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I think a lot of human understanding is basically intuition about topological invariants in various "spaces". If you go around asking famous thinkers what they
by dkarapetyan 10y ago
I think a lot of human understanding is basically intuition about topological invariants in various "spaces". If you go around asking famous thinkers what they see when they think they all describe similar kinds of imagery, fuzzy shapes that merge and unmerge in various ways as they probe the subject.
One good book I've found on the subject is https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From.
- catnaroek 10y agoIntuition quickly becomes unreliable when you move to spaces with weird topologies, like non-Hausdorff and non-(pseudo)metrizable spaces. When your intuition stops being useful, you actually need to calculate.
- dkarapetyan 10y agoI suspect a few folks that studied p-adic numbers extensively would disagree. And in general topologists and algebraists that study non-euclidean things in general.
- catnaroek 10y agoThe p-adic numbers can be equipped with a metric. The induced topology isn't Euclidean, but it's pretty tame compared to what you can see in a general topological space.