Quantum theory provides us with a striking illustration of the fact that we can fully understand a connection though we can only speak of it in image… - Werner Heisenberg

The interest of research workers has frequently been focused on the phenomenon of regularly shaped crystals suddenly forming from a liquid, e.g. a supersaturated salt solution. According to the atomic theory the forming force in this process is to a certain extent the symmetry characteristic of the solution to Schrödinger's wave equation, and to that extent crystallization is explained by the atomic theory. Nevertheless this process retains a statistical and — one might almost say — historical element which cannot be further reduced: even when the state of the liquid is completely known before crystallization, the shape of the crystal is not determined by the laws of quantum mechanics. The formation of regular shapes is just far more probable than that of a shapeless lump. But the ultimate shape owes its genesis partly to an element of chance which in principle cannot be analysed further.

The words "position" and "velocity" of an electron... seemed perfectly well defined... and in fact they were clearly defined concepts within the mathematical framework of Newtonian mechanics. But actually they were not well defined, as seen from the relations of uncertainty. One may say that regarding their position in Newtonian mechanics they were well defined, but in their relation to nature, they were not. This shows that we can never know beforehand which limitations will be put on the applicability of certain concepts by the extension of our knowledge into the remote parts of nature, into which we can only penetrate with the most elaborate tools. Therefore, in the process of penetration we are bound sometimes to use our concepts in a way which is not justified and which carries no meaning. Insistence on the postulate of complete logical clarification would make science impossible. We are reminded... of the old wisdom that one who insists on never uttering an error must remain silent.

Cautious deliberation based on purely rational arguments can save us from many errors and dangers. ...But ...there will always be a fundamental complementarity between deliberation and decision. ...The decision finally... pushing away all the arguments... The decision may be the result of deliberation, but it is... complementary... it excludes deliberation. Even the most important decisions... contain this inevitable element of irrationality. ...[I]t cannot be avoided that some real or apparent truth form the basis of life; and this fact should be acknowledged with regard to those groups... whose basis is different from our own.