 However, relations between mental and material states can also be conceived in a non-reductive fashion, e.g. in terms of emergence relations (Stephan 1999). Mental states and/or properties can be considered as emergent if the material brain is not necessary or not sufficient to explore and understand  them.[4]  This leads to a dualistic picture (less radical and more plausible than Cartesian dualism) in which residua remain if one attempts to reduce the mental to the material. Within a dualistic scheme of thinking, it becomes almost inevitable to discuss the question of causal influence between mental and material states. In particular, the causal efficacy of mental states upon brain states (“downward causation”) has recently attracted growing interest (Velmans, 2002; Ellis et al.  2011).[5]  The most popular approaches along those lines as far as quantum behavior of the brain is concerned will be discussed in  Section 3,  “Quantum Brain”. 