The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Popular Science)

For those people who didn't make it through the book, here is a (perhaps oversimplified) summary.

Assumption 1 : Machines function algorithmically. The human brain functions at least partly non-algorithmically

Assumption 2 : There are some mathematical problems that can not be solved by algorithms f.i. proving the correctness of a self-referring statement.

Conclusion from 1 and 2 : Humans are able to solve problems that machines will never be able to solve.

Assumption 3 : Intelligence means being able to solve every possible problem.

Conclusion : Humans are intelligent, machines will never be intelligent.

My thoughts on this :

assumption 1 : Non-algorithmically ? There is not a shred of evidence of non-algorithmic thinking in humans. There are on the other hand plenty of mechanisms taking place in the brain that are clearly algorithmic (like vision, pattern recognition etc.)

assumption 2 : Apparently Penrose believes that humans are able to solve these problems. I am not so sure. I challenge you to answer the next question correctly : Will you answer "no" to this question ? It cannot be answered correctly. It is in the nature of the problem itself. The problems Penrose mentions are of the same nature.

assumption 3 : We don't know the nature of consciousness. We have no understanding of what intelligence implies. Penrose believes it implies that an intelligent creature is able to solve EVERY problem. Therefore, if there is one problem a machine can not solve, the machine is not intelligent.

So the only thing Penrose has to do to prove his point is ask a question that has no correct answers : ask the machine to overcome the incompleteness theorem of G?del, or to answer the above question correctly. (and ignore the fact that people cannot answer it correctly either).

I have enjoyed the book in a way ... while seeking arguments to demolish Penrose's theory.

I don't think I can finish the book in its entirety--partly because it's clumsy and difficult and partly because Penrose has given me no reason to buy into the big-picture arguments he makes on consciousness.
Whether his motivation is theism or simply a "science is presumptuous and arrogant" mindset, it seems to me that Penrose fundamentally operates in a nonscientific manner here. He takes an incompletely-understood effect (human consciousness), rejects the simplest explanation (materialism), and crafts a clouded and speculative alternative explanation instead.
Whatever happened to Occam's Razor? Do we really need to invoke such esoteric explanations for human consciousness? And at what biological level does Penrose believe that algorithmic, materialist processes stop accounting for the observed level of awareness--bacterium? Insect? Chimpanzee?
Another reader characterized this book as "a poor man's Gödel, Escher, Bach." I agree, in that it reiterates many of the topics that Hofstadter's brilliant work covered nearly a decade earlier. There are at least two huge differences, though: first, the magic of GEB is the remarkable way that Hofstadter tied everything together into his grand thesis. In contrast, Penrose throws in ideas like non-periodic tiling but does not manage to integrate them into his whole. Of course, the huge difference is that GEB was a great ode to the limitlessness of conscious reason (whether human or not), while this book seems like little more than a rear-guard lament.
Granted, some will still read my review as an arrogant, presumptuous, and ill-informed diatribe. Well, I'll stick to science and progressivism. We still haven't lost a knowledge battle--there are just some we haven't won yet.

A wonderful survey of physics, mathematics, philosophy, and the mind. It is a welcome reality check to "Strong AIers" who are for the most part people who have read too much science fiction.

Five hundred pages of extremely dense technical exposition leading up to a somewhat disappointing sixty-page argument. If you already know advanced physics and discrete mathematics at an academic level, you can probably follow his explanations. But then you wouldn't need them - you could just skip to the end. If you don't already know this stuff, you're in for a real battle. To keep from giving up in despair, I recommend additional web research on the topics as you go along to complement the book.

My copy of this book is now 21 years old, but I thought it appropriate to write a short historical review. When I first read this book I was interested to read in a semi-technical way about many of the Physics and Computation ideas of Roger Penrose. I am sure that many are still interested in the book for that reason. Since then Penrose has written other books, but this provides an introduction to his ideas which is half way between popular science and textbook. What has happened in the years that have followed is that this work has undoubtedly stimulated many researchers and others.

The other aspect of the book was his specific arguments about AI: which have ired many critics. Indeed his later book (Shadows of the Mind) contained a revised argument and dealt with about 20 criticisms of the AI argument from this book. Nevertheless this was not enough and more criticisms appeared which he later discussed in other works. So there is quite a trail to follow here for those who wish to take these topics seriously.

I would now suggest that he was really trying to make the case for the importance of non-Turing-Computability in this book. That it is important in scientific arguments from Cognition Theory and AI to Quantum Physics. Non-Turing computability is a very subtle topic to discuss (it was the subject of Turing's logic Ph.D) especially in a philosophically broad way. Many of the topics like Fractals and Penrose Tiling which found their way into this book, and do not immediately seem relevant to the arguments, are there to emphasise and display some non-computable mathematical entities. Oversimplifications of Penrose's arguments usually miss the significance of non-computability in them.

Having said all this I think that were this book to be written now, then some sections could be reworded. As a specific detail I think that in discussing the historical evolution of "algorithm" the definition of that term changes in the book without being noticed. It took me a few readings to notice this.

So if you want to delve into the debate about non-computability in physics and AI this is a book to read, but be aware that it is only the beginning of a longer story. The physics/cosmology discussions are a good introduction to his approach to those topics too.

When I first encountered the book in my college library, I brushed it aside as I had heard of Roger Penrose as a famous theoretical Cosmologist and disingenuousness of him writing a popular science book put me off from reading it (Martin Gardner, in preface also states this). But curiosity got better off me, I was hooked when I read the first chapter - where such fundamental questions as What is mind? Do computers think? What is intelligence? are all discussed with such ease that we fail to grasp that we are being led to his magnum opus with the best possible introduction ever. Once Penrose has taken his stand in first chapter that he is a skeptic of the boastfulness of proponents of strong Artificial Intelligence (AI), he slowly and surely develops the background for his argument in the next few chapters, in possibly the best ever introduction to computer science and Quantum Mechanics (QM).

His thesis is that Godel's Theorem, Turing's solution to Halting problem and exposition of theoretical limits of computation, non computability of classical systems and the mysteriousness of collapse of QM wave function at the instant of measurement (classical and QM world collide) are all indications that current theories are insufficient to describe the operations of mind. He also touches on the incompatibility between general theory and QM as a source of revolutionary new workings in science of mind. And also that human mind is no algorithmic computer. Human thought process transcends strict logical algorithms through what he calls as "insight" - which he terms as the non algorithmic part of mathematics. Penrose also proposes vignettes of his novel explanation of the working of mind and intelligence in the last two chapters of the book.

This is a carefully argued book with concise and precise introductions of most of modern physics and computer science. Second and fourth chapters are little demanding for non specialists. The book has everything in range to cater to an informed enthusiast and also to the most proficient practitioner of the subjects. (Try derive the Turing number of a Universal Turing Machine) Mr. Penrose will come across as an individual with strong belief in the methods of science but, as the boy in the preface is, unafraid to ask some uncomfortable questions at the current state of thinking related to some of the most fundamental human interest conundrums. I do agree that strong AI is now not as prominent as it was in late 60s till 80s, but the relevance of the book according to me is the timeless nature of his explanations of physics and computers in his peerless classic pedagogical language, which makes it a classic of excellent science writing. I have observed that this book being sold in even some very ordinary book stalls, which itself attests to the continued popularity of the classic.

After reading this book twice and having it in my book shelf for last 6 years, I couldnt but marvel at the breadth and the authority with which the material is covered in this book, so much so that if I ever get stranded in an island and can have only one scientific book with me, it would be "Emperors New Mind".

I bought this book thinking that it was written for scientific non-experts. I was very wrong. I have a masters degree in electrical engineering, so I probably have more scientific background than most of the general public. Even so, I found Penrose's book to be almost impenetrable. The topics range from soup to nuts: classical physics; general relativity; quantum mechanics; Mandelbrot sets and fractals; thermodynamics; cosmology and the big bang; computer science; physiology of the brain. Every so often, Schrodinger's wave function and black holes are thrown in for good measure. Unfortunately, these diverse topics are never brought together into a coherent thesis.

Furthermore, I found many of the ideas presented in this book as being outdated and incorrect. Examples of some of the egregious errors I found in the book include the statement that black holes destroy information and that entropy equals missing information. A more modern (and more technically correct) treatment of entropy and information can be found in "A Farewell to Entropy" by Arieh Ben-Naim, and Stephen Hawking changed his mind about black holes -- they don't destroy information.

Penrose makes the claim that the second law of thermodynamics is a consequence of quantum gravity. A more modern (and correct) view is exactly the reverse. As Erik Verlinde has shown, gravity is an entropic force that emerges from the second law.

Penrose repeatedly reverts to a very outdated reductionist description of reality, which assumes that the whole is equal to the sum of its parts; i.e., physical systems are linear superpositions of complex quantum-mechanical wave functions. The Schrodinger's Cat "paradox" is resurrected for the upteenth time, even though there really is no paradox. (I thought the tired notion of a quantum-mechanical cat that is simultaneously dead and alive had been finally laid to rest decades ago.)

It came as no surprise when Penrose articulated the reductionist evaluation of the human brain: "In fact, there are a lot of similarities between the action of a great number of interconnected neurons and the wires and logic gates ... It would not be hard, in principle, to set up a a computer simulation of the action of a given such system of neurons. The brain is a thinking machine, no different than with consciousness an algorithm that is carried out by electrical impulses transmitted among neurons. A natural question arises: does this not mean that whatever the detailed wiring of the brain may be, it can always be modelled by the action of a computer?" In other words, is the whole (the brain) equal to the sum of its parts (the neurons)? Is consciousness nothing more than a computer algorithm carried out by cellular logic gates?

Penrose brought the quantum-mechanical processes, U and R, into the discussion of consciousness. (Along with Schrodinger's Cat, U and R are repeatedly dragged into practically every topic in this book. U represents the linear, deterministic superposition of complex quantum wave functions and R represents the reduction, or "collapse", of the wave function into real, probabilistic actualities. Penrose states that in addition to causing the second law of thermodynamics, gravity, specifically the graviton particle, is responsible for triggering the R process.) After some hand-waving, Penrose concludes that even U and R are not up to the task of explaining consciousness, and therefore something "beyond" quantum mechanics is required to explain it. But what is "beyond" QM? Unfortunately, the book leaves that question unanswered.

A great example of how not to write a non-science book. Just awful. Save your money for someone who knows how to write these kinds of books, like Brian Greene, Kip Thorne or Sean Carroll.

My mind is still spinning.The first third of the book covered Turing machines, non-recursivity in the Mandelbrot set, and non-computability in lambda calculus. Supposedly the phenomenon of knowing/understanding/consciousness is proven by Goedel’s theorem not to be possible to explain in terms of an algorithm, but I didn’t understand the argument. I found it very confusing. I am used to authors that do not explain things well, but in this case I got the impression that many of the subjects were just too much for me. There were too many moving parts for my brain to juggle at once to be able to understand. I was impressed.
The second third of the book covered subjects more familiar to me, such as relativity, quantum mechanics, and phase space. At this point the feeling of being inadequate was replaced by a feeling that the subjects were being explained rather poorly. After applying myself for some time and making guesses as to what the author probably meant, I believe I finally understand Hilbert space (a term I had heard before, but had never had explained to me), but I am still totally lost when it comes to the Riemann sphere. Here, the author went down numerous tangents unimportant to his case, including Newtonian mechanics, special relativity, tessellation, tidal forces, non-Euclidean geometries, and numerous details as to exactly how quantum superpositions are calculated. Everything that could have been covered in one page was covered in three or more.
The final third of the book wrapped up his main argument and contained fewer diagrams and equations than the first two thirds. He continued to go down numerous tangents (such as mapping out all the major parts of the brain) and also take a long time getting to his point. He would break things down unnecessarily, yet still without explaining it. Also, several times it would seem as if he would conclude something to be impossible, only to raise an objection I had thought was already answered, only to then claim that this was in fact equivalent to the old objection (still without explaining well or proving his claim) and conclude the something to be impossible again, only to then raise yet another equivalent objection.
Even now, I am left confused about several things. At one point, he dismisses one of the alternate interpretations of quantum physics (there are several), saying the collapse of the wave function is deterministic and non-random, but later in the book he requires that it is random to make up for the information loss thought to occur in black holes. In one part of the book he claims that there is nothing in known physics to explain the asymmetry of time (which is why his hypothesis is needed), yet later claims that the WEYL component of general relativity (a part of known physics since 1915) does just that.
Despite all this, I still give the book four stars for sheer ingenuity in tying several things together to explain several persistent problems in physics. His solution (though he admits it still needs some working-out in the mathematical details) simultaneously makes compatible gravity and quantum mechanics, explains how quasicrystals (non-periodicity!) can form, explains how it is we live in a universe with such low entropy, and paves the way for an understanding of consciousness. It would be impossible for me to explain it in writing in any reasonable amount of time, and I don’t want to spoil the book for you, so you’ll have to buy it.

i find this book to be the only one i know on what is close to being computational neuroscience translated to popular science material.