Maurice Merleau-Ponty's phenomenological philosophy suggests the search for the self and consciousness need not be focused on the space within our skulls. Instead, we should turn our attention to the lived body. 

Our scientific and philosophical search for the self and the place of consciousness in the world has tended to focus between our ears -- although Descartes, as the originator of the modern mind-body problem, held the conscious mind had (as non-material) no location. In the last hundred years or so, materialist-leaning theories have been especially inclined to locate mind and self in the head. In both computational/information-processing and biological theorizing about consciousness and the self, the question to be answered is often seen as one about where to localize this mind/self -- whether those critical properties were best modeled as information processing or as more fundamentally biological.

This is sometimes such a fundamental background assumption that it's even taken by some as fueling a kind of reductio ad absurdum argument against understanding consciousness or the self within a scientific perspective: Reasons for skepticism about reduction or localization of consciousness and self are commonly taken as reasons to infer that we should either (a) prejudge eventual failure for any attempt to scientifically explicate consciousness and self (as advocates of the "unbridgable explanatory gap" like David Chalmers do), or (b) get rid of the notions entirely, as (as anti-self “illusionists” like Thomas Metzinger suggest).