This paper reviews four current theories of brain-consciousness relations—classical Cartesian Dualism, the Identity Theory, Eliminative Materialism, and a new form of Substance Dualism that includes a modified form of the Cartesian theory. This entails a critical examination of our basic concepts of what consciousness is, of the nature of the body image, and the relation of phenomenal space to physical space. This investigation reaches the same result as that attained recently by the physicist Bernard Carr (2008)—that what is needed is (...) a paradigm shift in our basic concepts of the geometry of the Universe. In order to understand phenomenal consciousness we need to replace the present four-dimensional model with a higher-dimensional structure, in which a phenomenal space (with its contents) and physical space (with its contents) are different cross-sections (branes) of a higher-dimensional space (the bulk). Keywords: brain—consciousness—mechanisms—substance dualism—brane theory. (shrink)