The suggestion is that the book should be approached in a state of ignorance, setting aside all that one knows and thinks. In this way only, can one be receptive to the variety of different pictures of the universe that physicists are now exploring.
The book doesn't take us to anything like a proof of these principles, but it is an important milestone along the way. Penrose's Universe is made up of three worlds --a trinity-- whose links are still deeply mysterious.

There is, first, the physical world, some aspects of which we are getting to understand after much effort.

The second is the mental world, enclosing all our experiences, thoughts and understandings.

The third is the "Platonic world," of mathematical truths: beautiful abstract entities which, though mental in kind, seem to have an existence independent of our discovery of them.

The circle is finally closed by the realization that the first world, the physical one, depends at its foundation on the Platonic mathematical truths.

Penrose maintains too, that people, in the physical world, "have mentality," that is, they are linked to the second, the mental world. In turn, part of this mental world (the part to which Penrose has dedicated his life) lies in the third, Platonic world.

The focus of the book concentrates on the physical-mental link. Penrose argues that the mental operation of 'understanding' --which he regards as crucial to human consciousness-- points to a process that is essentially different from any of the processes that can be performed on computers as we now understand them: such a process is said to be "non-computational". He takes this as implying that a new physical process is at work in the brain, and, since classical physics is necessarily computational, it has to be a process that operates in the non-classical domain of quantum mechanics.

An array of clues gleaned from his experience in many fields leads him to point to a future theory that embraces quantum theory and gravitation as the prime suspect for the physics of consciousness.
The real point he claims, is that it is impossible for a mechanical process to give rise to any of the emotions and sensations of which we are all conscious, because of the fundamental difference in kind between these subjective experiences and the mechanism that are supposed to give rise to them. In careful, though necessarily rather technical account, he then puts forward his own application of the quantum theory to explain how brains are linked to these subjective experiences.

Dr. Fox, your pithy commentary is certain to attract readers. I feel the impulse to ask, "How can non-classical, subatomic, quantum mechanics be extant in a macroscopic world like the brain? Why the 'non-computational' process? Gravity, what has it to weigh on mental processes? And,'The impossibility of a mechanical process'... What is 'mechanical'? Is it a grand-father's clock? When we talk about quantum MECHANICS, the subject becomes quite complex --not just a clockwork is at stake.

The subdivision in three worlds is fine, but ONLY for a heuristic purpose. BECAUSE everything is PHYSICS. Subdivisions, as Psychology, Logic, Law, History..., are in turn sub-divisions of Philosophy. Mathematics I'd place in a special, prominent pedestal, because it would appear to be the heart of Physics.

Dr. Fox, now I'm going to tell you about a different book, which, as usual, I've not read nor will (I'm reading a love story called "The Notebook"). Listen, please: I received Newsweek's 6 July issue, and what do I find? An article about Edward O. Wilson, a Harvard savant, who has been writing for decades on understanding the World, and has now published "Consilience: The Unity of Knowledge." I repair to the dictionary, finding that consilience is the act of bringing the results of different areas of learning into a whole body, in order to explain the world. I'll cite only the following words of the critic.

And I say, "So happy to make your acquaintance, Mr. Wilson, Naturalist. Now I know that there is somebody who says things that glide easily with my own along a common rail."

Well, reader, 'Consilience' is an EMERGENT, because by unifying knowledge from several disciplines, a Super-discipline is created. And I would dare to guess, until more material is brought forward on Penrose's thought, that he just is not aware of COMPLEXITY, which is the way of calling the presence of a lot of Emergents and Resultants. And, certainly, our brain does not operate computationally --it does so Super-computationally! What is, after all, Artificial Intelligence, but the expected result of computing at higher levels? No more than three or four, as explained in my essay on geometric axioms.