The key to the solution of the consciousness-brain problem was provided by C.D. Broad in 1923, when he proposed that the phenomenal space of consciousness and physical space are two different slices in a higher-dimensional space (as we can cut two different planes in a cube).
This theory was later supported and further developed by H.H. Price, Bertrand Russell, Lord Brain, and John Smythies.
The physicist Bernard Carr has recently proposed that this theory is a logical development of brane theory in contemporary physics, and, as such, constitutes a major paradigm shift in physics and cosmology. Brane theory suggests that what is currently considered to constitute "the" physical universe is actually just one of a vast number of other parallel universes located in higher-dimensional space. The new paradigm shift suggests that some of these individual parallel universes contain a consciousness module, defined as the events contained in a person's spatio-temporal phenomenal world of sensations, images and thoughts. A person's consciousness module is related to that person's brain by relations of causality, not identity.
In other words a human organism consists not just of a physical body, but of a physical body plus a consciousness module. These two ontologically independent units nevertheless operate as a unity. These causal relations link events in two separate parallel universes across the dimensional interface between them.
Think of activity in one Flatland modulating events in a second parallel Flatland. This theory makes it much simpler to describe the role of the brain in modulating the contents of consciousness than does the rival Identity Theory. The latter runs into intractable binding problems and infractions of Leibniz's Law of the Identity of Indescernibles.