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Controversial, I know—but I wonder how deep that connection actually is... 'the points equidistant from a specific point' and 'X^2+Y^2=1' are both description

Controversial, I know—but I wonder how deep that connection actually is... 'the points equidistant from a specific point' and 'X^2+Y^2=1' are both descriptions that we know how to parse and and evaluate into the same thing. Don't get me wrong, I do think it's a super interesting property of the systems of description we formulate that it's possible to talk about the same things with different abstractions (which happens a lot in math: https://en.wikipedia.org/wiki/Duality_(mathematics) https://en.wikipedia.org/wiki/Duality_(mathematics)), even with very high degrees of precision—but I have a hard time seeing how this could be a property of space rather than of human conceptual structure/language.

posterboy 9y ago
The last bit can be said about anything. It might be relevant if the notion is intrinsically motivated by an instinctive search for closed forms. "Space" being emptiness would be isomorphic (dual) to many experiences of limits. In contrast, mystifying the unknown might inspire curiosity at best, reserving free space in the back of the mind, or philosophic arguments at infinitum at worst. The article is somewhere in the middle with its talk around gravitational waves and einsteinian curvature of space, without directly mentioning them.