Roger Penrose, a great astrophysicist, did some moonlighting in the worlds of neurology and neuropsychology in the late 1980s, and he developed a theory a quantum theory of consciousness. The idea behind it was (and is, in later more-developed forms) that microtubules, particularly those in neurons, are small enough so that quantum effects become pertinent in understanding their operations. Penrose contended that quantum physics allows for deterministic but non-algorithmic processes, and that these may be harnessed by the operations of the brain, resulting in consciousness. To put the idea crudely, using an old image, the microtubule is the closed box inside which a “cat” is both dead and alive. To refine that a bit: Penrose tells us that there must be a border zone where quantum effects still exist but are becoming of less salience as scales increase toward those of the world of Newtonian physics, the world of what Bertrand Russell once called "medium sized dry goods." The...