10 ms·
It doesn't make sense to me because a glass of water is a discrete set. If we only had two molecules you could just interchange them (with a 180 degree rotation
by fiso64 3y ago
It doesn't make sense to me because a glass of water is a discrete set. If we only had two molecules you could just interchange them (with a 180 degree rotation), without any fixed points.
- tgv 3y agoI'd guess the example of the glass of water was made as an afterthought, or as a vivid example of the potential complexity of the theorem. As your example shows, it simply cannot be true. If you think of a vase with marbles, it is also clear. Or if you think of an (ideal) gas in a closed system: would there be at least one particle that always(!) stays in the same place?
- mbeex 3y agoShow me a mathematical continuum in the real-world. And this is just the domain, nothing said about the mapping yet (the continuous function). Every analogy has its limits.
- tomrod 3y agoThe space represented in a flat piece of paper. The space is continuous even if we can only measure down to the Planck length.
- mbeex 3y agoKey here: "represented" I'm only a mathematician, no physicist. But I think to remember, that the concept of a continuous physical space becomes quite muddled at this scale.
- nerdponx 3y ago"The space represented by the water in a convex container"
- hgsgm 3y agoIf you get to assume continuous paper, then I get assumed continuous paper. If you don't want to assume continuity, then you get it back by rephrasing your theorems as "within a margin of error equal to the distance between discrete objects".