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John Barrow

Impossibility

Technology progresses at such speed that one sometime wonders whether there are any limits to what can be achieved. On the other hand science is built on laws which restrict our ability to do things - we can't travel faster than light or produce energy out of nothing. In Impossibility John Barrow looks such limits, and asks what consequences they will have in future. The book is actually much more positive than the title suggests, and the only things which seem to be really impossible are those which have been mathematically proved to be so. In truth the book is a wide ranging speculation of the possible directions our technology might follow. If you like this sort of peek into the future then this is a book you should read.

I had expected this book to be essentially a collection of separate chapters, each one dealing with a different kind of impossibility. In fact the chapters form more of a continuing discussion of what may become possibile in the future. In a sense the book is an answer to John Horgan's The End of Science. Some people might think that Barrow tries to cover too wide an area in this book and skims over the details too much - but he does provide plenty of notes at the end for those wanting to look further into the material covered.

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Paperback 304 pages
ISBN: 0195130820
Salesrank: 200141
Weight:0.66 lbs

Published: 1999 Oxford University Press, USA

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Hardcover 296 pages
ISBN: 0198518900
Salesrank: 1010896
Weight:1.55 lbs

Published: 1998 Oxford University Press

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Paperback 304 pages
ISBN: 0195130820
Salesrank: 724964
Weight:0.66 lbs

Published: 1999 Oxford University Press

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Product Description
In Impossibility, John D. Barrow--one of our most elegant and accomplished science writers--argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. Barrow first examines the limits of the human mind: our brain evolved to meet the demands of our immediate environment, and much that lies outside this small circle may also lie outside our understanding. He investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines deeper theoretical restrictions on our ability to know, including Godel's theorem, which proved that there were things that could not be proved. Finally, having explored the limits imposed on us from without, Barrow considers whether there are limits we should impose upon ourselves. Weaving together this intriguing tapestry, Barrow illuminates some of the most profound questions of science, from the possibility of time travel to the very structure of the universe.

Product Description

In Impossibility, John D. Barrow--one of our most elegant and accomplished science writers--argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. Barrow first examines the limits of the human mind: our brain evolved to meet the demands of our immediate environment, and much that lies outside this small circle may also lie outside our understanding. He investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines deeper theoretical restrictions on our ability to know, including Godel's theorem, which proved that there were things that could not be proved. Finally, having explored the limits imposed on us from without, Barrow considers whether there are limits we should impose upon ourselves. Weaving together this intriguing tapestry, Barrow illuminates some of the most profound questions of science, from the possibility of time travel to the very structure of the universe.

The End of Science ***
This work is informative, but far less profound/informative/entertaining (in my opinion)than the easily read/understood "opus" by John Horgan entitled...."The End of Science."

The End of Science ***

This work is informative, but far less profound/informative/entertaining (in my opinion)than the easily read/understood "opus" by John Horgan entitled...."The End of Science."

The impossible dream... *****
"I believe that knowledge is fractal. Whatever we learn -- what remains however small it seems -- is infinitely complex." Isaac Asimov, from his autobiography "I Asimov" In 1896, the US Patent Office seriously considered closing down on the theory that everything that was to be discovered had already been discovered. One need not look merely at the past one hundred or so years to see that there is no danger that plans to close the patent office will not soon be resurrected. In this book, Oxford University's John Barrow considers the inherent limits of knowability...an endeavor particularly germaine in the wake of Heisenberg's uncertainty, Einstein's relativity and of course Godel's incompleteness theorem...a subject DEFINATELY separate and apart from the closure of the US Patent Office because the whereas the closure of the US Patent Office would denote a completion of discovery, considerations of impossibility denote the limits of knowledge itself. Significantly, Barrow recognizes and addresses three key areas wherein a "the science limits and the limits of science" play a role: 1) Observer bias: In other words, the inherent limits of the human ability to percieve. In this regard, our partial view of the spectrum of visible light, auditory sound, and experiential feeling are but three examples; 2) The limits of technology: In other words, the inherent limits of the tools we use to devine truth. Our microscopes only view so microscopically. Our technologies only piece reality so deeply. 3) The limits of knowability itself: In this regard, Heisenberg's uncertainty priniciple that we cannot know both a subatomic particles speed and location is an easy example. However for Barrow, Godel's incompleteness theorem is a harder example. According to Barrow while its true that Godel's theorem says that any system sufficiently complicated to involve Godelian arithematic would suffer the production of formally unprovable propositions, for Barrow it is not a given that an ultimate theory of everything as denoted by modern physics would constitute such a "theory of everthing." As he puts it, even Euclidian geomotry would not constitute such a system. Barrow's understandable conservatism aside, it seems unlikely to be gainsaid that modern string theory -- consisting of anywhere from 10 to 26 dimensions -- let alone Einsteinian relativism would constitute such a system. In other words, while covering the main points, perhaps Barrow is a tad to conservative in hedging his bets that ultimate truth -- as would posited by a theory of everything -- is unknowable. In his closing chapters, Barrow addresses impossibility in relation to free will. If complete knowledge is unknowable then certainly such unknowability impacts free will. Perhaps Barrow himself or others will return to write on this important topic and when they do perhaps they will find that free will observes the same parementers outlined by choas theory...that the disorder yields itself to predictable patterns or order. In that sense, perhaps a complete survey of impossibility will outline the outer contours of what, itself, ultimately is.

The impossible dream... *****

"I believe that knowledge is fractal. Whatever we learn -- what remains however small it seems -- is infinitely complex."

Isaac Asimov, from his autobiography "I Asimov"

In 1896, the US Patent Office seriously considered closing down on the theory that everything that was to be discovered had already been discovered. One need not look merely at the past one hundred or so years to see that there is no danger that plans to close the patent office will not soon be resurrected.

In this book, Oxford University's John Barrow considers the inherent limits of knowability...an endeavor particularly germaine in the wake of Heisenberg's uncertainty, Einstein's relativity and of course Godel's incompleteness theorem...a subject DEFINATELY separate and apart from the closure of the US Patent Office because the whereas the closure of the US Patent Office would denote a completion of discovery, considerations of impossibility denote the limits of knowledge itself.

Significantly, Barrow recognizes and addresses three key areas wherein a "the science limits and the limits of science" play a role:

1) Observer bias: In other words, the inherent limits of the human ability to percieve. In this regard, our partial view of the spectrum of visible light, auditory sound, and experiential feeling are but three examples;

2) The limits of technology: In other words, the inherent limits of the tools we use to devine truth. Our microscopes only view so microscopically. Our technologies only piece reality so deeply.

3) The limits of knowability itself: In this regard, Heisenberg's uncertainty priniciple that we cannot know both a subatomic particles speed and location is an easy example. However for Barrow, Godel's incompleteness theorem is a harder example.

According to Barrow while its true that Godel's theorem says that any system sufficiently complicated to involve Godelian arithematic would suffer the production of formally unprovable propositions, for Barrow it is not a given that an ultimate theory of everything as denoted by modern physics would constitute such a "theory of everthing." As he puts it, even Euclidian geomotry would not constitute such a system.

Barrow's understandable conservatism aside, it seems unlikely to be gainsaid that modern string theory -- consisting of anywhere from 10 to 26 dimensions -- let alone Einsteinian relativism would constitute such a system.

In other words, while covering the main points, perhaps Barrow is a tad to conservative in hedging his bets that ultimate truth -- as would posited by a theory of everything -- is unknowable.

In his closing chapters, Barrow addresses impossibility in relation to free will. If complete knowledge is unknowable then certainly such unknowability impacts free will.

Perhaps Barrow himself or others will return to write on this important topic and when they do perhaps they will find that free will observes the same parementers outlined by choas theory...that the disorder yields itself to predictable patterns or order.

In that sense, perhaps a complete survey of impossibility will outline the outer contours of what, itself, ultimately is.

Rich in interesting ideas Understanding through understanding what we cannot understand *****
I read a text like this with the understanding that I am not going to understand everything in it. I read a text like this also with the understanding that I will probably at certain points disagree with it. But I first and above all read a text like this to extend my own thought, to learn new ideas, to go beyond the understanding I have previously had of the subject. The subject of ' impossibility' has been with me since I was a small child. I have always tried to understand how God could understand and know everything, when 'everything' seemed to me to be often so tremendously small and trivial, as if for instance the size and weight as they are changing of every particule of dirt and dust. The famous paradoxes of ' impossibility' relating to God are analyzed by Barrow in this book , the question of whether God can create a stone too heavy for God to lift - The answers which would seem to make God's existence and omniscence incompatible, it seems to me can always be trumped by the idea that our logic and our thought may simply not comprehend a 'dimension' of being , which is God's alone. In any case Barrow studies the idea of impossibility here in a variety of different contexts. In one he wants to show how crucial it is to the development of scientific inquiry and the establishing of laws of Nature. In all of this work I find Barrow's tone and intelligence admirable. He shows a great deal of modesty despite his great grasp of very complicated subjects. I will just cite one sample of this from his concluding chapter. "All the great questions about the nature of the Universe- from its beginning to its end- turn out to be unanswerable. There is a fundamental divide between the part of the Universe that we can observe, and the entire, possibly, infinite whole. There is a visusal horizon beyoned which we cannot see or know. Again there is a positive side to this limitation. If it did not exist, then nor would we: every movement of every star and galaxy would be felt here and now." His fundamental idea is in a sense that our limitations in knowledge add to our world and being. As he concludes, "Ultimately, we may even find that the fractal edge of our knowledge of the Universe defines its character more precisely than its contents, that what cannot be known is more revealing than what can" This is wonderfully rich work of thought, and most highly recommended to all who would better understand our world, through understanding what we cannot understand about it .

Rich in interesting ideas Understanding through understanding what we cannot understand *****

I read a text like this with the understanding that I am not going to understand everything in it. I read a text like this also with the understanding that I will probably at certain points disagree with it.
But I first and above all read a text like this to extend my own thought, to learn new ideas, to go beyond the understanding I have previously had of the subject.
The subject of ' impossibility' has been with me since I was a small child. I have always tried to understand how God could understand and know everything, when 'everything' seemed to me to be often so tremendously small and trivial, as if for instance the size and weight as they are changing of every particule of dirt and dust. The famous paradoxes of ' impossibility' relating to God are analyzed by Barrow in this book , the question of whether God can create a stone too heavy for God to lift - The answers which would seem to make God's existence and omniscence incompatible, it seems to me can always be trumped by the idea that our logic and our thought may simply not comprehend a 'dimension' of being , which is God's alone.
In any case Barrow studies the idea of impossibility here in a variety of different contexts. In one he wants to show how crucial it is to the development of scientific inquiry and the establishing of laws of Nature.
In all of this work I find Barrow's tone and intelligence admirable. He shows a great deal of modesty despite his great grasp of very complicated subjects. I will just cite one sample of this from his concluding chapter.
"All the great questions about the nature of the Universe- from its beginning to its end- turn out to be unanswerable. There is a fundamental divide between the part of the Universe that we can observe, and the entire, possibly, infinite whole. There is a visusal horizon beyoned which we cannot see or know. Again there is a positive side to this limitation. If it did not exist, then nor would we: every movement of every star and galaxy would be felt here and now."
His fundamental idea is in a sense that our limitations in knowledge add to our world and being. As he concludes, "Ultimately, we may even find that the fractal edge of our knowledge of the Universe defines its character more precisely than its contents, that what cannot be known is more revealing than what can"
This is wonderfully rich work of thought, and most highly recommended to all who would better understand our world, through understanding what we cannot understand about it .

Very unimpressive **
There are plenty of science books for the layman that I like. This sure isn't one of them. We start by discovering that there are some things which are impossible! For example, given the definitions of two, four, and five, two plus two can't equal five and not four. You may reply that since I'm only human, can I be sure of this? After all, humans can be wrong. Well, yes, if you say that two plus two is five, um, I know which human will be wrong! Similarly, nobody can make two plus two into five. Or pi into five. We may need to be a little more careful with pi, and define it as four times the arctangent of 1, because the measured circumferences of real circles (in curved space) are often something other than pi times their measured diameters, of course. But nobody can make pi into 5, not even God. Um, does that mean that God is not really all-powerful? If you think that what I've said so far is profound, maybe this book is for you! We also learn some more elementary stuff, such as c being the maximum speed, and that there is a limit to the accuracy with which we can simultaneously know both a particle's position and its momentum. The author then makes fun of Comte, the originator of Positivism. Comte sure had some really silly ideas. Still, the basic idea of basing one's knowledge on empirical data is totally sound, and I think we ought to give him some credit for that. Barrow then talks about three of the problems that Du Bois-Raymond said were unsolvable, back in 1880. These are the origin of natural forces and the nature of matter, the origin and nature of consciousness and sensation, and the problem of free will. Obviously, we've made plenty of progress on the first two problems (using empirical data, no less!) and the third problem may turn out to be mostly semantic. After that, the book goes downhill. We see discussions of the limits of science, of complexity, of possibilities for manipulating our environment, and of the difficulty of predicting an unambiguous future given a set of initial conditions. But I found all this very unimpressive. The sixth chapter is on cosmology, and it's certainly the best chapter of the book. It even gets into questions such as the natural selection of universes and whether the Universe had a beginning. Unfortunately, we then get into an amazingly weak and idiotic chapter on time travel. Look, folks, going into the past is totally impossible, for semantic reasons. Even if we could appear to do it, we'd have to call it something else in order to communicate in an unambiguous manner. In theory, we might be able to go into something similar to the past (but different, since we were not part of it originally). Or bring the past into the present. But it isn't English to say we could go into the past. Barrow ignores all this, and wonders about "grandfather paradoxes!" If you went into the something like the past, could you kill what appeared to be your now dead grandfather? Well, obviously you could. Would that be a paradox? No. If we changed the "past" would it ever have existed? Yes. After all, people die, but we do not claim that they never existed! Barrow is simply out of his depth in this chapter. The book concludes with a discussion of Godel's incompleteness theorem. Godel showed that some truth of some mathematical statements can not be ascertained. Now, does this stymie Physics? To his credit, Barrow speculates that it may not, and he has a reasonable argument here. And there is some discussion of implications about free will, which also seems reasonable. Still, this book has remarkably little content, and I did not like it. Nor do I recommend it. Barrow and Tipler's "The Anthropic Cosmological Principle," although it has some problems as well, is a much better book

Very unimpressive **

There are plenty of science books for the layman that I like. This sure isn't one of them.

We start by discovering that there are some things which are impossible! For example, given the definitions of two, four, and five, two plus two can't equal five and not four. You may reply that since I'm only human, can I be sure of this? After all, humans can be wrong. Well, yes, if you say that two plus two is five, um, I know which human will be wrong!

Similarly, nobody can make two plus two into five. Or pi into five. We may need to be a little more careful with pi, and define it as four times the arctangent of 1, because the measured circumferences of real circles (in curved space) are often something other than pi times their measured diameters, of course. But nobody can make pi into 5, not even God. Um, does that mean that God is not really all-powerful?

If you think that what I've said so far is profound, maybe this book is for you!

We also learn some more elementary stuff, such as c being the maximum speed, and that there is a limit to the accuracy with which we can simultaneously know both a particle's position and its momentum.

The author then makes fun of Comte, the originator of Positivism. Comte sure had some really silly ideas. Still, the basic idea of basing one's knowledge on empirical data is totally sound, and I think we ought to give him some credit for that. Barrow then talks about three of the problems that Du Bois-Raymond said were unsolvable, back in 1880. These are the origin of natural forces and the nature of matter, the origin and nature of consciousness and sensation, and the problem of free will. Obviously, we've made plenty of progress on the first two problems (using empirical data, no less!) and the third problem may turn out to be mostly semantic.

After that, the book goes downhill. We see discussions of the limits of science, of complexity, of possibilities for manipulating our environment, and of the difficulty of predicting an unambiguous future given a set of initial conditions. But I found all this very unimpressive.

The sixth chapter is on cosmology, and it's certainly the best chapter of the book. It even gets into questions such as the natural selection of universes and whether the Universe had a beginning.

Unfortunately, we then get into an amazingly weak and idiotic chapter on time travel. Look, folks, going into the past is totally impossible, for semantic reasons. Even if we could appear to do it, we'd have to call it something else in order to communicate in an unambiguous manner. In theory, we might be able to go into something similar to the past (but different, since we were not part of it originally). Or bring the past into the present. But it isn't English to say we could go into the past. Barrow ignores all this, and wonders about "grandfather paradoxes!" If you went into the something like the past, could you kill what appeared to be your now dead grandfather? Well, obviously you could. Would that be a paradox? No. If we changed the "past" would it ever have existed? Yes. After all, people die, but we do not claim that they never existed! Barrow is simply out of his depth in this chapter.

The book concludes with a discussion of Godel's incompleteness theorem. Godel showed that some truth of some mathematical statements can not be ascertained. Now, does this stymie Physics? To his credit, Barrow speculates that it may not, and he has a reasonable argument here. And there is some discussion of implications about free will, which also seems reasonable. Still, this book has remarkably little content, and I did not like it. Nor do I recommend it. Barrow and Tipler's "The Anthropic Cosmological Principle," although it has some problems as well, is a much better book

A torturous text on paradoxes of knowing what is unknowable ****
Is science fast coming to an end? Can we arrive at a so-called theory of everything? Are there limits to our abilities to discover the nature of reality? In trying to tackle such questions, Astronomer John D. Barrow invites readers to an intriguing journey which I understood as twofold. First, it promises to show how the notion of impossibility is far subtler than everyday language suggests and to demonstrate how fundamental are the limitations to science (in the broadest sense of human capability to discover and know things). To support this contention, he serves up a menu of what seems like disjointed readings into the limits of human endeavor as demonstrated in findings in different fields such as astronomy, mathematics, psychology, economics, and others. Each of these readings, which are sub-sections of chapters, is individually interesting and the book overall is not deeply technical, -- and thus remains accessible to the truly curious generalist reader. It covers some familiar basic ideas in different fields, which all depict the notions of limits and impossibility, whether in scientific discovery or in social decision-making. The topics range from the technical bounds to scientific experiments, such the speed of light and difficulties of producing the extremely high temperatures not found on earth which are needed to test our version of the forces of nature, to Arrow's impossibility theorem on the inability to generate a consistent ranking of social preferences based on an aggregation of ranking of individual preferences. Unfortunately, these sub-sections of chapters, while individually very interesting and clearly written, tend to conflate different ideas of impossibility rather than leading to a straightforward conclusion on the fundamental limitations of human endeavors of creation and discovery. The secondary thrust of the book is on the nature of reality itself. Barrow argues that the kind of limitations he enumerates defines the universe more powerfully than a list of what we think is possible. In fact, he contends that this ?impossible? nature of the universe is what itself allows the self-reflection consciousness of humans, a rather intriguing, if not entirely novel, proposition. My judgment on this book is a complex as the range of subjects the author attempts to cover. It is without doubt an intriguing set of propositions loosely connected with some related discussion on the history of scientific thought. I found the discussion of nineteenth century notions of impossibility very informative. However, the book may achieve its appeal by overstating its case (QUOTE the astronomers? desire to understand the structure of the universe is doomed merely to scratch the surface of the cosmological problem UNQUOTE) and resorting to fast and loose comparisons of paradoxes and limits which are well-known to practitioners in a number of different fields. Ultimately, the book gives a sense of having covered too much, and thus providing too little in any given area. I confess that notwithstanding these reservations, I enjoyed reading this somewhat unusual book. If you do have the stamina to complete this book, you might choose to do so in a non-linear fashion by working through the clear summaries of each chapter first, and then going through the chapters in your order of preference. If you manage to do all this, you are likely to enjoy another book on a different but related topic on the nature of the human mind entitled ?Figments of Reality? by Stewart and Cohen which I have also reviewed on this site.

A torturous text on paradoxes of knowing what is unknowable ****

Is science fast coming to an end? Can we arrive at a so-called theory of everything? Are there limits to our abilities to discover the nature of reality?

In trying to tackle such questions, Astronomer John D. Barrow invites readers to an intriguing journey which I understood as twofold. First, it promises to show how the notion of impossibility is far subtler than everyday language suggests and to demonstrate how fundamental are the limitations to science (in the broadest sense of human capability to discover and know things). To support this contention, he serves up a menu of what seems like disjointed readings into the limits of human endeavor as demonstrated in findings in different fields such as astronomy, mathematics, psychology, economics, and others. Each of these readings, which are sub-sections of chapters, is individually interesting and the book overall is not deeply technical, -- and thus remains accessible to the truly curious generalist reader. It covers some familiar basic ideas in different fields, which all depict the notions of limits and impossibility, whether in scientific discovery or in social decision-making. The topics range from the technical bounds to scientific experiments, such the speed of light and difficulties of producing the extremely high temperatures not found on earth which are needed to test our version of the forces of nature, to Arrow's impossibility theorem on the inability to generate a consistent ranking of social preferences based on an aggregation of ranking of individual preferences.

Unfortunately, these sub-sections of chapters, while individually very interesting and clearly written, tend to conflate different ideas of impossibility rather than leading to a straightforward conclusion on the fundamental limitations of human endeavors of creation and discovery.

The secondary thrust of the book is on the nature of reality itself. Barrow argues that the kind of limitations he enumerates defines the universe more powerfully than a list of what we think is possible. In fact, he contends that this ?impossible? nature of the universe is what itself allows the self-reflection consciousness of humans, a rather intriguing, if not entirely novel, proposition.

My judgment on this book is a complex as the range of subjects the author attempts to cover. It is without doubt an intriguing set of propositions loosely connected with some related discussion on the history of scientific thought. I found the discussion of nineteenth century notions of impossibility very informative. However, the book may achieve its appeal by overstating its case (QUOTE the astronomers? desire to understand the structure of the universe is doomed merely to scratch the surface of the cosmological problem UNQUOTE) and resorting to fast and loose comparisons of paradoxes and limits which are well-known to practitioners in a number of different fields. Ultimately, the book gives a sense of having covered too much, and thus providing too little in any given area.

I confess that notwithstanding these reservations, I enjoyed reading this somewhat unusual book. If you do have the stamina to complete this book, you might choose to do so in a non-linear fashion by working through the clear summaries of each chapter first, and then going through the chapters in your order of preference. If you manage to do all this, you are likely to enjoy another book on a different but related topic on the nature of the human mind entitled ?Figments of Reality? by Stewart and Cohen which I have also reviewed on this site.

Disappointing. **
Barrow, of anthropic cosmological principle fame, undertakes to examine the logical, practical, and psychological limits to human [scientific] knowledge. The result is a sometimes interesting, but more often disappointing exposition in the history of science and of philosophy. In a volume that is essentially a philosophical treatise, we find that even Cambridge mathematicians can expound rather sloppy logic, actually evidencing the limits imposed on human investigations by human psychological encumbrances (one of the author's themes). The author's first chapter consideration of visual and linguistic paradoxes features a feeble apologia for agnosticism, which employs a linguistic paradox as an argument against the existence of an omniscient being. Barrow, who seems to be fairly well studied in philosophy, should know that Augustine decisively trashed this type of argument 1600 years ago for reasons that seem apparent in Barrow's own choice of language. [Barrow's cited paradox attests merely that no finite being can know everything. Further, a variation of the paradox attests that no one could ever know that an omniscient being does not exist.] In the second chapter, discussing the limits of the human mind revealed by Immanuel Kant, Barrow states that we understand these problems "as Kant did not" to be explained by natural selection. Natural selection is, of course, a tautological proposition (stating that if gene a is more likely to succeed than gene b, then gene a is more likely to succeed than gene b). As Kant explained, and as any student of logic knows, a tautology explains nothing. Given Barrow's skeptical consideration of various other attempts at explanation, his non-analytical and repetitive alighting on this sacrosanct tautology is unfortunate. Barrow's opening fusillades here may be his weakest, but it doesn't get a great deal better. There are some discussions that I did enjoy: the author's consideration of selective as opposed to absolute limits; and his [re]visitation of a few of the fundamental 'coincidences' contributing to the anthropic principle (chapter 5). Barrow's consideration of the human mind ("What are minds for?", chapter 4) is essentially useless. His conclusions (chapters 8 and 9) are interesting but don't warrant reading the entire book to reach them: "If this book has taught the reader anything, I hope that the notion of impossibility is far subtler than naïve assumptions ... would lead you to believe." Likely, this is one of John Barrow's weakest efforts. To the reader interested in the interplay of physics and philosophy I recommend Paul Davies' The Mind of God. For the reader who is interested in logic, this book may suffice as a brief introduction to the idea of limit and to Gödel's Incompleteness Theorem. Reading Immanuel Kant, one of the most finely disciplined minds in scholastic history, would be of greater value. Pass on this one.

Disappointing. **

Barrow, of anthropic cosmological principle fame, undertakes to examine the logical, practical, and psychological limits to human [scientific] knowledge. The result is a sometimes interesting, but more often disappointing exposition in the history of science and of philosophy. In a volume that is essentially a philosophical treatise, we find that even Cambridge mathematicians can expound rather sloppy logic, actually evidencing the limits imposed on human investigations by human psychological encumbrances (one of the author's themes). The author's first chapter consideration of visual and linguistic paradoxes features a feeble apologia for agnosticism, which employs a linguistic paradox as an argument against the existence of an omniscient being. Barrow, who seems to be fairly well studied in philosophy, should know that Augustine decisively trashed this type of argument 1600 years ago for reasons that seem apparent in Barrow's own choice of language. [Barrow's cited paradox attests merely that no finite being can know everything. Further, a variation of the paradox attests that no one could ever know that an omniscient being does not exist.] In the second chapter, discussing the limits of the human mind revealed by Immanuel Kant, Barrow states that we understand these problems "as Kant did not" to be explained by natural selection. Natural selection is, of course, a tautological proposition (stating that if gene a is more likely to succeed than gene b, then gene a is more likely to succeed than gene b). As Kant explained, and as any student of logic knows, a tautology explains nothing. Given Barrow's skeptical consideration of various other attempts at explanation, his non-analytical and repetitive alighting on this sacrosanct tautology is unfortunate. Barrow's opening fusillades here may be his weakest, but it doesn't get a great deal better. There are some discussions that I did enjoy: the author's consideration of selective as opposed to absolute limits; and his [re]visitation of a few of the fundamental 'coincidences' contributing to the anthropic principle (chapter 5).
Barrow's consideration of the human mind ("What are minds for?", chapter 4) is essentially useless. His conclusions (chapters 8 and 9) are interesting but don't warrant reading the entire book to reach them: "If this book has taught the reader anything, I hope that the notion of impossibility is far subtler than naïve assumptions ... would lead you to believe."
Likely, this is one of John Barrow's weakest efforts. To the reader interested in the interplay of physics and philosophy I recommend Paul Davies' The Mind of God. For the reader who is interested in logic, this book may suffice as a brief introduction to the idea of limit and to Gödel's Incompleteness Theorem. Reading Immanuel Kant, one of the most finely disciplined minds in scholastic history, would be of greater value. Pass on this one.

Misson Impossible *****
Recurring fascination with the question: whether or not the ever-expanding frontiers of science are subject to limits, led me to the study of John Barrow's 'Impossibility'. Barrow asserts that there are definite limits to the development of science due to philosophical, sociological, biological, technological, mathematical and logical factors as well as Laws of Physics, like finite speed of light, cosmic singularity theorems, inflationary cosmology, relative time travel; and 'Anthropic Cosmology', which states that there must be physical constants (viz. the mass of the proton) to allow for the existnece and emergence of living creatures; and Godel's theorem, which has been used to argue that a computer may never be as smart as a human being because the extent of its knowledge base is limited by a fixed set of algorithms, whereas a person may discover unexpected truths. Without minimising the great merit in Barrow's approach, I feel that finding limits to scientific development is like learning to swim: no matter how much the instructor tells you before hand, you only learn after you have stepped into the water. While it is useful and desirable to have an idea of the limits which may beset scientific inquiry, it is imperative that scientists, at any given time, pursue research on the premise that further progress in science is always achievable.

Misson Impossible *****

Recurring fascination with the question: whether or not the ever-expanding frontiers of science are subject to limits, led me to the study of John Barrow's 'Impossibility'. Barrow asserts that there are definite limits to the development of science due to philosophical, sociological, biological, technological, mathematical and logical factors as well as Laws of Physics, like finite speed of light, cosmic singularity theorems, inflationary cosmology, relative time travel; and 'Anthropic Cosmology', which states that there must be physical constants (viz. the mass of the proton) to allow for the existnece and emergence of living creatures; and Godel's theorem, which has been used to argue that a computer may never be as smart as a human being because the extent of its knowledge base is limited by a fixed set of algorithms, whereas a person may discover unexpected truths.

Without minimising the great merit in Barrow's approach, I feel that finding limits to scientific development is like learning to swim: no matter how much the instructor tells you before hand, you only learn after you have stepped into the water. While it is useful and desirable to have an idea of the limits which may beset scientific inquiry, it is imperative that scientists, at any given time, pursue research on the premise that further progress in science is always achievable.

Philosophy rather than science ****
This book surprised me in that it was more about philosophy than science or mathematics. Somehow (was it the blurb or the title?) I expected this book to be a complement or development of the ideas in Rudy Rucker's 'Infinity and the Mind', or som3e of the works of Raymond Smullyan. But it shied away from technical aspects in preference to more general exposition. I thought, on starting the book, that I might have learned more about those mathematicians who work without reference to differential or integral calculus because of underlying difficulties in the rationale for using limits in analysis. However, I did enjoy the book and it did have insights that interested me.

Philosophy rather than science ****

This book surprised me in that it was more about philosophy than science or mathematics. Somehow (was it the blurb or the title?) I expected this book to be a complement or development of the ideas in Rudy Rucker's 'Infinity and the Mind', or som3e of the works of Raymond Smullyan. But it shied away from technical aspects in preference to more general exposition. I thought, on starting the book, that I might have learned more about those mathematicians who work without reference to differential or integral calculus because of underlying difficulties in the rationale for using limits in analysis. However, I did enjoy the book and it did have insights that interested me.

A fascinating journey through the science of limits ***
This is an interesting book and presents some issues which were unfamiliar to me. I had heard of most of the arguments before but some were completely refreshing especially those concerning Goedel, the Arrow Impossibility theorem and Donald McKay. Like some of the other reviewers I found the book to be a little muddled in terms of making clear points in each chapter but overall it was good. I would have been interested if Barrow had looked at some other ways of looking at the world such as Goethean science, unlike Kant, which notes that it is possible to truly experience what is real, or the approach of intuition which Goedel himself notes "I don't see any reason why we should have less confidence in this kind of perception, ie mathematical intuition ..." or for that matter the logical approach first created by Spencer Brown in his "Laws of Form". There are times when much is assumed which of course is not unexpected since Barrow is a hard scientist who stays well within the expected bounds of science. It is good to see the text interspersed with humorous asides such as those of Douglas Adams and many others. As usual Barrow has done his research in the accepted areas very well being thorough and at times insightful. All in all a fascinating journey through the (normal) science of limits.

A fascinating journey through the science of limits ***

This is an interesting book and presents some issues which were unfamiliar to me. I had heard of most of the arguments before but some were completely refreshing especially those concerning Goedel, the Arrow Impossibility theorem and Donald McKay. Like some of the other reviewers I found the book to be a little muddled in terms of making clear points in each chapter but overall it was good. I would have been interested if Barrow had looked at some other ways of looking at the world such as Goethean science, unlike Kant, which notes that it is possible to truly experience what is real, or the approach of intuition which Goedel himself notes "I don't see any reason why we should have less confidence in this kind of perception, ie mathematical intuition ..." or for that matter the logical approach first created by Spencer Brown in his "Laws of Form". There are times when much is assumed which of course is not unexpected since Barrow is a hard scientist who stays well within the expected bounds of science. It is good to see the text interspersed with humorous asides such as those of Douglas Adams and many others. As usual Barrow has done his research in the accepted areas very well being thorough and at times insightful. All in all a fascinating journey through the (normal) science of limits.