Cosmic Foresight

There exist five Platonic solids of perfect symmetry. Three (the tetrahedron, octahedron and icosahedron) have triangular faces. One (the cube) has square faces. And one (the dodecahedron) has pentagonal (five-sided) faces. Plato believed that the first four solids corresponded to the four elements of which the world was thought to be composed: earth, air, fire, and water. The dodecahedron, however, corresponded to "quintessence" -- the element, according to Plato, of which the heavens were made. "God used this solid for the whole universe," he declared, "embroidering figures on it."

Fittingly, in October 2003, Jean-Pierre Luminet and his colleagues at the Paris Observatory published a paper in the esteemed journal Nature arguing, on the basis of data collected by a satelite called the Wilkinson Microwave Anisotropy Probe (WMAP), that the universe is, in fact, a dodecahedron!

[The Economist explains: "This American satellite has been examining the microwave radiation (Cosmic Microwave Background or Cosmic Background Radiation) generated shortly after the universe began. The wavelength of this radiation is remarkably pure, but like a musical note it has harmonics associated with it. These harmonics, like those of a note, reflect the shape of the object in which the waves were generated. In the case of the note, that object is a musical instrument. In the case of the microwave background, that object is the universe itself.

"The most widely accepted model of the universe suggests that it is both flat and infinite. In this case, flatness does not mean it is two-dimensional, but that the space of which it is composed has no large-scale curves in it. (Small curves induced by gravitational fields, and predicted by the theory of relativity, do exist.) WMAP's data are in close agreement with this model, but that agreement is not perfect. In particular, the second and third harmonics of the microwave radiation are weaker than expected. Dr Luminet's calculations suggest that this weakness can be explained if the universe is finite and dodecahedron-shaped. Of course, things are not quite that simple. Familiar dodecahedrons have an inside and an outside. What Dr Luminet is proposing is actually something called a dodecahedral space, first described by his countryman Jules-Henri Poincar? in the 19th century. Such a space has no boundary, even though it has a finite volume. But it is, quintessentially, a dodecahedron."]

[Plato, who considered mathematical abstractions to be the highest form of human thought, had an inscription placed over the entrance to the Academy in Athens: "Let no one ignorant of mathematics enter here."]

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