[bane]

"Let's say you're moving nearly as fast as the speed of light. Are you flying side by side with light particles? No, because if they were, you would measure their speed as being close to zero relative to you. The theory says you will STILL measure the beams of light as flying away from you at the speed of light relative to you."

Something you said just clicked. I think I may now clearly "grok" relativity for the first time.

It reminded me of the http://en.wikipedia.org/wiki/Mahalanobis_distance

which calculates different distances given a vector field w/r to a Euclidian space.

It's not the same thing, but when thinking about what Mahalanobis distances measure, I used a helpful mental model of the measure forcing the vector field apart, enforcing a kind of constant distance between the vectors and then measuring that delta. It seems like a similar concept is at play here, only what we're measuring is different.

I'm aimlessly musing here, but I feel a kind of grokiness I haven't felt before after your post.