"One of the most profound advances in science in recent years is the way researchers from a variety of fields are beginning to formulate the problem of consciousness in mathematical terms, in particular using information theory. That's largely thanks to a relatively new theory that consciousness is a phenomenon which integrates information in the brain in a way that cannot be broken down. Now a group of researchers has taken this idea further using algorithmic theory to study whether this kind of integrated information is computable. They say that the process of integrating information is equivalent to compressing it. That allows memories to be retrieved but it also loses information in the process. But they point out that this cannot be how real memory works; otherwise, retrieving memories repeatedly would cause them to gradually decay. By assuming that the process of memory is non-lossy, they use algorithmic theory to show that the process of integrating information must noncomputable. In other words, your PC can never be conscious in the way you are. That's likely to be a controversial finding but the bigger picture is that the problem of consciousness is finally opening up to mathematical scrutiny for the first time."
