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Physical intuition isn’t going to help when you’re dealing with infinite-dimensional vector spaces, abstract groups and rings, topological spaces, mathematical
by chongli 3y ago
Physical intuition isn’t going to help when you’re dealing with infinite-dimensional vector spaces, abstract groups and rings, topological spaces, mathematical logic, or countless other topics you learn in mathematics.
- 12345hn6789 3y agoYou're just throwing jargon at the wall to dismiss folks who want to learn
- peanutcrisis 3y agoWell, can you visualize vector spaces beyond 3 dimensions?
- ndriscoll 3y agoYou just visualize 2 or 3 and say "n" or "infinite" out loud. A lot of the ideas carry over with some tweaks, even in infinite dimensions. Like spectral theorems mostly say that given some assumption, you have something like SVD. Now module theory, there's something I don't know how to visualize.
- chongli 3y agoYour intuitions can often lead you astray. For example, the curse of dimensionality [1] deceives our intuitions about volume at high dimensions. [1] https://en.wikipedia.org/wiki/Curse_of_dimensionality https://en.wikipedia.org/wiki/Curse_of_dimensionality
- chongli 3y agoNot at all! I fully endorse learning. My point is that physical intuition will only get you so far in mathematics. Eventually you have to make the leap to working abstractly. At some point the band-aid has to come off!