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Aren't you presupposing that lines are themselves a continuum? It's a reasonable abstraction, but as far as we know, it's not physical real. If a line were jus
by acjohnson55 8y ago
Aren't you presupposing that lines are themselves a continuum? It's a reasonable abstraction, but as far as we know, it's not physical real.
If a line were just a collection of discrete points related by some formula, there's no reason two lines that aren't parallel should have to intersect, from the perspective of sharing a point.
- vladTheInhaler 8y agoYou're absolutely right that it might not reflect physical reality. I don't think it's known whether space is fundamentally discrete or not. But I can definitely say that continuous space meshes a lot more with my experience as a human being, and that because of that, the real numbers are motivated by more than just taking square roots. They model the human experience of space.