Well, what I *really* want to see is not so much a handedness..
perhaps _something_ capable of showing where it fits in the
greater context of where it is used and what it is used for.
I suppose what I'm thinking of is to bring in a distinction of
purpose. Zero has multiple uses and is quite powerful.
It is used as a placeholder.
It is used as a marker of "Start" for the number line.
It is considered the lowest Even number.
It is used as a marker for "Success" in balancing systems (such
as economics)
It obliterates identity entirely; a number loses its
positiveness and negativeness and its quantity.
Conceptually, it's the "empty bucket".
Conceptually, it's non-movement or stillness or balance.
Conceptually, it's potential as it either *could have once*
represented something or it *could* in the future represent
something.
Conceptually, it's absence.
Conceptually, it's "I can't know" of a very strong form.
This is off the top of my head; please correct me if I'm
mistaken in these things.
But it seems to me that, perhaps zero serves too many purposes
without distinction, leading to confusion.
I have a similar issue with the modern concept of impetus versus
the Newtonian usage. Impetus that is external or internal are
considered the same now; both external; but in Newton's time and
before, Impetus was a pretty hot topic.
But that's with Science. At least in mathematics, the Axiom
would be the intrinsic impetus and the Proof would be the
extrinsic impetus, in my viewpoint creating a marvelous engine
which drives mathematics both from without and within.
Yeah, I tend to conceptually analogize to machines.
