| HN Mirror

Right, the post was not intended to be any kind of introduction or tutorial, but rather more of an announcement to those already familiar with the subject that there exists another way of doing the math that doesn't require inverting the dimensionality of points and planes. I will be writing some much longer that introduces the material properly and goes into much more detail with plenty of figures.

Here's an excerpt from pages 153-154 in FGED1 (https://www.amazon.com/dp/0985811749/?tag=terathon-20) that explains my reasoning about "anti" and "pseudo" with regard to vectors, but it also applies to everything else:

In the n-dimensional Grassmann algebra, a 1-vector and its complement, which is an (n - 1)-vector, both have n components. We give the complement of a vector the special name antivector because it corresponds to all of the directions in space that are perpendicular to the vector, excluding only the one direction to which the vector corresponds. An antivector is everything that a vector is not, and vice versa. T hey are opposites of each other and stand on equal ground with perfect symmetry. Since vectors and antivectors have the same numbers of components, a clear distinction is not always made between the two in much of the existing literature, and an antivector is often called a pseudovector because its transformation properties are different from an ordinary vector. However, the prefix "pseudo" tends to induce a characterization of lower status through its meaning of "false" without adding any descriptive value to the term, whereas the prefix "anti" accurately depicts an antivector as something that "opposes" its complementary vector.