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Space seen as shaped like a soccer ball

Scientists have kicked around many possibilities for the shape of the cosmos. Now one group says it is set up something like the surface of a soccer ball, with cosmic patches stitched together.
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Scientists have kicked around many possibilities for the shape of the cosmos and whether or not it has a boundary. Now one group says the big house is set up something like the surface of a soccer ball, with cosmic patches stitched together to form a decidedly finite universe.

THE STRUCTURE can also be likened to a funhouse of perplexing mirrors generating multiple images of one reality.

But the new theoretical conjuring is no joke. It’s based on real-world observations of radiation leftover from the Big Bang, data that do not fit the current leading view of an infinite universe.

The strange geometry has been suggested before. What’s new is how neatly it fits with the latest data. After some two millennia of speculation, the scientists involved in the work say, observations may be on the verge of determining whether the universe is infinite or finite.

An infinite or open universe would result from an infinite amount of matter. A finite amount of matter would generate a finite, or closed universe.


The new idea involves blocks of space “with opposite faces abstractly glued together,” the researchers write in the Oct. 9 issue of the journal Nature. An object sliding off an edge of one block will instantly slide into view at the edge of its opposing block.

In a telephone interview, researcher Jeff Weeks, a freelance mathematician and co-author of the Nature paper, explained the geometry.

Imagine a sheet of paper with the left and right edges rolled toward one another to make a cylinder, Weeks suggests. Suppose you could shrink and stand on the paper. Start at the seam and walk west in a straight line.

“Nothing funny happens along the way.” Weeks says. “Then lo-and-behold you’re back at the starting point and surprised to be there.”

Now if you could roll the sheet of paper in two directions — without the inevitable crumpling — so that things moving off the top would appear at the bottom, then you’d have created a universe much like the one Weeks and his colleagues imagine.

The real universe is more complex than a sheet of paper, of course.

The new study, led by Jean-Pierre Luminet of the Paris Observatory, suggests the universe is a dodecahedron — a complex pattern of 12 pentagonal shapes — with opposite faces connected up in pairs, like the opposite edges of the sheet of paper described above. A traveler exiting the dodecahedron through any face returns from the opposite face.

The dodecahedron is geometrically tweaked so that it makes a spherical universe — one that can be likened to the look of a soccer ball.


If the theory is right — and the researchers say more work is needed to bear it out — then light should experience the same travel patterns as you did while walking around the paper cylinder. That would mean astronomers should be able to find multiple images of a single object in space. Weeks thinks of it this way: On the paper cylinder, a person could look east and west and, in both directions, see light coming from a single object that’s on the far side of the cylinder.

The concept has implications for space travel, or at least for pondering its potential extremes.

“Hypothetically speaking, if you head off into space you can travel in a straight line and come back to the starting point,” Weeks said. “But it would take a long time.”

This latest twist on decades-old theory arose from observed density fluctuations in cosmic microwave background (CMB) radiation, a leftover of the early days of the universe. The density fluctuations are in essence the vibrational overtones of space, the researchers say. Just as the vibrations of a bell can’t exceed the size of the bell, the density fluctuations of space can’t be larger than space itself.

But measurements of the CMB, provided recently by NASA’s WMAP probe, do not match up with expectations set by cosmology’s leading model, which maintains the universe is geometrically flat, but infinite. Some fudge factors are needed to reconcile theory with what’s been observed.


The dodecahedral model explains the observations with no fudging required, says George Ellis, a mathematician at the University of Cape Town in South Africa. For anyone who is bewildered by the idea of infinite space, the new model could prove slightly comforting. It suggests we live in a relatively small, closed universe, Ellis writes in an accompanying analysis for Nature.

“This topology, unlike many others, is supported by” the WMAP data, says Ellis, who was not involved in the study.

If the universe is closed, though, then what is beyond the universe? Weeks took his best shot at answering this confounding question:

“The universe is finite,” he said, “but there’s no boundary to it,” implying that there is no beyond, or that if there is, then its nature is left to your imagination and is outside the closed system that astronomers can ever hope to see.

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