What do you think?
Rate this book
The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics
Will a computer eventually be able to do everything a human can do? For decades, proponents of artificial intelligence have argued yes. In The Emperor's New Mind, eminent physicist Roger Penrose argues that there are facets of human thinking, of human imagination, that can never be emulated by a machine. Exploring a dazzling array of topics —complex numbers, black holes, entropy, quasicrystals, the structure of the brain, and the physical processes of consciousness— Penrose demonstrates that laws even more wondrously complex than those of quantum mechanics are essential for the operation of a mind.
466 pages, Paperback
First published January 1, 1989
1571 people are currently reading
18188 people want to read
About the author
Roger Penrose
104 books1,318 followersSir Roger Penrose is a British mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge, and University College London.
Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity".
Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity".
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 363 reviews
July 12, 2025
I've been reading this one since June and it's now 3 days til Christmas!
Roger Penrose is a famous mathematician who worked with Stephen Hawking on black holes and who has done ground breaking work elsewhere (including on the surprisingly fundamental issue of tiling 2D spaces!).
The book is about the nature of intelligence and whether it really can be an emergent property of algorithmic procedure (i.e. Turing Machines, i.e. computers as we know them). Many people believe that intelligence can arise from sufficiently complex algorithms operating on sufficiently powerful computers. Penrose is in a minority that doesn't.
In order to make his point Penrose starts with issues of non-computability. A Turing Machine represents every possible algorithmic computer (including all the ones we've made), and there are many questions (regarding whether certain processes will stop or not) that Turing Machines can be proved to be unable to answer. This relates to Godel's proof that in any formal system (like mathematics) it is possible to pose questions that can't be answered within the system.
Penrose says that the human brain can answer many such unanswerable questions (in a similar way to that in which it discovers new mathematics) using inspiration.
I have reservations about this whole "the brain can answer unanswerable questions bit". I mean, sure, the brain can give an answer in these cases where a Turing machine might not be able to. But is it the correct answer? Can the brain prove it to be correct? I'm not so sure. It seems more that we just have a heuristic limit to how far we'll spend on a question...
In order to consider how the brain might be capable of things that Turing Machines are not Penrose then spends 85% of his fat book on a tour through science. And I mean pretty much the whole of physics plus some more. This is of course a whistle-stop tour, through mechanics, relativity, electro-magneticism, quantum mechanics, the formation and death of the universe etc ... To someone with a physics degree it constitutes a refresher course. I'm worried that to pretty much any one else it would be dull and incomprehensible. Additionally, given that most readers will not, in the time and detail available, really grasp much of it ... it's fairly pointless. The basics/feel of his final arguments could have been delivered by a less extensive tour of the whole of physics.
At the end of it Penrose needs to postulate a quantum mechanical source for the brain's proposed ability to do what a computer (of any Turing Machine sort (including quantum computers, apparently) can't. This is a hard sell as entanglement and other quantum phenomena don't seem to have macroscopic impact in a hot/noisy environment such as that brain. However, Penrose does lay out an interesting possible architecture for quantum gravity and the way in which the quantum and classical world may be unified within a theory. These suggestions also play interestingly into the business of time/the flow of time/the fact we perceive a present, past and future. And yes, at the end of it all he even manages to get his tiling into it.
Most of all, for me, this a heartening book not so much for the solutions it offers but for showing/reminding me just how much we don't know and that there are plenty of dark spaces in our knowledge/theories where all manner of surprises (including ones about the nature of intelligence) may lurk.
A good read wrapped around an over-long physics 101 that's too complex for pretty much anyone without a physics degree.
[it should be noted that I do have a physics degree, a math-based PhD, and years of experience working on research problems in the 'AI' area.]
Join my Patreon
Join my 3-emails-a-year newsletter #prizes
...
Roger Penrose is a famous mathematician who worked with Stephen Hawking on black holes and who has done ground breaking work elsewhere (including on the surprisingly fundamental issue of tiling 2D spaces!).
The book is about the nature of intelligence and whether it really can be an emergent property of algorithmic procedure (i.e. Turing Machines, i.e. computers as we know them). Many people believe that intelligence can arise from sufficiently complex algorithms operating on sufficiently powerful computers. Penrose is in a minority that doesn't.
In order to make his point Penrose starts with issues of non-computability. A Turing Machine represents every possible algorithmic computer (including all the ones we've made), and there are many questions (regarding whether certain processes will stop or not) that Turing Machines can be proved to be unable to answer. This relates to Godel's proof that in any formal system (like mathematics) it is possible to pose questions that can't be answered within the system.
Penrose says that the human brain can answer many such unanswerable questions (in a similar way to that in which it discovers new mathematics) using inspiration.
I have reservations about this whole "the brain can answer unanswerable questions bit". I mean, sure, the brain can give an answer in these cases where a Turing machine might not be able to. But is it the correct answer? Can the brain prove it to be correct? I'm not so sure. It seems more that we just have a heuristic limit to how far we'll spend on a question...
In order to consider how the brain might be capable of things that Turing Machines are not Penrose then spends 85% of his fat book on a tour through science. And I mean pretty much the whole of physics plus some more. This is of course a whistle-stop tour, through mechanics, relativity, electro-magneticism, quantum mechanics, the formation and death of the universe etc ... To someone with a physics degree it constitutes a refresher course. I'm worried that to pretty much any one else it would be dull and incomprehensible. Additionally, given that most readers will not, in the time and detail available, really grasp much of it ... it's fairly pointless. The basics/feel of his final arguments could have been delivered by a less extensive tour of the whole of physics.
At the end of it Penrose needs to postulate a quantum mechanical source for the brain's proposed ability to do what a computer (of any Turing Machine sort (including quantum computers, apparently) can't. This is a hard sell as entanglement and other quantum phenomena don't seem to have macroscopic impact in a hot/noisy environment such as that brain. However, Penrose does lay out an interesting possible architecture for quantum gravity and the way in which the quantum and classical world may be unified within a theory. These suggestions also play interestingly into the business of time/the flow of time/the fact we perceive a present, past and future. And yes, at the end of it all he even manages to get his tiling into it.
Most of all, for me, this a heartening book not so much for the solutions it offers but for showing/reminding me just how much we don't know and that there are plenty of dark spaces in our knowledge/theories where all manner of surprises (including ones about the nature of intelligence) may lurk.
A good read wrapped around an over-long physics 101 that's too complex for pretty much anyone without a physics degree.
[it should be noted that I do have a physics degree, a math-based PhD, and years of experience working on research problems in the 'AI' area.]
Join my Patreon
Join my 3-emails-a-year newsletter #prizes
...
February 2, 2025
What is Consciousness? To answer this scientific question, which touches our deepest being, does not currently have any theory. And, not knowing how to define this notion satisfactorily, how could she find a rigorous method to approach the question of its nature?
However, we have a subjective perception of consciousness since we are aware. However, we cannot express this perception in terms of scientific objectivity. Thus, we find ourselves faced with a curious paradox: the only absolute certainty that any conscious being can have, the existence of one's consciousness, remains inaccessible to scientific explanation today.
Many scientists evade the question by considering consciousness to be only an emergent phenomenon resulting from the brain's activity, which is regarded as similar to that of a computer.
This question is not Roger Penrose's opinion. In this book, this great mathematician and physicist strives to rigorously address this difficult question of the nature and functioning of consciousness. Admittedly, he cannot, for the moment, formulate a rigorous theory. Still, he takes us on a fantastic journey into the world of scientific discoveries of the twentieth century, a journey designed so that he can give us the fascinating tracks that he glimpses avenues that may one day allow science to understand consciousness and the spirit.
He clearly and rigorously presents valuable concepts for this reflection, such as algorithms, Turing machines, determinism, and computability. It gives us an overview of quantum physics, general relativity, and the problems posed by the incompatibility between these two grand theories. His analysis leads him to believe that a future unifying theory that solves this problem would provide a way to understand the nature of consciousness.
His reflections led him to imagine a link between quantum non-locality and consciousness, to formulate audacious hypotheses to account for both the growth of quasi-crystals and the functioning of the brain. He makes us feel the troubling role of time in the nature and functioning of consciousness.
As you will understand, this book is an excellent source of reflection for anyone deeply intrigued by consciousness and, ultimately, by who we are.
But beware: Although Roger Penrose proves to be an excellent popularizer and presents his ideas with great clarity, this book does not read like a novel. Also, if you are allergic to equations, you may suffer!
However, we have a subjective perception of consciousness since we are aware. However, we cannot express this perception in terms of scientific objectivity. Thus, we find ourselves faced with a curious paradox: the only absolute certainty that any conscious being can have, the existence of one's consciousness, remains inaccessible to scientific explanation today.
Many scientists evade the question by considering consciousness to be only an emergent phenomenon resulting from the brain's activity, which is regarded as similar to that of a computer.
This question is not Roger Penrose's opinion. In this book, this great mathematician and physicist strives to rigorously address this difficult question of the nature and functioning of consciousness. Admittedly, he cannot, for the moment, formulate a rigorous theory. Still, he takes us on a fantastic journey into the world of scientific discoveries of the twentieth century, a journey designed so that he can give us the fascinating tracks that he glimpses avenues that may one day allow science to understand consciousness and the spirit.
He clearly and rigorously presents valuable concepts for this reflection, such as algorithms, Turing machines, determinism, and computability. It gives us an overview of quantum physics, general relativity, and the problems posed by the incompatibility between these two grand theories. His analysis leads him to believe that a future unifying theory that solves this problem would provide a way to understand the nature of consciousness.
His reflections led him to imagine a link between quantum non-locality and consciousness, to formulate audacious hypotheses to account for both the growth of quasi-crystals and the functioning of the brain. He makes us feel the troubling role of time in the nature and functioning of consciousness.
As you will understand, this book is an excellent source of reflection for anyone deeply intrigued by consciousness and, ultimately, by who we are.
But beware: Although Roger Penrose proves to be an excellent popularizer and presents his ideas with great clarity, this book does not read like a novel. Also, if you are allergic to equations, you may suffer!
March 12, 2009
I suggested that one could imagine Albertine's gang in A L'Ombre Des Jeunes Filles En Fleurs as a kind of wave function of girls (see my review), and that made me think of The Emperor's New Mind. Given that it's all about quantum mechanics, I suppose it's appropriate that I have two different and completely incompatible reactions to it. On one hand, I am annoyed with Penrose. OK, he is a great genius in his own field, but why does that give him a license to come in and pronounce on the things I do, hardly even bothering to quote anyone who actually works in Artificial Intelligence? How would he feel if, say, Peter Norvig were to write a book on quantum theory, quoting only AI and computer science people, and making it sound like all the real quantum theorists were irrelevant? Many other AI people I know who have have read the book feel similarly.
On the other hand, Penrose's suggestion that we should think of people's minds as quantum-mechanical systems is interesting. In fact, I'd go further than that: it's sometimes a useful thing to do in real life! At least, I find myself thinking that more often than you might suppose. Here's what I mean. Often, it makes little sense to ask whether a person "really" thinks A, or if they rather think its opposite, B. It's more useful to imagine that they are in a superposed state, which is a combination of A and B. You can perform an observation, and force them into an eigenstate: then they will indeed have to take a stand as to whether it's A or B. But doing this changes the situation; you may wish you'd been sensible enough not to carry out the observation, and just left things superposed.
I think these observations are particularly relevant in serious romantic quarrels. Next time you are unfortunate enough to get into one, and if you are sufficiently interested in these issues to remember the experiment you're supposed to do, consider whether it's intuitively reasonable to model the other person's state as a superposition of "actually still loves you", "totally pissed off, had enough", and possibly other eigenstates. If you do think this is reasonable, consider whether your best strategy is to try and force them into an eigenstate, or leave it superposed. (I would LOVE data here). Personally, I think it's often best to try to leave the state superposed. Is this just a fancy way of describing a conflict-avoiding cop-out strategy, or is it some kind of insight? Again, my answer would be the one you so often get in quantum theory: both, even though they seem to contradict each other.
As you can see, I am eagerly awaiting the publication of A Quantum Theory of Love. Please, won't someone hurry up and write it? But I think Penrose is the wrong guy to do this job.
On the other hand, Penrose's suggestion that we should think of people's minds as quantum-mechanical systems is interesting. In fact, I'd go further than that: it's sometimes a useful thing to do in real life! At least, I find myself thinking that more often than you might suppose. Here's what I mean. Often, it makes little sense to ask whether a person "really" thinks A, or if they rather think its opposite, B. It's more useful to imagine that they are in a superposed state, which is a combination of A and B. You can perform an observation, and force them into an eigenstate: then they will indeed have to take a stand as to whether it's A or B. But doing this changes the situation; you may wish you'd been sensible enough not to carry out the observation, and just left things superposed.
I think these observations are particularly relevant in serious romantic quarrels. Next time you are unfortunate enough to get into one, and if you are sufficiently interested in these issues to remember the experiment you're supposed to do, consider whether it's intuitively reasonable to model the other person's state as a superposition of "actually still loves you", "totally pissed off, had enough", and possibly other eigenstates. If you do think this is reasonable, consider whether your best strategy is to try and force them into an eigenstate, or leave it superposed. (I would LOVE data here). Personally, I think it's often best to try to leave the state superposed. Is this just a fancy way of describing a conflict-avoiding cop-out strategy, or is it some kind of insight? Again, my answer would be the one you so often get in quantum theory: both, even though they seem to contradict each other.
As you can see, I am eagerly awaiting the publication of A Quantum Theory of Love. Please, won't someone hurry up and write it? But I think Penrose is the wrong guy to do this job.
February 3, 2013
First of all, I absolutely love Penrose.
His style simply amazes me! There's this feeling that he wants to tell you SO MUCH and that he's trying hard to control himself so that he doesn't end up with a book several thousand pages long. Also, it's obvious that he enjoys science and mathematics on a really profound level. Those two things are really what kept me on the edge of my seat (when I wasn't reading while walking) while I was reading this book!
As someone interested both in neuroscience and mathematical physics I found this book absolutely brilliant and fascinating. If you came to this book from the purely neuroscience side and really don't like mathematics and physics, then MAYBE this book isn't for you, but personally, I like how Penrose isn't afraid at all to go into mathematically detailed stuff when he feels it is necessary to do so... and some things are not so trivial to understand!
One more thing... I've seen many people (including a decent number of reviewers here) claiming that Penrose is nuts and that this book is filled with bollocks and nonsense, that he isn't logical, factual and whatnot...
So, I was very careful and skeptical about this book and I have to say that people who say so are not fair to Penrose. Whenever he introduced something that wasn't widely accepted or something extremely speculative, he explicitly stated so, over and over again!
Besides, it's not like he doesn't know what he's talking about... we should never appeal to authority as an argument (and I'm not doing that), but keep in mind that he isn't just some crazy old guy who doesn't know anything!
Bottom line, you should form your own opinion about it, but I strongly recommend this book and I'm looking forward to reading Penrose's Road to Reality!
His style simply amazes me! There's this feeling that he wants to tell you SO MUCH and that he's trying hard to control himself so that he doesn't end up with a book several thousand pages long. Also, it's obvious that he enjoys science and mathematics on a really profound level. Those two things are really what kept me on the edge of my seat (when I wasn't reading while walking) while I was reading this book!
As someone interested both in neuroscience and mathematical physics I found this book absolutely brilliant and fascinating. If you came to this book from the purely neuroscience side and really don't like mathematics and physics, then MAYBE this book isn't for you, but personally, I like how Penrose isn't afraid at all to go into mathematically detailed stuff when he feels it is necessary to do so... and some things are not so trivial to understand!
One more thing... I've seen many people (including a decent number of reviewers here) claiming that Penrose is nuts and that this book is filled with bollocks and nonsense, that he isn't logical, factual and whatnot...
So, I was very careful and skeptical about this book and I have to say that people who say so are not fair to Penrose. Whenever he introduced something that wasn't widely accepted or something extremely speculative, he explicitly stated so, over and over again!
Besides, it's not like he doesn't know what he's talking about... we should never appeal to authority as an argument (and I'm not doing that), but keep in mind that he isn't just some crazy old guy who doesn't know anything!
Bottom line, you should form your own opinion about it, but I strongly recommend this book and I'm looking forward to reading Penrose's Road to Reality!
February 6, 2016
The contents of quantum mechanics is the highest peak
Among every physics books.
Climax of this book Quantum gravity theory is not currently elucidated.
Description of the structure of the brain is very weak,
Currently, neuroscience is progressing rapidly
Books in the system are better than this book.
What is consciousness?
The answer has not yet been answered.
We should expect the book of the future of neuroscience.
I also am going to read the recent books in this system.
because fMRI and PET have been developed, human brain is easy to inspect and measure.
Continuum hypothesis has not yet been proven.
Since the beginning of the 20th century
Quantum mechanics and molecular biology have been to lead the modern science.
The last item quantum gravity theory and neuroscience.
This is currently under investigation.
The former is not yet known.
The latter has been elucidated little by little by the spread of medical equipment.
Among every physics books.
Climax of this book Quantum gravity theory is not currently elucidated.
Description of the structure of the brain is very weak,
Currently, neuroscience is progressing rapidly
Books in the system are better than this book.
What is consciousness?
The answer has not yet been answered.
We should expect the book of the future of neuroscience.
I also am going to read the recent books in this system.
because fMRI and PET have been developed, human brain is easy to inspect and measure.
Continuum hypothesis has not yet been proven.
Since the beginning of the 20th century
Quantum mechanics and molecular biology have been to lead the modern science.
The last item quantum gravity theory and neuroscience.
This is currently under investigation.
The former is not yet known.
The latter has been elucidated little by little by the spread of medical equipment.
April 13, 2012
After scanning the host of negative reviews of this book, I feel compelled to speak my piece. I've read this book more than once, and often return to it and find a few more nuggets. Is seems to me that there are few other books that grapple as honestly with the nature of consciousness. The AI community, and materialist scientists who start with the premise that --- it's all in the brain; we don't know how or where but one day we will know, are the people that Penrose challenges. This book predictably annoys them. Since the book's publication in 1989, when Penrose asserted that the nature of consciousness will not be explained in materialistic terms, his prediction has proved true. We're no closer to understanding consciousness than we were then.Perhaps, as Penrose suggests, we're like scientists trying to build a perpetual motion machine, who still don't accept the second law of thermodynamics, stating that such a machine cannot be built. It's a blow to our human hubris when a scientist makes a proposition that begins with the words: "It is not possible..." Using arguments based on Godel's theorem of incompleteness, and the work of Turing, Penrose makes a credible case for why consciousness will never be explained in materialistic terms. In so doing he steps on a lot of toes. But maybe he's right. 2 plus 2 will never be 5 either.
October 24, 2008
It's hard for me to rate this one:
the bulk of the book was a great deal of fun,
in the vein of "Goedel, Escher, Bach";
the concluding section seemed astonishingly
ill-conceived. There's a big debate around
this, but the connections he makes strike
me as terribly wrong. Incompleteness doesn't
prove the human mind does something no machine
can do, and microtubules do not allow brain-wide
coherence for special quantum-supercharged
thinking that results in consciousness.
But watching Icarus crash and burn might be as much
fun as watching him soar high and proud until then,
so I certainly recommend this book to anyone who
enjoys following a brilliant mind broadly exploring
math and science.
the bulk of the book was a great deal of fun,
in the vein of "Goedel, Escher, Bach";
the concluding section seemed astonishingly
ill-conceived. There's a big debate around
this, but the connections he makes strike
me as terribly wrong. Incompleteness doesn't
prove the human mind does something no machine
can do, and microtubules do not allow brain-wide
coherence for special quantum-supercharged
thinking that results in consciousness.
But watching Icarus crash and burn might be as much
fun as watching him soar high and proud until then,
so I certainly recommend this book to anyone who
enjoys following a brilliant mind broadly exploring
math and science.
November 3, 2012
This is a great mathematical book, which goes deep into many mathematical and philosophical ideas.I was 17 when i first picked it up at a library and this book was my introduction to many mathematical concepts and quantum mechanics.
The basic premise of the author in this book is that human consciousness cannot be simulated computationally.his hypothesis that the human brain is a quantum-mechanical structure is very interesting.
Not an easy read, but definitely worth going through.
October 7, 2008
First, the good. Penrose weaves tales of science, philosophy, and history that few others can, due to his wide-ranging and vast intellect. He touches on a wealth of interesting subjects in this book and his enthusiasm for them bleeds through the pages. In particular, this book offered the most illuminating introduction to entropy (in the "Cosmology and the arrow of time" chapter) that I have ever read. In short, before I read it, I didn't believe in the second law of thermodynamics. After I read it, I could interpret the entire world through "entropy goggles". In other books, entropy was some esoteric concept; here it is a beautiful and central feature of our universe.
Now, the irritating. Penrose's stated goal in this book is to convince the reader that strong AI will not be realized. In other words, what human brains do, no computer ever could. Yet, however many fascinating ideas he introduces, his core evidence is little more than hope that what he does as a mathematician is unique; that human "aha!" moments are somehow distinguished from anything a computer ever does.
Penrose fervently declares that he is no "formalist", claiming that the mere idea of a computer arriving at mathematical proofs makes the pursuit of mathematical truth "meaningless". Why? A computer may arrive at such a truth, but it is the human's role to make human meaning out of it. Meaning isn't some quality embedded into the fabric of our universe. It is a manufactured human ideal - a wonderful, enjoyable one at that.
Penrose goes on to cite the vague notion of "reflection principles" (the imprecise methods by which the human mind discovers mathematical truth "upon reflection") as above and beyond algorithms. He uses these "aha!" moments as support for his argument that algorithms cannot possibly imitate what we do. Yet, how can we be so sure that these "aha!" moments do not arise from some complicated algorithm themselves?
Perhaps, any human-created set of mathematical axioms will always be subject to "reflection principles" and only a more intelligent species could create a set for which there are no human-generated "reflection principles". Perhaps the notion of computability simply refers to a hierarchy of skill among complex adaptive systems. (If anyone knows of a book or research on such an idea, please let me know)
Finally, on Penrose in general. Penrose's books tend to occupy a literary no-man's-land between popular science and technical writing: too technical for the average hobbyist yet not deep enough for a student in the sciences. It seems he's just too damn smart to recognize what falls into each category (for example, he might spend half a chapter explaining fractions and then breeze through Hamiltonians in half a paragraph). For me, he's best as a connector of mathematical and physical ideas after I've been formally introduced to them.
As any good book should do, this one did leave me with a few questions (besides the above):
Which is a deeper truth - math or physics?
In reflecting on the story non-Euclidean geometry, what else are our evolutionary adaptations leading us to falsely assume?
Has anyone checked whether Hamiltonians would be deterministic for computable universal constants and discrete input?
Can we really separate dynamical equations from boundary conditions? Are not boundary conditions simply consequences of other not-yet-understood dynamical equations?
March 26, 2010
Here's what I think: Roger Penrose is wrong, and smart enough to convince himself he's right. I know he's smart because the journey he provides to his thesis is so rich with disparate concepts (I awarded an entire extra star just for the chapter that introduces quantum mechanics, for example). Unfortunately the logic that ties the whole thing together doesn't speak to me.
The purpose of the book is to argue that strong AI is fundamentally impossible. He argues this from the last place I think is left for such a position. If we can simulate the action of a neuron, and if it's possible to know how neurons are connected, then in principle we can duplicate a brain and thus, it seems, a mind. Therefore, strong AI is possible, UNLESS brains depend on exotic physics not yet understood. He's very careful to distinguish between intelligence and consciousness: technical advances may make it possible for software to write symphonies, but that software, he claims, won't be conscious without taking advantage of certain quantum gravity effects which have not yet been observed and which are currently explained by no rigorously tested theory.
There's a lot of suspense building to the thesis at the end, which he keeps well hidden up to then, intentionally or not. The author doesn't jump ahead to give a peek at how the chapter in question fits into the big picture; rather, he restates his thesis and promises again and again that he's about to prove it. In the end, the logic is underwhelming. Part of his argument actually rests on the impossibility of genetic programming, a technique that became popular a decade after publishing.
I can easily allow the possibility that brains take advantage of exotic physics to perform computations; biology is a top down discipline, and in many respects the bottom, the basic physical reality of the phenomena in question, is nowhere in sight. But I'm less convinced that consciousness can't arise without those effects; and, anyway, it remains possible to simulate THOSE effects in a computer, and thus to build a strong AI. The whole thing smells like the scientific writings of an intelligent, scientifically read creationist, doing whatever logical gymnastics are necessary to prove the desired point, as much to oneself as to anyone else.
One possibility the author allows for is that the quantum gravity effects he's postulating are deterministic, but non-computable. That is, that the state of a system, if it were known, implies how the state will evolve next with no possible randomness, yet the state in the future cannot be CALCULATED, even in principle. It's a neat idea that may or may not be sensible and I don't have any more to say about it.
It's a good book. The math, physics, and computer science are all intensive, but Penrose is a good writer and pleasant to read. I don't regret the several weeks it took me to finish.
The purpose of the book is to argue that strong AI is fundamentally impossible. He argues this from the last place I think is left for such a position. If we can simulate the action of a neuron, and if it's possible to know how neurons are connected, then in principle we can duplicate a brain and thus, it seems, a mind. Therefore, strong AI is possible, UNLESS brains depend on exotic physics not yet understood. He's very careful to distinguish between intelligence and consciousness: technical advances may make it possible for software to write symphonies, but that software, he claims, won't be conscious without taking advantage of certain quantum gravity effects which have not yet been observed and which are currently explained by no rigorously tested theory.
There's a lot of suspense building to the thesis at the end, which he keeps well hidden up to then, intentionally or not. The author doesn't jump ahead to give a peek at how the chapter in question fits into the big picture; rather, he restates his thesis and promises again and again that he's about to prove it. In the end, the logic is underwhelming. Part of his argument actually rests on the impossibility of genetic programming, a technique that became popular a decade after publishing.
I can easily allow the possibility that brains take advantage of exotic physics to perform computations; biology is a top down discipline, and in many respects the bottom, the basic physical reality of the phenomena in question, is nowhere in sight. But I'm less convinced that consciousness can't arise without those effects; and, anyway, it remains possible to simulate THOSE effects in a computer, and thus to build a strong AI. The whole thing smells like the scientific writings of an intelligent, scientifically read creationist, doing whatever logical gymnastics are necessary to prove the desired point, as much to oneself as to anyone else.
One possibility the author allows for is that the quantum gravity effects he's postulating are deterministic, but non-computable. That is, that the state of a system, if it were known, implies how the state will evolve next with no possible randomness, yet the state in the future cannot be CALCULATED, even in principle. It's a neat idea that may or may not be sensible and I don't have any more to say about it.
It's a good book. The math, physics, and computer science are all intensive, but Penrose is a good writer and pleasant to read. I don't regret the several weeks it took me to finish.
April 6, 2014
I did a back-of-the-envelope calculation and told Roger that the decoherence times were at least ten orders of magnitude too low for the brain to be a quantum computer. No response. Then Max did it more carefully and said they were twenty orders of magnitude too low. Any advance on twenty?
Sigh. I love Roger, but sometimes he just won't listen.
Sigh. I love Roger, but sometimes he just won't listen.
June 30, 2013
I got so bored... too much formalism with having to explain all the mathematical and physical principles from the ground up before adding his own thoughts to the theme of consciousness. It all became too mucky to follow and keep track of, it felt more like a textbook for Penrose's ideas rather than an enlightening conversation that could offer me food for thought which I could digest.
July 14, 2024
Roger Penrose's commentary ably dispels "Strong AI" proponents' belief that it is possible to create machines that possess true human-like cognitive abilities with arguments ranging from microtubular quantum effects in human brain function to Gödel's Incompleteness Theorems.
January 16, 2021
Penrose's magnum opus, The Road to Reality, is supposed to be great but notoriously difficult, so I went for this one, aimed at a general reader. Penrose claims that his arguments "do not require mathematical knowledge beyond that of elementary school", but seems to have a high opinion of elementary schools, covering inter alia the lambda calculus, the Argand plane of complex numbers, Hamiltonian mechanics, the Lorentz equation, Hilbert space, quantum gravity, cosmology and algorithmic complexity theory. In fact the goal of this quick tour through some of the twentieth century's push to the foundations of mathematical and physical reality is to put forward a theory of mind. Although not following every detail, I thought I had a general sense of what was going on most of the time, but still could not tell you what a Ricci tensor is.
The essential bit of this book is an attack on the computational theory of mind, popular among researchers and practitioners in AI (undergoing a "winter" when this book came out in 1989), whereby the brain is essentially nothing different from a universal Turing machine, implemented in wetware, just with some algorithmic and processing tweaks that make it better at identifying bicycles in pictures, appreciating poetry and feeling conscious, and which advances in hardware and AI algorithms will soon be able to replicate. There are all kinds of objections to this theory, philosophical and technical, but Penrose focuses on one closer to his area of expertise: that the brain is able to process things which are essentially uncomputable. In his preface hie gives the example of Goodstein numbers, which are unprovable by the regular axioms of maths, but still can be proven to terminate in zero. The broader idea is that there exist facts that we know despite being infinitely recursive by serial calculation, implying that our brains must work by some other mechanism.
Penrose's thesis is that this has to do with quantum uncertainty. Despite being highly regarded in his field (including winning the most recent Physics Nobel), this theory seems to be considered a bit out there both by neuroscientists/psychologists and by physicists, but Penrose sticks to his guns (most recently in this podcast) while cheerfully acknowledging that he is a lone voice. When you are this famous, you get one crazy idea - just ask Avi Loeb!
The book gives a potted history of physics, classifying theories as superb (there are very few of these), useful, tentative and misguided. Even the superb theories are just approximations of reality and break down at a certain resolution, but their extreme closeness to reality is awe-inspiring. From Euclid to Galileo, from Newton to Maxwell to Einstein, it has often occurred that physical discoveries are based on some new and beautiful maths. This surprising connection strengthens Penrose's belief in the reality of at least some mathematical Platonic objects (e.g. Mandelbrot sets!) - a view known as realism - while conceding that not every equation must have Platonic reality. Finally he reaches quantum electrodynamics, fundamentally an attempt to resolve the classical contradiction between everything being particles (as in Newtonian mechanics) and everything being fields (as in Maxwell's equations). The bizarre conclusion of the physicists, that the particle's state seems to change based on whether we are observing it or not, is to Penrose connected to the mystery of consciousness, and he speculates that the collapse of the wave-function might be related to what goes on in conscious brains. The final chapter of the book contains a summary of how brains work and where such a theory might fit in. Penrose points out that some think the unconscious mysterious but conscious thought understandable (after all, we can recall and explain it), but he thinks the unconscious understandable (since the primitive "lizard brain" mostly follows simple rules) but consciousness very hard! He muses on the connection between the two in creative thought, when the unconscious sometimes seems to shoot out ideas, which are then evaluated by the conscious mind.
Some things have changed since Penrose wrote this book (amusingly, he says that the truth of Fermat's Last Theorem "is still unknown", just four years before Andrew Wiles proved it). AI has gotten a lot better, and is much in the public eye. Nonetheless, the essential points Penrose makes all still obtain, and we will probably wait much longer - perhaps forever - before understanding this issue fully.
A note on the audiobook: the narrator reads mathematical notation literally, ignoring the fact that it is often easier to speak such statements than to write them, so for example "1 + Tₙ(n) × H(n;n) = Tₖ(n)" is read as "one plus T n open parenthesis n close parenthesis times H open parenthesis n n close parenthesis = T k open parenthesis n close parenthesis", rather than "Turing machine n given n times Turing machine H given n and n equals Turing machine k given n", which is longer to write but much easier to say and understand. This is even worse when discussing the lambda calculus with all its parentheses!
The essential bit of this book is an attack on the computational theory of mind, popular among researchers and practitioners in AI (undergoing a "winter" when this book came out in 1989), whereby the brain is essentially nothing different from a universal Turing machine, implemented in wetware, just with some algorithmic and processing tweaks that make it better at identifying bicycles in pictures, appreciating poetry and feeling conscious, and which advances in hardware and AI algorithms will soon be able to replicate. There are all kinds of objections to this theory, philosophical and technical, but Penrose focuses on one closer to his area of expertise: that the brain is able to process things which are essentially uncomputable. In his preface hie gives the example of Goodstein numbers, which are unprovable by the regular axioms of maths, but still can be proven to terminate in zero. The broader idea is that there exist facts that we know despite being infinitely recursive by serial calculation, implying that our brains must work by some other mechanism.
Penrose's thesis is that this has to do with quantum uncertainty. Despite being highly regarded in his field (including winning the most recent Physics Nobel), this theory seems to be considered a bit out there both by neuroscientists/psychologists and by physicists, but Penrose sticks to his guns (most recently in this podcast) while cheerfully acknowledging that he is a lone voice. When you are this famous, you get one crazy idea - just ask Avi Loeb!
The book gives a potted history of physics, classifying theories as superb (there are very few of these), useful, tentative and misguided. Even the superb theories are just approximations of reality and break down at a certain resolution, but their extreme closeness to reality is awe-inspiring. From Euclid to Galileo, from Newton to Maxwell to Einstein, it has often occurred that physical discoveries are based on some new and beautiful maths. This surprising connection strengthens Penrose's belief in the reality of at least some mathematical Platonic objects (e.g. Mandelbrot sets!) - a view known as realism - while conceding that not every equation must have Platonic reality. Finally he reaches quantum electrodynamics, fundamentally an attempt to resolve the classical contradiction between everything being particles (as in Newtonian mechanics) and everything being fields (as in Maxwell's equations). The bizarre conclusion of the physicists, that the particle's state seems to change based on whether we are observing it or not, is to Penrose connected to the mystery of consciousness, and he speculates that the collapse of the wave-function might be related to what goes on in conscious brains. The final chapter of the book contains a summary of how brains work and where such a theory might fit in. Penrose points out that some think the unconscious mysterious but conscious thought understandable (after all, we can recall and explain it), but he thinks the unconscious understandable (since the primitive "lizard brain" mostly follows simple rules) but consciousness very hard! He muses on the connection between the two in creative thought, when the unconscious sometimes seems to shoot out ideas, which are then evaluated by the conscious mind.
Some things have changed since Penrose wrote this book (amusingly, he says that the truth of Fermat's Last Theorem "is still unknown", just four years before Andrew Wiles proved it). AI has gotten a lot better, and is much in the public eye. Nonetheless, the essential points Penrose makes all still obtain, and we will probably wait much longer - perhaps forever - before understanding this issue fully.
A note on the audiobook: the narrator reads mathematical notation literally, ignoring the fact that it is often easier to speak such statements than to write them, so for example "1 + Tₙ(n) × H(n;n) = Tₖ(n)" is read as "one plus T n open parenthesis n close parenthesis times H open parenthesis n n close parenthesis = T k open parenthesis n close parenthesis", rather than "Turing machine n given n times Turing machine H given n and n equals Turing machine k given n", which is longer to write but much easier to say and understand. This is even worse when discussing the lambda calculus with all its parentheses!
June 5, 2010
Penrose sets out to prove that strong AI (minds simulated on digital computer being equivalent to biological minds) is impossible. He argues that minds depend on a physical process which, while perhaps deterministic, is non-computable and therefore can't be simulated on a Turing machine. This was quite convincingly argued, and in the process Penrose takes you through probably the most comprehensible description of quantum theory that I've read in popular form. Not shying away from using the odd formula helps keep the ideas concrete and generally didn't freak out this reader too much.
His reason for covering so much physics in order to explain his opinion on AI is that he thinks the process that turns quantum physics on the very tiny scale into classical physics on human scales is the non-computable process essential to consciousness (and is necessarily tied to quantum gravity).
The discussion of the limitations of current theories seems much more insightful than the typical very speculative and fantastical projections of possible future physics found in popular cosmology. In particular, Penrose makes an interesting prediction about a future more complete theory: it will be time asymmetric (whereas current theories don't care what direction you run time in), and a low entropy start to the universe will be an essential feature of it (explaining the 2nd law of thermodynamics).
He does have the (rather odd) idea that the 'platonic world' of mathematical truths can be reached from the mind (via this non-computable physical process), which is how mathematicians can 'see' the truth of mathematical propositions which would stump a purely algorithmic mind (since that algorithmic mind can't figure out the truth of its gödel sentences).
I think it is more likely that these propositions are being analyzed in a more heuristic and error-prone way. But this implies cognitive closure which would be a shame.
This book didn't resolve any of my philosophical problems with consciousness...
Anyway, you should read this.
His reason for covering so much physics in order to explain his opinion on AI is that he thinks the process that turns quantum physics on the very tiny scale into classical physics on human scales is the non-computable process essential to consciousness (and is necessarily tied to quantum gravity).
The discussion of the limitations of current theories seems much more insightful than the typical very speculative and fantastical projections of possible future physics found in popular cosmology. In particular, Penrose makes an interesting prediction about a future more complete theory: it will be time asymmetric (whereas current theories don't care what direction you run time in), and a low entropy start to the universe will be an essential feature of it (explaining the 2nd law of thermodynamics).
He does have the (rather odd) idea that the 'platonic world' of mathematical truths can be reached from the mind (via this non-computable physical process), which is how mathematicians can 'see' the truth of mathematical propositions which would stump a purely algorithmic mind (since that algorithmic mind can't figure out the truth of its gödel sentences).
I think it is more likely that these propositions are being analyzed in a more heuristic and error-prone way. But this implies cognitive closure which would be a shame.
This book didn't resolve any of my philosophical problems with consciousness...
Anyway, you should read this.
July 10, 2012
بسم الله الرحمن الرحيم
"بالعربي و دغري و من الآخر" كتاب من أجمل ما قرأت في حياتي حتى الساعة!
الكتاب يبحث في السؤال الشهير: هل يمكن للآلة (الحاسوب) أن تقلد ذكاء الإنسان الصرف؟ و هل سيأتي زمن تصبح فيه الحواسيب ذات و عي وشعور؟!
وللإجابة على مثل هذه التساؤلات العلمية الفلسفية يذهب بك الكاتب في جولة على أهم وأشهر المفاهيم والنظريات الفيزيائية ويشرحها بأسلوب علمي دقيق جميل سلس يسهل على غير المختصين فهم الجزء الكبير منه. و الهدف من البحث في هذه المفاهيم و النظريات هو استخدامها في الإجابة على السؤال الذي يبدأ به الكتاب وهو هل سيكون للحاسوب ذكاء إنساني ووعي و شعور؟
هذه الرحلة التي يصحبك بها الكاتب لا تخلو من صعوبات، ففهم كل ما في الكتاب أمر عسير على غير المنختصين، و لكنه ممتع و يشعرك بالتحدي إن لم تكن من المختصين، وإياك أن يكون ذلك سبباً في عزوفك عن قراءة الكتاب، فكما يقول لك الكاتب إن الأمر ليس بالصعوبة التي تتوقعها. ومهما كنت بعيداً عن هذه المفاهيم وتلك النظريات فلن تخرج خاوي اليدين من قراءتك لهذا الكتاب، بل ستخرج بالكثير من المعلومات الممتعة والمفيدة عن القوانين التي تحكم كوننا هذا.
الكتاب في عشرة فصول. يبدأها الكاتب بفصل تحت عنوان:
01. أمن الممكنأن يكون للحاسوب عقل؟
وهو فصل يكاد يخلو من أية مفاهيم رياضية ويقتصر على المحاكمة العقلية والمناقشة الفلسفية. لذلك تستطيع قرائته مهما كنت بعيداً عن الفيزياء، ومثله في ذلك مثل الفصلان الآخيران ( التاسع والعاشر).
02. الخوارزميات وآلات تورنغ:
وهو فصل يتحدث فيه بشيء من التفصيل عن الخوارزميات، التي يزعم أنصار الذكاء الاصطناعي الذي يعتقدون بإمكانية الوصول للذكاء الاصطناعي (ويجبيون بـ نعم على السؤال المطروح في بداية الكتاب) والذين يزعمون أن عمل الدماغ يشابه خوارزمية معقدة لا أكثر، ويسعى الكاتب في بحثه و تعمقه في الخوارزميات أن يوصل لك الفكرة التي تبرهن عملياً أن الدماغ لا يمكن أن يكون كذلك. فكما قلت لك يهدف الكاتب في كل فصوله من تسخير هذه المفاهيم التي يشرحها لتخدم وجهة نظره في الإجابة على ذلك السؤال التاريخي.
03. الرياضيات والواقع
04. الحقيقة والبرهان والبصيرة
05. العالم الكلاسيكي
06. سحر النظرية الكمومية وغموضها
07. الكوسمولوجية (علم الكون) وسهم الزمن
08. البحث عن الثقالة الكمومية
في هذه الفصول يعرض الكاتب جملة من أشهر النظريات الفيزيائية - من النسبية إلى الكمومية و غيرها الكثير - و يشرحها ويجول معك في رحابها الجميلة بأسلوب قل نظيره! وفي سبيل الغاية ذاتها - الوصول إلى جواب مقنع للتساؤل الأول.
09. الأدمغة الحقيقية:
و يعرض لك فيها مقدمة رائعة عن بينة الأدمغة الحقيقية ومقارنتها بالحاسوب، ليصل بالنهاية إلى أن في العقل البشري شيئاً غير خوارزمي يكسبه ميزات الوعي و الشعور و الذكاء.
10. أين تكمن فيزياء العقل:
يلخص لك فيه وجهة نظره ويطرح فيه أفكاره في هذا السياق.
و بذلك ستنتهي مع هذا الكتاب رحلة أقل ما يقال عنها أنها خلابة و أجمل من الخيال!
وهذه بعض السطور من مقدمة المترجمين (محمد وائل الأتاسي، د. بسام المعصراني، مراجعة د. محمد المراياتي):
"نضع بين يدي القارىء العربي كتاباً متميزاً نال منذ صدوره شهرة كبيرة. فهو كتاب علمي بقدر ما هو فلسفي، جدي بقدر ما هو ممتع، شامل بقدر ما هو عميق. سعى كاتبه - الرياضي المعاصر الشهير روجر بنروز - إلى تفنيد الآراء التي تتحدث عن ذكاء اصطناعي وبين أن التفكير الإنساني يتمتع بمميزات كثيرة أهمها الشعور أو الوعي الذي لا يمكن للفيزياء في وضعها الراهن أن تفسره، ولا للآلة أن تقلده. وقد رأى المؤلف انه لا بد، لكي يثبت لنا ذلك، من أن يأخذنا في جولة استغرقت منه عشرة فصول مليئة بالمعلومات الشائقة المتنوعة التي قلما أتيح لكاتب أن يجمعها أو لكتاب واحد أن يضمها بين دفتيه. فهي تتضمن إلى جانب المعلومات المتنوعة معلومات عن الرياضيات وفلسفتها وعلم الكون وتنبؤاته وبينة الدماغ و فيزيولوجيته ومبادئها الأساسية..."
"بالعربي و دغري و من الآخر" كتاب من أجمل ما قرأت في حياتي حتى الساعة!
الكتاب يبحث في السؤال الشهير: هل يمكن للآلة (الحاسوب) أن تقلد ذكاء الإنسان الصرف؟ و هل سيأتي زمن تصبح فيه الحواسيب ذات و عي وشعور؟!
وللإجابة على مثل هذه التساؤلات العلمية الفلسفية يذهب بك الكاتب في جولة على أهم وأشهر المفاهيم والنظريات الفيزيائية ويشرحها بأسلوب علمي دقيق جميل سلس يسهل على غير المختصين فهم الجزء الكبير منه. و الهدف من البحث في هذه المفاهيم و النظريات هو استخدامها في الإجابة على السؤال الذي يبدأ به الكتاب وهو هل سيكون للحاسوب ذكاء إنساني ووعي و شعور؟
هذه الرحلة التي يصحبك بها الكاتب لا تخلو من صعوبات، ففهم كل ما في الكتاب أمر عسير على غير المنختصين، و لكنه ممتع و يشعرك بالتحدي إن لم تكن من المختصين، وإياك أن يكون ذلك سبباً في عزوفك عن قراءة الكتاب، فكما يقول لك الكاتب إن الأمر ليس بالصعوبة التي تتوقعها. ومهما كنت بعيداً عن هذه المفاهيم وتلك النظريات فلن تخرج خاوي اليدين من قراءتك لهذا الكتاب، بل ستخرج بالكثير من المعلومات الممتعة والمفيدة عن القوانين التي تحكم كوننا هذا.
الكتاب في عشرة فصول. يبدأها الكاتب بفصل تحت عنوان:
01. أمن الممكنأن يكون للحاسوب عقل؟
وهو فصل يكاد يخلو من أية مفاهيم رياضية ويقتصر على المحاكمة العقلية والمناقشة الفلسفية. لذلك تستطيع قرائته مهما كنت بعيداً عن الفيزياء، ومثله في ذلك مثل الفصلان الآخيران ( التاسع والعاشر).
02. الخوارزميات وآلات تورنغ:
وهو فصل يتحدث فيه بشيء من التفصيل عن الخوارزميات، التي يزعم أنصار الذكاء الاصطناعي الذي يعتقدون بإمكانية الوصول للذكاء الاصطناعي (ويجبيون بـ نعم على السؤال المطروح في بداية الكتاب) والذين يزعمون أن عمل الدماغ يشابه خوارزمية معقدة لا أكثر، ويسعى الكاتب في بحثه و تعمقه في الخوارزميات أن يوصل لك الفكرة التي تبرهن عملياً أن الدماغ لا يمكن أن يكون كذلك. فكما قلت لك يهدف الكاتب في كل فصوله من تسخير هذه المفاهيم التي يشرحها لتخدم وجهة نظره في الإجابة على ذلك السؤال التاريخي.
03. الرياضيات والواقع
04. الحقيقة والبرهان والبصيرة
05. العالم الكلاسيكي
06. سحر النظرية الكمومية وغموضها
07. الكوسمولوجية (علم الكون) وسهم الزمن
08. البحث عن الثقالة الكمومية
في هذه الفصول يعرض الكاتب جملة من أشهر النظريات الفيزيائية - من النسبية إلى الكمومية و غيرها الكثير - و يشرحها ويجول معك في رحابها الجميلة بأسلوب قل نظيره! وفي سبيل الغاية ذاتها - الوصول إلى جواب مقنع للتساؤل الأول.
09. الأدمغة الحقيقية:
و يعرض لك فيها مقدمة رائعة عن بينة الأدمغة الحقيقية ومقارنتها بالحاسوب، ليصل بالنهاية إلى أن في العقل البشري شيئاً غير خوارزمي يكسبه ميزات الوعي و الشعور و الذكاء.
10. أين تكمن فيزياء العقل:
يلخص لك فيه وجهة نظره ويطرح فيه أفكاره في هذا السياق.
و بذلك ستنتهي مع هذا الكتاب رحلة أقل ما يقال عنها أنها خلابة و أجمل من الخيال!
وهذه بعض السطور من مقدمة المترجمين (محمد وائل الأتاسي، د. بسام المعصراني، مراجعة د. محمد المراياتي):
"نضع بين يدي القارىء العربي كتاباً متميزاً نال منذ صدوره شهرة كبيرة. فهو كتاب علمي بقدر ما هو فلسفي، جدي بقدر ما هو ممتع، شامل بقدر ما هو عميق. سعى كاتبه - الرياضي المعاصر الشهير روجر بنروز - إلى تفنيد الآراء التي تتحدث عن ذكاء اصطناعي وبين أن التفكير الإنساني يتمتع بمميزات كثيرة أهمها الشعور أو الوعي الذي لا يمكن للفيزياء في وضعها الراهن أن تفسره، ولا للآلة أن تقلده. وقد رأى المؤلف انه لا بد، لكي يثبت لنا ذلك، من أن يأخذنا في جولة استغرقت منه عشرة فصول مليئة بالمعلومات الشائقة المتنوعة التي قلما أتيح لكاتب أن يجمعها أو لكتاب واحد أن يضمها بين دفتيه. فهي تتضمن إلى جانب المعلومات المتنوعة معلومات عن الرياضيات وفلسفتها وعلم الكون وتنبؤاته وبينة الدماغ و فيزيولوجيته ومبادئها الأساسية..."
March 3, 2015
I read this book when it first came out and I was still a student of science so my memory on specific details is sketchy. There is no doubt that it is interesting and lively. I recall agreeing with Penrose's skepticism about artificial intelligence through his discussion of the Chinese Room Problem and the idea that if it were possible to write down the "program" of a person's mind in a book then the book, in a very slowed down sense, would be intelligent. From this I recall that his skepticism is about what some call the Strong AI hypothesis, which the Chinese Room Problem and the example of the book illustrate. His argument is that the functioning of the mind is inherently a quantum phenomenon and, because of the indeterminacy of states inherent in quantum systems, the mind cannot be embodied in a machine (like a Turing machine) that progresses through definite states. In fact, Penrose (again from distant memory!) says that the human mind is uniquely and inextricably bound to the human brain. Thus all the grandiose claims of the proponents of AI are in a way like the praises the fabled naked emperor receives from his courtiers as he bestrides his throne room and thus the book's title.
All of this is very good and, I think, weakens the plausibility of materialism which is the philosophical pedestal on which most scientists stand; though I realize this was probably not Penrose's intention. (It weakens it because it illustrates a reductio ad absurdum of the materialistic point of view.)
Another interesting book, expressing skepticism toward AI is Hubert Dreyfus', "What Computers Can't Do". Dreyfus is a phenomenologist and tackles the problem from that point of view and not one based on modern physics.
All of this is very good and, I think, weakens the plausibility of materialism which is the philosophical pedestal on which most scientists stand; though I realize this was probably not Penrose's intention. (It weakens it because it illustrates a reductio ad absurdum of the materialistic point of view.)
Another interesting book, expressing skepticism toward AI is Hubert Dreyfus', "What Computers Can't Do". Dreyfus is a phenomenologist and tackles the problem from that point of view and not one based on modern physics.
August 9, 2022
Me: mom, can we have Gödel, Escher, Bach?
Mom: we have Gödel, Escher, Bach at home.
Gödel, Escher, Bach at home: ...
Mom: we have Gödel, Escher, Bach at home.
Gödel, Escher, Bach at home: ...
August 31, 2023
In 1989, I was in the middle of a demanding career as a software engineer at a small, local company best known for accounting software. I was working on completing a new software package to replace an aging investment accounting package for insurance companies. We had already sold the new package to some large insurers and mutual funds such as Allstate, American General., State Farm, and Putnam. We considered our package state-of-the art for the 1980s and used a rudimentary “expert system” to generate code. Expert systems were a small part of the artificial intelligence revolution then. Some expert systems were used by oilfield services companies to aid in discovering productive oil fields. I developed an active interest in artificial intelligence to speed up and improve the quality of programming work.
I was immediately captivated by the thesis of The Emperor’s New Mind (ENM) by Roger Penrose. This 1989 book subtitled, “Concerning Computers, Minds, and the Laws of Physics,” promised to show that “strong AI,” or artificial general intelligence (AGI), was impossible. That argument begins with Gödel’s Incompleteness Theorem. Penrose’s treatment is entirely mathematical and, therefore, not accessible to many people. But ENM was not my first encounter with Gödel or his famous theorem. I had read Gödel, Escher, Bach: An Eternal Golden Braid (GEB) ten years earlier and had spent considerable effort understanding the paradox it was based on.
One approach to understanding Gödel’s Incompleteness Theorem begins with the “liar’s paradox.” Originally attributed to the Greek philosopher Epimenides in the 6th century BCE, it develops as follows:
Hofstadter refers to this paradox in its simpler version, “This statement is false.”
Gödel’s breakthrough occurred when he found a way to formalize the liar’s paradox as a mathematical theorem. This is the equivalent of a theorem stating, “This theorem is unprovable.” If the theorem is proved true, then it asserts its own unprovability. GEB provides a detailed representation of the constructed proof for a theorem asserting its own unprovability based on simple arithmetic.
Most people faced with a statement like “This sentence is false” intuitively sense that something is wrong even if they can’t say why. It took Gödel’s genius to formulate the wrongness in mathematical terms. The full expression of the Incompleteness Theorem goes something like this:
A formal system is consistent if it does not allow proofs of theorems that are false. Consistency is vital for understanding Gödel’s theorem. Any formal system that allows false axioms or theorems asserting a falsehood can then prove anything, such as 1+1 = 3.
When the theorem was introduced in 1931, it caused significant disruption to a project undertaken by Alfred North Whitehead and Bertrand Russell to formalize all of mathematics based on their work, Principia Mathematica. Nevertheless, controversy abounds on the theorem’s interpretation when applied to other topics. And Penrose’s application of the theorem to human consciousness is very controversial indeed.
His first step is to conclude that human intelligence must have a capability beyond the calculations of formal logic. If that were not true, Gödel would not have been able to create the Incompleteness Theorem, which makes a claim beyond what the formal system F can prove. This is consistent with the intuitive judgment of most people who sense the wrongness of paradoxical statements.
Penrose also concludes that “strong AI” or artificial general intelligence will have the same limitation since it is based on a formal system of calculation. Although ENM appeared more than twenty years before the advent of large language models (LLMs) like ChatGPT, they are based on mathematical calculations subject to Gödel’s limitations on completeness.
On July 8th, 2023, The Atlantic Magazine published a piece by Douglas Hofstadter about an incident involving ChatGPT. The article is titled “Gödel, Escher, Bach, and AI: A Dazzlingly Fast Chatbot Cannot Replace the Authentic and Reflective Voice of a Thinking, Living Human Being.” Hofstadter’s article describes how a fan sent him an essay by ChatGPT on why Hofstadter had written GEB. Hofstadter was horrified and disturbed. He labeled the piece “a saccharine mixture of pomposity and humility.” And evaluated its imitation of him as “so far from my real voice and so far from GEB’s real story that it is ludicrous.”
He also points out that he wrote a genuine story about GEB in its 20th-anniversary edition. ChatGPT attributes Hofstadter’s motive as his “passion for uncovering hidden connections.” Hofstadter replies:
Roger Penrose drills like a laser into Hofstadter’s main passion for understanding human consciousness. Having deduced that human consciousness can discern truth beyond formal logic, he developed a hypothesis about the mind based on quantum theory (QT). This is probably even more controversial than his use of Gödel’s theorem. Physicists have been reluctant to discuss QT and consciousness for good reasons.
From the early days of quantum theory, there has been a puzzle called the “measurement problem” or even “measurement paradox.” QT asserts that a quantum particle’s state (location, momentum, spin, etc.) (electron, photon, proton, neutron, etc.) cannot be known until measured or observed. The Copenhagen interpretation of QT asserts that both the wave and particle nature of elementary particles are required for a complete description of physical matter.
When a measurement or observation occurs, the “wave” nature collapses, and the “particle” is localized. The circular question arises: Did conscious observation “cause” the particle to be localized? This is the Schrodinger’s Cat paradox. Colloquially, if a tree falls in the forest and nobody hears it, did it fall? Or, is the moon there if I don’t see it? Does consciousness cause reality, or does reality have an independent existence? We don’t observe puzzling quantum effects on large objects, so most people believe that reality has an independent, objective existence. Quantum theory asserts that it may not have an independent, objective existence.
Currently, no rule in QT requires wave nature to collapse. The phenomenon is always determined empirically.
Roger Penrose’s solution to this paradox is to postulate that the wave nature of physical matter objectively collapses even if it is not observed or measured. He proposes a theory of quantum gravity that suggests conditions under which the particle becomes localized.
Theories of quantum gravity have been extensively pursued. It has been recognized for some time that Quantum Theory and Einstein’s General Relativity are not easily reconciled. Billions of dollars and decades have been invested in String Theory to little avail. String Theory has proved intractable due to an overabundance of mathematical solutions. As yet, there is no experimental confirmation. See The Trouble with Physics by Lee Smolin.
Both ENM and Penrose’s subsequent book, Shadows of the Mind, represent his working out the details of quantum gravity by writing about the issues involved in their integration. It isn’t easy to summarize what his theory claims. I have concluded that objective collapse of the wave function is a “real” phenomenon, even if not a result of quantum gravity. Penrose calls it Objective Reduction (OR). Penrose’s most compelling argument is that QT produces incredibly accurate results for predictions when time is assumed to progress into the future. But it has nonsensical answers when we ask the time-reverse question, “What happened to produce a measured result?”
His example of the time-reverse analysis goes like this. In a traditional photon-splitting experiment, a photon of light is projected at a half-silvered mirror. There is a 50% probability that the photon will pass through the mirror and strike a detector. There is also a 50% probability that the mirror will reflect the photon and hit the wall housing the experiment. QT calculations agree with the 50-50 split of possibilities when the experiment is analyzed from the perspective of the photon’s destination.
But what if we ask a different question? If the photon strikes the detector, where did it originate? Now, QT gives the nonsensical answer that the photon has a 50% probability of being emitted by the wall! In truth, the photon has a 100% probability of being emitted by the projector. This argument suggests but doesn’t prove, that OR might be taking place even if it is not a result of quantum gravity.
The primary conclusion of ENM is that human consciousness, intelligence, and judgment are not based on a mathematical algorithm. This conclusion points to the basis of consciousness being biological or biochemical, governed by the laws of chemistry and quantum physics. Penrose argues that quantum physics must be modified by OR for its use in applying it to the mind. The specifics of this modification are continued in Shadows of the Mind, and my review will continue there.
I did not need much convincing of this conclusion. I have spent my entire career working with computers and algorithms. I do not believe that mathematical calculations, no matter how sophisticated, can lead to human consciousness, intelligence, or sentience. However, many people will not agree. The counter argument asserts that the human mind might also be constrained by Gödel’s Incompleteness Theorem. The human mind might simply be doing more reasoning about counterfactuals. From David Lewis (Counterfactuals, 1973), an example of a counterfactual condition is, “If kangaroos had no tails, they would topple over.” So, if Gödel was wrong, mathematics would be a mess! One must pursue Penrose’s next book, Shadows of the Mind, to see how QT can do counterfactual calculations.
I was immediately captivated by the thesis of The Emperor’s New Mind (ENM) by Roger Penrose. This 1989 book subtitled, “Concerning Computers, Minds, and the Laws of Physics,” promised to show that “strong AI,” or artificial general intelligence (AGI), was impossible. That argument begins with Gödel’s Incompleteness Theorem. Penrose’s treatment is entirely mathematical and, therefore, not accessible to many people. But ENM was not my first encounter with Gödel or his famous theorem. I had read Gödel, Escher, Bach: An Eternal Golden Braid (GEB) ten years earlier and had spent considerable effort understanding the paradox it was based on.
One approach to understanding Gödel’s Incompleteness Theorem begins with the “liar’s paradox.” Originally attributed to the Greek philosopher Epimenides in the 6th century BCE, it develops as follows:
“Epimenides the Cretan says, ‘that all the Cretans are liars,’ but Epimenides is himself a Cretan; therefore, he is himself a liar. But if he is a liar, what he says is untrue, and consequently, the Cretans are veracious; but Epimenides is a Cretan, and therefore what he says is true; saying the Cretans are liars, Epimenides is himself a liar, and what he says is untrue. Thus, we may go on alternately proving that Epimenides and the Cretans are truthful and untruthful.” (Thomas Fowler, 1869, The Elements of Deductive Logic).
Hofstadter refers to this paradox in its simpler version, “This statement is false.”
Gödel’s breakthrough occurred when he found a way to formalize the liar’s paradox as a mathematical theorem. This is the equivalent of a theorem stating, “This theorem is unprovable.” If the theorem is proved true, then it asserts its own unprovability. GEB provides a detailed representation of the constructed proof for a theorem asserting its own unprovability based on simple arithmetic.
Most people faced with a statement like “This sentence is false” intuitively sense that something is wrong even if they can’t say why. It took Gödel’s genius to formulate the wrongness in mathematical terms. The full expression of the Incompleteness Theorem goes something like this:
“Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.” (Raatikainen, Panu, “Gödel’s Incompleteness Theorems,” The Stanford Encyclopedia of Philosophy (Spring 2022 Edition), Edward N. Zalta (ed.))
A formal system is consistent if it does not allow proofs of theorems that are false. Consistency is vital for understanding Gödel’s theorem. Any formal system that allows false axioms or theorems asserting a falsehood can then prove anything, such as 1+1 = 3.
When the theorem was introduced in 1931, it caused significant disruption to a project undertaken by Alfred North Whitehead and Bertrand Russell to formalize all of mathematics based on their work, Principia Mathematica. Nevertheless, controversy abounds on the theorem’s interpretation when applied to other topics. And Penrose’s application of the theorem to human consciousness is very controversial indeed.
His first step is to conclude that human intelligence must have a capability beyond the calculations of formal logic. If that were not true, Gödel would not have been able to create the Incompleteness Theorem, which makes a claim beyond what the formal system F can prove. This is consistent with the intuitive judgment of most people who sense the wrongness of paradoxical statements.
Penrose also concludes that “strong AI” or artificial general intelligence will have the same limitation since it is based on a formal system of calculation. Although ENM appeared more than twenty years before the advent of large language models (LLMs) like ChatGPT, they are based on mathematical calculations subject to Gödel’s limitations on completeness.
On July 8th, 2023, The Atlantic Magazine published a piece by Douglas Hofstadter about an incident involving ChatGPT. The article is titled “Gödel, Escher, Bach, and AI: A Dazzlingly Fast Chatbot Cannot Replace the Authentic and Reflective Voice of a Thinking, Living Human Being.” Hofstadter’s article describes how a fan sent him an essay by ChatGPT on why Hofstadter had written GEB. Hofstadter was horrified and disturbed. He labeled the piece “a saccharine mixture of pomposity and humility.” And evaluated its imitation of him as “so far from my real voice and so far from GEB’s real story that it is ludicrous.”
He also points out that he wrote a genuine story about GEB in its 20th-anniversary edition. ChatGPT attributes Hofstadter’s motive as his “passion for uncovering hidden connections.” Hofstadter replies:
“I have never been driven by any such passion, although I do enjoy finding unexpected connections from time to time. But I was indeed driven by a passion when I wrote GEB – namely, my intense desire to reveal what I believed consciousness (or an 'I') is, which in the book I called 'strange loop.' I was on fire to explain the 'strange loop' notion, and I did my best to show how this elusive notion was concretely epitomized by the unexpected self-referential structure lying at the heart of Gödel’s incompleteness theorem.”
Roger Penrose drills like a laser into Hofstadter’s main passion for understanding human consciousness. Having deduced that human consciousness can discern truth beyond formal logic, he developed a hypothesis about the mind based on quantum theory (QT). This is probably even more controversial than his use of Gödel’s theorem. Physicists have been reluctant to discuss QT and consciousness for good reasons.
From the early days of quantum theory, there has been a puzzle called the “measurement problem” or even “measurement paradox.” QT asserts that a quantum particle’s state (location, momentum, spin, etc.) (electron, photon, proton, neutron, etc.) cannot be known until measured or observed. The Copenhagen interpretation of QT asserts that both the wave and particle nature of elementary particles are required for a complete description of physical matter.
When a measurement or observation occurs, the “wave” nature collapses, and the “particle” is localized. The circular question arises: Did conscious observation “cause” the particle to be localized? This is the Schrodinger’s Cat paradox. Colloquially, if a tree falls in the forest and nobody hears it, did it fall? Or, is the moon there if I don’t see it? Does consciousness cause reality, or does reality have an independent existence? We don’t observe puzzling quantum effects on large objects, so most people believe that reality has an independent, objective existence. Quantum theory asserts that it may not have an independent, objective existence.
Currently, no rule in QT requires wave nature to collapse. The phenomenon is always determined empirically.
Roger Penrose’s solution to this paradox is to postulate that the wave nature of physical matter objectively collapses even if it is not observed or measured. He proposes a theory of quantum gravity that suggests conditions under which the particle becomes localized.
Theories of quantum gravity have been extensively pursued. It has been recognized for some time that Quantum Theory and Einstein’s General Relativity are not easily reconciled. Billions of dollars and decades have been invested in String Theory to little avail. String Theory has proved intractable due to an overabundance of mathematical solutions. As yet, there is no experimental confirmation. See The Trouble with Physics by Lee Smolin.
Both ENM and Penrose’s subsequent book, Shadows of the Mind, represent his working out the details of quantum gravity by writing about the issues involved in their integration. It isn’t easy to summarize what his theory claims. I have concluded that objective collapse of the wave function is a “real” phenomenon, even if not a result of quantum gravity. Penrose calls it Objective Reduction (OR). Penrose’s most compelling argument is that QT produces incredibly accurate results for predictions when time is assumed to progress into the future. But it has nonsensical answers when we ask the time-reverse question, “What happened to produce a measured result?”
His example of the time-reverse analysis goes like this. In a traditional photon-splitting experiment, a photon of light is projected at a half-silvered mirror. There is a 50% probability that the photon will pass through the mirror and strike a detector. There is also a 50% probability that the mirror will reflect the photon and hit the wall housing the experiment. QT calculations agree with the 50-50 split of possibilities when the experiment is analyzed from the perspective of the photon’s destination.
But what if we ask a different question? If the photon strikes the detector, where did it originate? Now, QT gives the nonsensical answer that the photon has a 50% probability of being emitted by the wall! In truth, the photon has a 100% probability of being emitted by the projector. This argument suggests but doesn’t prove, that OR might be taking place even if it is not a result of quantum gravity.
The primary conclusion of ENM is that human consciousness, intelligence, and judgment are not based on a mathematical algorithm. This conclusion points to the basis of consciousness being biological or biochemical, governed by the laws of chemistry and quantum physics. Penrose argues that quantum physics must be modified by OR for its use in applying it to the mind. The specifics of this modification are continued in Shadows of the Mind, and my review will continue there.
I did not need much convincing of this conclusion. I have spent my entire career working with computers and algorithms. I do not believe that mathematical calculations, no matter how sophisticated, can lead to human consciousness, intelligence, or sentience. However, many people will not agree. The counter argument asserts that the human mind might also be constrained by Gödel’s Incompleteness Theorem. The human mind might simply be doing more reasoning about counterfactuals. From David Lewis (Counterfactuals, 1973), an example of a counterfactual condition is, “If kangaroos had no tails, they would topple over.” So, if Gödel was wrong, mathematics would be a mess! One must pursue Penrose’s next book, Shadows of the Mind, to see how QT can do counterfactual calculations.
April 10, 2025
If you are considering reading this with the assumption that it has any up to date information on artificial intelligence, you will be discouraged cursing it as outdated. However, I found this 40 year old pop science book to remain relevant and inspiring. He has a sincere and humble way of proposing theories, never trying to convince you of the absolute truth. Rather, you accompany him through mental exercises and possibilities that he is exploring. I found the way he presents the Mandelbrot set particularly captivating, with his elegant breakdown of the system of complex numbers. In fact, I found every mathematical set he illustrates throughout the book to be fascinating and quite beautiful. He possesses a unique ability to visualize maths -a true geometer. Or perhaps that is the Platonist in him.
June 3, 2015
Uno de los mejores libros que he leído sin duda, me dejó con muchas cosas que pensar acerca de la realidad física y me aclaró muchos puntos en los que tenía las cosas tan claras.
Además aprendí de muchos otros temas avanzados de la física(aunque someramente), de los que no tenía la mínima idea. Es un libro obligado para todas las personas que gusten de la ciencia.
En cuanto al tema principal con el que inicia el libro, estoy completamente de acuerdo con la conclusión del autor, y nunca había visto o siquiera vislumbrado la posibilidad de que en nuestro cerebro ocurran procesos físicos que aún no pueden ser explicados por las teorías actuales. Me tomó tiempo leerlo por la dificultad técnica(y ciertas partes a duras penas puedo decir que las entendí), pero es un libro que vale completamente la pena.
Para las personas que les apasiona la computación es un libro que les fascinará porque trata las teorías básicas de la coputación, computabilidad, cálculo Lambda, complejidad de algoritmos, sistemas lógicos y el teorema de la Incompletitud de Gödel.
Parecerá que el autor le está dando muchas vueltas a el asunto antes de llegar a una conclusión útil relacionada con el tema del libro, pero los temas que se tratan ahí son necesarios para llegar a una comprensión fuerte y bien argumentada de porque se llega a esa conclusión.
No es un libro para todas las personas, sólo aquellas que de verdad disfurtan del aprendizaje acerca del mundo físico.
Además aprendí de muchos otros temas avanzados de la física(aunque someramente), de los que no tenía la mínima idea. Es un libro obligado para todas las personas que gusten de la ciencia.
En cuanto al tema principal con el que inicia el libro, estoy completamente de acuerdo con la conclusión del autor, y nunca había visto o siquiera vislumbrado la posibilidad de que en nuestro cerebro ocurran procesos físicos que aún no pueden ser explicados por las teorías actuales. Me tomó tiempo leerlo por la dificultad técnica(y ciertas partes a duras penas puedo decir que las entendí), pero es un libro que vale completamente la pena.
Para las personas que les apasiona la computación es un libro que les fascinará porque trata las teorías básicas de la coputación, computabilidad, cálculo Lambda, complejidad de algoritmos, sistemas lógicos y el teorema de la Incompletitud de Gödel.
Parecerá que el autor le está dando muchas vueltas a el asunto antes de llegar a una conclusión útil relacionada con el tema del libro, pero los temas que se tratan ahí son necesarios para llegar a una comprensión fuerte y bien argumentada de porque se llega a esa conclusión.
No es un libro para todas las personas, sólo aquellas que de verdad disfurtan del aprendizaje acerca del mundo físico.
May 11, 2020
Pedazo de libro. Del mismo estilo que el Gödel, Escher, Bach de Douglas Hofstadter. Habla acerca de aproximadamente dieciocho mil quinientas ramas interesantes de la ciencia y el conocimiento. Es, desde luego, merecedor de la segunda lectura (y sucesivas), porque es imposible absorberlo todo a la primera.
Hacia el final se le va la bola con non sequiturs (como no podemos explicar la conciencia entonces el cerebro humano nunca podrá ser imitado por una maquina, y otras movidas cuánticas más abstrusas todavía), pero se le perdona la tontería por el buen rato previo.
Hacia el final se le va la bola con non sequiturs (como no podemos explicar la conciencia entonces el cerebro humano nunca podrá ser imitado por una maquina, y otras movidas cuánticas más abstrusas todavía), pero se le perdona la tontería por el buen rato previo.
June 15, 2019
I feel like the book would be very useful for someone without prior knowledge of modern CS/physical fundamentals and who wants to glimpse into its connections with modern philosophy of mind. Otherwise the book is quite thought provoking.
September 18, 2020
Incredible, Insightful, and Lucid, from the Master Mathematician / Physicist, the one and only, Sir Roger Penrose.. I found resonance here for many of the ideas I was looking to develop . Shall keep this one close to me for frequent revisits.
March 3, 2021
Me ha gustado bastante poco este libro. Considero que el autor se plantea principalmente tres objetivos, siendo el tercero el más importante para él: 1) entretener, 2) divulgar teorías físicas, matemáticas y de ciencia de la computación y 3) exponer nuevas teorías especulativas o intuiciones sobre las mismas. En mi opinión, no consigue ninguno de los tres, ya que los materiales para entretener son simple formalismo que además el lector de un libro así no desea; la divulgación no es tal, ya que expone las teorías de manera bastante técnica, aunque, eso sí, renombrando algunas palabras atemorizantes y aliñando con admiraciones, y, en cuanto a la parte exploratoria, tiene bastante poco rigor.
El capitulo en el que muestra sus teorías y en el que supuestamente converge todo el libro (aunque tres cuartos del equipaje que recogemos por el camino sobra) es el último. En el Penrose defiende que para entender el fenómeno de la conciencia hacen falta nuevas teorías físicas, en concreto de la gravedad cuántica. Los capítulos anteriores han supuestamente mostrado las piezas teóricas que apuntan en esta dirección.
En los primeros capítulos (1-4) se presentan la teoría de la computabilidad y se hace un repaso —bastante bueno en mi opinión— por las máquinas de Turing, los teoremas de la incompletitud de Gödel, y las consecuencias teóricas de ambos. La principal moraleja que hay que obtener de ellos es que no todo lo cierto es computable; ya que nuestra mente nos permite «ver la verdad matemática» (el autor habla en estos términos, poniendo comillas en «ver» y ahorrádose definiciones precisas) en situaciones en los que es demostrable que esa verdad no es computable dentro del sistema en el que tiene sentido. Básicamente, intenta apuntar hacia las consecuencias psicológicas de los teoremas de Gödel. Recuperará este hilo para proponer que sistema algorítmico no puede alcanzar toda verdad matemática por principio, mientras que la conciencia humana por principio sí. También menciona su convicción de que los objetos matemáticos tienen existencia propia en un mundo platónico (y los matemáticos no los inventan, sino que los descubren), sin embargo, ejemplificando el tono de pensamiento especulativo del libro, añade que «un decidido platonista como [él] mismo puede honestamente empezar a dudar» [p. 182] de su existencia.
En los siguientes capítulos (5-8) se resumen los distintos marcos teóricos de la física: la física clásica, incluyendo la relatividad general de Einstein, y la física cuántica. Uno de los principales resultados indicados en estos es que, en física clásica, no todo proceso determinista es un proceso computable. Recuperará este hilo para plantear que la mente puede ser determinista (Penrose tiene una visión fisicalista —si obviamos su insistencia en el mundo platónico matemático— del mundo y la mente) pero seguir procesos no computables. Respecto a la mecánica cuántica, expone que en la teoría actual hay dos procesos de evolución distintos (la evolución unitaria determinista y la medición probabilista no lineal ni unitaria). Esto solo es así en las interpretaciones más clásicas de la teoría, pero él lo da por sentado. Su propuesta es que ambos procesos son aproximaciones a un proceso más fundamental que los englobaría. Da dos tipos de indicios de que esta teoría más fundamental esté relacionada con el problema de la gravedad cuántica: que, según él, el colapso de la función de onda ocurre a escalas en las que entra en juego al menos un gravitón (opinión que no es para nada mayoritaria en la comunidad) y la paradoja de la pérdida de información en los agujeros negros. Parece no tener graves problemas con que su teoría implique la acción instantánea a distancia (ninguna teoría que reproduzca los resultados medibles de la mecánica cuántica puede ser determinista y con causalidad local), según él esto será posiblemente consecuencia de el gran cambio que dará nuestro concepto de «tiempo». Su nueva teoría, por cierto, no sería simétrica respecto a inversión temporal.
En el capítulo 9 habla de neurociencia.
En el último capítulo (10) define (sorprendentemente) la conciencia como la capacidad de tener intuición directa de las verdades matemáticas. Quizá por esta razón considera que algunos objetos matemáticos tienen más existencia propia que otros: algunos son más fácilmente alcanzables por la conciencia. (Esto ontológicamente parece contradictorio.) Considera que gatos o perros tienen conciencia (dice que es evidente) pero que una máquina no puede tenerla (algo que, según él, es evidente para un niño, pero sobre lo cual algunos expertos, de tanto pensar en ello, acaban confundidos). Parece que es consciente de la estrechez de su definición de conciencia e intenta ampliarla dando indicios de que los juicios de verdad matemática están relacionados con los juicios estéticos, aunque no expone ninguna teoría al respecto.
Podemos trenzar ahora los hilos. Su propuesta es que la misma física, todavía desconocida, que consigue paliar lo que él considera la principal carencia de la mecánica cuántica, será también la física que solucione el problema de la gravedad cuántica y, más aún, sea la física necesaria para entender por qué un cerebro tiene conciencia y un ordenador nunca puede tenerla. Propone que sea física determinista (no como la mecánica cuántica actual) pero no computable (y por tanto no reproducible con un ordenador). Los aspectos no computables de esta teoría que entren en juego en el cerebro serían, de alguna manera, los que nos permiten tener acceso directo a las verdades matemáticas.
Algunas cuestiones más:
Muchos de sus argumentos sobre la conciencia se asientan en las «intuiciones» y el «sentido común», llegando a defender que debe haber «algún modo de comportamiento que es característico de la conciencia (incluso aunque no sea _siempre_ manifestado por la conciencia) y al que somos sensibles a través de nuestras "intuiciones del sentido común"» (p. 582).
Hay que perdonar que en el momento de publicación del libro no había tenido lugar la revolción de las redes neuronales artificiales y su uso en machine learning como estamos viviendo ahora. Tenemos intuiciones mucho más claras hoy día sobre procesos emergentes de aprendizaje y elaboración de juicios gracias a ellas. En mi opinión, esto da la clave para desmontar el principal argumento del libro: un sistema puede ser algorítmico en un nivel inferior de emergencia («substrato») pero establecer con bastante seguridad juicios no algorítmicos en un nivel superior («epifenómeno»).
Llega a plantear que el cerebro puede tener trabajar en algún tipo de sperposición cuántica, al modo de los ordenadores cuánticos (ya teorizados cuando se escribió el libro).
Los matemáticos pueden comunicarse sus descubrimientos porque cada uno tiene un acceso directo a la «verdad» (p. 610).
Se atreve a sugerir que esta nueva física pueda tener alguna influencia en la evolución natural, pudiendo quizá así explicar las sospechas teleológicas que nos suscita (p. 593). Creo que añadiendo esto al problema de la conciencia y el origen del universo (que, por ser una singularidad, necesita de una teoría de la gravedad cuántica como la que él plantea) alcanza en pretensiones respecto a lo que quiere solventar con su teoría a lo que un teólogo pretendería con la idea de Dios.
Plantea (p. 613-4) que el mundo físico pueda en realidad ser el mismo que el mundo platónico matemático.
Es interesante la idea de _determinismo fuerte_ (p. 616). Una teoría sobre nuestro universo sería de este tipo si además de determinista no tiene varibles sin fijar, esto es, no hay condiciones de contorno. Toda la historia del universo de principio a fin estaría fijada completamente por la teoría.
Por último, en (p. 616-7) plantea como contraargumento al determinismo fuerte que uno podría calcular su propio estado futuro y actuar contra la predicción (como el libre albedrío dictamina que podemos hacer), dando lugar a una paradoja. Este tipo de paradojas, aunque para él sea definitiva, se pueden resolver de distintas maneras, como considerando las condiciones de contorno de nuestro propio cuerpo (que han de incluir la llegada de información sobre su propio futuro) o, como hizo ya Gödel en su día, tomándose en serio la hipótesis que la supuesta paradoja ataca: que el mismo libre albedrío emerge del sustrato físico.
El capitulo en el que muestra sus teorías y en el que supuestamente converge todo el libro (aunque tres cuartos del equipaje que recogemos por el camino sobra) es el último. En el Penrose defiende que para entender el fenómeno de la conciencia hacen falta nuevas teorías físicas, en concreto de la gravedad cuántica. Los capítulos anteriores han supuestamente mostrado las piezas teóricas que apuntan en esta dirección.
En los primeros capítulos (1-4) se presentan la teoría de la computabilidad y se hace un repaso —bastante bueno en mi opinión— por las máquinas de Turing, los teoremas de la incompletitud de Gödel, y las consecuencias teóricas de ambos. La principal moraleja que hay que obtener de ellos es que no todo lo cierto es computable; ya que nuestra mente nos permite «ver la verdad matemática» (el autor habla en estos términos, poniendo comillas en «ver» y ahorrádose definiciones precisas) en situaciones en los que es demostrable que esa verdad no es computable dentro del sistema en el que tiene sentido. Básicamente, intenta apuntar hacia las consecuencias psicológicas de los teoremas de Gödel. Recuperará este hilo para proponer que sistema algorítmico no puede alcanzar toda verdad matemática por principio, mientras que la conciencia humana por principio sí. También menciona su convicción de que los objetos matemáticos tienen existencia propia en un mundo platónico (y los matemáticos no los inventan, sino que los descubren), sin embargo, ejemplificando el tono de pensamiento especulativo del libro, añade que «un decidido platonista como [él] mismo puede honestamente empezar a dudar» [p. 182] de su existencia.
En los siguientes capítulos (5-8) se resumen los distintos marcos teóricos de la física: la física clásica, incluyendo la relatividad general de Einstein, y la física cuántica. Uno de los principales resultados indicados en estos es que, en física clásica, no todo proceso determinista es un proceso computable. Recuperará este hilo para plantear que la mente puede ser determinista (Penrose tiene una visión fisicalista —si obviamos su insistencia en el mundo platónico matemático— del mundo y la mente) pero seguir procesos no computables. Respecto a la mecánica cuántica, expone que en la teoría actual hay dos procesos de evolución distintos (la evolución unitaria determinista y la medición probabilista no lineal ni unitaria). Esto solo es así en las interpretaciones más clásicas de la teoría, pero él lo da por sentado. Su propuesta es que ambos procesos son aproximaciones a un proceso más fundamental que los englobaría. Da dos tipos de indicios de que esta teoría más fundamental esté relacionada con el problema de la gravedad cuántica: que, según él, el colapso de la función de onda ocurre a escalas en las que entra en juego al menos un gravitón (opinión que no es para nada mayoritaria en la comunidad) y la paradoja de la pérdida de información en los agujeros negros. Parece no tener graves problemas con que su teoría implique la acción instantánea a distancia (ninguna teoría que reproduzca los resultados medibles de la mecánica cuántica puede ser determinista y con causalidad local), según él esto será posiblemente consecuencia de el gran cambio que dará nuestro concepto de «tiempo». Su nueva teoría, por cierto, no sería simétrica respecto a inversión temporal.
En el capítulo 9 habla de neurociencia.
En el último capítulo (10) define (sorprendentemente) la conciencia como la capacidad de tener intuición directa de las verdades matemáticas. Quizá por esta razón considera que algunos objetos matemáticos tienen más existencia propia que otros: algunos son más fácilmente alcanzables por la conciencia. (Esto ontológicamente parece contradictorio.) Considera que gatos o perros tienen conciencia (dice que es evidente) pero que una máquina no puede tenerla (algo que, según él, es evidente para un niño, pero sobre lo cual algunos expertos, de tanto pensar en ello, acaban confundidos). Parece que es consciente de la estrechez de su definición de conciencia e intenta ampliarla dando indicios de que los juicios de verdad matemática están relacionados con los juicios estéticos, aunque no expone ninguna teoría al respecto.
Podemos trenzar ahora los hilos. Su propuesta es que la misma física, todavía desconocida, que consigue paliar lo que él considera la principal carencia de la mecánica cuántica, será también la física que solucione el problema de la gravedad cuántica y, más aún, sea la física necesaria para entender por qué un cerebro tiene conciencia y un ordenador nunca puede tenerla. Propone que sea física determinista (no como la mecánica cuántica actual) pero no computable (y por tanto no reproducible con un ordenador). Los aspectos no computables de esta teoría que entren en juego en el cerebro serían, de alguna manera, los que nos permiten tener acceso directo a las verdades matemáticas.
Algunas cuestiones más:
Muchos de sus argumentos sobre la conciencia se asientan en las «intuiciones» y el «sentido común», llegando a defender que debe haber «algún modo de comportamiento que es característico de la conciencia (incluso aunque no sea _siempre_ manifestado por la conciencia) y al que somos sensibles a través de nuestras "intuiciones del sentido común"» (p. 582).
Hay que perdonar que en el momento de publicación del libro no había tenido lugar la revolción de las redes neuronales artificiales y su uso en machine learning como estamos viviendo ahora. Tenemos intuiciones mucho más claras hoy día sobre procesos emergentes de aprendizaje y elaboración de juicios gracias a ellas. En mi opinión, esto da la clave para desmontar el principal argumento del libro: un sistema puede ser algorítmico en un nivel inferior de emergencia («substrato») pero establecer con bastante seguridad juicios no algorítmicos en un nivel superior («epifenómeno»).
Llega a plantear que el cerebro puede tener trabajar en algún tipo de sperposición cuántica, al modo de los ordenadores cuánticos (ya teorizados cuando se escribió el libro).
Los matemáticos pueden comunicarse sus descubrimientos porque cada uno tiene un acceso directo a la «verdad» (p. 610).
Se atreve a sugerir que esta nueva física pueda tener alguna influencia en la evolución natural, pudiendo quizá así explicar las sospechas teleológicas que nos suscita (p. 593). Creo que añadiendo esto al problema de la conciencia y el origen del universo (que, por ser una singularidad, necesita de una teoría de la gravedad cuántica como la que él plantea) alcanza en pretensiones respecto a lo que quiere solventar con su teoría a lo que un teólogo pretendería con la idea de Dios.
Plantea (p. 613-4) que el mundo físico pueda en realidad ser el mismo que el mundo platónico matemático.
Es interesante la idea de _determinismo fuerte_ (p. 616). Una teoría sobre nuestro universo sería de este tipo si además de determinista no tiene varibles sin fijar, esto es, no hay condiciones de contorno. Toda la historia del universo de principio a fin estaría fijada completamente por la teoría.
Por último, en (p. 616-7) plantea como contraargumento al determinismo fuerte que uno podría calcular su propio estado futuro y actuar contra la predicción (como el libre albedrío dictamina que podemos hacer), dando lugar a una paradoja. Este tipo de paradojas, aunque para él sea definitiva, se pueden resolver de distintas maneras, como considerando las condiciones de contorno de nuestro propio cuerpo (que han de incluir la llegada de información sobre su propio futuro) o, como hizo ya Gödel en su día, tomándose en serio la hipótesis que la supuesta paradoja ataca: que el mismo libre albedrío emerge del sustrato físico.
August 18, 2019
Uno dei libri piú belli che abbia mai letto, la scienza che contiene é spiegata in modo semplice ma completo, ti fa' veramente appassionare alla scienza dei computer e alla matrmatica.
March 21, 2012
Computers can defeat humans in a game of chess, and perform mathematical operations much faster than humans can. A robot can be built that detects when its batteries are running low and when this happens, goes off to find a power socket to plug itself in and recharge. Computers can be programmed to answer questions as a human being would.
But can a computer solve every problem that a human being can solve? Could computers ever be aware of, and actually understand what they are doing? Could the entire contents of the brain be stored on a digital device? To state that a computer behaves as a human being, is it enough that it gives us answers that are indistinguishable from those of a human being? Can computers actually be intelligent; will they feel, think, and have minds?
The defenders of "strong-AI" say yes, but Penrose doesn't think so. He argues that there is a lack of understanding of the laws of physics at the scale of the human brain that prevents us from penetrating the concept of "mind" in physical or logical terms. In other words, there is a piece of the puzzle missing.
To explain his viewpoints, Penrose takes us on a ride through the developments in artificial intelligence (as it was in the end of the 1980s when he wrote the book), the workings of the Turing machine, the foundations of mathematics and Gödel's theorem, quantum theory and electromagnetism, and he does that really well. Penrose is a very creative thinker with an astonishing mastery of many fields of science. It is therefore disappointing that what follows in the last few chapters is no more than speculation; his suggestion that consciousness is the result of quantum gravity effects in certain areas of the human brain has since been refuted by other scientists.
I am still glad to have read The Emperor’s New Mind, as it provides an interesting contrast with Hofstadter's views on artificial intelligence, and I certainly learned a lot from the science chapters. However, I doubt whether it is worth going through such an awful lot of math for a somewhat outdated theory.
But can a computer solve every problem that a human being can solve? Could computers ever be aware of, and actually understand what they are doing? Could the entire contents of the brain be stored on a digital device? To state that a computer behaves as a human being, is it enough that it gives us answers that are indistinguishable from those of a human being? Can computers actually be intelligent; will they feel, think, and have minds?
The defenders of "strong-AI" say yes, but Penrose doesn't think so. He argues that there is a lack of understanding of the laws of physics at the scale of the human brain that prevents us from penetrating the concept of "mind" in physical or logical terms. In other words, there is a piece of the puzzle missing.
To explain his viewpoints, Penrose takes us on a ride through the developments in artificial intelligence (as it was in the end of the 1980s when he wrote the book), the workings of the Turing machine, the foundations of mathematics and Gödel's theorem, quantum theory and electromagnetism, and he does that really well. Penrose is a very creative thinker with an astonishing mastery of many fields of science. It is therefore disappointing that what follows in the last few chapters is no more than speculation; his suggestion that consciousness is the result of quantum gravity effects in certain areas of the human brain has since been refuted by other scientists.
I am still glad to have read The Emperor’s New Mind, as it provides an interesting contrast with Hofstadter's views on artificial intelligence, and I certainly learned a lot from the science chapters. However, I doubt whether it is worth going through such an awful lot of math for a somewhat outdated theory.
April 22, 2019
This is the first book of Sir Roger Penrose that I read by now and it left me mesmerized by the originality of his ideas no matter how much speculative they may be. Sir Penrose is a mathematician of first rate and it is very evident from his take on the hard problems which is beyond the mainstream approach of physicists. I am very much biased towards new ideas that can knit a multitude of problems together yet possessing a scientific ring of falsifiability, predictability and testability. This book was written back in the late 80s with so rich ideas which can leave one thinking about it even today.
In this book the author speculates an approach to answer the nature of consciousness which necessitates a modification of quantum and classical physics to an unification of both.
Such unification is the holy grail of physics and much work is done on it and still ongoing. But the approach which Sir Penrose posits is quite a different one from the conventional line of thought of our present times. Moreover such approach ties not just classical and quantum worlds but also that of our consciousness as well. Although very speculative and much work needs to be done on this (even the author presently has somewhat moved on from his theory of one graviton criterion presented in this book) the essence of his approach remains the same and active research is being done at present. This approach being a gravitational collapse of the quantum wave function.
To describe the book:
Firstly the author questions the possibility of present day digital computers of having a mind or not. Such computers are run on algorithms which much of our brain functionality also does however the attribute of a conscious interpretation or judgement need to transcend this algorithmic nature and be non-algorithmic. The author describes computers that pass the Turing test and AI with complex algorithms have a good calculation power but the essence of understanding is something non-computational that remains lacking in these machines.
The Author then delves into the meaning and details of algorithm, stretching to its limit of the most important insolubility of Hilbert's Halting problem of finding a mathematical procedure to ascertain the solution of all mathematical problems belonging to broad well defined class. It turns out to have no general algorithm to find such solutions in general for various mathematical problems.
The famous incompleteness theorem given by Kurt Gödel does present to us the very limit of formalism of any one kind in particular which is applicable for all formal systems nevertheless.
There are problems of Hamiltonian circuit and travelling salesman problem which belongs to the category of problem whose solution doesn't have an algorithm in specific determined time range. These are termed as NP complete. The more general algorithms being referred as P which possess algorithm for its solution in deterministic time. As of now P and NP are understood as different.
Also the famous mathematical problem of tiling in which the author himself is a significant contributor towards aperiodic tiling structures, has no algorthimic decision procedure of its solution.
Armed with all these concepts and the famous branch of non-recursive mathematics, the author posits that there should be a non-algorithmic nature of our consciousness which is much capable of judgement and insights.
The best part of reading books by such high rank mathematicians and physicists as the author himself is that the reader's basic ideas in the field of mathematics and physics gets well strengthened.
Sir Penrose magnificently described the world of mathematics , classical and quantum physics in each of which there are hints of non-algorithmic , deterministic but non-computational & non-local attributes respectively.
Penrose is a Platonist giving the timeless realm of mathematical world a certain reality of its own.
Finally the author arrives at his speculation namely one graviton criterion. Here Penrose tries to provide a possible mechanism as to how the complex weighted linear superposition of quantum wave function collapses to form a observable aspect of our classical world out of the several orthogonal alternatives which coexists in quantum world giving it a non-local feature. Locality gets imbued , according to this theory , when the difference between initial and final mass distribution as a part of the superposition achieves a gravitational field difference to that of 1/100 of Planck mass.
With several interesting phenomena of quasicrystals where a 5-fold symmetry ( tiling in 5fold symmetry was worked out by Penrose ) occurs need a nonlocal quantum superposition description to attain it in a minimum energy. With such an analogy the author speculates the growth and contraction of dendrites (having synaptic connecrions) of neurons of our brain can occur in a similar fashion then such a superposition would collapse upon meeting the one graviton criterion within a certain small amount of time. Within this time several nonlocal activity may be achieved simultaneously which when collapses takes the form of a judgement or conscious decision.
This collapse which slides from the deterministic Schrödinger wave function(superposed) evolution to the stochastic reduction of wave function requires a new quantum gravity theory with a non-algirithmic property.
Also in this book Penrose subtely touches on an interdependency of quantum state vector reduction and a null value of tidal flow field given by the Weyl curvature tensor of the equations of the famous Einstein's general theory of relativity. This constraint of Weyl curvature tensor being zero is theorized to be present at the Big bang singularity imparting our Universe the second law of thermodynamics which states that irreversible events occur towards a higher entropic state with a lower entropic state preceding it.
The nature of brilliant insights or spark of ideas which comes up in our mind altough having a non-algorithmic nature it nevertheless depend on the otherwise various algorithmic/computational activities of our brain carried out involuntarily.
This book is a collection of several deep and insightful ideas. I have seldom written such a lengthy review in goodreads owing to my inability to manage time. But for this book I lost track of time and length of my review.
This book is a mandatory read for those who strive for diverse ideas for various mysteries of our reality.
In this book the author speculates an approach to answer the nature of consciousness which necessitates a modification of quantum and classical physics to an unification of both.
Such unification is the holy grail of physics and much work is done on it and still ongoing. But the approach which Sir Penrose posits is quite a different one from the conventional line of thought of our present times. Moreover such approach ties not just classical and quantum worlds but also that of our consciousness as well. Although very speculative and much work needs to be done on this (even the author presently has somewhat moved on from his theory of one graviton criterion presented in this book) the essence of his approach remains the same and active research is being done at present. This approach being a gravitational collapse of the quantum wave function.
To describe the book:
Firstly the author questions the possibility of present day digital computers of having a mind or not. Such computers are run on algorithms which much of our brain functionality also does however the attribute of a conscious interpretation or judgement need to transcend this algorithmic nature and be non-algorithmic. The author describes computers that pass the Turing test and AI with complex algorithms have a good calculation power but the essence of understanding is something non-computational that remains lacking in these machines.
The Author then delves into the meaning and details of algorithm, stretching to its limit of the most important insolubility of Hilbert's Halting problem of finding a mathematical procedure to ascertain the solution of all mathematical problems belonging to broad well defined class. It turns out to have no general algorithm to find such solutions in general for various mathematical problems.
The famous incompleteness theorem given by Kurt Gödel does present to us the very limit of formalism of any one kind in particular which is applicable for all formal systems nevertheless.
There are problems of Hamiltonian circuit and travelling salesman problem which belongs to the category of problem whose solution doesn't have an algorithm in specific determined time range. These are termed as NP complete. The more general algorithms being referred as P which possess algorithm for its solution in deterministic time. As of now P and NP are understood as different.
Also the famous mathematical problem of tiling in which the author himself is a significant contributor towards aperiodic tiling structures, has no algorthimic decision procedure of its solution.
Armed with all these concepts and the famous branch of non-recursive mathematics, the author posits that there should be a non-algorithmic nature of our consciousness which is much capable of judgement and insights.
The best part of reading books by such high rank mathematicians and physicists as the author himself is that the reader's basic ideas in the field of mathematics and physics gets well strengthened.
Sir Penrose magnificently described the world of mathematics , classical and quantum physics in each of which there are hints of non-algorithmic , deterministic but non-computational & non-local attributes respectively.
Penrose is a Platonist giving the timeless realm of mathematical world a certain reality of its own.
Finally the author arrives at his speculation namely one graviton criterion. Here Penrose tries to provide a possible mechanism as to how the complex weighted linear superposition of quantum wave function collapses to form a observable aspect of our classical world out of the several orthogonal alternatives which coexists in quantum world giving it a non-local feature. Locality gets imbued , according to this theory , when the difference between initial and final mass distribution as a part of the superposition achieves a gravitational field difference to that of 1/100 of Planck mass.
With several interesting phenomena of quasicrystals where a 5-fold symmetry ( tiling in 5fold symmetry was worked out by Penrose ) occurs need a nonlocal quantum superposition description to attain it in a minimum energy. With such an analogy the author speculates the growth and contraction of dendrites (having synaptic connecrions) of neurons of our brain can occur in a similar fashion then such a superposition would collapse upon meeting the one graviton criterion within a certain small amount of time. Within this time several nonlocal activity may be achieved simultaneously which when collapses takes the form of a judgement or conscious decision.
This collapse which slides from the deterministic Schrödinger wave function(superposed) evolution to the stochastic reduction of wave function requires a new quantum gravity theory with a non-algirithmic property.
Also in this book Penrose subtely touches on an interdependency of quantum state vector reduction and a null value of tidal flow field given by the Weyl curvature tensor of the equations of the famous Einstein's general theory of relativity. This constraint of Weyl curvature tensor being zero is theorized to be present at the Big bang singularity imparting our Universe the second law of thermodynamics which states that irreversible events occur towards a higher entropic state with a lower entropic state preceding it.
The nature of brilliant insights or spark of ideas which comes up in our mind altough having a non-algorithmic nature it nevertheless depend on the otherwise various algorithmic/computational activities of our brain carried out involuntarily.
This book is a collection of several deep and insightful ideas. I have seldom written such a lengthy review in goodreads owing to my inability to manage time. But for this book I lost track of time and length of my review.
This book is a mandatory read for those who strive for diverse ideas for various mysteries of our reality.
April 1, 2017
Another longtime companion of mine, this book is by turns brilliant and exasperating. It's a bulky layman's discourse on Artificial Intelligence, seeking the answer to the question "Can a computer ever possess true intelligence?" Its brilliance lies in fascinating and lucid coverage of a variety of subjects in mathematics, classical and quantum physics, relativity, and all of the philosophical underpinnings. Unfortunately in the tumble of information Penrose neglects to pull the threads together and support a thesis. I always looks back, say, at a chapter on the Mandelbrot set or Godel's Theorem, or whatever, thinking - that was great and fascinating, but what does it have to do with the nature of intelligence? Exactly what is the link between black holes and brains? Penrose's thesis - that human thought and self-awareness are non-algorithmic - is supported indirectly, if at all.
December 24, 2008
My reaction to this book and its follow up, Shadows of the Mind, were pretty much the same.
Yes, it's true we can't reconcile gravity and quantum mechanics
Yes, reconciling how intelligence arises in a purely mechanical system is not understood
Yes, Godel's incompleteness stuff and Turing halting stuff are weird and not at all obvious
But, no, I am very far from convinced that a mechanism that allowed us to reconcile General Relativity and Quantum Mechanics would allow us to understand how intelligence can arise and avoid the Godel paradox
That being said, Penrose is a tad smarter than I am.
Maybe it's a case of the reader blaming the authors for the reader's shortcomings
Yes, it's true we can't reconcile gravity and quantum mechanics
Yes, reconciling how intelligence arises in a purely mechanical system is not understood
Yes, Godel's incompleteness stuff and Turing halting stuff are weird and not at all obvious
But, no, I am very far from convinced that a mechanism that allowed us to reconcile General Relativity and Quantum Mechanics would allow us to understand how intelligence can arise and avoid the Godel paradox
That being said, Penrose is a tad smarter than I am.
Maybe it's a case of the reader blaming the authors for the reader's shortcomings
Displaying 1 - 30 of 363 reviews