Abstract
Riemann has shown that as there are different kinds of lines and surfaces, so there are different kinds of space of three dimensions; and that we can only find out by experience to which of these kinds the space in which we live belongs. In particular, the axioms of plane geometry are true within the limits of experiment on the surface of a sheet of paper, and yet we know that the sheet is really covered with a number of small ridges and furrows, upon which (the total curvature not being zero) these axioms are not true. Similarly, he says although the axioms of solid geometry are true within the limits of experiment for finite portions of our space, yet we have no reason to conclude that they are true for very small portions; and if any help can be got thereby for the explanation of physical phenomena, we may have reason to conclude that they are not true for very small portions of space.
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© 1976 Springer Science+Business Media Dordrecht
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Clifford, W.K. (1976). On the Space-Theory of Matter. In: Čapek, M. (eds) The Concepts of Space and Time. Boston Studies in the Philosophy of Science, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1727-5_50
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DOI: https://doi.org/10.1007/978-94-010-1727-5_50
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-0375-0
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