Is Consciousness Computable? Quantifying Integrated Information Using   Algorithmic Information Theory
  In this article we review Tononi's (2008) theory of consciousness as integrated information. We argue that previous formalizations of integrated information (e.g. Griffith, 2014) depend on information loss. Since lossy integration would necessitate continuous damage to existing memories, we propose it is more natural to frame consciousness as a lossless integrative process and provide a formalization of this idea using algorithmic information theory. We prove that complete lossless integration requires noncomputable functions. This result implies that if unitary consciousness exists, it cannot be modelled computationally. 
Phil Maguire, Philippe Moser, Rebecca Maguire, Virgil Griffith
cs.IT math.IT q-bio.NC