They're equivalent in a limited context.
That, to me, is the point of metaphors: the limiting of context
comes with it for free.
A computer mouse is equivalent to a real mouse in the sense that
it has a similar shape to a mouse and, prior to wireless mice,
had a form of a tail.
They are equivalent in a limited sense. I see equivalent as
running from very weak to strong, in the same manner that
metaphors run from very weak to strong. I'm simply extending the
strong into the realm of very strong, which would be
mathematics. It's not that much of a stretch.
Thank you for the points. I'm keeping a tally someplace. I'm
doing well, but I have a ways to go, hence why I bring up my
ideas while they're still in the formative stages - in order to
get the necessary challenges to my thinking to help me
correct/modify them, as we're doing now.
Believe me when I say, I appreciate the challenge.