Here is Penrose in his own words at page 12 of Shadows of the Mind:
"It seems to me there are at least four different viewpoints -- or extremes of viewpoint -- that one may reasonably hold on the matter:
A. All thinking is computation; in particular feelings of conscious awareness are evoked merely by the carrying out of appropriate computations.
B. Awareness is a feature of the brain's physical action; and whereas any physical action can be simulated computationally, computational simulation cannot by itself invoke awareness.
C. Appropriate physical action of the brain evokes awareness, but this physical action cannot even be properly simulated computationally.
D. Awareness cannot be explained by physical, computational, or any other scientifc means.
"The point of view expressed in "D", which negates the physicalist position altogether and regards the mind as something that is entirely inexplicable in scientific terms, is the viewpoint of the mystic; and at least some ingredient of "D" seems to be involved in the acceptance of religious doctrine. My own position is that the questions of the mind, though they lie uncomfortably with present-day scientific understanding, should not be regarded as being forever outside the realm of science. If science is yet incapable of saying much that is of significance concerning matters of the mind, then eventually science must enlarge its scope so as to accommodate such matters, and perhaps even modify its very procedures. Whereas I reject mysticism in its negation of scientifc criteria for the furtherance of knowledge, I believe that within an expanded science and mathematics there will be found sufficient mystery ultimately to accommodate even the mystery of the mind ..."
At page 7, he writes:
"In this book, I shall attempt to address the question of consciousness from a scientific standpoint. But I shall strongly contend -- by use of scientific argument -- that an essential ingredient is missing from our present-day scientific picture. The missing ingredient would be needed in order that the central issues of human mentality could ever be accommodated within a coherent scientific world-view. I shall maintain that this ingredient is itself something that is not beyond science -- although, no doubt, it is an appropriately expanded scientific world-view that we shall need ...
And at page 8:
"A scientific world-view which does not profoundly come to terms with the problem of conscious minds can have no serious pretentions of completeness. Consciousness is part of our universe, so any physical theory which makes no proper place for it falls fundamentally short of providing a genuine description of the world. I would maintain that there is yet no physical, biological, of computational theory that comes very close to explaining our consciousness and consequent intelligence; but that should not deter us from striving to search for one. It is with such asperations in mind that the arguments of this book are presented ..."
Boldings and underlinings are mine. Physicist, this is definitively not Materialism and I do not disagree with Penrose. This is a rejection of Materialism.
I agree fully with your reading of Penrose's statements and wish to add these two observations:
2. In Emporer's New Mind Penrose emphasizes math which pre-exists (like the Mandelbrot set) and was later discovered. Though it is evidently offensive to some, pre-existence seems obvious to me. For instance, Schwarzchild Geometry was not created by Schwarzchild, it was discovered by him.
At any rate, I agree that he is not a materialist. I would say he is a true scientist who has indentified the point at which current science fails and new science is needed to go any further.
It absolutely is not. His viewpoint is C, which begins, "Appropriate physical action of the brain evokes awareness". How could he be more explicitly materialist? Furthermore, Penrose is quite clear in stating that he "shall maintain that this ingredient is itself something that is not beyond science -- although, no doubt, it is an appropriately expanded scientific world-view that we shall need ". In other words, he thinks that physical material is fully up to the task; it is only our understanding of material that (currently and correctably) falls short. We don't know everything, but materialism isn't about what we do or do not know; it's about how things work.
Phaedrus, you wrote: "this is definitively not Materialism and I do not disagree with Penrose. This is a rejection of Materialism."
I agree with your assessment. It looks to me like Penrose is saying, with Wolfram, with Evan Harris Walker, that we really do need a "new kind of science."
Here's Walker: "Maybe the way out of the Bell's theorem problem and the measurement problem in quantum mechanics is to stop denying the obvious answer. Quantum mechanics requires that we take into account the fact that conscious observers exist as unique entities, as a part of the total reality of the world. What we have to do now is find a way to understand what consciousness itself is.... Consciousness should have long since been the topic of reasoned scientific study, and yet it has largely been ignored....
"Bell's theorem was an effort to escape this obvious conclusion about quantum mechanics, and that effort failed. It failed because it was an attempt to design a universe that would leave out consciousness. The way out of our difficulty, the path we must take now, is to try to understand what was previously rejected. We must recognize that objective reality is a flawed concept, that state vector collapse does arise from some interaction with the observer, and that indeed consciousness is a negotiable instrument of reality. Our entire conception of reality must be rethought. We stand at the threshold of a revolution in thinking that transcends anything that has happened in a thousand years. Now the observer, consciousness, something self-like or mind-like, becomes a provable part of a richer reality than physics or any science has ever dared to envision."