If we take the hamming cube and project a point through its vertives, we get the 7 point geometry.
Obviously, the distance along the line of the point to the geometries plane affects the scaling it of the geometry.
Imagine the scale of our geometry is diminishing, until the circle of the normalizer has radius 1 (ie a norm of 1). This is accomplished by moving the projection point away.
So what is the relationship between the distances on the projection line and the rate of scaling of the plane.
Dont know why, but i imagine the 1d line to be a log scale, whereas the plane scaling is linear in reduction of radius, proportioned to each ban on the projection line.
Why didnt i ask this before?