- #26

mathwonk

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Well, that spares you a long post.

Here is just the last sentence from it: Professor Bott (a famous engineer - turned - topologist] used to say a cocyle, i.e. differential form, is something that "hovers over the space, looking for a cycle [i.e. a path], and when it sees one, it pounces on it gobbles it up, and spits out a number".

What is more visual than that!? Sort of like a hungry bird of prey.

Most of my post was devoted to recalling how the familiar coordinate functions x and y on the euclidean plane are covectors, and the grid of parallel lines on a graph paper are the corresponding parallel families of "level sets" for those covectors, i.e. sets where the coordinate takes the same value.

This lets us picture at least the level sets of covectors within the vector space it self.