2 ms·
Seems like an odd choice when talking about the cross product, since the cross product is only a thing in 3D. You can define analogous things in other dimension
by jameshart 3y ago
Seems like an odd choice when talking about the cross product, since the cross product is only a thing in 3D. You can define analogous things in other dimensions but it becomes clearer and clearer that it’s not meaningfully a ‘product’.
So it doesn’t matter if your visual intuition for a cross product breaks down in higher dimensions - a cross product is only a thing in three.
- jacobolus 3y agoThis is very off topic, but the wedge product absolutely is "meaningfully a product", generalizes fine to arbitrary dimension, and has a perfectly reasonable visual/spatial/geometric interpretation. (Indeed, we should entirely scrap the cross product in undergraduate level technical instruction and replace it with the wedge product; one happy effect will be replacing students' misleading spatial intuitions with better ones.)
- jameshart 3y agoOr bivectors, or k-vectors, or blades…
- nilstycho 3y agoGood point; you're right. I might be misremembering the cross product. I do remember that he didn't even teach the geometric interpretation of vector addition.