Full Moon and Quarter Moon

When half the earth-facing hemisphere of the moon is illuminated we
(in the U.S.) call the lunar phase: "quarter".

When the whole earth-facing hemisphere of the moon is illuminated we
call the lunar phase: "full".

Is it any wonder that so many children in the U.S. have difficulty
understanding science and fractions (math)?

Of course, there are reasons for the names we use; but I don't believe
there are any "good" reasons for the mutually contradictory terms used
for the above mentioned lunar phases.

It's enough to make one wonder if some organization (comparable to the
IAU) long, long ago felt there was no choice but to accept a
compromise between two lunar phase nomenclature systems. After all,
the current system has all appearances of having been adopted by a
group of lunatics!

Does this discrepancy exist in other countries?

Would the IAU be willing to draft and adopt a more rational,
scientific, lunar phase nomenclature?

Wouldn't it be nice if two halves equaled one whole (or two quarters
equaled one half) in astronomy just as it does in mathematics?

Willie R. Meghar
Observational Notes at:
http://meghar.blogspot.com/