Geometric evidence – really?
Peace and blessings. I have seen in some of the rabbi’s letters that the rabbi treats the laws of geometry (between every two points there is one straight line, etc.) as evidential truths – truths that are self-evident to all of us and do not require proof. As far as I know, it is now known that Euclidean geometry, which is based on these axioms, does not accurately describe reality. Shouldn’t we therefore abandon such careless adoption of axioms, or is it better to reject the scientific world that claims that our world is not Euclidean because it contradicts the axioms that are laid down in our minds?
First, if you give up adopting such axioms you will not be able to know anything. Every claim is proven on the basis of axioms and without axioms we have no information at all. Therefore we have no option to give them up. Are you suggesting thinking without axioms? You understand that there is no such thinking at all. What would you rely on? On what you see? This is also a reckless axiom, that our vision is reliable. Moreover, it is really not true, since there are also optical illusions.
Our intuition is an uncertain tool, but we cannot do without it. Therefore, it should be treated with respect and suspicion. What my intuition says is true in my opinion, but I will try to test it and see if it is really so.
Euclidean geometry is self-evident for us, and it is indeed true for Euclidean space. The mistake is in assuming that our world is Euclidean. This is a wrong intuition. But it is important to understand that the deviation from Euclideanity is completely negligible. In other words, this intuition is also correct (except for tiny deviations that are somehow impossible to notice). It is just like the axiom that our vision is reliable, which I mentioned above. There are exceptions, but they are marginal. Overall, this intuition is correct.
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