This is consistent with a new theory of consciousness being advocated by physicist Sir Roger Penrose and Dr. Stuart Hameroff. Penrose and Hameroff suggest that consciousness is something applied to the brain, not generated by it.

Came to the comments to mention Hammeroff. He's an anesthesiologist who thinks consciousness arises out of the quantum states of microtubules within the neuron. Basically, the brain is more a quantum antenna than a computer. Really fascinating stuff, and interesting that it comes from a guy who's an expert in turning consciousness off (and hopefully back on again).