I Stand Corrected
Although another book lists wu-wei as fire, Alex is correct that it is earth. By arranging the 12 elements in a circle, they pair off sequentially. Since these pairs are earth, wood, fire, and then water, the last pair must also be earth, completing the system. The beauty of the system is in its mathematical integrity. Alex's statement that he had to learn about the triple element combos empirically seems unconvincing. Anyone arranging the 12 elements in a sequential circle will see that triangles of every fourth element form automatically. Furthermore, those elements located on the four corners of the circle (tze, mao, wu, yu) decide what each triangle will be, in terms of the new element for all three. For example, the mao-wei-hai triad has to be wood, because mao is the corner element.