## Impossibility : The Limits of Science and the Science of Limits: The Limits of Science and the Science of LimitsAre there some things we can never think, or know, let alone do? In this fascinating book, acclaimed author John Barrow reveals the often paradoxical limits on knowledge and achievement, and shows that the notion of `impossibility' has played, and continues to play, a striking role in our thinking, and in the way in which we understand the universe and ourselves. - ;What are the true limits of science and human endeavour? The end of each century leads to a stocktaking of human achievement and our expectation about the future. This new book by John D. Barrow looks at what limits there might be to human discovery and what we might find, ultimately, to be unknowable, undoable, or unthinkable. Weaving together a tapestry of surprises, Barrow explores the frontiers of knowledge, taking in surrealism, impossible figures, time travel, paradoxes of logic and perspective, theological speculations about Beings for whom nothing is impossible -- all stimulate us to contemplate something more that what is. With sufficient time and money at our disposal, why should we find anything impossible? Barrow explores the limits that may be imposed upon a full understanding of the physical Universe by constraints of technology, computes, cost, and complexity. He considers how the nature of the universe's structure prevents us from answering the deepest questions about its beginning, its structure, and its future. And he delves into the deep limits imposed by the nature of knowledge itself, which have profound implications for any quest for complete knowledge. They take us into the debates over the problems of free will and consciousness. G--ouml--;del's famous theorem about our inability to capture the truths of mathematics by rules and axioms is explored to see if it has any implications for science. Clearly and engagingly written, and using simple explanations, this book reveals that impossibility is a deep and powerful notion: that any Universe complex enough to contain conscious beings will contain limits on what those beings can know about their Universe: that what we cannot know defines reality as surely as what we can know. Impossibility is a two-edged sword: it threatens the completeness of the scientific enterprise yet without it there would be no laws of Nature, no science, and no scientists. - ;In this illuminating, well-written account of Limits (with capital L), John D. Barrow chronicles and explains the limits of science as a reality-generation mechanism and why it matters.So for about as good an account as you're going to get of where science stops, read this book. It won't tell you any final answer. But the journey is far more interesting - and important - than the destination. - Nature |

### Contents

The art of the impossible | 1 |

Linguistic paradox | 19 |

Progress and prejudice | 37 |

Summary | 55 |

Selective and absolute limits | 68 |

How many discoveries are there still to be made? | 83 |

Counting on words | 91 |

The frontier spirit | 107 |

Summary | 153 |

Chaotic inflation | 169 |

the final frontier | 182 |

Paradoxes | 195 |

Consistency | 197 |

Impossible constructions | 211 |

Gödel logic and the human mind | 230 |

Summary | 246 |

### Other editions - View all

### Common terms and phrases

ability arithmetic astronomical atoms axioms behaviour believe black hole brain choice complexity concept constants cosmic cosmological create critical defined discover discovery Einstein's elementary particles energy environment Euclidean geometry evolution example exist expanding expanding universe fact fine structure constant finite fundamental future galaxies geometry Gödel Gödel's theorem Grandfather Paradoxes gravity horizon human mind idea impossible incompleteness individual infinite inflation inflationary universe investigation J.D. Barrow knowledge laws of Nature limits logical London look machine mathematical mathematicians matter means natural selection observations outcomes Oxford University Press paradox past patterns philosopher physicists picture possess possible predict Presburger arithmetic principle problems quantum quantum mechanics realm reason result Roger Penrose scientists self-organized critical simple smaller solve space speed of light stars statement structure superstring theory symmetry technological Theory of Everything things truth Type ultimate understanding visible universe voters York