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Sunday, July 17, 2011

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A new world: The AuthaGraph map projection of the Earth developed by Tokyo-based architect-cum-artist Hajime Narukawa. By accurately representing all the areas of land and sea, Narukawa's projection corrects those distortions in the 1569 Mercator projection (bottom of the story), which remains the standard view we have of the world to this day. © AUTHAGRAPH CO. LTD.

WEEK 3

The world according to AuthaGraph


Staff writer

In today's wired world, it's easy to learn about issues anywhere that might affect us or be of interest. So news of a disaster, for example, can be instantly transmitted, shared and discussed by people wherever they might be.

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Hajime Narukawa SATOKO KAWASAKI PHOTO

In this global village, though, few people seem to question the image of the physical world that they have in their heads — most commonly, a world map that uses the Mercator projection.

Named after geographer Gerardus Mercator, who was from a part of Flanders in present-day Belgium, the two-dimensional view of the world he revealed in 1569 has been the dominant image people have had of the planet ever since.

Hajime Narukawa, however, may change that.

The Tokyo-based architect-cum-artist says he has created a new world map which, while employing the same rectangular shape as Mercator's projection, succeeds in showing the world's physical components — its continents and seas, etc. — scaled as accurately as is possible.

Indeed, no less than the former astronaut Mamoru Mohri, who is currently CEO of the Tokyo-based National Museum of Emerging Science and Innovation (Miraikan), was so impressed by Narukawa's work — the AuthaGraph — that he incorporated it into the museum's interactive data-visualization project that kicked off in June.

Narukawa, 40, took his first steps on the road to accurately redrawing the map of the world nearly 20 years ago at the Shibaura Institute of Technology in Tokyo, where his interest in geometry led to him studying the so-called geodesic dome structures developed by U.S. engineer, designer and inventor Buckminster Fuller (1895-1983).

"He expressed a completely different view of the world through his architecture," Narukawa said during a recent interview with The Japan Times at his office in Tokyo — pointing to an architecture textbook with a picture of Fuller's famous "Biosphere," a dome structure made of numerous steel and acrylic triangular cells that was the U.S. pavilion at the 1967 World Expo in Montreal, Canada.

"He envisioned a whole new world, and came up with concrete projects to realize his ideal," Narukawa said with admiration.

It so happened that Fuller, whose architecture and whose quest for an alternative lifestyle helped inspire the hippie movement of the 1960s, also created an alternative to the conventional Mercator-projection map that he named the Dymaxion map. Featuring jagged edges, this map is rendered on a cut-out version of an icosahedron — a regular polyhedron with 20 identical triangular faces.

In inventing his Dymaxion map, Fuller aimed to solve the fundamental flaw in Mercator's projection: its great distortions of area ratios — distortions that grow worse toward the North and South poles.

Since it was conceived by Mercator as an opened-up cylinder, the projection has the lines of latitude (including the Equator) and longitude all invariably crossing at right angles — and with all the lines of latitude the same length, despite the fact that they actually get progressively shorter in both directions poleward from the Equator.

However, by mapping the world in this way on a rectangular sheet, Mercator made it possible for sailors or explorers on land to draw straight lines between places, measure the angle and then follow the bearing using a compass.

So in no small measure, it was Mercator's faulty projection that allowed those from countries with the will and means to travel long distances to reach out to the four corners of the world, whether for the purpose of conquest or trade, or both.

However, as Narukawa pointed out, those distortions in area that get worse on Mercator's map the closer to the poles you look, end up showing places such as Greenland and Antarctica much larger than their true size. The map is also unable to help us visualize such phenomena as the depletion of the ozone layer, which is most marked right above the South Pole.

The Dymaxion map tried to address such concerns, and it manages to project relative sizes and shapes of areas much more accurately. But its biggest drawback is its irregular shape that, among other things, breaks up ocean areas. Consequently, ocean currents, which are crucial in the study of climate change and marine ecology, for instance, cannot be adequately illustrated.

This is where Narukawa's map comes in. In fact, prior to creating a map, Narukawa, greatly inspired by Fuller, had long studied how he could image our three-dimensional world on a two-dimensional surface with as little distortion as possible. That was when he was pursuing his graduate degree in the late 1990s at the Berlage Institute in the Netherlands.

At that time, Narukawa even published a paper about pictures he took with a special distortion-reducing camera he had made himself. This comprised a black box with two tiny holes facing each other on two opposite sides that he kept covered until he wanted to take a picture. Inside the box, he positioned photographic paper folded into the shape of an icosahedron that was split into two halves.

When he shot pictures of a landscape, the images captured on the inner surfaces of the angled planes of the icosahedron were of things it wasn't possible to see simultaneously in an image taken through a regular lens. There were far wider angles, for instance, than could be shot using any wide-angle lens — and they were distortion-free, too. But when you unfold the photographic paper, its edges are still ragged and it doesn't make a rectangle.

Narukawa's breakthrough came, though, in the fall of 1999. While fiddling with the plastic, tetrahedron-shaped wrapping of a plum-flavored candy, he suddenly remembered his childhood experience of toying with a Tetra Pak milk carton after a school lunch.

"I used to play by breathing air into the emptied tetrahedral package and then stamping on it with my feet. I used to think, 'Hmm. When it's flattened, (the milk package) becomes a rectangle.' "

Yet it still took Narukawa more time to decide how to change a spherical surface into a tetrahedral shape, which he said was a bigger challenge. He eventually came up with the idea, he said, of dividing the spherical surface into 96 regions and turning it into an inflated tetrahedron first, and then distorting it again into a regular tetrahedron — which, when it's cut out, makes a rectangle that maintains land ratios and land shapes similar to those in the spherical surface. Using 3-D modeling software, he said he simulated the distortion process countless times on the way to creating his AuthaGraph map.

He also explained how his map can be "tiled," or tessellated, so that various different world maps can be created. Hence by cutting out different parts of the tessellated AuthaGraph images, you can create a map featuring anywhere in the world at its center. This way, the world will be free from existing perceptions such as "Far East" or "Western," Narukawa said. He also noted that his map will be mentioned in an upcoming high school geography textbook in Japan.

But Narukawa is also realistic, saying that the AuthaGraph will not gain currency overnight. That is because, he said, people are so used to the Mercator projection that, despite its disadvantages and inconveniences, "It will be difficult to change what people are so accustomed to."

"For example, there is a theory about how the most popular modern typewriter keyboard layout — known as QWERTY — was created to be intentionally inconvenient. That was because with a previous layout of the keys, typists were getting so fast that they would often break the machines — so the layout was changed to slow them down. The same keyboard has survived to this day. I think maps are like that, too."

So Narukawa is not expecting to cash in on his invention anytime soon. He does, however, still dream about putting a new camera on the market that would allow people to shoot much more wide-angled pictures. "I would like to capture an image from right above our head and on the ground — at the same time," he said.

For more on the AuthaGraph map, visit www.authagraph.com

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