EDIT: To add a simple analogy: Is a parabola only x^2 -- just another polynominal -- or is a parabola a conic section first and foremost? polynominal in x ==

EDIT: To add a simple analogy: Is a parabola only x^2 -- just another polynominal -- or is a parabola a conic section first and foremost? polynominal in x == "flatland" view