it can't be that difficult ...

the metaphor is a space spawn by different base vectors which represent features, if ++ and + are not parallel the cartesian product has either an additional dimension or the vectors are not orthogonal anymore.

But it's just a graphic metaphor, because you can hardly represent a computer language as a primitive n-dimensional vector space.

Thats why you need a more abstract model from Universal Algebra (which BTW is used in CS and Math) .