Sphere-world

The idea of a sphere-world was constructed by Henri Poincaré who, while pursuing his argument for conventionalism (see philosophy of space and time), offered a thought experiment about a sphere with strange properties.

Poincaré asks us to imagine a sphere of radius R. The temperature of the sphere decreases from its maximum at the center to absolute zero at its extremity such that a body’s temperature at a distance r from the center is proportional to ${\displaystyle R^{2}-r^{2}}$.

In addition, all bodies have the same coefficient of dilatation so every body shrinks and expands in similar proportion as they move about the sphere. To finish the story, Poincaré states that the index of refraction will also vary with the distance r, in inverse proportion to ${\displaystyle R^{2}-r^{2}}$.

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