Thursday, May 27, 2010

Diaspora Chapter 17: Partition of Unity - Greg Egan

"Rotation in a single plane

In Chapter 17 of Diaspora, an artifact is discovered near the “rotational pole” of a star in the 5-dimensional macrosphere; this pole is described as the single 2-sphere on the star's 4-dimensional hypersurface that stays fixed in space as the star rotates.

To see why this is possible (but actually not very likely), first consider the case in 3 dimensions. If a planet in 3 dimensions rotates as a perfectly rigid body, it has a stationary axis running through it which intersects the 2-dimensional surface at two points, the familiar rotational poles. But another way to characterise this motion is by the direction of the plane of the rotation: a slice through the planet along any plane parallel to the equator will reveal the rock to be moving only within that plane. At the centre of each plane the rock won't be moving at all; taken together, all these fixed centres constitute the axis of rotation."

4.5 out of 5

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