SIDELIGHTS ON RELATIVITY

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with respect to one another, namely, with parts of the earth,
measuring-lines, measuring-wands, etc. It is clear that the system
of concepts of axiomatic geometry alone cannot make any assertions
as to the relations of real objects of this kind, which we will
call practically-rigid bodies. To be able to make such assertions,
geometry must be stripped of its merely logical-formal character
by the co-ordination of real objects of experience with the empty
conceptual frame-work of axiomatic geometry. To accomplish this,
we need only add the proposition:--Solid bodies are related, with
respect to their possible dispositions, as are bodies in Euclidean
geometry of three dimensions. Then the propositions of Euclid contain
affirmations as to the relations of practically-rigid bodies.

Geometry thus completed is evidently a natural science; we may in
fact regard it as the most ancient branch of physics. Its affirmations
rest essentially on induction from experience, but not on logical
inferences only. We will call this completed geometry "practical