The boundaries of the problem are defined by assumption and then within those boundaries vertical thinking proceeds to find a solution. Very often, however, the boundaries are imaginary and the solution may lie outside them. Take the apocryphal story of Columbus and the egg. When his friends taunted him, saying that discovering America was really easy since only had to point west and keep going, he asked them to stand an egg on end. They tried but failed. Then Columbus took the egg, flattened one end and stood it up. Naturally his friends protested that they had thought the egg could not be damaged. His friends had assumed for the egg problem limits which did not in fact exist. But they had also assumed that it would not be possible to point west and keep on sailing. This feat of navigation seemed easy only after Columbus had shown that their assumptions were imaginary.