Describe Yams to the English - "they're like potatoes", only they're not. You realise that when you first taste them, feel cheated by the description others have offered you, then find yourself using it yourself, for want of a better. So it is with books on modern physics, or modern mathematics. These are subjects in which the inmates are in charge of the asylums. It doesn't have to be so, but looks like being so for the forseeable future, for organisational and economic reasons. Who can exorcise, in six hundred pages, the terror of fifteen years of incompetent teaching, half-baked syllabuses, and horrifying examinations? Most attempts merely repeat that trauma. This book is quite the best account of modern physics and mathematics that I have ever come across. It's written by a visionary who has the deep respect of both physicists and mathematicians, and, to me at least, seems to represent a popularisation of the merging of pure mathematics with the mathematic! s of physics, which has been going on since the time of Dirac and Eddington. Penrose makes you believe that it's reasonable to cross the corridors of academe from Quantum Mechanics to Algebraic Topology, and back via Logic and Machine theory without being conscious of barriers; and, that it's reasonable that the people who pay for these games with their taxes might be initiated into them. A beautiful, brilliant book, by a master mathematician at the height of his powers. How do we relate to a subject? In my view, through inspirational journalism. We all "know" that mathematics is a game for young men; because elderly, elegant, Hardy told us so, despite being an obvious counterexample. Just about every distinguished mathematician is rushing into print with their own impenetrable view of the world. In a situation in which the unreadable "Brief History of Time" is an international best seller, you'd suspect that no-one could come up with an account of mat! hematics which is accurate but which also captures the shee! r joy of being involved in it. If anyone has managed that, it is Penrose, with this incredible book.

First published in 1972, it is remarkable that this book is still in print, and this fact attests to the current interest in singularity theorems in general relativity. The author of course is well-known for his contributions in this area, and he has written these series of lectures primarily for the mathematician whose speciality is differential topology, and who is curious about its applications to general relativity. The author thinks in pictures in this book, and so it is well-suited for the physicist reader also. Detailed proofs are omitted for the singularity theorems, but references are given. Much work and discussion has taken place since this book was published, but it can still serve as an introduction to modern developments.

Section 1 sets the mathematical definitions and conventions used in the later sections. Spacetime is defined as a real, four-dimensional connected smooth Hausdorff manifold on which is defined a global smooth nondegenerate Lorentzian metric. In addition, it is assumed that spacetime is time-orientable, which is not too big a restriction since as the author remarks, one can always find a time-orientable twofold covering of spacetime. Jacobi fields are introduced also, with the goal of eventually using them to study maximal geodesics. Known to physicists as the equation of geodesic deviation, the author derives the Jacobi equation, the solutions of which form an 8-dimensional vector space of Jacobi fields.

In section 2, the author gives definitions that allow one to discuss causality and time ordering for curves on spacetime. Special types of non-smooth curves, called trips, which (piecewise) are future-oriented timelike geodesics, are used to define a chronological ordering of points on spacetime. Causal trips are more restrictive, in that the curves are causal geodesics. The chronological ordering is shown to imply causal ordering, and both orderings are shown to be transitive. This allows the partitioning of spacetime into chronological future and past, and causal future and past. The topological properties of these sets are studied, and conditions are given in terms of null geodesics and timelike curves for causal and chronological ordering.

The next section considers the properties of future and past sets. A future (past) set is one that is equal to the chronological future (past) of some set in spacetime. In addition, subsets of spacetime that do not contain any points that are chronologically related, called achronal sets, and subsets that are boundaries are considered. It is shown that spacetime can be written as the disjoint union of an achronal boundary, and a unique past and future set. It is also shown that achronal boundaries are fairly well-behaved objects: they are 3-dimensional topological manifolds.

In order to rule out "pathological" spacetimes that contain closed trips or closed causal trips, the author studies global causality conditions in section 4. Thus the author defines a spacetime to be future (past)-distinguishing if for any two distinct points, their chronological future (past) sets are unequal. He then defines a spacetime to be strongly causal if every point in it has arbitrarily small causally convex neighborhoods (causally convex meaning that it does not intersect a trip in a disconnected set). The author offers examples to show that local violations of causal convexity can be avoided, and so violations of strong causality at a point are due to the global structure of the spacetime. He shows that a spacetime which is strongly causal at a point must be future and past distinguishing at the point. The converse is not true, and the author gives a counterexample. The Alexandrov topology for spacetime is defined in this section also. Given two points in spacetime, a basis for the open sets for this topology is given by the intersection of the chronological future set of one point with the chronological past set of the other. The author shows that spacetime is strongly causal iff the Alexandrov topology equals the manifold topology iff the Alexandrov topology is Hausdorff. Defining a vicious point to be one through which passes a closed trip, and concentrating attention on the set of all vicious points, the author gives five conditions for strong causality to fail at a point, these conditions involving the boundary of the set of vicious points. He concludes the section by showing that if spacetime is compact, it must contain a closed trip.

Motivated by the notion of an initial value set from physicial considerations, the author defines in the next section domains of dependence for achronal subsets of spacetime, along with the future, past, or total Cauchy horizon for closed achronal subsets. These are related to the familiar Cauchy hypersurfaces from the theory of partial differential equations. It is proven that spacetime is globally hyperbolic iff a Cauchy hypersurface exists for it.

The space of causal curves is defined in the next section, on which is defined the C0-topology. It is shown to be compact under certain conditions. The study of geodesics as curves of maximal length is taken up in section 7. This entails matters of a more purely differential geometric point of view. The important inequality involving the Ricci curvature and an element of volume (or area) on a hypersurface. The author discusses briefly the importance of this inequality in the singularity theorems.

The last section is (unfortunately) very brief, wherein the author discusses the applications of the preceeding sections in singularity theorems. Referring to S. Hawking for the full proof, he gives a general argument and discusses the conditions as to when spacetime will have a past-endless geodesic in M which has a finite length. He defines a future-trapped set as one where the "future horizon" of the set, defined as the difference between its causal and chronological future, is compact. He then outlines a proof of the result that no spacetime can have the property that it contain no closed trips, have endless causal geodesics containing a pair of conjugate points, and contain a future-trapped set.

If you've got a fair background in beginning Calculus and elementary physics, you may find this book very worthwhile. I wouldn't know.

Don't be fooled, however, by reviewers who claim that Feynman explains things in such a way that even without those basic tools, the book isn't incomprehensible. I've HAD basic calculus, albeit a LONG time ago, and I'm a tad rusty. And I have even less grounding in physics. But I'm far from mathematically illiterate, or incapable. And it isn't true that I got nothing out of my reading of this book; the sixth chapter did, in fact, answer the question that I'd hoped to have answered when I bought it. But by and large, the book was close to impenetrable. Now, clearly, this may well be due to my lack of preparation in the prerequisites for understanding it. But it definitely is NOT the first step in the process of understanding physics, as one reviewer actually called it and others implied. Read "Six Easy Pieces" first, and brush up on first-year Calculus. THEN consider tackling this book.

These lectures where designed to give the student the reasoning behind relativity. Unlike some books, this book does not just explain the results or phenomena of relativity. Feynman actually explains the problems with Newton's laws and actually derives and gives the reasoning for Einstein's theories about relativity. These lectures need only some calculus and basic physics knowledge to appreciate. However, as with most bonfide scientific literature, the more "mathematically and scientifically mature" the reader the better. Feynman uses pieces of calculus (very basic stuff), algebra (symmetry, vector notation, cross products, and dot products), geometry (non-Euclidian), and basic physics knowledge (conservation laws, Newton's laws, Maxwell's equations etc). You don't need all of this to listen and understand the lectures, but obviously the more the better. Feynman also does a good job of explaining some the mathematics involved as well. The lectures pretty much follow the book so you can read along while you listen. These are actual lectures that Feynman gave at Caltech to undergraduates so they are very rigorous. In short, the lectures were clear, very understandable, and offer something to everyone. You don't need anything more than a solid background in calculus and introductory physics to get something out of these lectures.

Six Not-So-Easy Pieces is the sequel to the book Six Easy Pieces. The first book is a collection of six of the easier lectures from Feynman's freshman and sophomore physics classes at CalTech. Six Not-So-Easy Pieces are some of the more difficult lectures from those classes. In contrast to the first book, these lessons are much more mathematical. Freshman calculus is definitely a prerequisite to reading this book. Courses in vector calculus and differential equations will help the reader to more completely understand the works, but they are not absolutely necessary. However, without much mathematical knowledge, one can just take Feynman at his word for all the equations, reading mainly the conceptual explanations, but one will invariably miss out on some of the points. For anyone reading the book, Feynman's teaching style is something that can be enjoyed. He explains the concepts in a comprehensive and not-too-difficult manner and seems to have a full understanding of what the student in the lecture hall is thinking. The six topics (chapters) covered in this book are: Vectors, Symmetry in Physical Laws, The Special Theory of Relativity, Relativistic Energy and Motion, Space-Time, and Curved Space. This book is in no way a survey of physics. It is more of a sampling of Feynman's teaching. However, the common thread that runs through the six pieces is that they all relate to understanding relativity. For the layman who has a mathematical background and wants to understand the concept of relativity, this book is an excellent help. I would suggest reading Six Easy Pieces before reading this book, but it is not necessary. If you enjoyed reading the first book, I would highly recommend this one and vice versa.

...and almost succeeds in uniting the dissimilar worlds of Biochemistry/cellular mechanics with the subatomic and atomic worlds. Undoubtedly if this book (series of essays/thoughts/lectures) had been written twenty years later, it would be quite different, but as is, it makes some startlingly accurate predictions about the nature of heredity in biological systems. This book is NOT 'quantum mechanics explains life', it is however, the masterwork of one of quantum theories brightest stars, relating the abstract world of subatomic particles to, well, DNA, before anyone knew what it did. Alas, for poor Schrodinger, probabalistic interpretation is much less useful at such a macroscopic level, and the mathematics behind even 'good approximations' of VERY SMALL macromolecules are nearly infinitely more complex than those for, say helium, which cannot be solved exactly (too many variables) itself. But he knew that already, and shows it here. But regardless of any 'after-the-fact' criticism, Schrodinger built something palpable and incredible out of scaling and deduction from the quantum level up. The fact that he struck so close to the mark speaks volumes for the man and for quantum theory in general. Biology is rather more difficult to quantify with wave equations than an alpha particle...not that Schrodinger attempts such an undertaking here, but the point should be understood as pertaining to his background, at least. At any rate, this book is probably not the most pedestrian work one could find on the subject, nor the easiest read. It is however, some awfully foresighted ideas about nature, and is heartily recomended reading for anyone with an in-depth knowledge of biology and chemistry (quantum chemistry/physics would be a good *background* course here), and should be required reading for any molecular biology/biochemistry regimen. This book deserves five stars, and if it wasn't for that article in the late fifties that used quantum tunneling theory to dispute the fact that DNA could be the genetic material of the cell, (not authored by Schrodinger, but using an extension of his ideas, as in most quantum computation) it would have gotten them. Barring that, this is, to my knowledge, the best book about life ever written by a physicist, and contains philosophical insight befitting the greatest sages and philosophers. Or Dr. Schrodinger.

What Is Life? Erwin Schrodinger This book is the compilation of a series of lectures by a Nobel Luareate in quantum physics and attempts to reconcile the biological requirements of living cells to the probabalistic nature of the atom as defined by quantum mechanics. These lectures were originally give in the 1940's and 50's prior to the discovery of DNA, RNA, gene mapping, and other techniques taken for granted by today's biologists. The basic tenant of quantum physics is that all atomic structure can be described only by the mathematics of probability. The exact orbit of an electron or its velocity cannot be determined. One can only state the probability of the location or velocity. Protons and neutrons are thought to change back and forth into one another in a random fashion. The very process of physical measurement introduces errors which preclude accurate measurements. This is modern physics - random events governed by probabilities. Compare this to the biology of living cells. Genetics reproduce specific inherited characteristic for generations. Why does the random atomic behavior not interrupt or change genetic traits? How does humanity think logically using randomly behaving atoms and hence molecules and compounds? This little book attempts and succeeds in theoretically reconciling these two worlds. The author predicts the structure of DNA. He anticipates current studies in how small numbers of randomly acting atoms are constrained to be deterministic. In the latter lectures, he enters the world of metaphysics to discuss "Mind and Matter, Determinism and Free Will, Ethics, and Science and Religion." This book is less than 300 pages long, but encylopic in scope. Be warned that it must be savored to be understood. It cannot be speed read nor can it be read only once to be understood. Finally, two much later in time companion books are "The Quantum Self" and "The Dancing Wu Li Masters" expand the concepts presented by this book. Both are available from Amazon. Joseph I. Schwartz, April 23, 1997

It is not surprising that a genius would have interesting things to say. Physicist Erwin Schrodinger was an affable genius whose comments about life, molecular biology, mind, qualia, and a number of topics are interesting and relevant even today.

This edition of 'What is Life?' by Cambridge University Press also contains Schrodinger's essay entitled 'Mind and Matter,' along with some autobiographical notes. What is Life? is a well paced 1944 version of molecular genetics that is still valid today. Crick and Watson didn't discover the structure of DNA til 1953, so Schrodinger didn't know of replisomes and error correcting polymerase III, but this essay shows how well developed molecular biology was by this time. Crick and Watson were certainly in the right place at the right time by clearing up a minor bottleneck in the broader science of molecular genetics. Mainly what Schrodinger, the formulator of the quantum mechanical wave equation of atoms, wants to accomplish is to reconcile quantum effects with biology. What is Life? makes an excellent synthesis of quantum physics and biology. Where modern scientists like physicist Roger Penrose and chemist Graham Cairns-Smith fail at this correlation Schrodinger is eminently successful. Although this essay is somewhat dated it is stimulating and rewarding to read.

The second essay entitled 'Mind and Matter' written in 1956 is very similar to modern efforts in describing abstract neuro and cognitive science. It tackles many of the same topics as moderns Daniel Dennett, Gerald Edelman, and Antonio Damasio do. Schrodinger artfully blends the idealism of Schopenhauer with his own personal physicist's point of view and crafts a perfectly enjoyable, reflective discussion on the concept of mind. I actually enjoyed Mind and Matter more than What is Life? as it showed the intellectual range of Schrodinger better. His discussion of what he calls objectivation, or how the subjective and objective dynamics of the scientific observer influence one another was great.

Lastly, a brief selection of Schrodinger's writing about his own life rounds out this brief, thoughtful collection of essays by a world class scientist. This relaxing little book still exhibits the ability to invoke serious thought about the nature of life and the implications of consciousness.

A great book, about some of the coolest and most cutting edge theories out there. Certainly not for the layman though. Most of the chapters are filled with equation after equation however those with advanced math and a good math program will have lots of fun. This book is the real deal! Read it all and you just might fry your brain! It would get five stars if it was better organized. The best use of this book is for quick reference if you have a specific idea or question about the topics contained and don't or can't get to the internet. Not a must buy but worth the money.

This book makes the greatest mousepad I've ever had. Good book.

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.)

Roger Penrose's original and provocative ideas about the large-scale physics of the Universe, the small-scale world of quantum physics and the physics of the mind have been the subject of controversy and discussion. These ideas were proposed in his best-selling books The Emperor's New Mind and Shadows of the Mind. In this book, he summarises and updates his current thinking in these complex areas to present a masterful summary of those areas of physics in which he feels there are major unresolved problems. Through this, he introduces radically new concepts which he believes will be fruitful in understanding the workings of the brain and the nature of the human mind. These ideas are challenged by three distinguished experts from different backgrounds: Abner Shimony and Nancy Cartwright as philosophers of science and Stephen Hawking as a theoretical physicist and cosmologist. Roger Penrose concludes with a response to their thought-provoking criticisms.
To see a scientist of Penrose's ability, stature and achievement toss large parts of modern physics into the air as though juggling balls and try to keep them aloft while marshalling them into a coherent pattern is a thing to behold. It is a wonderful illustration of a first-rate scientist doing what first-rate scientists have always done: make bold conjectures and display them for others to confirm, refute or amend

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! :)

Roger Penrose has written a book which transcends all other efforts in probing the patterns of human reasoning. Although the book has generated controversy amongst mathematicians, few who have reviewed this work have stated categorically that he is wrong. Penrose's conclusions are unpleasant for those who believe in strong AI but they may very well be right. The potential reader considering purchasing this book should be aware that the book is technical and requires thought. Penrose does not make allowances for sloppy thinking (although, one has the feeling Penrose thinks he is making allowances). If you are open minded, not given to leaping to conclusions, and genuinely curious about science and human thought, this book plus The Emperor's New Mind, are definitely books for you.

This book is one of the most exciting of its kind.To me,the best science book I ever read. When talking about human brains it is not longer a matter of Computation or the Quantum Model. It's also a quest of one of our primary needs:the knowledge of our selves.Explained from a scientific point of view.It highlights however in a certain way the spiritual dimension of human beings.Without telling us directly,Penrose introduce on the reader's mind phylosophique and religious issues,as possible links on the explanation of the whole. It's true,we can't conclude(after reading the book)we have a definitive explanation,which has been proved right.However on this book,to my knowledge,it's the first time a scientist establish the link:Our Brains:Consciousness and the Quantum Model! If I compare to others books of its kind,such as Stephen Hawkins and Sir Roger Penrose in Space and Time,1995;Leon Lederman in God Particle,1995,Fred A.Wolf in Taking the Quantum Leap,1982 and Star Wave,1984;and finally the previous book of Penrose:The Emperor's New Mind,1990 I have to conclude on the fact that Penrose,on Shadows of the Mind goes beyond frontiers others could not reach before. And I have to analyze briefly the new aspects Penrose approach in a such visionary way:1)The strong possibility that physics(of particles)could be the basis of the appearance of high intellectual functions in our brains(which is quite opposite to the traditional scientific knowledge of the chemical basis being the cause)2)The strong possibility of the emerge of the highest intellectual function:consciousness into the most complex part of our brains:the neuronal synapses(microtubules)and 3)the possibility certain human brains could react differently from the average,because of a different physical arrangement. Of course,conclusions have not ben proved yet.However R.Penrose already advance on his book as examples, some clinical experiments which uses different anaesthetic on patients who loss consciousness;in order to prove his proposal of the new physical basis being the cause of that effect. To me these proposals,if some day proved right are revolutionary on the field of science and on the knowledge of our selves. The link he suggest between the Quantum Model applied to consciousness is not only unique up to now(to my knowledge),but could be the pathway which could lead us to the comprehension of one of the most intriguing,fascinating and really unknowed mystery:Our Brains:How come our consciousness could emerge on it and make us different from animals!And moreover it allows the reader to think on others possible dimensions of his proposals. I do agree:the book isn't for everybody.We have to like the subject and have already a certain knowledge on the matter. If you belong to that category,don't miss it!It's great! (...)

Between the beautifully written prologue and epilogue, this book approaches a range of topics in modern physics in a unique and readable way. Through a continuation of some earlier work, Penrose furthers an argument for brain function and conciousness that many in the artificial intelligence field will not appreciate. He presents his case that the human mind will never be simulated with digital a computer, no matter how complex. But that is not his main focus of this book.

Even more facinating are his calculations which indicate how mathematically unique our existence is under the 2nd law of thermodynamics. To me, it's ultimately ironic that the physical principal which orders our universe and makes intelligent life possible (the 2nd law), is the result of an unimaginably improbable set of initial conditions. Although Penrose never invokes the concept of a creator or supreme being, in my mind, this poses an interesting challenge to those in the scientific community who claim our universe is simply the result of random particle collisions over a long period of time.

If we combine the concepts of similar structures scaling across space and time (tensegrity and fractals), with Penrose's ideas that consciousness may be associated with quantum gravity interactions in microtubules (present in all living cells), perhaps there is far more mystery and beauty to this existence than some would now believe...

This book was satisfying and throught provoking, and I highly recommend it to anyone interested in the mysteries of the very large and the very small.

While parts of this book devoted to the popular description of concepts of modern physics and mathematics hold a pedagogical value for a lay reader, the rest of the book is really poor. The author makes an extremely loose connections between completely unconnected problems, and with surprising immodesty puts forward an extremely contrived theory of mind without providing any semblance of logic, let alone proof. For any scientist familiar with both quantum mechanics and some basic knowledge of biology of the CNS, the main thesis of the book that consciousness is somehow connected to the quantum mechanics of the brain function should certainly look ridiculous; it's a completely arbitrary connection, and no proof is even suggested. The author in effect attempts to employ a very cheap trick to solve two of the greatest problems of modern science and philosophy, the problem of consciousness and the problem of (apparent) ambiguities in the formulation of quantum physics, by deciding to cancel them against each other, linking them with an arbitrary mental construction. How convenient! The suggestion that Godel's theorem proves that human thought is non-algorithmic is laughable; while the theorem is one of the greatest achievements of modern logic, it is only relevant for symbol-based computation, and our brain certainly isn't a purely symbol-manipulating machine: most neural-network computations are not based on applying symbolic rules, although they can be implicitly algorithmic. Besides, to suggest that humans can never encounter a statement that can be neither proved nor disproved is almost humorous in its arrogance: the problem of consciousness alone holds lots of such examples; problems of ethics is another great example. Penrose's argument will only be applicable when we discover a theory of everything and there will be no philosophical questions left to be solved for humanity; only in that case one could say that there are no contradictory statements for a human mind. ...I could go on and on, but this is too long already. I personally find it fascinating that an undoubtedly talented scientist like Penrose, one of the greatest mathematicians of our times, can come up with something as absurd. I guess this can teach the rest of us something about how the human brain works, after all...

No, I'm joking. This is by far the best exposition of...what ? Basically, all the stuff, ranging from AI & algorithms to classical and quantum mechanics, thermodynamics and basic tenets of Big Bang cosmology, is densely packed in 480+ pages & rushes vertiginously the the author's central interest- brain/mind problem & his particular answer to the "why consciousness" mystery. On the strong side- Penrose has most lucidly expounded classical and quantum paradigmata ( plus thermodynamics and orthodox cosmology ). I think his finest writing is contained in these chapters/passages. Chapters from 1-4 ( with the possible exception of chapter 3. ) are a dry read & not illuminating at all. Frankly, I'd say the entire AI, the Turing machine & computability "mythology" is just a scholiasts's fodder, a scholastic verbiage lacking in true cognitive strength.

Ultimately: where does Penrose stand ?

Evidently- he is a "refined" reductionist/epiphenomenalist. I'd say his "consciousness" theory ( he's done not a few papers with Stuart Hameroff on Orch OR model ) is not a breakthrough at all. For better works on quantum physics, one should consult David Bohm's works ( apart from classical textbooks of Landau, Messiah or Sakurai ); for a more thought-provoking "brain" musings- Jean Pierre Changeux & his L'Homme Neuronal. So, although the author has not shown much conceptual audacity and originality, I'm giving this book 4 stars for excellent exposition of chunks of physics for laymen.

The Emperor's New Mind by Roger Penrose is thought provoking and absorbing. Not being a physicist, I thought this work was going to be daunting, but to my surprise the author made the subject readable and understandable.

The physics and mathematics within this book is not hard to understand, but as a layperson quantum mechanics and quasicrystals were rather complex concepts. There are mathematical formulae in this book, but as the author points out read the words and the formula will play out...in other words if you understand the concept the formula only confirms the logic. But as I understand, Heisenberg's Uncertainty principle also tells us that when we try to measure both position and momentum of a particle, not only are we incapable of measuring both simultaneously, but far more incomprehensibly, both the position and momentum cannot exist at the same time. Now, the implication here is that such properties, which we are inclined to think of as inherent properties of the particle, do not exist until they are measured, the Copenhagen Interpretation of quantum mechanics. Particles are really nothing more than probability wave functions that expand infinitely across the universe. So, in the terminology of quantum mechanics, the act of measurement collapses the wave funtction... counter intuitive.

Artificial intelligence will some day match a human mind... awareness and understanding, but to understand the human mind first is what Penrose is trying to explain.

If you have a serious interest in physics, mathematics, philosophy, and artificial intelligence you will like this book.
White and black holes, the structure of the brain and understanding the physicial processes of consciousness all come into play.

This is not light reading, but read it.

To understand the mind, is to understand mankind

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For this novel, in fact, I think 3 stars is a bit generous, although 2 would be too harsh. There are some interesting flashes, but too much of it is philosophising in a preachy sort of way, and when science fiction takes its stand with Chimborazo it seems almost out of place. Most of this novel seems to be set in a desert anywhere on the Earth - I had none of the real alien feel that Mars should give, as so well done by Philip K Dick and C S Lewis in radically different ways, even Ray Bradbury - and who can forget Samuel Delany's 'Triton' - these were real places to visit, really alien and challenging.

And then the people in 'White Mars' seem to be placed there in the ethnically acceptable mix just as they were in 'Star Trek' - a pretty old scenario in present times. I also wonder why so many utopian or alternative societies have to be built on deprived or degraded environments. Even imagined societies I admired immensely, such as Ursula LeGuin's anarchic society in 'The Dispossessed'. About the only way of avoiding the difficulties of evolving a society from where we are today, seems to be by setting it vastly in the future as in H G Wells's 'Time Machine' and W H Hudson's 'A Crystal Age.' To me, I would be much more impressed to have a new social order develop under my nose as I read about it, from the base of our current world and mix of societies.

I am also displeased in that an 'alien' influence seems to be required to 'help' people develop their social skills. Humankind may not be the ideal society we would dream of, but we have achieved enormously and I have confidence that we can keep pushing forward, even through the dark times, into a new and better world and by our own initiative.

In all, I was disappointed in this novel, partly because I have admired so much of Mr Aldiss's earlier work.

The discussion of how to build a better society is central to this book, and it is good. Cut off from Earth by an economic disaster, several thousand Mars colonists are thrown back on their own resources to sustain themselves. The focus is almost exclusively on the Mars of the mind-what kind of society can be formed/should be formed in the isolation of the Martian frontier? The characters endlessly discuss what it means to be human under these conditions. What institutions are necessary, and which ones can be avoided? How are we to raise children? How are we to conduct ourselves in a larger society? How are we to cope with our variegated behaviors when freedom brings us into conflict with one another? These questions and more are raised and raised again.

I don't agree with many of the answers White Mars seems to provide, and so I was tempted to give the book three stars. For example, I don't agree that Mars should be set aside as a scientific preserve. However, I believe the most important thing is that the questions were asked and various opinions aired. White Mars is a valuable addition to the debate on Mars and on how human beings interact with our society.

The science is really beside the point, which also tempted me to give White Mars three stars. The discussion on physics and the quest for meaning at the sub-particle level is half-developed and never really tied into the main story. There's also the discovery of native life on Mars, which is more science fantasy than science fiction. The more mundane science of maintaining a community of several thousand in total isolation on Mars is completely ignored, which is also a disappointment. As an answer to Kim Stanley Robinson's Mars trilogy, White Mars falls so short in this department that I can't even say there was an effort at competition.

At its heart, however, White Mars is a discussion on values and humanity. All other factors aside, this discussion makes the book worth reading and pondering.

After having read "A Brief History of Time", "Black Holes and Baby Universes and Other Essays", "The Cambridge Lectures" and "The Universe In a Nutshell" by the esteemed Professor Hawking, as well as Brian Greene's "The Elegant Universe", I figured this book would be yet another great educational read!

It appears that my initial logic was somewhat flawed.

While the book states at it's outset that it requires an understanding of physics, I believe that it requires either the equivalent mind-power of a Einstein with the cocaine-induced flashes of Freud, or the equivalent computing power of everything Seymour Cray ever built...after several upgrades!

After (during?!) the first chapter, I simply couldn't keep my thoughts from blurring into obscure thoughts of the fact that GM is killing the Camaro after 35 successful years...the price of inkjet printer supplies... Bill...Gates keeps getting away with it...and essentially ANY OTHER TOPIC than that which I was "attempting" to read at the time!

While one of the girls at the coffee shop (I get wired on caffeine, and I read...) who, I must admit, was absolutely, captivatingly exotic, and her mere presence drew my eye more often that I care to admit, using her as an excuse for my distraction would really only be secondary at best.

The fact remains that the book simply isn't written for laymen; it's for scientists...and not just "good" scientists either, but the "truly rare" breed...unfortunately, that breed does not appear to include me. Sure, I can get into Mensa...but this book was almost completely beyond me! (I GOT THE INDEX!!!)

I'd very highly reccommend any or ALL (obviously my choice) of the books I've noted above for anyone with an interest, but as for this one...if you're not working for a PHD, Masters, or at least a Bachelor's degree, save your money, because this'll only make you tear your hair out...for many, it's probably falling quickly enough on its own already.

Not me, of course, as I'm just so pretty my face decided to annex surrounding territory for expansion purposes.

Well...theoretics are theoretics, right?

This was an early attempt to capitalize on Hawking's commercial success with the Brief History. Roger Penrose, Hawking's PhD advisor, has also written some really fascinating books for lay readers on philosophical implications of physics such as on the nature of intelligence. However, combining the two in a debate, the form of this book, cancels out the reader-friendly accessibility of their solo works as their egos take charge and they try to outperform each other. It makes sense after the fact that if they're debating, they must be discussing matters on which they disagree, and since physics is so well settled and understood on all but the most esoteric and advanced questions, the subject matter of their disagreements must lie in that advanced realm. Of course, "advanced" is a vastly relative term to apply to physics, since many ordinary readers would balk at any physics material. But I have a degree in physics, albeit only a BS - and after the initial material I have to struggle to follow anything they're saying! They should stamp this book's cover with a caveat emptor; this is no "Brief History of Time" or "Elegant Universe." They even mention at the outset that they assume the reader has a basic understanding of physics, but these guys' idea of a basic understanding is a Ph.D. specializing in general relativity. Having said all that, the book still makes for heady reading from what I could pick up here and there, so it's a thrill if you're up to it.

In spite of the errors mentioned in another review the discussion was fairly interesting but not as great a "debate" as I anticipated. I'd spend my money on Penrose's "The Emporer's New Mind" before this one. For those interested in Black Holes, Kip Thorne's "Black Holes and Time Warps ..." is exceptionally well written and rewarding for the reader. For the technically [mathematically] apt who wants an fascinating treatice on spacetime, try John Wheeler and Ignazio Ciufolini's book on Geometrodynamics (Princeton Univ. Press).