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operation "square" that the square of any number was positive. The
extension to imaginary numbers abandons this property and proposes
defining NEW entities whose square is negative.
So too, here it is proposed to define NEW entities whose absolute value
is negative.
abs(Q) + abs(1) = 0 is no more perverse than i^2 +1^2 = 0
Whether this leads to anything useful is another question, but it is
conceptually feasible.