Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Superb, 31 Oct 2008
This book is really well written by not just an expert in the field but someone who is able to make very complex ideas intelligable to non-specialists. I enjoyed this book immensely and recommend it to anyone who is either interested in particle physics or like me who has to teach it!

Crystal Clear, 07 Oct 2008
Wilczek got his Nobel Prize for his part in developing Chromodynamics, the theory of quarks and gluons and their strong force interaction. In this book we get an awe-inspiring jaunt through the most modern views of the quantum vacuum (which W. calls "The Grid") and unification theories (including SUSY).

Lots of stuff I hadn't understood before - for example, the mass of protons and neutrons (actually hadrons in general) is not at all a primary attribute. Instead it's Nature's optimisation compromise between the energy in the colour field (decreases as quarks and antiquark, for example, get closer together) and the increasing energy of 'localisation' as the said quarks and antiquarks are constrained into the same place: (more precision in location means higher momentum and energy). This energy (E/c2) is what turns out to be the proton or neutron mass: the quarks and gluons themselves are almost massless.

Wilczek writes in a humorous and crystal clear way, which makes his book that rarity in popularisations - a bit of a page turner! Warning: you need to be comfortable with the conceptual basis of 'undergraduate' quantum mechanics and special relativity to engage with this book.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Superb, 31 Oct 2008
This book is really well written by not just an expert in the field but someone who is able to make very complex ideas intelligable to non-specialists. I enjoyed this book immensely and recommend it to anyone who is either interested in particle physics or like me who has to teach it!

Crystal Clear, 07 Oct 2008
Wilczek got his Nobel Prize for his part in developing Chromodynamics, the theory of quarks and gluons and their strong force interaction. In this book we get an awe-inspiring jaunt through the most modern views of the quantum vacuum (which W. calls "The Grid") and unification theories (including SUSY).

Lots of stuff I hadn't understood before - for example, the mass of protons and neutrons (actually hadrons in general) is not at all a primary attribute. Instead it's Nature's optimisation compromise between the energy in the colour field (decreases as quarks and antiquark, for example, get closer together) and the increasing energy of 'localisation' as the said quarks and antiquarks are constrained into the same place: (more precision in location means higher momentum and energy). This energy (E/c2) is what turns out to be the proton or neutron mass: the quarks and gluons themselves are almost massless.

Wilczek writes in a humorous and crystal clear way, which makes his book that rarity in popularisations - a bit of a page turner! Warning: you need to be comfortable with the conceptual basis of 'undergraduate' quantum mechanics and special relativity to engage with this book.

Not really what I was expecting, 29 Nov 2008
From the blurb and the title I was expecting a book that would help deepen my understanding of quantum mechanics, and give me new and subtle insights into the implications of the Aspect/Gisin quantum entanglement experiments, possibly including some implications for thought and consciousness, a-la-Penrose. This turns out not to be the book's purpose at all however. It's hard to determine who the intended audience is. While the discussion on Quantum Mechaincs is pitched at layman's level, the discussion around it would seem more aimed at academics in the arts and humanities. It is a wide-ranging book touching on far more than QM. I found the book, informative, provocative, irritating, and in the end, rather moving. I'm glad I persisted with it though I can't say I agree with everything in it.

The introduction announces a post-modernist malaise in the academic humanities, rooted, the authors claim, in the removal of mind from the material world by Cartesian Dualism. This was surprising for me because, as a reader in Cognitive Science and Philosophy of Mind, I know that the modern scientific currency is reductive materialism. I had no idea that there was a community of folks out there who presumed dualism, and deduced pessimism.

The first half of the book then gives a layman's (non-mathematical) description of quantum mechanics. It's a bit sloppy. Terms are introduced without definition. Conclusions are drawn from premises without explanation. Schrodinger's cat is trotted out again, as usual, without qualification, so yet more credible folks will come away thinking that there is something magical about conscious observerhood that collapses superposed quantum states. The dual slit experiment is explained pretty well. Then we come to an exposition of Bell's inequality theorm as an intro to the Aspect/Gisin experiments. We gather that the implications are that Bohr's Copenhagen Interpretation is now incontrovertible, Einstein's Realism is refuted, and the hopes for deeper breakthroughs, such as hidden variable approaches, restoring it are shattered once and for all. The authors then specify a 'logic of complementarity' required to do constructive thinking about quantum phenomena, and point out along the way how Relativity requires the same kind of logic when thinking about space and time. This latter point I did find quite illuminating.

We then get a couple of chapters looking at aspects of Biology and Human Evolution where similar complementarity logic might be applicable. We are essentially looking at emergence, and how wholes can be greater than than sum of parts. We look at how co-operation operates alongside Darwinian competition as a dynamic in evolution, and we look at how culture could have driven the evolution of the physical substrates of human language in a virtuous spiral. Whether complementarity is fruitful of original insights in these areas, or merely provides analogies is hard to say.

The last third of the book gets to its main point which is to use the logic of complemantarity, derived from quantum mechanics, to bring solace to all these languishing postmodernist academics, and show them a way out of their pessimism.

I should say before I go much further that as a scientist who believes in a world out there, that gets on with it regardless of whether we do or can observe it, I don't have a lot of patience with post-modernist thought. The notion that science is a mythical social construction, promulgated by the power elite, is just institutionalised solipsism, and the money spent maintaining serious academic careers and filling our children's heads with this nonsense would be better spent on alleviating poverty or putting a person on Mars.

We get an intellectual history of post-modernism, tracing a line of descent from Descartes, through Nietzche, Husserl, Sartre and Existentialism, the post-structuralists and then the Derridas, Foucaults, etc. We have discovered that language can only ever refer to itself. That nothing meaningful can be said or deduced about the world outside our minds, and that all our thoughts have been hijacked by the power elite so they can get on with oppressing minorities of various pursuasions. Here, I just lose it. The Power elite does it's thing with violence and the exploitation of ignorance, pure and simple. They don't need to control our thoughts and language to do that, and the fact that they don't is what gives us hope for the future. Eventually we learn that the logic of complementarity allows the meanings of words to signify things in the external world and language is saved from the power elite. This is great because I hate to think of these postmodernists suffering needlessly.

We then get a chapter on the implications of the nonlocality implied by the Copenhagen Interpretation and the Aspect/Gisin experiments. Quantum entanglement from the big bang ensures that all particles/quanta in the universe are ultimately bound up in a single whole across all of space and time which is ultimately unknowable, in principle, to science. There can never be ontology, a science or knowledge of what's actually out there. I'm familiar with this understanding and have made my peace with it. The book makes the point that most of the science community simply adopt an ostrich approach to the full implications of nonlocality, so long as the maths works out.

The authors see things in terms of C.P.Snow's culture war between the disaffected postmodernists and the pragmatic mentality of science, a rift that itself follows the complementarity paradigm. In the final chapter they argue that that a dialogue is required between the two cultures if the ecological catastrophe, for which they present a very incisive analysis, facing humanity is to be confronted successfully. They here make a very moving appeal for the rift to be healed and a new complimentarity based unified system of thought to be developed as the basis for a completely new form of religion, shorn of all anthropomorphism and compatible with science but which speaks to all aspects of the human being. Their logic is that only a belief system with the force of a religion will be powerful enough to transform global society into something that can reach a sustainable realtionship with the world. I kind of agree, which is why I found it moving, but I have little optimism of it happening and less so that a shift in rational perspectives will provide the foundation for it.

So a very wide ranging book with some interesting points to make, none of which you'd suspect from the title. As a layman's introduction to Quantum Mechanics, I know there are better ones out there.


important and well written - perhaps flawed, 17 Jul 2007
Sometimes the language of this book, with its long flowing sentences and abstract ideas sounds a little Hegelian, but the vast majority of it is down-to-earth, well thought out and sticks to the task of describing some of the most difficult conceptual areas in science. Quantum Mechanics can never be easy because it is not visualisable as such. There may be some flaws in the argument however (why I marked it down!). The author's explanation of entanglement is solely in terms of non-locality. However they seemed to have ignored the alternative of retro-causality. They actually describe an important retro-causal experiment, but do not seem to incorporate it into their arguments. A further problem seems to occur when they go on to extend the idea of complementarity beyond physics (following Niels Bohr). They describe how `biological reality' might be affected by the same measurement difficulties as physical reality at the micro level. But biology is far too complex, in my opinion, to be able to isolate such an effect. It seems an unwarranted generalisation.

Simple yet technically superb, 21 Sep 2006
Anyone interested in the area of quantum mechanics should read this book. It is easy to understand, yet detailed and technically superb - explaining the various different interpretations that are available. This book is particularly impressive in bridging the knowledge gap that most books on the subject leave - the gap between quantum mechanics and what it implies for the human mind and our everyday lives. For anyone that thinks quantum mechanics has nothing (or very little) to do with reality - think again!

The main strength of this book is its uncompromising tenacity in explaining and staying with the facts. Where little is known, the authors explain the various thories that are around and their likely implications. For me, this book is the best available explanation of quantum mechanics and its unexpected possibilities.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Superb, 31 Oct 2008
This book is really well written by not just an expert in the field but someone who is able to make very complex ideas intelligable to non-specialists. I enjoyed this book immensely and recommend it to anyone who is either interested in particle physics or like me who has to teach it!

Crystal Clear, 07 Oct 2008
Wilczek got his Nobel Prize for his part in developing Chromodynamics, the theory of quarks and gluons and their strong force interaction. In this book we get an awe-inspiring jaunt through the most modern views of the quantum vacuum (which W. calls "The Grid") and unification theories (including SUSY).

Lots of stuff I hadn't understood before - for example, the mass of protons and neutrons (actually hadrons in general) is not at all a primary attribute. Instead it's Nature's optimisation compromise between the energy in the colour field (decreases as quarks and antiquark, for example, get closer together) and the increasing energy of 'localisation' as the said quarks and antiquarks are constrained into the same place: (more precision in location means higher momentum and energy). This energy (E/c2) is what turns out to be the proton or neutron mass: the quarks and gluons themselves are almost massless.

Wilczek writes in a humorous and crystal clear way, which makes his book that rarity in popularisations - a bit of a page turner! Warning: you need to be comfortable with the conceptual basis of 'undergraduate' quantum mechanics and special relativity to engage with this book.

Not really what I was expecting, 29 Nov 2008
From the blurb and the title I was expecting a book that would help deepen my understanding of quantum mechanics, and give me new and subtle insights into the implications of the Aspect/Gisin quantum entanglement experiments, possibly including some implications for thought and consciousness, a-la-Penrose. This turns out not to be the book's purpose at all however. It's hard to determine who the intended audience is. While the discussion on Quantum Mechaincs is pitched at layman's level, the discussion around it would seem more aimed at academics in the arts and humanities. It is a wide-ranging book touching on far more than QM. I found the book, informative, provocative, irritating, and in the end, rather moving. I'm glad I persisted with it though I can't say I agree with everything in it.

The introduction announces a post-modernist malaise in the academic humanities, rooted, the authors claim, in the removal of mind from the material world by Cartesian Dualism. This was surprising for me because, as a reader in Cognitive Science and Philosophy of Mind, I know that the modern scientific currency is reductive materialism. I had no idea that there was a community of folks out there who presumed dualism, and deduced pessimism.

The first half of the book then gives a layman's (non-mathematical) description of quantum mechanics. It's a bit sloppy. Terms are introduced without definition. Conclusions are drawn from premises without explanation. Schrodinger's cat is trotted out again, as usual, without qualification, so yet more credible folks will come away thinking that there is something magical about conscious observerhood that collapses superposed quantum states. The dual slit experiment is explained pretty well. Then we come to an exposition of Bell's inequality theorm as an intro to the Aspect/Gisin experiments. We gather that the implications are that Bohr's Copenhagen Interpretation is now incontrovertible, Einstein's Realism is refuted, and the hopes for deeper breakthroughs, such as hidden variable approaches, restoring it are shattered once and for all. The authors then specify a 'logic of complementarity' required to do constructive thinking about quantum phenomena, and point out along the way how Relativity requires the same kind of logic when thinking about space and time. This latter point I did find quite illuminating.

We then get a couple of chapters looking at aspects of Biology and Human Evolution where similar complementarity logic might be applicable. We are essentially looking at emergence, and how wholes can be greater than than sum of parts. We look at how co-operation operates alongside Darwinian competition as a dynamic in evolution, and we look at how culture could have driven the evolution of the physical substrates of human language in a virtuous spiral. Whether complementarity is fruitful of original insights in these areas, or merely provides analogies is hard to say.

The last third of the book gets to its main point which is to use the logic of complemantarity, derived from quantum mechanics, to bring solace to all these languishing postmodernist academics, and show them a way out of their pessimism.

I should say before I go much further that as a scientist who believes in a world out there, that gets on with it regardless of whether we do or can observe it, I don't have a lot of patience with post-modernist thought. The notion that science is a mythical social construction, promulgated by the power elite, is just institutionalised solipsism, and the money spent maintaining serious academic careers and filling our children's heads with this nonsense would be better spent on alleviating poverty or putting a person on Mars.

We get an intellectual history of post-modernism, tracing a line of descent from Descartes, through Nietzche, Husserl, Sartre and Existentialism, the post-structuralists and then the Derridas, Foucaults, etc. We have discovered that language can only ever refer to itself. That nothing meaningful can be said or deduced about the world outside our minds, and that all our thoughts have been hijacked by the power elite so they can get on with oppressing minorities of various pursuasions. Here, I just lose it. The Power elite does it's thing with violence and the exploitation of ignorance, pure and simple. They don't need to control our thoughts and language to do that, and the fact that they don't is what gives us hope for the future. Eventually we learn that the logic of complementarity allows the meanings of words to signify things in the external world and language is saved from the power elite. This is great because I hate to think of these postmodernists suffering needlessly.

We then get a chapter on the implications of the nonlocality implied by the Copenhagen Interpretation and the Aspect/Gisin experiments. Quantum entanglement from the big bang ensures that all particles/quanta in the universe are ultimately bound up in a single whole across all of space and time which is ultimately unknowable, in principle, to science. There can never be ontology, a science or knowledge of what's actually out there. I'm familiar with this understanding and have made my peace with it. The book makes the point that most of the science community simply adopt an ostrich approach to the full implications of nonlocality, so long as the maths works out.

The authors see things in terms of C.P.Snow's culture war between the disaffected postmodernists and the pragmatic mentality of science, a rift that itself follows the complementarity paradigm. In the final chapter they argue that that a dialogue is required between the two cultures if the ecological catastrophe, for which they present a very incisive analysis, facing humanity is to be confronted successfully. They here make a very moving appeal for the rift to be healed and a new complimentarity based unified system of thought to be developed as the basis for a completely new form of religion, shorn of all anthropomorphism and compatible with science but which speaks to all aspects of the human being. Their logic is that only a belief system with the force of a religion will be powerful enough to transform global society into something that can reach a sustainable realtionship with the world. I kind of agree, which is why I found it moving, but I have little optimism of it happening and less so that a shift in rational perspectives will provide the foundation for it.

So a very wide ranging book with some interesting points to make, none of which you'd suspect from the title. As a layman's introduction to Quantum Mechanics, I know there are better ones out there.


important and well written - perhaps flawed, 17 Jul 2007
Sometimes the language of this book, with its long flowing sentences and abstract ideas sounds a little Hegelian, but the vast majority of it is down-to-earth, well thought out and sticks to the task of describing some of the most difficult conceptual areas in science. Quantum Mechanics can never be easy because it is not visualisable as such. There may be some flaws in the argument however (why I marked it down!). The author's explanation of entanglement is solely in terms of non-locality. However they seemed to have ignored the alternative of retro-causality. They actually describe an important retro-causal experiment, but do not seem to incorporate it into their arguments. A further problem seems to occur when they go on to extend the idea of complementarity beyond physics (following Niels Bohr). They describe how `biological reality' might be affected by the same measurement difficulties as physical reality at the micro level. But biology is far too complex, in my opinion, to be able to isolate such an effect. It seems an unwarranted generalisation.

Simple yet technically superb, 21 Sep 2006
Anyone interested in the area of quantum mechanics should read this book. It is easy to understand, yet detailed and technically superb - explaining the various different interpretations that are available. This book is particularly impressive in bridging the knowledge gap that most books on the subject leave - the gap between quantum mechanics and what it implies for the human mind and our everyday lives. For anyone that thinks quantum mechanics has nothing (or very little) to do with reality - think again!

The main strength of this book is its uncompromising tenacity in explaining and staying with the facts. Where little is known, the authors explain the various thories that are around and their likely implications. For me, this book is the best available explanation of quantum mechanics and its unexpected possibilities.


Exploring the Unexplorable, 07 Jul 2003
Abbott's Flatland will always remain a classical inspiration for our understanding of higher-dimensional spaces. In drawing the analogy of the way that two dimensional people understand three dimensional space, Abbott allows the reader to ponder ways of investigating higher-dimensional space without the baggage of mathematical formalism.

However as Abbott's age and background are firmly rooted in the latter half of the 19th century, it would be thought that the finer nuances alluded to by the author would pass into obscurity. Here, the ingenuity of Ian Stewart comes to the fore. Prof Stewart refreshes Abbott's text with his annotations, detailing every minuscule reference that Abbott makes in his 19th century world. The result is an informed invigoration of a classic and opens more paths to inspiration in diverse disciplines such as theology and partical physics.

The book does require at least two readings; once for the story itself to bring alive the narrative of A Square, the second to fit in the background provided by Stewart around the story. One could almost say that Stewart uses a fourth dimension of time to expand a three dimensional tale that belongs in more dimensions.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Superb, 31 Oct 2008
This book is really well written by not just an expert in the field but someone who is able to make very complex ideas intelligable to non-specialists. I enjoyed this book immensely and recommend it to anyone who is either interested in particle physics or like me who has to teach it!

Crystal Clear, 07 Oct 2008
Wilczek got his Nobel Prize for his part in developing Chromodynamics, the theory of quarks and gluons and their strong force interaction. In this book we get an awe-inspiring jaunt through the most modern views of the quantum vacuum (which W. calls "The Grid") and unification theories (including SUSY).

Lots of stuff I hadn't understood before - for example, the mass of protons and neutrons (actually hadrons in general) is not at all a primary attribute. Instead it's Nature's optimisation compromise between the energy in the colour field (decreases as quarks and antiquark, for example, get closer together) and the increasing energy of 'localisation' as the said quarks and antiquarks are constrained into the same place: (more precision in location means higher momentum and energy). This energy (E/c2) is what turns out to be the proton or neutron mass: the quarks and gluons themselves are almost massless.

Wilczek writes in a humorous and crystal clear way, which makes his book that rarity in popularisations - a bit of a page turner! Warning: you need to be comfortable with the conceptual basis of 'undergraduate' quantum mechanics and special relativity to engage with this book.

Not really what I was expecting, 29 Nov 2008
From the blurb and the title I was expecting a book that would help deepen my understanding of quantum mechanics, and give me new and subtle insights into the implications of the Aspect/Gisin quantum entanglement experiments, possibly including some implications for thought and consciousness, a-la-Penrose. This turns out not to be the book's purpose at all however. It's hard to determine who the intended audience is. While the discussion on Quantum Mechaincs is pitched at layman's level, the discussion around it would seem more aimed at academics in the arts and humanities. It is a wide-ranging book touching on far more than QM. I found the book, informative, provocative, irritating, and in the end, rather moving. I'm glad I persisted with it though I can't say I agree with everything in it.

The introduction announces a post-modernist malaise in the academic humanities, rooted, the authors claim, in the removal of mind from the material world by Cartesian Dualism. This was surprising for me because, as a reader in Cognitive Science and Philosophy of Mind, I know that the modern scientific currency is reductive materialism. I had no idea that there was a community of folks out there who presumed dualism, and deduced pessimism.

The first half of the book then gives a layman's (non-mathematical) description of quantum mechanics. It's a bit sloppy. Terms are introduced without definition. Conclusions are drawn from premises without explanation. Schrodinger's cat is trotted out again, as usual, without qualification, so yet more credible folks will come away thinking that there is something magical about conscious observerhood that collapses superposed quantum states. The dual slit experiment is explained pretty well. Then we come to an exposition of Bell's inequality theorm as an intro to the Aspect/Gisin experiments. We gather that the implications are that Bohr's Copenhagen Interpretation is now incontrovertible, Einstein's Realism is refuted, and the hopes for deeper breakthroughs, such as hidden variable approaches, restoring it are shattered once and for all. The authors then specify a 'logic of complementarity' required to do constructive thinking about quantum phenomena, and point out along the way how Relativity requires the same kind of logic when thinking about space and time. This latter point I did find quite illuminating.

We then get a couple of chapters looking at aspects of Biology and Human Evolution where similar complementarity logic might be applicable. We are essentially looking at emergence, and how wholes can be greater than than sum of parts. We look at how co-operation operates alongside Darwinian competition as a dynamic in evolution, and we look at how culture could have driven the evolution of the physical substrates of human language in a virtuous spiral. Whether complementarity is fruitful of original insights in these areas, or merely provides analogies is hard to say.

The last third of the book gets to its main point which is to use the logic of complemantarity, derived from quantum mechanics, to bring solace to all these languishing postmodernist academics, and show them a way out of their pessimism.

I should say before I go much further that as a scientist who believes in a world out there, that gets on with it regardless of whether we do or can observe it, I don't have a lot of patience with post-modernist thought. The notion that science is a mythical social construction, promulgated by the power elite, is just institutionalised solipsism, and the money spent maintaining serious academic careers and filling our children's heads with this nonsense would be better spent on alleviating poverty or putting a person on Mars.

We get an intellectual history of post-modernism, tracing a line of descent from Descartes, through Nietzche, Husserl, Sartre and Existentialism, the post-structuralists and then the Derridas, Foucaults, etc. We have discovered that language can only ever refer to itself. That nothing meaningful can be said or deduced about the world outside our minds, and that all our thoughts have been hijacked by the power elite so they can get on with oppressing minorities of various pursuasions. Here, I just lose it. The Power elite does it's thing with violence and the exploitation of ignorance, pure and simple. They don't need to control our thoughts and language to do that, and the fact that they don't is what gives us hope for the future. Eventually we learn that the logic of complementarity allows the meanings of words to signify things in the external world and language is saved from the power elite. This is great because I hate to think of these postmodernists suffering needlessly.

We then get a chapter on the implications of the nonlocality implied by the Copenhagen Interpretation and the Aspect/Gisin experiments. Quantum entanglement from the big bang ensures that all particles/quanta in the universe are ultimately bound up in a single whole across all of space and time which is ultimately unknowable, in principle, to science. There can never be ontology, a science or knowledge of what's actually out there. I'm familiar with this understanding and have made my peace with it. The book makes the point that most of the science community simply adopt an ostrich approach to the full implications of nonlocality, so long as the maths works out.

The authors see things in terms of C.P.Snow's culture war between the disaffected postmodernists and the pragmatic mentality of science, a rift that itself follows the complementarity paradigm. In the final chapter they argue that that a dialogue is required between the two cultures if the ecological catastrophe, for which they present a very incisive analysis, facing humanity is to be confronted successfully. They here make a very moving appeal for the rift to be healed and a new complimentarity based unified system of thought to be developed as the basis for a completely new form of religion, shorn of all anthropomorphism and compatible with science but which speaks to all aspects of the human being. Their logic is that only a belief system with the force of a religion will be powerful enough to transform global society into something that can reach a sustainable realtionship with the world. I kind of agree, which is why I found it moving, but I have little optimism of it happening and less so that a shift in rational perspectives will provide the foundation for it.

So a very wide ranging book with some interesting points to make, none of which you'd suspect from the title. As a layman's introduction to Quantum Mechanics, I know there are better ones out there.


important and well written - perhaps flawed, 17 Jul 2007
Sometimes the language of this book, with its long flowing sentences and abstract ideas sounds a little Hegelian, but the vast majority of it is down-to-earth, well thought out and sticks to the task of describing some of the most difficult conceptual areas in science. Quantum Mechanics can never be easy because it is not visualisable as such. There may be some flaws in the argument however (why I marked it down!). The author's explanation of entanglement is solely in terms of non-locality. However they seemed to have ignored the alternative of retro-causality. They actually describe an important retro-causal experiment, but do not seem to incorporate it into their arguments. A further problem seems to occur when they go on to extend the idea of complementarity beyond physics (following Niels Bohr). They describe how `biological reality' might be affected by the same measurement difficulties as physical reality at the micro level. But biology is far too complex, in my opinion, to be able to isolate such an effect. It seems an unwarranted generalisation.

Simple yet technically superb, 21 Sep 2006
Anyone interested in the area of quantum mechanics should read this book. It is easy to understand, yet detailed and technically superb - explaining the various different interpretations that are available. This book is particularly impressive in bridging the knowledge gap that most books on the subject leave - the gap between quantum mechanics and what it implies for the human mind and our everyday lives. For anyone that thinks quantum mechanics has nothing (or very little) to do with reality - think again!

The main strength of this book is its uncompromising tenacity in explaining and staying with the facts. Where little is known, the authors explain the various thories that are around and their likely implications. For me, this book is the best available explanation of quantum mechanics and its unexpected possibilities.


Exploring the Unexplorable, 07 Jul 2003
Abbott's Flatland will always remain a classical inspiration for our understanding of higher-dimensional spaces. In drawing the analogy of the way that two dimensional people understand three dimensional space, Abbott allows the reader to ponder ways of investigating higher-dimensional space without the baggage of mathematical formalism.

However as Abbott's age and background are firmly rooted in the latter half of the 19th century, it would be thought that the finer nuances alluded to by the author would pass into obscurity. Here, the ingenuity of Ian Stewart comes to the fore. Prof Stewart refreshes Abbott's text with his annotations, detailing every minuscule reference that Abbott makes in his 19th century world. The result is an informed invigoration of a classic and opens more paths to inspiration in diverse disciplines such as theology and partical physics.

The book does require at least two readings; once for the story itself to bring alive the narrative of A Square, the second to fit in the background provided by Stewart around the story. One could almost say that Stewart uses a fourth dimension of time to expand a three dimensional tale that belongs in more dimensions.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Superb, 31 Oct 2008
This book is really well written by not just an expert in the field but someone who is able to make very complex ideas intelligable to non-specialists. I enjoyed this book immensely and recommend it to anyone who is either interested in particle physics or like me who has to teach it!

Crystal Clear, 07 Oct 2008
Wilczek got his Nobel Prize for his part in developing Chromodynamics, the theory of quarks and gluons and their strong force interaction. In this book we get an awe-inspiring jaunt through the most modern views of the quantum vacuum (which W. calls "The Grid") and unification theories (including SUSY).

Lots of stuff I hadn't understood before - for example, the mass of protons and neutrons (actually hadrons in general) is not at all a primary attribute. Instead it's Nature's optimisation compromise between the energy in the colour field (decreases as quarks and antiquark, for example, get closer together) and the increasing energy of 'localisation' as the said quarks and antiquarks are constrained into the same place: (more precision in location means higher momentum and energy). This energy (E/c2) is what turns out to be the proton or neutron mass: the quarks and gluons themselves are almost massless.

Wilczek writes in a humorous and crystal clear way, which makes his book that rarity in popularisations - a bit of a page turner! Warning: you need to be comfortable with the conceptual basis of 'undergraduate' quantum mechanics and special relativity to engage with this book.

Not really what I was expecting, 29 Nov 2008
From the blurb and the title I was expecting a book that would help deepen my understanding of quantum mechanics, and give me new and subtle insights into the implications of the Aspect/Gisin quantum entanglement experiments, possibly including some implications for thought and consciousness, a-la-Penrose. This turns out not to be the book's purpose at all however. It's hard to determine who the intended audience is. While the discussion on Quantum Mechaincs is pitched at layman's level, the discussion around it would seem more aimed at academics in the arts and humanities. It is a wide-ranging book touching on far more than QM. I found the book, informative, provocative, irritating, and in the end, rather moving. I'm glad I persisted with it though I can't say I agree with everything in it.

The introduction announces a post-modernist malaise in the academic humanities, rooted, the authors claim, in the removal of mind from the material world by Cartesian Dualism. This was surprising for me because, as a reader in Cognitive Science and Philosophy of Mind, I know that the modern scientific currency is reductive materialism. I had no idea that there was a community of folks out there who presumed dualism, and deduced pessimism.

The first half of the book then gives a layman's (non-mathematical) description of quantum mechanics. It's a bit sloppy. Terms are introduced without definition. Conclusions are drawn from premises without explanation. Schrodinger's cat is trotted out again, as usual, without qualification, so yet more credible folks will come away thinking that there is something magical about conscious observerhood that collapses superposed quantum states. The dual slit experiment is explained pretty well. Then we come to an exposition of Bell's inequality theorm as an intro to the Aspect/Gisin experiments. We gather that the implications are that Bohr's Copenhagen Interpretation is now incontrovertible, Einstein's Realism is refuted, and the hopes for deeper breakthroughs, such as hidden variable approaches, restoring it are shattered once and for all. The authors then specify a 'logic of complementarity' required to do constructive thinking about quantum phenomena, and point out along the way how Relativity requires the same kind of logic when thinking about space and time. This latter point I did find quite illuminating.

We then get a couple of chapters looking at aspects of Biology and Human Evolution where similar complementarity logic might be applicable. We are essentially looking at emergence, and how wholes can be greater than than sum of parts. We look at how co-operation operates alongside Darwinian competition as a dynamic in evolution, and we look at how culture could have driven the evolution of the physical substrates of human language in a virtuous spiral. Whether complementarity is fruitful of original insights in these areas, or merely provides analogies is hard to say.

The last third of the book gets to its main point which is to use the logic of complemantarity, derived from quantum mechanics, to bring solace to all these languishing postmodernist academics, and show them a way out of their pessimism.

I should say before I go much further that as a scientist who believes in a world out there, that gets on with it regardless of whether we do or can observe it, I don't have a lot of patience with post-modernist thought. The notion that science is a mythical social construction, promulgated by the power elite, is just institutionalised solipsism, and the money spent maintaining serious academic careers and filling our children's heads with this nonsense would be better spent on alleviating poverty or putting a person on Mars.

We get an intellectual history of post-modernism, tracing a line of descent from Descartes, through Nietzche, Husserl, Sartre and Existentialism, the post-structuralists and then the Derridas, Foucaults, etc. We have discovered that language can only ever refer to itself. That nothing meaningful can be said or deduced about the world outside our minds, and that all our thoughts have been hijacked by the power elite so they can get on with oppressing minorities of various pursuasions. Here, I just lose it. The Power elite does it's thing with violence and the exploitation of ignorance, pure and simple. They don't need to control our thoughts and language to do that, and the fact that they don't is what gives us hope for the future. Eventually we learn that the logic of complementarity allows the meanings of words to signify things in the external world and language is saved from the power elite. This is great because I hate to think of these postmodernists suffering needlessly.

We then get a chapter on the implications of the nonlocality implied by the Copenhagen Interpretation and the Aspect/Gisin experiments. Quantum entanglement from the big bang ensures that all particles/quanta in the universe are ultimately bound up in a single whole across all of space and time which is ultimately unknowable, in principle, to science. There can never be ontology, a science or knowledge of what's actually out there. I'm familiar with this understanding and have made my peace with it. The book makes the point that most of the science community simply adopt an ostrich approach to the full implications of nonlocality, so long as the maths works out.

The authors see things in terms of C.P.Snow's culture war between the disaffected postmodernists and the pragmatic mentality of science, a rift that itself follows the complementarity paradigm. In the final chapter they argue that that a dialogue is required between the two cultures if the ecological catastrophe, for which they present a very incisive analysis, facing humanity is to be confronted successfully. They here make a very moving appeal for the rift to be healed and a new complimentarity based unified system of thought to be developed as the basis for a completely new form of religion, shorn of all anthropomorphism and compatible with science but which speaks to all aspects of the human being. Their logic is that only a belief system with the force of a religion will be powerful enough to transform global society into something that can reach a sustainable realtionship with the world. I kind of agree, which is why I found it moving, but I have little optimism of it happening and less so that a shift in rational perspectives will provide the foundation for it.

So a very wide ranging book with some interesting points to make, none of which you'd suspect from the title. As a layman's introduction to Quantum Mechanics, I know there are better ones out there.


important and well written - perhaps flawed, 17 Jul 2007
Sometimes the language of this book, with its long flowing sentences and abstract ideas sounds a little Hegelian, but the vast majority of it is down-to-earth, well thought out and sticks to the task of describing some of the most difficult conceptual areas in science. Quantum Mechanics can never be easy because it is not visualisable as such. There may be some flaws in the argument however (why I marked it down!). The author's explanation of entanglement is solely in terms of non-locality. However they seemed to have ignored the alternative of retro-causality. They actually describe an important retro-causal experiment, but do not seem to incorporate it into their arguments. A further problem seems to occur when they go on to extend the idea of complementarity beyond physics (following Niels Bohr). They describe how `biological reality' might be affected by the same measurement difficulties as physical reality at the micro level. But biology is far too complex, in my opinion, to be able to isolate such an effect. It seems an unwarranted generalisation.

Simple yet technically superb, 21 Sep 2006
Anyone interested in the area of quantum mechanics should read this book. It is easy to understand, yet detailed and technically superb - explaining the various different interpretations that are available. This book is particularly impressive in bridging the knowledge gap that most books on the subject leave - the gap between quantum mechanics and what it implies for the human mind and our everyday lives. For anyone that thinks quantum mechanics has nothing (or very little) to do with reality - think again!

The main strength of this book is its uncompromising tenacity in explaining and staying with the facts. Where little is known, the authors explain the various thories that are around and their likely implications. For me, this book is the best available explanation of quantum mechanics and its unexpected possibilities.


Exploring the Unexplorable, 07 Jul 2003
Abbott's Flatland will always remain a classical inspiration for our understanding of higher-dimensional spaces. In drawing the analogy of the way that two dimensional people understand three dimensional space, Abbott allows the reader to ponder ways of investigating higher-dimensional space without the baggage of mathematical formalism.

However as Abbott's age and background are firmly rooted in the latter half of the 19th century, it would be thought that the finer nuances alluded to by the author would pass into obscurity. Here, the ingenuity of Ian Stewart comes to the fore. Prof Stewart refreshes Abbott's text with his annotations, detailing every minuscule reference that Abbott makes in his 19th century world. The result is an informed invigoration of a classic and opens more paths to inspiration in diverse disciplines such as theology and partical physics.

The book does require at least two readings; once for the story itself to bring alive the narrative of A Square, the second to fit in the background provided by Stewart around the story. One could almost say that Stewart uses a fourth dimension of time to expand a three dimensional tale that belongs in more dimensions.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

The Key Reference for its Field, 26 Aug 2004
A fragmentary edition of this book was published online in 1994, and has already been an academic "underground hit". The subject matter (probability as the only consistent, universal logic of uncertain inference) is relevant to nearly every field in science where evidence has to be assessed.

Edwin Jaynes was a great scientific writer and his breadth of learning, concern for real-world applications and wit clearly show through in this book. His comments on opposing views are very harsh by academic standards, but Jaynes' writing shows up how bland and how disconnected from real-world problems the academic writing on Bayesianism usually is.

This book combines two principles and shows how they can produce a Bayesian mathematical system which illuminates and unifies problems of reasoning and decision. His examples are sometimes delightfully original and range from court-room decisions to complex engineering problems.

The first principle is the Cox Proof, explained at length in Chapter 2. Probability is normally justified in terms of rational betting behaviour or in terms of sensible preferences between options. The Cox Proof, by contrast, derives probability from consistency constraints on the form of a system of inference. Hence non-probabilistic systems (such as those in orthodox statistics or fuzzy logic) are inconsistent; a very important result.

The other principle is the idea that one's expectations have an information content, which can be measured using the mathematics of Information Theory. Ideally, your beliefs should contain no more information than what is allowed by the evidence you have so far. Spelled out mathematically, this gives what is known as the Maximum Entropy (or "maxent") principle.

As a doctoral student in the philosophy of science, I found this the most useful source about induction, probability and statistics. Even though a lot of the maths was too advanced for me, Jaynes puts the mathematical proofs in context and explains why they are so important for science.

If more philosophers would read the first few chapters of this book, then a lot of collective misconceptions about probability would be cleared up and a lot of "new" discoveries would be shown to be already part of Jaynes' sophisticated system. AI researchers interested in the representation of uncertainty will also find it essential.

Really understand probability!, 30 Sep 2003
The book quotes Bernoulli (1713): "I cannot conceal the fact here that in the [application of probability theory], I foresee many things happening which can cause one to be badly mistaken if he does not proceed cautiously.", and indeed shows that throughout the history of probability theory this has happened all too often.

Jaynes starts with some deceptively simple requirements for the rules of reasoning in the face of uncertainty. He then proceeds systematically and with confident ease, to deduce the rules and practice of probability theory, showing along the way how to avoid the controversies and paradoxes usually associated with this field. He shows that these rules are the only consistent ones and any method that violates them is necessarily inconsistent.

The bulk of the book is about inference, or inverse probability problems. It is therefore highly recommended for all users of probability theory for inference. (This specifically includes engineers working on all types of automatic speech processing.) The reader is freed from the restrictive frequency interpretation of probability and can then start to develop a deep understanding of inference.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Superb, 31 Oct 2008
This book is really well written by not just an expert in the field but someone who is able to make very complex ideas intelligable to non-specialists. I enjoyed this book immensely and recommend it to anyone who is either interested in particle physics or like me who has to teach it!

Crystal Clear, 07 Oct 2008
Wilczek got his Nobel Prize for his part in developing Chromodynamics, the theory of quarks and gluons and their strong force interaction. In this book we get an awe-inspiring jaunt through the most modern views of the quantum vacuum (which W. calls "The Grid") and unification theories (including SUSY).

Lots of stuff I hadn't understood before - for example, the mass of protons and neutrons (actually hadrons in general) is not at all a primary attribute. Instead it's Nature's optimisation compromise between the energy in the colour field (decreases as quarks and antiquark, for example, get closer together) and the increasing energy of 'localisation' as the said quarks and antiquarks are constrained into the same place: (more precision in location means higher momentum and energy). This energy (E/c2) is what turns out to be the proton or neutron mass: the quarks and gluons themselves are almost massless.

Wilczek writes in a humorous and crystal clear way, which makes his book that rarity in popularisations - a bit of a page turner! Warning: you need to be comfortable with the conceptual basis of 'undergraduate' quantum mechanics and special relativity to engage with this book.

Not really what I was expecting, 29 Nov 2008
From the blurb and the title I was expecting a book that would help deepen my understanding of quantum mechanics, and give me new and subtle insights into the implications of the Aspect/Gisin quantum entanglement experiments, possibly including some implications for thought and consciousness, a-la-Penrose. This turns out not to be the book's purpose at all however. It's hard to determine who the intended audience is. While the discussion on Quantum Mechaincs is pitched at layman's level, the discussion around it would seem more aimed at academics in the arts and humanities. It is a wide-ranging book touching on far more than QM. I found the book, informative, provocative, irritating, and in the end, rather moving. I'm glad I persisted with it though I can't say I agree with everything in it.

The introduction announces a post-modernist malaise in the academic humanities, rooted, the authors claim, in the removal of mind from the material world by Cartesian Dualism. This was surprising for me because, as a reader in Cognitive Science and Philosophy of Mind, I know that the modern scientific currency is reductive materialism. I had no idea that there was a community of folks out there who presumed dualism, and deduced pessimism.

The first half of the book then gives a layman's (non-mathematical) description of quantum mechanics. It's a bit sloppy. Terms are introduced without definition. Conclusions are drawn from premises without explanation. Schrodinger's cat is trotted out again, as usual, without qualification, so yet more credible folks will come away thinking that there is something magical about conscious observerhood that collapses superposed quantum states. The dual slit experiment is explained pretty well. Then we come to an exposition of Bell's inequality theorm as an intro to the Aspect/Gisin experiments. We gather that the implications are that Bohr's Copenhagen Interpretation is now incontrovertible, Einstein's Realism is refuted, and the hopes for deeper breakthroughs, such as hidden variable approaches, restoring it are shattered once and for all. The authors then specify a 'logic of complementarity' required to do constructive thinking about quantum phenomena, and point out along the way how Relativity requires the same kind of logic when thinking about space and time. This latter point I did find quite illuminating.

We then get a couple of chapters looking at aspects of Biology and Human Evolution where similar complementarity logic might be applicable. We are essentially looking at emergence, and how wholes can be greater than than sum of parts. We look at how co-operation operates alongside Darwinian competition as a dynamic in evolution, and we look at how culture could have driven the evolution of the physical substrates of human language in a virtuous spiral. Whether complementarity is fruitful of original insights in these areas, or merely provides analogies is hard to say.

The last third of the book gets to its main point which is to use the logic of complemantarity, derived from quantum mechanics, to bring solace to all these languishing postmodernist academics, and show them a way out of their pessimism.

I should say before I go much further that as a scientist who believes in a world out there, that gets on with it regardless of whether we do or can observe it, I don't have a lot of patience with post-modernist thought. The notion that science is a mythical social construction, promulgated by the power elite, is just institutionalised solipsism, and the money spent maintaining serious academic careers and filling our children's heads with this nonsense would be better spent on alleviating poverty or putting a person on Mars.

We get an intellectual history of post-modernism, tracing a line of descent from Descartes, through Nietzche, Husserl, Sartre and Existentialism, the post-structuralists and then the Derridas, Foucaults, etc. We have discovered that language can only ever refer to itself. That nothing meaningful can be said or deduced about the world outside our minds, and that all our thoughts have been hijacked by the power elite so they can get on with oppressing minorities of various pursuasions. Here, I just lose it. The Power elite does it's thing with violence and the exploitation of ignorance, pure and simple. They don't need to control our thoughts and language to do that, and the fact that they don't is what gives us hope for the future. Eventually we learn that the logic of complementarity allows the meanings of words to signify things in the external world and language is saved from the power elite. This is great because I hate to think of these postmodernists suffering needlessly.

We then get a chapter on the implications of the nonlocality implied by the Copenhagen Interpretation and the Aspect/Gisin experiments. Quantum entanglement from the big bang ensures that all particles/quanta in the universe are ultimately bound up in a single whole across all of space and time which is ultimately unknowable, in principle, to science. There can never be ontology, a science or knowledge of what's actually out there. I'm familiar with this understanding and have made my peace with it. The book makes the point that most of the science community simply adopt an ostrich approach to the full implications of nonlocality, so long as the maths works out.

The authors see things in terms of C.P.Snow's culture war between the disaffected postmodernists and the pragmatic mentality of science, a rift that itself follows the complementarity paradigm. In the final chapter they argue that that a dialogue is required between the two cultures if the ecological catastrophe, for which they present a very incisive analysis, facing humanity is to be confronted successfully. They here make a very moving appeal for the rift to be healed and a new complimentarity based unified system of thought to be developed as the basis for a completely new form of religion, shorn of all anthropomorphism and compatible with science but which speaks to all aspects of the human being. Their logic is that only a belief system with the force of a religion will be powerful enough to transform global society into something that can reach a sustainable realtionship with the world. I kind of agree, which is why I found it moving, but I have little optimism of it happening and less so that a shift in rational perspectives will provide the foundation for it.

So a very wide ranging book with some interesting points to make, none of which you'd suspect from the title. As a layman's introduction to Quantum Mechanics, I know there are better ones out there.


important and well written - perhaps flawed, 17 Jul 2007
Sometimes the language of this book, with its long flowing sentences and abstract ideas sounds a little Hegelian, but the vast majority of it is down-to-earth, well thought out and sticks to the task of describing some of the most difficult conceptual areas in science. Quantum Mechanics can never be easy because it is not visualisable as such. There may be some flaws in the argument however (why I marked it down!). The author's explanation of entanglement is solely in terms of non-locality. However they seemed to have ignored the alternative of retro-causality. They actually describe an important retro-causal experiment, but do not seem to incorporate it into their arguments. A further problem seems to occur when they go on to extend the idea of complementarity beyond physics (following Niels Bohr). They describe how `biological reality' might be affected by the same measurement difficulties as physical reality at the micro level. But biology is far too complex, in my opinion, to be able to isolate such an effect. It seems an unwarranted generalisation.

Simple yet technically superb, 21 Sep 2006
Anyone interested in the area of quantum mechanics should read this book. It is easy to understand, yet detailed and technically superb - explaining the various different interpretations that are available. This book is particularly impressive in bridging the knowledge gap that most books on the subject leave - the gap between quantum mechanics and what it implies for the human mind and our everyday lives. For anyone that thinks quantum mechanics has nothing (or very little) to do with reality - think again!

The main strength of this book is its uncompromising tenacity in explaining and staying with the facts. Where little is known, the authors explain the various thories that are around and their likely implications. For me, this book is the best available explanation of quantum mechanics and its unexpected possibilities.


Exploring the Unexplorable, 07 Jul 2003
Abbott's Flatland will always remain a classical inspiration for our understanding of higher-dimensional spaces. In drawing the analogy of the way that two dimensional people understand three dimensional space, Abbott allows the reader to ponder ways of investigating higher-dimensional space without the baggage of mathematical formalism.

However as Abbott's age and background are firmly rooted in the latter half of the 19th century, it would be thought that the finer nuances alluded to by the author would pass into obscurity. Here, the ingenuity of Ian Stewart comes to the fore. Prof Stewart refreshes Abbott's text with his annotations, detailing every minuscule reference that Abbott makes in his 19th century world. The result is an informed invigoration of a classic and opens more paths to inspiration in diverse disciplines such as theology and partical physics.

The book does require at least two readings; once for the story itself to bring alive the narrative of A Square, the second to fit in the background provided by Stewart around the story. One could almost say that Stewart uses a fourth dimension of time to expand a three dimensional tale that belongs in more dimensions.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

The Key Reference for its Field, 26 Aug 2004
A fragmentary edition of this book was published online in 1994, and has already been an academic "underground hit". The subject matter (probability as the only consistent, universal logic of uncertain inference) is relevant to nearly every field in science where evidence has to be assessed.

Edwin Jaynes was a great scientific writer and his breadth of learning, concern for real-world applications and wit clearly show through in this book. His comments on opposing views are very harsh by academic standards, but Jaynes' writing shows up how bland and how disconnected from real-world problems the academic writing on Bayesianism usually is.

This book combines two principles and shows how they can produce a Bayesian mathematical system which illuminates and unifies problems of reasoning and decision. His examples are sometimes delightfully original and range from court-room decisions to complex engineering problems.

The first principle is the Cox Proof, explained at length in Chapter 2. Probability is normally justified in terms of rational betting behaviour or in terms of sensible preferences between options. The Cox Proof, by contrast, derives probability from consistency constraints on the form of a system of inference. Hence non-probabilistic systems (such as those in orthodox statistics or fuzzy logic) are inconsistent; a very important result.

The other principle is the idea that one's expectations have an information content, which can be measured using the mathematics of Information Theory. Ideally, your beliefs should contain no more information than what is allowed by the evidence you have so far. Spelled out mathematically, this gives what is known as the Maximum Entropy (or "maxent") principle.

As a doctoral student in the philosophy of science, I found this the most useful source about induction, probability and statistics. Even though a lot of the maths was too advanced for me, Jaynes puts the mathematical proofs in context and explains why they are so important for science.

If more philosophers would read the first few chapters of this book, then a lot of collective misconceptions about probability would be cleared up and a lot of "new" discoveries would be shown to be already part of Jaynes' sophisticated system. AI researchers interested in the representation of uncertainty will also find it essential.

Really understand probability!, 30 Sep 2003
The book quotes Bernoulli (1713): "I cannot conceal the fact here that in the [application of probability theory], I foresee many things happening which can cause one to be badly mistaken if he does not proceed cautiously.", and indeed shows that throughout the history of probability theory this has happened all too often.

Jaynes starts with some deceptively simple requirements for the rules of reasoning in the face of uncertainty. He then proceeds systematically and with confident ease, to deduce the rules and practice of probability theory, showing along the way how to avoid the controversies and paradoxes usually associated with this field. He shows that these rules are the only consistent ones and any method that violates them is necessarily inconsistent.

The bulk of the book is about inference, or inverse probability problems. It is therefore highly recommended for all users of probability theory for inference. (This specifically includes engineers working on all types of automatic speech processing.) The reader is freed from the restrictive frequency interpretation of probability and can then start to develop a deep understanding of inference.

Learn maths the easy way , 17 Mar 2008
I wish I had found this book long ago. It explains concepts in the easist way possible. You will find many details that are very relevant in applied mathematics in it and it will be very clear to you that they are important.

Again, not a book for someone that just wants proofs for theorems etc. but a book that allows you to apply your knowledge in physics and science in general in quite a strict mathematical manner. I would think, however, that you get the most of it only if you know some mechanics and/or thermodynamics.

On the other hand I was very curious about how the authors would attack vector calculus and wave theory in their easy to read style. In the end, I feel they really struggled with the last two chapters and is more evidence, in my opinion, that these are just hard topics (although you WILL know how to solve problems in vector calculus if you read this book).

Finally, if you ALSO want to know what you are really doing, I would not encourage you to learn from this book only and I would use it as a reference and fast revision text instead. If you want to learn, say calculus, from a more basic point of view (even if applied) I recommend Thomas' calculus which is a bit more rigorous.





Well structured book, which explains the material really well, 09 Aug 2006
This is an excellent book which explains the material really well. The best thing about it is the way it is structured, with fast track questions to see whether you can skip a section, and then ready to study questions, to make sure that you have the background knowledge to understand the chapter. Examples are clearly explained, as well as answers to questions in the text. It doesn't miss out crucial lines in a derivation, and it doesn't say 'This is obviously...' when it's not obvious to me, and if it was, I wouldn't have needed to look it up in the first place.

The maths is backed up by examples from physical sciences, which is really helpful and puts the whole thing in context.

It didn't cover all my course, so I had to use other books for part of the course. But it was so much better than the books which did cover the whole course, I'd buy it again.

A criticism for the publisher to put right - the index gives the section number, but there is no easy way to find a section, because it is not written on each page. The same problem in the answer sections, the answers are R1, T1 etc but doesn't say what chapter.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

Superb, 31 Oct 2008
This book is really well written by not just an expert in the field but someone who is able to make very complex ideas intelligable to non-specialists. I enjoyed this book immensely and recommend it to anyone who is either interested in particle physics or like me who has to teach it!

Crystal Clear, 07 Oct 2008
Wilczek got his Nobel Prize for his part in developing Chromodynamics, the theory of quarks and gluons and their strong force interaction. In this book we get an awe-inspiring jaunt through the most modern views of the quantum vacuum (which W. calls "The Grid") and unification theories (including SUSY).

Lots of stuff I hadn't understood before - for example, the mass of protons and neutrons (actually hadrons in general) is not at all a primary attribute. Instead it's Nature's optimisation compromise between the energy in the colour field (decreases as quarks and antiquark, for example, get closer together) and the increasing energy of 'localisation' as the said quarks and antiquarks are constrained into the same place: (more precision in location means higher momentum and energy). This energy (E/c2) is what turns out to be the proton or neutron mass: the quarks and gluons themselves are almost massless.

Wilczek writes in a humorous and crystal clear way, which makes his book that rarity in popularisations - a bit of a page turner! Warning: you need to be comfortable with the conceptual basis of 'undergraduate' quantum mechanics and special relativity to engage with this book.

Not really what I was expecting, 29 Nov 2008
From the blurb and the title I was expecting a book that would help deepen my understanding of quantum mechanics, and give me new and subtle insights into the implications of the Aspect/Gisin quantum entanglement experiments, possibly including some implications for thought and consciousness, a-la-Penrose. This turns out not to be the book's purpose at all however. It's hard to determine who the intended audience is. While the discussion on Quantum Mechaincs is pitched at layman's level, the discussion around it would seem more aimed at academics in the arts and humanities. It is a wide-ranging book touching on far more than QM. I found the book, informative, provocative, irritating, and in the end, rather moving. I'm glad I persisted with it though I can't say I agree with everything in it.

The introduction announces a post-modernist malaise in the academic humanities, rooted, the authors claim, in the removal of mind from the material world by Cartesian Dualism. This was surprising for me because, as a reader in Cognitive Science and Philosophy of Mind, I know that the modern scientific currency is reductive materialism. I had no idea that there was a community of folks out there who presumed dualism, and deduced pessimism.

The first half of the book then gives a layman's (non-mathematical) description of quantum mechanics. It's a bit sloppy. Terms are introduced without definition. Conclusions are drawn from premises without explanation. Schrodinger's cat is trotted out again, as usual, without qualification, so yet more credible folks will come away thinking that there is something magical about conscious observerhood that collapses superposed quantum states. The dual slit experiment is explained pretty well. Then we come to an exposition of Bell's inequality theorm as an intro to the Aspect/Gisin experiments. We gather that the implications are that Bohr's Copenhagen Interpretation is now incontrovertible, Einstein's Realism is refuted, and the hopes for deeper breakthroughs, such as hidden variable approaches, restoring it are shattered once and for all. The authors then specify a 'logic of complementarity' required to do constructive thinking about quantum phenomena, and point out along the way how Relativity requires the same kind of logic when thinking about space and time. This latter point I did find quite illuminating.

We then get a couple of chapters looking at aspects of Biology and Human Evolution where similar complementarity logic might be applicable. We are essentially looking at emergence, and how wholes can be greater than than sum of parts. We look at how co-operation operates alongside Darwinian competition as a dynamic in evolution, and we look at how culture could have driven the evolution of the physical substrates of human language in a virtuous spiral. Whether complementarity is fruitful of original insights in these areas, or merely provides analogies is hard to say.

The last third of the book gets to its main point which is to use the logic of complemantarity, derived from quantum mechanics, to bring solace to all these languishing postmodernist academics, and show them a way out of their pessimism.

I should say before I go much further that as a scientist who believes in a world out there, that gets on with it regardless of whether we do or can observe it, I don't have a lot of patience with post-modernist thought. The notion that science is a mythical social construction, promulgated by the power elite, is just institutionalised solipsism, and the money spent maintaining serious academic careers and filling our children's heads with this nonsense would be better spent on alleviating poverty or putting a person on Mars.

We get an intellectual history of post-modernism, tracing a line of descent from Descartes, through Nietzche, Husserl, Sartre and Existentialism, the post-structuralists and then the Derridas, Foucaults, etc. We have discovered that language can only ever refer to itself. That nothing meaningful can be said or deduced about the world outside our minds, and that all our thoughts have been hijacked by the power elite so they can get on with oppressing minorities of various pursuasions. Here, I just lose it. The Power elite does it's thing with violence and the exploitation of ignorance, pure and simple. They don't need to control our thoughts and language to do that, and the fact that they don't is what gives us hope for the future. Eventually we learn that the logic of complementarity allows the meanings of words to signify things in the external world and language is saved from the power elite. This is great because I hate to think of these postmodernists suffering needlessly.

We then get a chapter on the implications of the nonlocality implied by the Copenhagen Interpretation and the Aspect/Gisin experiments. Quantum entanglement from the big bang ensures that all particles/quanta in the universe are ultimately bound up in a single whole across all of space and time which is ultimately unknowable, in principle, to science. There can never be ontology, a science or knowledge of what's actually out there. I'm familiar with this understanding and have made my peace with it. The book makes the point that most of the science community simply adopt an ostrich approach to the full implications of nonlocality, so long as the maths works out.

The authors see things in terms of C.P.Snow's culture war between the disaffected postmodernists and the pragmatic mentality of science, a rift that itself follows the complementarity paradigm. In the final chapter they argue that that a dialogue is required between the two cultures if the ecological catastrophe, for which they present a very incisive analysis, facing humanity is to be confronted successfully. They here make a very moving appeal for the rift to be healed and a new complimentarity based unified system of thought to be developed as the basis for a completely new form of religion, shorn of all anthropomorphism and compatible with science but which speaks to all aspects of the human being. Their logic is that only a belief system with the force of a religion will be powerful enough to transform global society into something that can reach a sustainable realtionship with the world. I kind of agree, which is why I found it moving, but I have little optimism of it happening and less so that a shift in rational perspectives will provide the foundation for it.

So a very wide ranging book with some interesting points to make, none of which you'd suspect from the title. As a layman's introduction to Quantum Mechanics, I know there are better ones out there.


important and well written - perhaps flawed, 17 Jul 2007
Sometimes the language of this book, with its long flowing sentences and abstract ideas sounds a little Hegelian, but the vast majority of it is down-to-earth, well thought out and sticks to the task of describing some of the most difficult conceptual areas in science. Quantum Mechanics can never be easy because it is not visualisable as such. There may be some flaws in the argument however (why I marked it down!). The author's explanation of entanglement is solely in terms of non-locality. However they seemed to have ignored the alternative of retro-causality. They actually describe an important retro-causal experiment, but do not seem to incorporate it into their arguments. A further problem seems to occur when they go on to extend the idea of complementarity beyond physics (following Niels Bohr). They describe how `biological reality' might be affected by the same measurement difficulties as physical reality at the micro level. But biology is far too complex, in my opinion, to be able to isolate such an effect. It seems an unwarranted generalisation.

Simple yet technically superb, 21 Sep 2006
Anyone interested in the area of quantum mechanics should read this book. It is easy to understand, yet detailed and technically superb - explaining the various different interpretations that are available. This book is particularly impressive in bridging the knowledge gap that most books on the subject leave - the gap between quantum mechanics and what it implies for the human mind and our everyday lives. For anyone that thinks quantum mechanics has nothing (or very little) to do with reality - think again!

The main strength of this book is its uncompromising tenacity in explaining and staying with the facts. Where little is known, the authors explain the various thories that are around and their likely implications. For me, this book is the best available explanation of quantum mechanics and its unexpected possibilities.


Exploring the Unexplorable, 07 Jul 2003
Abbott's Flatland will always remain a classical inspiration for our understanding of higher-dimensional spaces. In drawing the analogy of the way that two dimensional people understand three dimensional space, Abbott allows the reader to ponder ways of investigating higher-dimensional space without the baggage of mathematical formalism.

However as Abbott's age and background are firmly rooted in the latter half of the 19th century, it would be thought that the finer nuances alluded to by the author would pass into obscurity. Here, the ingenuity of Ian Stewart comes to the fore. Prof Stewart refreshes Abbott's text with his annotations, detailing every minuscule reference that Abbott makes in his 19th century world. The result is an informed invigoration of a classic and opens more paths to inspiration in diverse disciplines such as theology and partical physics.

The book does require at least two readings; once for the story itself to bring alive the narrative of A Square, the second to fit in the background provided by Stewart around the story. One could almost say that Stewart uses a fourth dimension of time to expand a three dimensional tale that belongs in more dimensions.

Ian Stewart has done it again!, 29 Nov 2008
What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.

The Key Reference for its Field, 26 Aug 2004
A fragmentary edition of this book was published online in 1994, and has already been an academic "underground hit". The subject matter (probability as the only consistent, universal logic of uncertain inference) is relevant to nearly every field in science where evidence has to be assessed.

Edwin Jaynes was a great scientific writer and his breadth of learning, concern for real-world applications and wit clearly show through in this book. His comments on opposing views are very harsh by academic standards, but Jaynes' writing shows up how bland and how disconnected from real-world problems the academic writing on Bayesianism usually is.

This book combines two principles and shows how they can produce a Bayesian mathematical system which illuminates and unifies problems of reasoning and decision. His examples are sometimes delightfully original and range from court-room decisions to complex engineering problems.

The first principle is the Cox Proof, explained at length in Chapter 2. Probability is normally justified in terms of rational betting behaviour or in terms of sensible preferences between options. The Cox Proof, by contrast, derives probability from consistency constraints on the form of a system of inference. Hence non-probabilistic systems (such as those in orthodox statistics or fuzzy logic) are inconsistent; a very important result.

The other principle is the idea that one's expectations have an information content, which can be measured using the mathematics of Information Theory. Ideally, your beliefs should contain no more information than what is allowed by the evidence you have so far. Spelled out mathematically, this gives what is known as the Maximum Entropy (or "maxent") principle.

As a doctoral student in the philosophy of science, I found this the most useful source about induction, probability and statistics. Even though a lot of the maths was too advanced for me, Jaynes puts the mathematical proofs in context and explains why they are so important for science.

If more philosophers would read the first few chapters of this book, then a lot of collective misconceptions about probability would be cleared up and a lot of "new" discoveries would be shown to be already part of Jaynes' sophisticated system. AI researchers interested in the representation of uncertainty will also find it essential.

Really understand probability!, 30 Sep 2003
The book quotes Bernoulli (1713): "I cannot conceal the fact here that in the [application of probability theory], I foresee many things happening which can cause one to be badly mistaken if he does not proceed cautiously.", and indeed shows that throughout the history of probability theory this has happened all too often.

Jaynes starts with some deceptively simple requirements for the rules of reasoning in the face of uncertainty. He then proceeds systematically and with confident ease, to deduce the rules and practice of probability theory, showing along the way how to avoid the controversies and paradoxes usually associated with this field. He shows that these rules are the only consistent ones and any method that violates them is necessarily inconsistent.

The bulk of the book is about inference, or inverse probability problems. It is therefore highly recommended for all users of probability theory for inference. (This specifically includes engineers working on all types of automatic speech processing.) The reader is freed from the restrictive frequency interpretation of probability and can then start to develop a deep understanding of inference.

Learn maths the easy way , 17 Mar 2008
I wish I had found this book long ago. It explains concepts in the easist way possible. You will find many details that are very relevant in applied mathematics in it and it will be very clear to you that they are important.

Again, not a book for someone that just wants proofs for theore