My default assumption is that it took humans that long to get a clue (or shift a paradigm). We are remarkably bad at creating new thinking patterns. In my area of interest, fundamental physics, there are similar patterns aplenty. It took several decades to get from the first black hole metric to understanding black hole horizons, even though no new math was required. Similarly, it took several decades from EPR to Bell, and the math there was… very elementary. The most glaring example is the Euclid’s Fifth Postulate (about parallel lines): It took some 2000 years (!) for mathematicians to notice what was literally in front of their eyes and under their feet: that there are cases where the first 4 postulates hold, but the 5th does not!
To be fair changing the 5th postulate requires some creative redefining of what a straight line is. In my experience when explaining non-euclidean geometries to muggles the hardest part is not the 5th postulate or its consequences but making people accept that on a sphere a straight line is really a great circle (the easier way being through the concept of a geodesic line but this was invented after non-euclidean geometries if I’m not mistaken.
Yeah, there are two equivalent definitions of a straight line, “don’t turn” and “shortest path”, both known to the ancient Greeks, I’m sure, but not formalizable in any easy way until differential calculus was invented, and not well until Riemann. Still, if someone actually asked Euclid “what do you think the closest thing to a straight line might be on a sphere, and which postulates hold there?” he would probably have done the rest.
My default assumption is that it took humans that long to get a clue (or shift a paradigm). We are remarkably bad at creating new thinking patterns. In my area of interest, fundamental physics, there are similar patterns aplenty. It took several decades to get from the first black hole metric to understanding black hole horizons, even though no new math was required. Similarly, it took several decades from EPR to Bell, and the math there was… very elementary. The most glaring example is the Euclid’s Fifth Postulate (about parallel lines): It took some 2000 years (!) for mathematicians to notice what was literally in front of their eyes and under their feet: that there are cases where the first 4 postulates hold, but the 5th does not!
To be fair changing the 5th postulate requires some creative redefining of what a straight line is. In my experience when explaining non-euclidean geometries to muggles the hardest part is not the 5th postulate or its consequences but making people accept that on a sphere a straight line is really a great circle (the easier way being through the concept of a geodesic line but this was invented after non-euclidean geometries if I’m not mistaken.
Yeah, there are two equivalent definitions of a straight line, “don’t turn” and “shortest path”, both known to the ancient Greeks, I’m sure, but not formalizable in any easy way until differential calculus was invented, and not well until Riemann. Still, if someone actually asked Euclid “what do you think the closest thing to a straight line might be on a sphere, and which postulates hold there?” he would probably have done the rest.