Roger Penrose, "one of the world's most knowledgeable and creative mathematical physicists," presents in his 1989 Emperor's New Mind one of the most intriguing and substantive popularizations of mathematical logic and physical theory that has ever been published. As a reader of many books written by scientists, I will say that few compare with this one. Penrose wrestles with what he sees as some of science's most inadequate or poorly developed (although popularly accepted) ideas. As certain physical theories are found wanting, his grapplings extend to some of the deepest questions of metaphysics. Of the deepest questions, Penrose says, "To ask for definitive answers to such grandiose questions would, of course, be a tall order. Such answers I cannot provide; nor can anyone else, though some may try to impress us with their guesses." While he speaks respectfully of individuals with whom he has certain differences of opinion, the "some" in that statement might be taken to be Hawking, Dawkins, Dennett, to suggest a few. The author here tends toward a more humble and questioning approach. Penrose's puzzlings are complex, creative, and speculative, and even his admirers might easily misrepresent certain of his opinions and conjectures. A case in point may be the fact that he finds cosmic inflation theories to have less explanatory power than others claim for them -- this doesn't mean he necessarily rejects inflation, rather he doubts claims that inflation significantly helps explain the specialness of the early universe. Positivists may be disposed to discount the problem but there appears to be good reason for Penrose's skepticism. However this is not treated in this volume.
Rigorously building a case against the fundamental arguments for strong AI, Penrose begins with what for him is to ultimately be 'le coup de grâce', considerations and arguments from mathematical logic. If the human mind works non-algorithmically, then we know of no way to digitize/program its processes. The mind does in fact function non-algorithmically, a fact demonstrated without much difficulty. It learns in intuitive, non-linear, and mysteriously creative ways. The idea that some non-algorithmic approach might achieve a program equivalent to the human mind is not supported by any "useful" (or better, see below) physical theory and is not mathematically tenable. Strong AI is thus relegated to a mere ideological preference (and obviously to sci-fi). In his mathematical considerations, Penrose is most interested in the work of Turing and Gödel and in the Platonic essence of mathematics itself. Concluding that the human mind cannot be reduced to an algorithm (or any set of algorithms), Penrose next questions whether the mind might be reducible physically. Here he finds the questions and answers less well defined than he has in mathematics. His tour of classical and quantum physics features interpretations and ideas that many readers may have not encountered (which makes the text fun). The problem of "correct quantum gravity" (that is, the incompleteness [or incorrectness?] of relativity and quantum theories) is one that Penrose and other theoreticians have struggled with for decades. Penrose wonders if this mysterious and conspicuously missing physical theory might be related to the also conspicuously missing science of mind. This speculation on his part is the theme also of his more recent books. As Erwin Schrödinger (like Einstein and Gödel, Platonists all) seems to be one whose ideas are of particular interest to Penrose, I will cite Schrödinger's view: "Consciousness cannot be accounted for in physical terms. For consciousness is absolutely fundamental. It cannot be accounted for in terms of anything else." But Penrose doesn't quite argue this view, although it would seem an obvious conclusion from his best arguments. Here is a classic example of how we may know 'something' without knowing everything: we can know that the human mind cannot be reduced to an algorithm -- or algorithm of algorithms -- and yet it is not known whether we can even know precisely what mind is. Particularly so if, as Schrödinger says, mind is irreducible.
The chapter on cosmology is excellent, as one might expect of a Roger Penrose. The consideration of the "specialness" of the initial [cosmological] conditions and of the relationship of this specialness to the second law of thermodynamics is also fascinating as it is precisely the second law that lends the "arrow of time" its apparent non-symmetrical aspect -- in other words, defines physical reality as we experience it. In this sense, the second law connects the human mind to the cosmos (which is interesting but does nothing to help us "reduce" mind).
Penrose suggests, and I cannot find any reason to disagree, that all scientific theories can be assigned to one of three broad categories, which he calls: (1.) SUPERB, (2.) USEFUL, (3.) TENTATIVE. All SUPERB theories (there are roughly a dozen) stand within the purvey of physics, and: "It is remarkable that all the SUPERB theories of Nature have proved to be extraordinarily fertile as sources of mathematical ideas. There is a deep and beautiful mystery in this fact: that these superbly accurate theories are also extraordinarily fruitful simply as mathematics. No doubt this is telling us something profound about the connections between the real world of our physical experiences and the Platonic world of mathematics." Over time, theories (particularly those that do not feature such mathematical beauty or fertility) may tend to move between the categories. Theories held to be SUPERB for centuries have dropped completely from the current categories; theories have faded and re-emerged. . . "we should not be too complacent that the pictures that we have formed at any one time are not to be overturned by some later and deeper view."
Some readers will not like the fact that, after extensive rumination on very difficult and deep questions (like "what is mind?"), the author doesn't conclude with a pretense that he, or anyone else, has definitive answers. This reader appreciated the integrity of Penrose's questionings and of his conclusions (or lack of conclusions). I will misappropriate one of Penrose's terms -- as a text examining mathematics, physics, and the human mind, this volume is SUPERB.
