio,” Andrasek writes in an email. “I can imagine embedding the golden ratio into different systems as additional ‘spice,’ but I can hardly imagine it driving the whole design as it did historically… it is way too simplistic.”

Giorgia Lupi of Accurat, the Italian design and innovation firm, says that, at best, the golden ratio is as important to designers as any other compositional rule, such as the rule of thirds: maybe a fine rule-of-thumb, but one that good designers will feel free to reject. “I don’t really know, in practice, how many designers deliberately employ the golden ratio,” she writes. “I personally have never worked with it our used it in my projects.”

Of the designers we spoke to, industrial designer Yves Béhar of Fuseproject is perhaps kindest to the golden ratio. “I sometimes look at the golden ratio as I observe proportions of the products and graphics we create, but it’s more informational than dogmatic,” he tells me. Even then, he never sets out to design something with the golden ratio in mind. “It’s important as a tool, but not a rule.”

Even designers who are also mathematicians are skeptical of the golden ratio’s use in design. Edmund Harriss is a clinical assistant professor in the University of Arkansas’ mathematics department who uses many formulas to help generate new works of art. But Harriss says that the golden ratio is, at best, just one of many tools at a mathematically inclined designer’s fingertips. “It is a simple number in many ways, and as a result it does turn up in a wide variety of places…” Harriss tells me by email. “[But] it is certainly not the universal formula behind aesthetic beauty.”

The Sacrament of the Last Supper, 1955, Salvador Dali

Why Does The Myth Persist?

If the golden ratio’s aesthetic merit is so flimsy, then why does the myth persist?

Devlin says it’s simple. “We’re creatures who are genetically programmed to see patterns and to seek meaning,” he says. It’s not in our DNA to be comfortable with arbitrary things like aesthetics, so we try to back them up with our often limited grasp of math. But most people don’t really understand math, or how even a simple formula like the golden ratio applies to complex system, so we can’t error-check ourselves. “People think they see the golden ratio around them, in the natural world and the objects they love, but they can’t actually substantiate it,” Devlin tells me. “They are victims to their natural desire to find meaning in the pattern of the universe, without the math skills to tell them that the patterns they think they see are illusory.” If you see the golden ratio in your favorite designs, you’re probably seeing things.

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09 Thursday May 2013

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23 Tuesday Oct 2012

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Landmark Houses: John Lautner’s Chemosphere

21 Saturday Apr 2012

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architecture, celebrity home, Chemosphere, la homes, LA Interior design, los angeles architecture, los angeles interior design

By Scott Timberg, Los Angeles Times Staff Writer

When Benedikt Taschen, a globe-trotting publisher of stylish art books, and his then-wife first laid eyes on Chemosphere in 1997, the iconic Los Angeles house had seen better days.

The sleek, octagonal design, arguably the boldest work by the singular architect John Lautner, is considered a masterpiece of California Modernism and is beloved by cultists of midcentury design.

But the Taschens saw dirty, disco-era, wall-to-wall carpet on much of its 2,200 square feet, an old aluminum door, smudged windows and seven layers of paint on what was originally a gently austere, exposed brick wall.

Still, “it was love at first sight,” says the laconic German, wearing a red Muhammad Ali bathrobe as he shows off the place on a hazy morning. The backlist of Taschen’s company — from homoerotic nudes to the original Lutheran Bible — includes books on Modernist homes, the architectural photographs of Julius Shulman, the works of Richard Neutra and the Case Study houses. Some of the titles, along with dozens of art magazines, are scattered around the house and its unobtrusive furniture.

Today, the place is serene and airy, with a simple, light-wood openness that suggests midcentury Scandinavian crossed with a ski chalet, and views that are pure Southern California.

“I bought it right away — as fast as possible,” says Taschen.

Frank Escher, who was brought in as restoration architect, vividly remembers the place’s condition.

“I have to give Benedikt credit for seeing past the disrepair and sad state the house had fallen into,” he says. “It looked like a rundown motel. It had been rented out for 10 to 12 years; it was like the ultimate party house.”

In fact, during much of that decade, the place had been on the market. “It was for sale for so long,” says Taschen, “that it was even in a ‘Simpsons’ episode: a house with a for-sale sign.”

“There was no market for that house,” says Julie Jones, the Realtor in the sale, who had watched the place languish after she listed the house. “Everybody loved Spanish, and then shabby chic came in.” Midcentury houses “would sit and sit and sit — you couldn’t give ’em away. People would want to see the view, and that was about it.”

The fate seemed unjust for a structure the Encyclopedia Britannica had judged “the most modern home built in the world,” and which had appeared in Brian De Palma’s “Body Double.” It’s hard not to see the house, which sits on a 29-foot-high, 5-foot-wide concrete column over a long-considered-unbuildable Hollywood Hills site, as a hovering flying saucer or a prototype for the 23rd century architecture of “The Jetsons.”

But the 1960 house is very much a work of its time and place.

Alan Hess, an architectural historian and author of “The Architecture of John Lautner,” considers Chemosphere as perfect an expression of Southland culture as Greene & Greene’s Gamble House, Charles and Ray Eames’ Case Study house and the finest work of Neutra and R.M. Schindler.

Chemosphere was characteristically Los Angeles of that time because “it didn’t have to look like a house,” says Hess. “It was an architecture newly defined. It could take on its own brand-new shape. It displays the optimism of its time: that technology can be used to solve any problem, just as Century City and Googie’s,” the Lautner-designed Sunset Boulevard coffee shop, did. “The West would not be possible without technology: Water, electricity, everything that it took to overcome dryness and distance was dependent in some form on technology.”

Hess finds the house fascinating partly because it was built for a couple and their four children. “And yet whenever that house is used in the movies, it’s always a decadent bachelor pad,” Hess says. “You have the reality of Southern California life, and the image of Southern California life, summed up in one house.”

It’s not the only contradiction the place contains.

“From the outside it looks like a spaceship which you cannot enter,” Angelika Taschen says from Berlin, where she now lives. (The couple were finalizing a divorce at the time of this article’s publication.) “But if you go inside, it feels very cozy … very Zen and calming. Maybe because you are floating above the city, above reality in the sky. You feel disconnected from the planet and completely free and happy.”

The house is the product of a fortuitous union of architect, client, time and place. Leonard Malin was a young aerospace engineer in late-1950s L.A. whose father-in-law had just given him a plot north of Mulholland Drive, near Laurel Canyon. The land was leafy and overgrown, with extravagant views of the San Fernando Valley.

“My philosophy at the time was, most people work their whole lives to build their dream house,” Malin says from Arizona, where he’s constructing a new home. “Why not build it now, and pay for it for the rest of my life?” This was a time, during L.A.’s postwar expansion, when a middle-class client could build in the Hollywood Hills on a modest budget: Malin had $30,000 to spare.

The only catch: At roughly 45 degrees, the slope was all but unbuildable. The plot may have remained empty had Malin not approached Lautner, whose work he knew from a nearby house. Lautner, a brilliant but reputedly prickly man, sketched a bold vertical line, a cross, and a curve above it. “Draw it up,” he told his assistant Guy Zebert.

Though Lautner could appear imperious, a quality he may have learned from his mentor Frank Lloyd Wright, he was also a deeply practical and hard-headed problem-solver. Lautner didn’t see the house as a flying saucer but as a sensible solution.

However counterintuitive the scheme, it was also one of very few imaginable that allowed the plot to be utilized. And because of a concrete pedestal, almost 20 feet in diameter, buried under the earth and supporting the post, the house has survived earthquakes and heavy rains. (The house is reached by a funicular.)

“What was great about Lautner,” Benedikt Taschen says, “is that he had this dualism about nature and the city.” He says the home’s northern edge, which contains the bedroom and his office, is very quiet. “It’s pure nature, with all kinds of animals: skunks, bobcats, coyotes, deer. They are not shy; you almost have nose prints on the window.

“And here,” Taschen says, walking toward the living room window that faces the Valley’s homes and skyscrapers along the 101 Freeway, “it’s all city.”

Taschen admires the bold dichotomies the architect worked with. “That’s the characteristic of great artists: They can make things simple.”

Hess points out that Lautner’s embrace of Modernist innovation and organic forms made him a more interesting architect but also contributed to his obscurity during much of his career. During the 1950s and ’60s, the starker, cooler Modernism of the Bauhaus and of Ludwig Mies van der Rohe reigned in intellectual circles, especially in Europe and on the East Coast.

“Organic Modernism was just as modern in its use of materials,” Hess says, “but it had a different sense of space, which was flowing. The way a building was put together was like a tree or a flower or a cave — natural forms. Wright was one of the founders of that approach to Modernism, and Lautner brought it to Southern California.”

Even out-of-state critics and scholars who could appreciate the sharply angular California Modernism of midcentury didn’t know what to make of Lautner’s merging of the modern with natural forms. “So they ignored him,” says Hess, “or put him in the category of undisciplined, far-out, do-whatever-you-want California architecture.”

Escher, the preservation architect, considers Lautner “the missing link between the classic Modernism of the Case Study Houses and the work we now associate with Los Angeles — the more expressive, more sculptural forms. Frank Gehry has said that as a student, he considered Lautner to be a god.”

Unlike a lot of the more didactic and theory-driven homes of Modernists from Le Corbusier to Philip Johnson, it’s actually pleasant, most of the time, to live inside a Lautner. The homes don’t force their inhabitants into an ant farm’s existence the way some houses do. Le Corbusier called his homes “machines for living in,” and sometimes they felt that way, with their narrow hallways and rigidly prescribed paths.

Chemosphere is bisected by a central, exposed brick wall with a fireplace, abutted by subdued seating, in the middle. One side of the house is public, with a small kitchen and blended living and dining rooms including built-in couches below glass windows. The house’s private half includes a master bedroom with bathroom, small storage and laundry rooms, an office made of two children’s bedrooms, and an additional bathroom. Despite being more compact than many new single-family houses, it has most of the essential elements.

Angelika Taschen, a PhD in art history, knew the house from Shulman’s photos before she saw the real thing. She worried it might be difficult to live there.

She said that besides limiting her trips out of the house because of the funicular, living there didn’t alter her behavior. “Day-to-day life is really easy,” she says, often easier “than in a conventional home where the architect has not thought so much about every single detail.”

Lautner, despite his reputation as having a strong personality, worked hard to suit his clients and their inner lives.

Angelika describes the place as having a spiritual impact, almost like a church. “With this house he found and expressed this almost religious spirit with a perfect architectural language in general, but also in detail.”

Benedikt likens the house to an eagle’s nest. “You feel safe. It’s warm and human, not a cold place. You would not expect it from outside.”

The only consistent problem with the house, Taschen says, is that its technology often fails in subtle but frustrating ways. “Every day there is something not working,” he says. “The maintenance is 10 times higher than in any other building. Everything is much more complicated. To get cable or Internet, they have to come 10 times.

“It’s like having a vintage car — a ’55 Mercedes. More difficult. But they have a personality to them, ya?”

In Escher’s first meeting with Taschen, the restoration architect pointed out which pieces were original, which needed to be replaced, and which details deserved restoration. “He interrupted me in about half a minute and said in German, ‘Herr Escher, why don’t you do what you think is right?'”

For Escher, a native of Switzerland who loves the rational, structure-inspired work of Lautner, Neutra and the late Pierre Koenig, this was a gift from the gods. His firm, which he runs with partner Ravi GuneWardena, had been partly inspired by classic California Modernism, and here he could delve into a great Modernist’s original conception. (Escher wrote the first book on Lautner a few years after moving to Los Angeles in 1988, and oversees the John Lautner Archives.)

The architect describes the job as a philosophical challenge.

“I think the hardest thing was developing an intellectual strategy for how to deal with it,” Escher says, calling the task, “a combination of research into history and technology, and to some degree into Lautner’s psychology. You can’t be afraid of a house like that: You have to, in some cases, be kind of forceful.”

The forcefulness was balanced with the architects’ own “sensitive and careful” respect for Lautner’s intentions: The goal was to undo the damage previous tenants had exacted, and to simplify. The restoration team removed layers of paint, paneled the walls with the same shade of ash wood used for the original built-in couches and cabinets (some of which needed repair or restoration), and replaced the fixed-paneled windows with frameless glass.

“We wanted to make it as invisible and elegant as possible,” says Escher. “That’s something that’s important to all our projects: We don’t try to draw attention to a detail. It should disappear.” GuneWardena compares the process to “pruning a garden, to reveal the clarity of the structure.”

They also tried to match what they thought Lautner would have chosen if he’d had access to contemporary workmanship and a larger budget: The original drawings, for instance, described a floor of random broken slate, but the day’s technology would not allow the stone to be cut thinly enough to keep from destabilizing the house. Escher’s restoration ran the flagstone pattern inside and out, across the bridge that connects the front door to the funicular.

One of the biggest challenges was bringing art into the house, difficult when a home already exerts a bold personality.

“The Taschens originally wanted to have more period pieces,” Escher says. “But we didn’t want the house to be a museum of the 1960s.”

Today, Chemosphere is furnished sparely with clean-lined pieces including Eames chairs and a coffee table and an oval Florence Knoll dining room table. Taschen commissioned the suspended lamps of bent plexiglass strips by Cuban-born L.A. artist Jorge Pardo and the pastiche rug designed by German painter Albert Oehlen.

“These Lautner houses are like custom-made clothes,” Escher says, “so you really have to find the right tenant for them. Taschen was perfect for the house — he immediately grasped what the house was about, and he was entirely open to our ideas for the place, like ripping out the glass and commissioning pieces by artists.”

During the first few years the Taschens lived there, the house became locally famous for their parties, where photographer Bill Claxton and his model wife Peggy Moffett would carouse with porn stars, jazz musicians and director Billy Wilder.

These days, now that Taschen has an office in Hollywood and a bookstore in Beverly Hills, the place has reverted to being, mostly, a house for him and fiancee Lauren Wiener. He canceled plans for a guesthouse designed by Rem Koolhaas at Chemosphere’s base because he feared it would visually compete with the main house. His only major plan is to replace the bird-cage-like funicular with a more open one.

Taschen remembers going to a Beverly Hills open house where “a fashionable Hollywood film star” was selling his Neutra home. The young actor, in the publisher’s estimate, “had robbed the soul of the house. If you make tiny changes that don’t fit the integrity of the house, you destroy it. It’s like a movie where you add a scene of someone with a mobile phone in 1958, or a style of shirt or car that wouldn’t have existed until years later.

“It’s the responsibility of the owner to preserve it for future generations,” Taschen says, “because a house like this doesn’t belong to one or two people: It belongs to mankind.”

The Chemosphere restoration won an award from the Los Angeles Conservancy as well as the approval of its original tenant.

“Today there are materials that weren’t available then,” Malin says. “The place is much better than when I was in there — and it’s in keeping with Lautner’s vision.”

Taschen says it’s hard to get bored with the place — despite the rain this winter — since the enormous windows offer an expansive view on the world. “It’s like a wide-screen movie,” he says. “Always changing.”

home@latimes.com

This article is adapted from a piece that originally was published in The Times’ Home section on April 14, 2005.

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