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Dr. Tononi’s theory is, potentially, very different. He and his colleagues are translating the poetry of our conscious experiences into the precise language of mathematics. To do so, they are adapting information theory, a branch of science originally applied to computers and telecommunications.

Dr. Tononi began to think of consciousness in a different way, as a particularly rich form of information. He took his inspiration from the American engineer Claude Shannon, who built a scientific theory of information in the mid-1900s. Mr. Shannon measured information in a signal by how much uncertainty it reduced.

Dr. Tononi and his colleagues have been expanding traditional information theory in order to analyze integrated information. It is possible, they have shown, to calculate how much integrated information there is in a network. Dr. Tononi has dubbed this quantity phi, and he has studied it in simple networks made up of just a few interconnected parts. How the parts of a network are wired together has a big effect on phi. If a network is made up of isolated parts, phi is low, because the parts cannot share information. But simply linking all the parts in every possible way does not raise phi much. “It’s either all on, or all off,” Dr. Tononi said. In effect, the network becomes one giant photodiode. Networks gain the highest phi possible if their parts are organized into separate clusters, which are then joined. “What you need are specialists who talk to each other, so they can behave as a whole,” Dr. Tononi said. He does not think it is a coincidence that the brain’s organization obeys this phi-raising principle.