Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift that quantum mechanics represented. Mathematical descriptions of the wave function can also fail to impart to the audience the true nature of the quantum measurement problem and its implications for our concept of reality. Presenting both Bell's theorem and Heisenberg's uncertainty principle in a heuristic framework allows for a conceptual-based discussion of quantum phenomena suitable for a mathematically naive undergraduate or an interested nonscientist. (Contains 4 figures.)