Rating: 
Summary: The clearest statement of Penrose's philosophy to date.
Review: A previous commentator claimed that this book was not readable enough for a mass audience--I have to disagree with this view wholeheartedly. I would say that his previous works, especially "Shadows of the Minds" were difficult to digest due to the amount of mathematics contained in almost all of the chapters (this doesn't negate the power of his ideas--he just makes them hard to understand). This latest work presents all of his major ideas on cosmology, quantum physics, and the nature of the mind in an extremely clear manner. His treatment of quantum physics is the best I've seen to date in a popular work. A short and rewarding read.
Rating:
Summary: The clearest statement of Penrose's philosophy to date.
Review: A previous commentator claimed that this book was not readable enough for a mass audience--I have to disagree with this view wholeheartedly. I would say that his previous works, especially "Shadows of the Minds" were difficult to digest due to the amount of mathematics contained in almost all of the chapters (this doesn't negate the power of his ideas--he just makes them hard to understand). This latest work presents all of his major ideas on cosmology, quantum physics, and the nature of the mind in an extremely clear manner. His treatment of quantum physics is the best I've seen to date in a popular work. A short and rewarding read.
Rating: 
Summary: A platonist speaks out
Review: According to Stephen Hawking, Roger Penrose is a Platonist, who believes there is a unique world of ideas that describes physical reality. I think it is a good thing that someone actually believes Plato was right all the way and makes the case for it concerning Relativity, Quantum Gravity and Consciousness. So, as inspiration I found the book a good read - But I don't particular believe all of Penroses arguments. Especially the part about that our brains can't be modeled by computational systems and hence that strong artificial intelligence will remain in science fiction was to me unconvincing.-Simon
Rating:
Summary: A platonist speaks out
Review: According to Stephen Hawking, Roger Penrose is a Platonist, who believes there is a unique world of ideas that describes physical reality. I think it is a good thing that someone actually believes Plato was right all the way and makes the case for it concerning Relativity, Quantum Gravity and Consciousness. So, as inspiration I found the book a good read - But I don't particular believe all of Penroses arguments. Especially the part about that our brains can't be modeled by computational systems and hence that strong artificial intelligence will remain in science fiction was to me unconvincing. -Simon
Rating:
Summary: With reservations, a fascinating discussion
Review: As my background is mainly in the brain sciences, I was most interested in what Penrose had to say about consciousness and the brain in this book, so I'll concentrate mostly on the chapter that had to do with that. This is not to say I didn't enjoy the other chapters, just that I'm not as qualified to critique those as I am the one on the brain. There has been a lot of speculation in recent years about such things as computability and the brain, quantum consciousness, and so on, and I was interested to find out what Penrose might have to say about that. One of Penrose's major ideas in this chapter is his demonstration that consciousness, although perhaps mathematical, isn't computable, in the sense that you could program a computer to simulate it. Penrose uses the example of geometric tilings or polyominos that are deterministic in their coverage of the Euclidean plane, but that aren't computable, to show this. Since, as Penrose points out, there are plenty of mathematical concepts that aren't computable and that can't be done on a computer, but that the human mind can understand, Penrose concludes that there is something beyond computability in both pure mathematics and the human brain. This is interesting, and Penrose might be right about that. However, I must point out that while consciousness itself may not be computable (and I'm not really prepared to conclude this for sure at this point, because of what I'm about to say), nevertheless, many aspects of the brain's functioning have been shown to be computable, so I'd like to discuss that briefly. For example, sensory neurophysiology has been shown to be both quite mathematical and computational as a result of the work of a pioneering mathematician by the name of David Marr 25 years ago, whose ideas revolutionized neurobiology almost overnight, after which the field was never the same. Marr examined a number of different fundamental sensory mechanisms, and showed, for the first time, that the way in which the visual system was processing light information was consistent with the operation of certain sophisticated spatial-frequency filtering transforms that are well-known in many engineering applications. To mention just a few of his important ideas, Marr's demonstrations that retinal receptive-field geometry could be derived by Fourier transformation of spatial-frequency sensitivity data, that edges and contours could be detected by finding zero crossings in the light gradient by taking the Laplacian or second directional derivative, that excitatory and inhibitory receptive fields could be constructed from "DOG" functions (the difference of two Gaussians), and that the visual system used a two-dimensional convolution integral with a Gaussian prefilter as an operator for bandwidth optimization on the retinal light distribution, were more powerful than anything that had been seen up to that time. It was as if vision research suddenly acquired its own Newtonian Principia Mathematica, or perhaps General Relativity Theory, in terms of the new explanatory power Marr's theories provided. Basically, in one fell swoop sensory neurobiology also became an area of theoretical physics rather than purely biology, giving the area a rigor and elegance never before seen--an amazing achievement for a young man who died so prematurely from leukemia at the age of 36. The main point of all this is that all of these mechanisms are both mathematical and computable, although the way in which they're done in the brain is probably more like how a computer would use numerical analysis to solve a differential equation, rather than using the original equations in a purely analytical way themselves. Since Marr's time, there has been further progress in this area, such as the great Bela Julesz's demonstrations that the visual system can extract and compute binocular disparity cues point-by-point for depth information from abstract, non-representational pictures or textures such as random-dot stereograms, the extension of Marr's ideas about monochromatic edge detection into color edge detection, the mathematical bases of non-linear visual field distortions present in optical illusions, and many other areas. Furthermore, in the last few years, the nature of consciousness itself has been shown to be composed of many different separate mechanisms in the brain that are being coordinated in time in order for consciousness to occur. It simply isn't one process or central program that runs in the brain, nor is there a "master" brain center that one can point to where it can be said that consciousness resides. I'm sure the progress of this research will also have implications for ideas about the nature and computability of consciousness. So overall, a fascinating and enjoyable discussion about the brain and consciousness by Penrose, even if I don't completely accept one of his major ideas about it for the reasons that I discuss above.
Rating:
Summary: A book about the Mind, NOT PHYSICS!
Review: I wrote this review because I felt that none of the reviews so far really got the main cause of this book. This is NOT a book about cosmology (as people would expect from Roger Penrose). In this tiny book, Penrose summarizes his idea that the mind cannot be understood by mathematical processes (something much different from the opinion of 99,99% of neurobiologists, such as Steven Pinker). This view is near to the Nobel laureate Murray Gell-Mann. The book is easy to understand and the ideas are very concise and its recommended for the ones that are interested in intelligence theories (thus, the author assumes that the reader know what a neuron is and how it works!). Some may think this is a difficult to understand book because they didn't had in mind that this book is about Penrose's point of view on intelligence. In fact, I'm not a physicist, nor a biologist, simply a high school student and I found the book very easy to understand, although I do not agree with Penrose's point of view. I think he forgot something very important. Read it and read the other point of view and you'll find what it is! :)
Rating:
Summary: Confused about the importance of Measurement in Schools?
Review: I'll have to read this book several times more. However one only needs to get to about page 5 to appreciate that the topic of space and measurement is complex and encompasses far more than mastery of dividing kilometres, litres, hours etc into handy sized bits. This book might help explain why space and measurement gets a separate rating on your childs report and may give you some hints on how to interest your child in the subject.It is, I think, a common misconception that this part of Math is for those who will do practical things in the "real" world. But where is the "real" world? If something is so small that we are not able to measure it can we be sure it exists at all?
Rating:
Summary: Confused about the importance of Measurement in Schools?
Review: I'll have to read this book several times more. However one only needs to get to about page 5 to appreciate that the topic of space and measurement is complex and encompasses far more than mastery of dividing kilometres, litres, hours etc into handy sized bits. This book might help explain why space and measurement gets a separate rating on your childs report and may give you some hints on how to interest your child in the subject.It is, I think, a common misconception that this part of Math is for those who will do practical things in the "real" world. But where is the "real" world? If something is so small that we are not able to measure it can we be sure it exists at all?
Rating:
Summary: Penrose: Science needs a "revolution".
Review: Let me first say something about Roger Penrose. One notices how certain other mathematicians and mathematical physicists speak of him. He is not only admired and respected; it seems that he is positively enjoyed! This may be a bit surprising when one notices that Penrose is something of a thorn in the side of several popular ideas in contemporary physics (and psychology). Cosmic inflation theories and ideas regarding the fundamental nature of quantum uncertainty find a formidable and articulate critic in the Oxford mathematician. Of the somewhat less popular, but ever fanciful "many-worlds" interpretation of quantum superpositioning, Penrose says "[the 'many-worlds' view] is not a very economical description of the Universe but I think things are rather worse than that for the many-worlds description. It is not just its lack of economy that worries me. The main problem is that it does not really solve the problem." He brings the same mental rapier to what he has called "the missing science" of mind and to the idea of computational / artificial intelligence. It is the problem of superpositioning described by Schrodinger and the decoherence caused by quantum measurement that prompt Penrose's search for an 'objective reduction' (OR) of quantum state vectors, the key ingredient in a "revolutionary" physical theory that remains a mystery. He speculates that this physical mystery may be related to the mystery of consciousness. He is unconvincing in this regard, but his ideas and arguments are quite interesting.
Well, let me now take this a bit further. Penrose also seems to terribly irk certain others! In particular he really raises the hackles of proponents of strong AI and the Dawkins/Dennett camp of 'consciousness-is-merely-mechanism' dogmatists. His views are much closer to those of perhaps most mathematicians and philosophers and stand on a deeper logical footing than do the doctrines that the human mind is mere biology. Let me say that I agree with Penrose in that the 'simple biology' view is never going to win this argument for reasons that can be demonstrated by the application of mathematical logic. To say that Penrose "doesn't understand biology" is to miss the point. The author freely admits, "there is a good deal of speculation in many of these ideas". Of course there is; science is largely -- we might even say wholly -- speculation. A more perceptive analysis would suggest that those committed to a rigid materialistic aesthetic don't understand (don't want to understand) the mathematics. Those who summarily dismiss Penrose do so unwisely. Given his contributions to mathematics (e.g., Penrose tiling, computability, mathematical logic) and his stature within the mathematics community, and given that the history of mathematics is essentially written by mathematicians, Roger Penrose may come to be considered the greatest mathematician of his generation. Given his work on black holes and space-time geometry (he recognizes the apparent "flatness" of the universe but suggests a more elegant geometry to describe that flatness), he may be one of his day's greatest physicists as well. Should his hunch ("OR") one day prove "true", his stature would approach that of a Newton or Einstein. The point being that any scientist who avoids or ignores Penrose's views, or is inclined to dismiss them by erroneously characterizing them, does so, as I say, unwisely.
Chapters 4, 5, and 6 are challenges to Penrose from A. Shimony, N. Cartwright, and S. Hawking, respectively. Apart from Shimony's discussion of A. N. Whitehead's views, its not on a par with the author's discourses; Cartwright suggests that nature may be a mess of "patchwork" laws (her view itself seems a horrible mess), and Hawking is disappointingly flippant. Penrose certainly meets these challenges.
I must say that the "controversy" over Penrose's Platonism is nothing less than nonsensical. Hawking complains "basically, he's a Platonist," as though calling him an offensive name and thereby granting the reader cause to disregard Penrose's arguments. That's unfortunate. Most of history's great minds have been Platonists; even Aristotle*, so often cited as the philosophical godfather of reductionism, was arguably a Platonist. Augustine, Kepler, Descartes, Pascal, Newton, Leibniz, Kant, Linnaeus, Einstein*, Schrödinger, Gödel, Whitehead -- the list of Platonists is long and impressive. As Penrose has said, "... it is my direct personal impression that the considerable majority of working mathematicians are at least 'weak' Platonists." Yet it seems as if some who call themselves "positivists" feel a calling to be science's mind-police. I suggest that this should be the real controversy... So-called positivists would do well to honesty consider Gödel's observation that the idea that mind/mentality is simply material is nothing more than the "prejudice of our time."
There is a rather child-like glee in the way Penrose sees and uses mathematics. His investigations and speculations are those of an extremely astute mind having fun! In his aggressive curiosity, his boldness, his clear-eyed honesty about the frailties of human thought and the limits of science, it seems to me that Penrose is something of a treasure and an inspiration. As he candidly states, "... the world-view that present-day physicists tend to present may well be grossly overstated as to its closeness to completion, or even to its correctness!" This volume presents a concise look at the Penrose ideas/arguments and even if nothing much ever comes of these arguments, they present a shining example of the kind of creative thinking that moves science into new frontiers.
*(footnote: While recognizing that it can easily be argued that Aristotle and Einstein were not "strong" Platonists, it seems obvious to me that they were each Platonists in some fundamental ways. I consider them to have been "weak" Platonists.)
Rating:
Summary: Typically good and heuristic Penrose
Review: My one line summary is praise enough, but I will say that one of your reviewers appears to be miffed because a particular paragraph appeared to be arcane. I had expected, then, to read something about, say, Penrose's writing style. How could I have had such an expectation when that reviewer writes, ". . . there are a number . . ." There are a man who should read books on different topics. There are a man who should buy a book on grammar. There are no chance that he will do so!
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