The Harry Potter Wand Test

[Carol]

Jen wrote: 
<snip> I can't decide if it's more like math or numerology when trying
to think of a RW equivalent.  Harmione would like the precision of 
math & it's taught by Prof. Vector.  But then, attempting to find 
logic for anything in the story having to do with maths may be a
losing battle.... 

Carol:
But it's the logic of etymology (which JKR is pretty good at) that we
need to consider here. "Arith" clearly relates to "arithmetic," which
is derived from "arithmos," the Greek word for "number," and "-mancy"
is an actual English suffix meaning "divination" derived from the
Greek word "mantis," meaning "diviner." So, apparently, divination is
okay with Hermione if it's based on something solid and predictable
like numbers; otherwise, it's "woolly." Alternatively, "-mantis" might
simply suggest magic or sorcery, as in "necromancy" (dark magic
involving the dead--I think that Voldemort's resurrection potion and
Inferi would qualify as necromancy--not taught at Hogwarts, of course!).

As for vector, I think that JKR expects the reader to connect the
concept with geometry (an imaginary line or something like that--I
hate abstract mathematical concepts)--vaguely mathematical but not
really related to Arithmancy, which I think of as divination based on
numbers. Or it might be equivalent to numerology, which Merriam
-Webster Online defines as "the study of the occult significance of
numbers." that would tie in with Tom Riddle's fascination with the
number seven.

Carol, wondering whether there's any "silly wand waving" in arithmancy
and thinking that it's more a matter of calculations