On page 197 Penrose divides scientific theories into three broad
categories: SUPERB, USEFUL, nad TENTATIVE.  (Yes, he uses caps)
The paragraph following this list reads:

    Into the SUPERB category must go all those I have been discussing
    in the paragraphs preceding this one [that is, relativity - both
    varieties - and quantum mechanics].  To qualify as SUPERB, I do
    not deem it necessary that the theory should apply without
    refutation to the phenomena of the world, but I do require that
    the range and accuracy with which it applies should, in some
    appropriate sense, be _phenomenal_.  The way that I am using the
    term `superb', it is an extraordinary remarkable fact that there
    are any theories in this category at all!  I am not aware of any
    basic theory in any other science which could properly enter this
    category.  Perhaps the theory of natural selection, as proposed by
    Darwin and Wallace, comes closest, but it is still some way off.

Anyone who wants to use Penrose as an example of someone "who reject[s]
some aspect of evol[ution]" had better think again!

Ken Smith

===================================================

The following quote from the forward of _The Emperor's New Mind_
may refresh your memory as to the main purpose of the book:

     Penrose's book is the most powerful attack yet written
     on strong AI. Objections have been raised in past centuries
     to the reductionist claim that a mind is a machine operated
     by known laws of physics, but Penrose's offensive is more
     persuasive because it draws on information not available to
     earlier writers.
--- Martin Gardner in the forward to _The Emperor's New Mind_

Indeed, the breadth of topics considered is truly amazing. In the last
chapter titled "Where lies the physics of mind" he has a section
dealing with natural selection in the context of his overall thrust
stated above. He begins this section ...

     If we suppose that the action of the human brain, conscious or
     otherwise, is merely the acting out of some complicated algorithm,
     then we must ask how such an extraordinarily effective algorithm
     came about. The standard answer, of course, would be 'natural
     selection'.
--- Roger Penrose, _The Emperor's New Mind_

He then goes on to summarize the basic ideas of natural selection as
they would apply to algorithms giving Dawkins (_The Blind Watchmaker_) as
a source for further reading. He continues ...

     Even according to my own viewpoint, there would have to be
     _some_ truth in this picture, since I envisage that much of the
     brain's action is indeed algorithmic, and - as the reader will
     have inferred from the above discussion - I am a strong believer
     in the power of natural selection. But I do not see how natural
     selection, in itself, can evolve algorithms which could have the
     kind of conscious judgements of the _validity_ of other algoritms
     that we seem to have.
--- Roger Penrose, _The Emperor's New Mind_

He elaborates on this idea further and takes into consideration such
arguments as "given enough time, ...", yet remains unconvinced that
natural selection provides the complete answer to the question
posed in his opening statement.

Another quote that may illustrate his point more clearly ...

     Nevertheless, one still might imagine some kind of natural
     selection process being effective for producing _approximately_
     valid algorithms. Personally, I find this very difficult to
     believe, however. Any selection process of this kind could act
     only on the _output_ of the algorithms and not directly on the
     ideas underlying the actions of the algoritms. This is not
     simply extremely inefficient; I believe that it would be totally
     unworkable. In the first place, it is not easy to ascertain
     what an algorithm actually is, simply by examining its output.
     (... deletion of example involving Turing machines ...)
     Moreover, the slightest 'mutation' (say a slight change in a
     Turing machine specification, or in its input tape) would tend
     to render it totally useless, and it is hard to see how actual
     _improvements_ in algorithms could arise in this random way.
     (Even _deliberate_ improvements are difficult without 'meanings'
     being available. ..... )
--- Roger Penrose, _The Emperor's New Mind_