  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.
