Quote: construct a consistent, non-Euclidean world as a sphere whose temperature decreases to zero at its surface, and whose lengths are proportional to temperature

Quotation

The Non-Euclidean World. ... [p. 65] Suppose, for example, a world enclosed in a large sphere and subject to the following laws:-The temperature is not uniform; it is greatest at the centre, and gradually decreases as we move towards the circumference of the sphere ... If R be the radius of the sphere, and r the distance of the point considered from the centre, the absolute temperature will be proportional to R^2-r^2. Further, ... the linear dilatation of any body is proportional to its absolute temperature. Finally, I shall assume that a body transported from one point to another of different temperatures is instantaneously in thermal equilibrium with its new environment. There is nothing in these hypotheses either contradictory or unimaginable. A moving object will become smaller and smaller as it approaches the circumference of the sphere. ... to its inhabitants [the world] will appear infinite. ... [p. 68] If they construct a geometry, it will not be like ours   Google-1   Google-2

Published before 1923

Related Topics

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Topic: geometry (33 items)