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Einstein starts by talking about what we have all learned in basic geometry. His point is that we have learned certain facts that we take as self-evident and unchallengeable. He says we are so convinced of these axioms that we "regard everyone with disdain who should pronounce even the most out-of-the-way proposition of this science to be untrue." He follows this with, "But perhaps this feeling of proud certainty would leave you immediately if someone were to ask, 'What, then, do you mean by the assertion that these propositions are true?'"

Geometry describes concepts we can draw on paper "with a rule and compasses " or build in three-dimensional space. Some of the facts we learn are that a point has no dimensions, two points define a line, and three points define a plane. The rest of Euclid's geometry is built upon these axioms. We accept such extensions as true when they are "...derived in the recognized manner from the axioms."

However, our confidence in the truth of the axioms takes us back to the above question. We find that there is no answer and that the question is, in fact, meaningless. We can say that geometry deals with points, lines, and planes. However, geometry deals with these entities and how they relate to each other. It doesn't purport to deal with objects in the real world.

Einstein continues by supplementing Euclidean geometry by proposing that two points on a rigid body always correspond to the same distance independently of any changes in the body's position. Geometry supplemented in this way can be treated as a branch of physics. Applying geometry to real objects, we can legitimately ask the question; we can now ask if the propositions are satisfied by real things. However, the conviction of the truth of geometrical axioms is limited by our incomplete experience with real things.

We can temporarily assume that the axioms of geometry remain true for rigid bodies. But this truth becomes limited upon further examination (revealed in general relativity).

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