Reference: Einstein’s 1920 Book
Section I (Part 1)
Physical Meaning of Geometrical Propositions
Please see Section I at the link above.
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Summary
We all believe in the propositions of Euclid’s geometry with total certainty. But what is meant by the assertion that these propositions are true?
If we look closely, we note that geometry is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.
Geometrical ideas correspond to more or less exact objects in nature. This prevents geometry from attaining largest possible logical unity of structure.
When we consider the geometrical points to always correspond to points on a practically rigid body, then the rigidity of measuring instruments, such as, ruler and compass, also becomes significant. We can then treat geometry as a branch of physics.
In this sense, we find that the conviction of the “truth” of the Euclidean propositions is founded exclusively on rather incomplete experience.
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Comments
The axioms and logic used in Euclidean geometry are idealistic rather than realistic. The distances measured in space do not maintain their exactness as geometry supposes them to. Therefore, when we use geometry to calculate distances in space, we are doing that based on incomplete experience.
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Comments
Euclidean geometry has proven to be a very useful set of tools. But it is also a limited and feeble attempt to mathematcally model our surroundings utilizing the limited set of sensors and computational capability with which we have been gifted. By extrapolation, the same limitation applies to even the most advanced forms of mathematical modeling including Einstein’s theories, Hawkin’s theories and beyond. One always ends up at a point prior to death where one must simply choose what to believe, or alternatively admit inability to fully comprehend.
Physical and spiritual are not separate or independent of each other. Math and physics try to concentrate on physical only. That doesn’t give you the full picture.