How old were you when you realize the cross product is not a real thing and that your elementary school teachers lied to you?
>>16970586>the cross product is not a real thingIt is though... unless you mean in the same sense that numbers are not real.
>>16970591A vector times a vector is equal to either a scalar or a bivector. Grassman algebras don't lie bro. Try defining a cross product in 6D and report back if you're so sure
>>16970610None of that contradicts that the cross product is well defined for 3-dimensional vector spaces.
>>16970586There are no "real things" in mathematics by definition.
>>16970615a bivector is not a vector bro. you can't measure an area with a vector
>>16970617You seem confused.
>>16970617You can't measure an area with [math] \nabla \times \vec A [/math] either
>>16970615This
[eqn] \mathbf F = q(\mathbf E + \mathbf v \times \mathbf B) [/eqn]>>16970617I'm adding a vector and a bivector. What are you going to do about it, fag?
>>16970716make sure i don't do an improper rotation
>>16970716>bold instead of arrowngmi
>>16970716>I'm adding a vector and a bivector. Now you're thinking with geometric algebra
So what's the difference between the scalar i and the pseudoscalar i? idgi, they're both the same and they both square to -1
>>16970769a scalar is an element of a vectorspace's underlying fielda pseudoscalar appears to be scalar that's computed from vectors, however it's sign flips when the vectors are transformed by a linear transformation with negative determinant
>>16970769the scalar is used by physicists.the pseudoscalar is used by pseudophysicists, aka mathematicians
>>16970818mathematicians are actually perfectly spherical linguists in a vacuum
>>16970993>mathematician>perfectmaybe in fantasy land (formal maths rigor)
>>16971007physicists are the ones who put perfectly spherical things into vacuums though....
