Impossibility : The Limits of Science and the Science of Limits

Rating:
Summary: Disappointing.
Review: 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.

Rating:
Summary: A torturous text on paradoxes of knowing what is unknowable
Review: 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.

Rating:
Summary: Misson Impossible
Review: 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.

Rating:
Summary: A personal selection of fascinating ideas
Review: The ideas in this book are huge. It is only fair to admit that I did not understand many of the sections. Nevertheless, my impression is that the book is at least in part a personal and perhaps idiosyncratic tour of topics that fascinate the author, collected under a framework that does have a logical beginning, middle, and end. I was particularly fascinated by the progression in Chapters 4 through 7. Perhaps like the universe, the notion of limits relentlessly expands farther and farther outward from our central location inside the human mind. If you want to feel unbelievably small, check out the "real" size of the universe in Chapter 6, Cosmological Limits! The footnotes contain a lifetime of philosophical reading from around the world, but many of the references would be hard to find in the USA. What I will use the most from this book, though, is the lucid discussion of crank science in Chapter 1, and Barrow's wise criteria for real science on page 3.

Rating:
Summary: Fascinating, insightful, worth the effort.
Review: This book is worth reading for the quotations alone. The text is slower reading and the middle is a bit of a muddle, but very deep insights are scattered throughout. No fluff, good science, careful effort of a fine mind.

Paradox is the source of existence, and impossibility is the source of meaning. The recognition of limits is a powerful new tool, not the "end of science". It allows us to transcend the spacetime metric and understand ultimate reality without the superstitious nonsense. That's my interpretation, and it's very true. The author may have meant something else, of course.

Rating:
Summary: Too many fields.
Review: This book shows us the actual state of the limits of science and of our thinking.
It covers as different fields as physics, mathematics, linguistics, economics, politics, science fiction, epistemology, informatics, internet, artificial intelligence, cosmology ...
It is too much and not enough: too many items and a too short treatment, with one exception: the comments on Gödel, physics and free will.

I still learned a lot (e.g. the Oklo natural reactor), but I can only recommend this book to people who are not familiar with the works of K. Arrow, F. Dyson, W. Heisenberg, R. Penrose, A. Turing and others, as well as the author's own heavily contested and, for my part, misleadingly (for humanity) hope promising tome 'The Anthropic Cosmological Principle'.

On the other hand, the chapters 7 and 8 should not be missed.

Rating:
Summary: Philosophy rather than science
Review: 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.

Rating:
Summary: A fascinating journey through the science of limits
Review: 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.