Various neutron interferometry experiments demonstrate the subtlety of the notions of duality and complementarity. We use this example to illustrate the proof of the weak duality theorem. These theorems belong to a larger class of duality theorems in optimization. One example of such a more general duality is from Galois theory. Ultimate truths, are phenomena free from the duality of apprehender and apprehended. Two theories related by a duality need not be string theories. It is based on taoistic duality of yin and yang. De Morgan's laws are an example of a more general concept of mathematical duality. This produced a duality of natures in Christ. The main illusions of this order are synthesis, autonomy, duality, and resemblance. All impurity comes from doubt and attachment to duality. That led to the creation of a particular terminological duality. The reason for this duality is hard to explain. Relations of semi-duality are similar to relations of duality. That move led to the creation of a particular terminological duality.