{"product_id":"the-road-to-reality-isbn-9780679776314","title":"The Road to Reality","description":"\u003cp\u003e\u003cb\u003eNobel Prize-winner Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive—and comprehensible—account of the physics of the universe. \u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eA \"guide to physics’ big picture, and to the thoughts of one of the world’s most original thinkers.”—\u003ci\u003eThe New York Times\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003eFrom the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, \u003ci\u003eThe Road to Reality\u003c\/i\u003e carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. \u003cbr\u003e\u003cbr\u003eHere, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.\u003c\/p\u003e\u003ci\u003ePreface \u003cbr\u003eAcknowledgements \u003cbr\u003eNotation \u003cbr\u003ePrologue \u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e1 The roots of science\u003c\/b\u003e \u003cbr\u003e1.1 The quest for the forces that shape the world \u003cbr\u003e1.2 Mathematical truth \u003cbr\u003e1.3 Is Plato’s mathematical world ‘real’? \u003cbr\u003e1.4 Three worlds and three deep mysteries \u003cbr\u003e1.5 The Good, the True, and the Beautiful \u003cbr\u003e\u003cbr\u003e\u003cb\u003e2 An ancient theorem and a modern question \u003c\/b\u003e\u003cbr\u003e2.1 The Pythagorean theorem \u003cbr\u003e2.2 Euclid’s postulates \u003cbr\u003e2.3 Similar-areas proof of the Pythagorean theorem \u003cbr\u003e2.4 Hyperbolic geometry: conformal picture \u003cbr\u003e2.5 Other representations of hyperbolic geometry \u003cbr\u003e2.6 Historical aspects of hyperbolic geometry \u003cbr\u003e2.7 Relation to physical space \u003cbr\u003e\u003cbr\u003e\u003cb\u003e3 Kinds of number in the physical world \u003c\/b\u003e\u003cbr\u003e3.1 A Pythagorean catastrophe? \u003cbr\u003e3.2 The real-number system \u003cbr\u003e3.3 Real numbers in the physical world \u003cbr\u003e3.4 Do natural numbers need the physical world? \u003cbr\u003e3.5 Discrete numbers in the physical world \u003cbr\u003e\u003cbr\u003e\u003cb\u003e4 Magical complex numbers \u003c\/b\u003e\u003cbr\u003e4.1 The magic number ‘i’ \u003cbr\u003e4.2 Solving equations with complex numbers \u003cbr\u003e4.3 Convergence of power series \u003cbr\u003e4.4 Caspar Wessel’s complex plane \u003cbr\u003e4.5 How to construct the Mandelbrot set \u003cbr\u003e\u003cbr\u003e\u003cb\u003e5 Geometry of logarithms, powers, and roots \u003c\/b\u003e\u003cbr\u003e5.1 Geometry of complex algebra \u003cbr\u003e5.2 The idea of the complex logarithm \u003cbr\u003e5.3 Multiple valuedness, natural logarithms \u003cbr\u003e5.4 Complex powers \u003cbr\u003e5.5 Some relations to modern particle physics \u003cbr\u003e\u003cbr\u003e\u003cb\u003e6 Real-number calculus\u003c\/b\u003e\u003cbr\u003e6.1 What makes an honest function? \u003cbr\u003e6.2 Slopes of functions \u003cbr\u003e6.3 Higher derivatives; C1-smooth functions \u003cbr\u003e6.4 The ‘Eulerian’ notion of a function? \u003cbr\u003e6.5 The rules of differentiation \u003cbr\u003e6.6 Integration \u003cbr\u003e\u003cbr\u003e\u003cb\u003e7 Complex-number calculus \u003c\/b\u003e\u003cbr\u003e7.1 Complex smoothness; holomorphic functions\u003cbr\u003e7.2 Contour integration \u003cbr\u003e7.3 Power series from complex smoothness \u003cbr\u003e7.4 Analytic continuation \u003cbr\u003e\u003cbr\u003e\u003cb\u003e8 Riemann surfaces and complex mappings\u003c\/b\u003e\u003cbr\u003e8.1 The idea of a Riemann surface\u003cbr\u003e8.2 Conformal mappings \u003cbr\u003e8.3 The Riemann sphere \u003cbr\u003e8.4 The genus of a compact Riemann surface \u003cbr\u003e8.5 The Riemann mapping theorem\u003cbr\u003e\u003cbr\u003e\u003cb\u003e9 Fourier decomposition and hyperfunctions\u003c\/b\u003e\u003cbr\u003e9.1 Fourier series \u003cbr\u003e9.2 Functions on a circle\u003cbr\u003e9.3 Frequency splitting on the Riemann sphere\u003cbr\u003e9.4 The Fourier transform \u003cbr\u003e9.5 Frequency splitting from the Fourier transform \u003cbr\u003e9.6 What kind of function is appropriate? \u003cbr\u003e9.7 Hyperfunctions \u003cbr\u003e\u003cbr\u003e\u003cb\u003e10 Surfaces \u003c\/b\u003e\u003cbr\u003e10.1 Complex dimensions and real dimensions \u003cbr\u003e10.2 Smoothness, partial derivatives \u003cbr\u003e10.3 Vector Fields and 1-forms \u003cbr\u003e10.4 Components, scalar products \u003cbr\u003e10.5 The Cauchy–Riemann equations \u003cbr\u003e\u003cbr\u003e\u003cb\u003e11 Hypercomplex numbers \u003c\/b\u003e\u003cbr\u003e11.1 The algebra of quaternions \u003cbr\u003e11.2 The physical role of quaternions?\u003cbr\u003e11.3 Geometry of quaternions\u003cbr\u003e11.4 How to compose rotations\u003cbr\u003e11.5 Clifford algebras \u003cbr\u003e11.6 Grassmann algebras \u003cbr\u003e\u003cbr\u003e\u003cb\u003e12 Manifolds of n dimensions \u003c\/b\u003e\u003cbr\u003e12.1 Why study higher-dimensional manifolds?\u003cbr\u003e12.2 Manifolds and coordinate patches \u003cbr\u003e12.3 Scalars, vectors, and covectors \u003cbr\u003e12.4 Grassmann products \u003cbr\u003e12.5 Integrals of forms \u003cbr\u003e12.6 Exterior derivative \u003cbr\u003e12.7 Volume element; summation convention \u003cbr\u003e12.8 Tensors; abstract-index and diagrammatic notation \u003cbr\u003e12.9 Complex manifolds\u003cbr\u003e\u003cbr\u003e\u003cb\u003e13 Symmetry groups \u003c\/b\u003e\u003cbr\u003e13.1 Groups of transformations \u003cbr\u003e13.2 Subgroups and simple groups \u003cbr\u003e13.3 Linear transformations and matrices\u003cbr\u003e13.4 Determinants and traces \u003cbr\u003e13.5 Eigenvalues and eigenvectors \u003cbr\u003e13.6 Representation theory and Lie algebras \u003cbr\u003e13.7 Tensor representation spaces; reducibility \u003cbr\u003e13.8 Orthogonal groups\u003cbr\u003e13.9 Unitary groups \u003cbr\u003e13.10 Symplectic groups \u003cbr\u003e\u003cbr\u003e\u003cb\u003e14 Calculus on manifolds \u003c\/b\u003e\u003cbr\u003e14.1 Differentiation on a manifold? \u003cbr\u003e14.2 Parallel transport \u003cbr\u003e14.3 Covariant derivative \u003cbr\u003e14.4 Curvature and torsion \u003cbr\u003e14.5 Geodesics, parallelograms, and curvature \u003cbr\u003e14.6 Lie derivative\u003cbr\u003e14.7 What a metric can do for you\u003cbr\u003e14.8 Symplectic manifolds \u003cbr\u003e\u003cbr\u003e\u003cb\u003e15 Fibre bundles and gauge connections \u003c\/b\u003e\u003cbr\u003e15.1 Some physical motivations for fibre bundles \u003cbr\u003e15.2 The mathematical idea of a bundle \u003cbr\u003e15.3 Cross-sections of bundles \u003cbr\u003e15.4 The Clifford bundle \u003cbr\u003e15.5 Complex vector bundles, (co)tangent bundles\u003cbr\u003e15.6 Projective spaces \u003cbr\u003e15.7 Non-triviality in a bundle connection \u003cbr\u003e15.8 Bundle curvature \u003cbr\u003e\u003cbr\u003e\u003cb\u003e16 The ladder of infinity \u003c\/b\u003e\u003cbr\u003e16.1 Finite fields\u003cbr\u003e16.2 A Wnite or inWnite geometry for physics? \u003cbr\u003e16.3 Different sizes of infinity \u003cbr\u003e16.4 Cantor’s diagonal slash \u003cbr\u003e16.5 Puzzles in the foundations of mathematics \u003cbr\u003e16.6 Turing machines and Gödel’s theorem \u003cbr\u003e16.7 Sizes of infinity in physics\u003cbr\u003e\u003cbr\u003e\u003cb\u003e17 Spacetime \u003c\/b\u003e\u003cbr\u003e17.1 The spacetime of Aristotelian physics \u003cbr\u003e17.2 Spacetime for Galilean relativity\u003cbr\u003e17.3 Newtonian dynamics in spacetime terms \u003cbr\u003e17.4 The principle of equivalence \u003cbr\u003e17.5 Cartan’s ‘Newtonian spacetime’ \u003cbr\u003e17.6 The fixed finite speed of light \u003cbr\u003e17.7 Light cones \u003cbr\u003e17.8 The abandonment of absolute time \u003cbr\u003e17.9 The spacetime for Einstein’s general relativity \u003cbr\u003e\u003cb\u003e\u003cbr\u003e18 Minkowskian geometry \u003c\/b\u003e\u003cbr\u003e18.1 Euclidean and Minkowskian 4-space \u003cbr\u003e18.2 The symmetry groups of Minkowski space \u003cbr\u003e18.3 Lorentzian orthogonality; the ‘clock paradox’ \u003cbr\u003e18.4 Hyperbolic geometry in Minkowski space \u003cbr\u003e18.5 The celestial sphere as a Riemann sphere \u003cbr\u003e18.6 Newtonian energy and (angular) momentum \u003cbr\u003e18.7 Relativistic energy and (angular) momentum \u003cbr\u003e\u003cbr\u003e\u003cb\u003e19 The classical Welds of Maxwell and Einstein \u003c\/b\u003e\u003cbr\u003e19.1 Evolution away from Newtonian dynamics \u003cbr\u003e19.2 Maxwell’s electromagnetic theory \u003cbr\u003e19.3 Conservation and flux laws in Maxwell theory \u003cbr\u003e19.4 The Maxwell Weld as gauge curvature \u003cbr\u003e19.5 The energy–momentum tensor \u003cbr\u003e19.6 Einstein’s field equation \u003cbr\u003e19.7 Further issues: cosmological constant; Weyl tensor \u003cbr\u003e19.8 Gravitational field energy\u003cbr\u003e\u003cbr\u003e\u003cb\u003e20 Lagrangians and Hamiltonians\u003c\/b\u003e\u003cbr\u003e20.1 The magical Lagrangian formalism \u003cbr\u003e20.2 The more symmetrical Hamiltonian picture \u003cbr\u003e20.3 Small oscillations\u003cbr\u003e20.4 Hamiltonian dynamics as symplectic geometry \u003cbr\u003e20.5 Lagrangian treatment of fields \u003cbr\u003e20.6 How Lagrangians drive modern theory \u003cbr\u003e\u003cbr\u003e\u003cb\u003e21 The quantum particle \u003c\/b\u003e\u003cbr\u003e21.1 Non-commuting variables \u003cbr\u003e21.2 Quantum Hamiltonians \u003cbr\u003e21.3 Schrödinger’s equation \u003cbr\u003e21.4 Quantum theory’s experimental background \u003cbr\u003e21.5 Understanding wave–particle duality \u003cbr\u003e21.6 What is quantum ‘reality’?\u003cbr\u003e21.7 The ‘holistic’ nature of a wavefunction \u003cbr\u003e21.8 The mysterious ‘quantum jumps’ \u003cbr\u003e21.9 Probability distribution in a wavefunction \u003cbr\u003e21.10 Position states \u003cbr\u003e21.11 Momentum-space description \u003cbr\u003e\u003cbr\u003e\u003cb\u003e22 Quantum algebra, geometry, and spin \u003c\/b\u003e\u003cbr\u003e22.1 The quantum procedures \u003cb\u003eU\u003c\/b\u003e and \u003cb\u003eR\u003c\/b\u003e \u003cbr\u003e22.2 The linearity of \u003cb\u003eU\u003c\/b\u003e and its problems for \u003cb\u003eR\u003c\/b\u003e \u003cbr\u003e22.3 Unitary structure, Hilbert space, Dirac notation \u003cbr\u003e22.4 Unitary evolution: Schrödinger and Heisenberg \u003cbr\u003e22.5 Quantum ‘observables’ \u003cbr\u003e22.6 YES\/NO measurements; projectors \u003cbr\u003e22.7 Null measurements; helicity \u003cbr\u003e22.8 Spin and spinors\u003cbr\u003e22.9 The Riemann sphere of two-state systems\u003cbr\u003e22.10 Higher spin: Majorana picture\u003cbr\u003e22.11 Spherical harmonics \u003cbr\u003e22.12 Relativistic quantum angular momentum \u003cbr\u003e22.13 The general isolated quantum object \u003cbr\u003e\u003cbr\u003e\u003cb\u003e23 The entangled quantum world \u003c\/b\u003e\u003cbr\u003e23.1 Quantum mechanics of many-particle systems \u003cbr\u003e23.2 Hugeness of many-particle state space \u003cbr\u003e23.3 Quantum entanglement; Bell inequalities \u003cbr\u003e23.4 Bohm-type EPR experiments\u003cbr\u003e23.5 Hardy’s EPR example: almost probability-free \u003cbr\u003e23.6 Two mysteries of quantum entanglement \u003cbr\u003e23.7 Bosons and fermions \u003cbr\u003e23.8 The quantum states of bosons and fermions \u003cbr\u003e23.9 Quantum teleportation \u003cbr\u003e23.10 Quanglement \u003cbr\u003e\u003cbr\u003e\u003cb\u003e24 Dirac’s electron and antiparticles \u003c\/b\u003e\u003cbr\u003e24.1 Tension between quantum theory and relativity \u003cbr\u003e24.2 Why do antiparticles imply quantum fields? \u003cbr\u003e24.3 Energy positivity in quantum mechanics \u003cbr\u003e24.4 Diffculties with the relativistic energy formula \u003cbr\u003e24.5 The non-invariance of d\/dt \u003cbr\u003e24.6 Clifford–Dirac square root of wave operator \u003cbr\u003e24.7 The Dirac equation\u003cbr\u003e24.8 Dirac’s route to the positron \u003cbr\u003e\u003cbr\u003e\u003cb\u003e25 The standard model of particle physics \u003c\/b\u003e\u003cbr\u003e25.1 The origins of modern particle physics \u003cbr\u003e25.2 The zigzag picture of the electron \u003cbr\u003e25.3 Electroweak interactions; reflection asymmetry \u003cbr\u003e25.4 Charge conjugation, parity, and time reversal\u003cbr\u003e25.5 The electroweak symmetry group \u003cbr\u003e25.6 Strongly interacting particles \u003cbr\u003e25.7 ‘Coloured quarks’ \u003cbr\u003e25.8 Beyond the standard model? \u003cbr\u003e\u003cbr\u003e\u003cb\u003e26 Quantum field theory \u003c\/b\u003e\u003cbr\u003e26.1 Fundamental status of QFT in modern theory \u003cbr\u003e26.2 Creation and annihilation operators \u003cbr\u003e26.3 Infinite-dimensional algebras \u003cbr\u003e26.4 Antiparticles in QFT \u003cbr\u003e26.5 Alternative vacua \u003cbr\u003e26.6 Interactions: Lagrangians and path integrals \u003cbr\u003e26.7 Divergent path integrals: Feynman’s response \u003cbr\u003e26.8 Constructing Feynman graphs; the S-matrix \u003cbr\u003e26.9 Renormalization \u003cbr\u003e26.10 Feynman graphs from Lagrangians \u003cbr\u003e26.11 Feynman graphs and the choice of vacuum \u003cbr\u003e\u003cbr\u003e\u003cb\u003e27 The Big Bang and its thermodynamic legacy \u003c\/b\u003e\u003cbr\u003e27.1 Time symmetry in dynamical evolution \u003cbr\u003e27.2 Submicroscopic ingredients \u003cbr\u003e27.3 Entropy \u003cbr\u003e27.4 The robustness of the entropy concept \u003cbr\u003e27.5 Derivation of the second law—or not? \u003cbr\u003e27.6 Is the whole universe an ‘isolated system’? \u003cbr\u003e27.7 The role of the Big Bang \u003cbr\u003e27.8 Black holes \u003cbr\u003e27.9 Event horizons and spacetime singularities \u003cbr\u003e27.10 Black-hole entropy \u003cbr\u003e27.11 Cosmology \u003cbr\u003e27.12 Conformal diagrams \u003cbr\u003e27.13 Our extraordinarily special Big Bang \u003cbr\u003e\u003cbr\u003e\u003cb\u003e28 Speculative theories of the early universe\u003c\/b\u003e\u003cbr\u003e28.1 Early-universe spontaneous symmetry breaking \u003cbr\u003e28.2 Cosmic topological defects \u003cbr\u003e28.3 Problems for early-universe symmetry breaking \u003cbr\u003e28.4 Inflationary cosmology \u003cbr\u003e28.5 Are the motivations for inflation valid? \u003cbr\u003e28.6 The anthropic principle \u003cbr\u003e28.7 The Big Bang’s special nature: an anthropic key? \u003cbr\u003e28.8 The Weyl curvature hypothesis \u003cbr\u003e28.9 The Hartle–Hawking ‘no-boundary’ proposal \u003cbr\u003e28.10 Cosmological parameters: observational status? \u003cbr\u003e\u003cbr\u003e\u003cb\u003e29 The measurement paradox \u003c\/b\u003e\u003cbr\u003e29.1 The conventional ontologies of quantum theory \u003cbr\u003e29.2 Unconventional ontologies for quantum theory \u003cbr\u003e29.3 The density matrix \u003cbr\u003e29.4 Density matrices for spin 1\/2: the Bloch sphere \u003cbr\u003e29.5 The density matrix in EPR situations \u003cbr\u003e29.6 FAPP philosophy of environmental decoherence \u003cbr\u003e29.7 Schrödinger’s cat with ‘Copenhagen’ ontology \u003cbr\u003e29.8 Can other conventional ontologies resolve the ‘cat’? \u003cbr\u003e29.9 Which unconventional ontologies may help? \u003cbr\u003e\u003cbr\u003e\u003cb\u003e30 Gravity’s role in quantum state reduction \u003c\/b\u003e\u003cbr\u003e30.1 Is today’s quantum theory here to stay?\u003cbr\u003e30.2 Clues from cosmological time asymmetry\u003cbr\u003e30.3 Time-asymmetry in quantum state reduction \u003cbr\u003e30.4 Hawking’s black-hole temperature\u003cbr\u003e30.5 Black-hole temperature from complex periodicity \u003cbr\u003e30.6 Killing vectors, energy flow—and time travel!\u003cbr\u003e30.7 Energy outflow from negative-energy orbits\u003cbr\u003e30.8 Hawking explosions \u003cbr\u003e30.9 A more radical perspective \u003cbr\u003e30.10 Schrödinger’s lump \u003cbr\u003e30.11 Fundamental conflict with Einstein’s principles \u003cbr\u003e30.12 Preferred Schrödinger–Newton states? \u003cbr\u003e30.13 FELIX and related proposals \u003cbr\u003e30.14 Origin of fluctuations in the early universe \u003cbr\u003e\u003cbr\u003e\u003cb\u003e31 Supersymmetry, supra-dimensionality, and strings \u003c\/b\u003e\u003cbr\u003e31.1 Unexplained parameters \u003cbr\u003e31.2 Supersymmetry \u003cbr\u003e31.3 The algebra and geometry of supersymmetry \u003cbr\u003e31.4 Higher-dimensional spacetime \u003cbr\u003e31.5 The original hadronic string theory \u003cbr\u003e31.6 Towards a string theory of the world \u003cbr\u003e31.7 String motivation for extra spacetime dimensions \u003cbr\u003e31.8 String theory as quantum gravity? \u003cbr\u003e31.9 String dynamics \u003cbr\u003e31.10 Why don’t we see the extra space dimensions? \u003cbr\u003e31.11 Should we accept the quantum-stability argument? \u003cbr\u003e31.12 Classical instability of extra dimensions \u003cbr\u003e31.13 Is string QFT finite? \u003cbr\u003e31.14 The magical Calabi–Yau spaces; M-theory \u003cbr\u003e31.15 Strings and black-hole entropy \u003cbr\u003e31.16 The ‘holographic principle’ \u003cbr\u003e31.17 The D-brane perspective \u003cbr\u003e31.18 The physical status of string theory? \u003cbr\u003e\u003cbr\u003e\u003cb\u003e32 Einstein’s narrower path; loop variables\u003c\/b\u003e\u003cbr\u003e32.1 Canonical quantum gravity \u003cbr\u003e32.2 The chiral input to Ashtekar’s variables \u003cbr\u003e32.3 The form of Ashtekar’s variable\u003cbr\u003e32.4 Loop variables \u003cbr\u003e32.5 The mathematics of knots and links \u003cbr\u003e32.6 Spin networks \u003cbr\u003e32.7 Status of loop quantum gravity? \u003cbr\u003e\u003cbr\u003e\u003cb\u003e33 More radical perspectives; twistor theory \u003c\/b\u003e\u003cbr\u003e33.1 Theories where geometry has discrete elements \u003cbr\u003e33.2 Twistors as light rays \u003cbr\u003e33.3 Conformal group; compactified Minkowski space\u003cbr\u003e33.4 Twistors as higher-dimensional spinors \u003cbr\u003e33.5 Basic twistor geometry and coordinates \u003cbr\u003e33.6 Geometry of twistors as spinning massless particles\u003cbr\u003e33.7 Twistor quantum theory \u003cbr\u003e33.8 Twistor description of massless fields \u003cbr\u003e33.9 Twistor sheaf cohomology \u003cbr\u003e33.10 Twistors and positive\/negative frequency splitting \u003cbr\u003e33.11 The non-linear graviton \u003cbr\u003e33.12 Twistors and general relativity \u003cbr\u003e33.13 Towards a twistor theory of particle physics \u003cbr\u003e33.14 The future of twistor theory? \u003cbr\u003e\u003cbr\u003e\u003cb\u003e34 Where lies the road to reality? \u003c\/b\u003e\u003cbr\u003e34.1 Great theories of 20th century physics—and beyond? \u003cbr\u003e34.2 Mathematically driven fundamental physics \u003cbr\u003e34.3 The role of fashion in physical theory \u003cbr\u003e34.4 Can a wrong theory be experimentally refuted? \u003cbr\u003e34.5 Whence may we expect our next physical revolution? \u003cbr\u003e34.6 What is reality? \u003cbr\u003e34.7 The roles of mentality in physical theory \u003cbr\u003e34.8 Our long mathematical road to reality \u003cbr\u003e34.9 Beauty and miracles \u003cbr\u003e34.10 Deep questions answered, deeper questions posed\u003cbr\u003e\u003cbr\u003e\u003ci\u003eEpilogue \u003cbr\u003eBibliography \u003cbr\u003eIndex \u003cbr\u003eContents\u003cbr\u003e\u003c\/i\u003e“A comprehensive guide to physics’ big picture, and to the thoughts of one of the world’s most original thinkers.”—\u003ci\u003eThe New York Times\u003c\/i\u003e \u003cbr\u003e\u003cbr\u003e“Simply astounding. . . . Gloriously variegated. . . . Pure delight. . . . It is shocking that so much can be explained so well. . . . Penrose gives us something that has been missing from the public discourse on science lately–a reason to live, something to look forward to.” —\u003ci\u003eAmerican Scientist\u003c\/i\u003e \u003cbr\u003e\u003cbr\u003e “A remarkable book . . . teeming with delights.”  —\u003ci\u003eNature\u003c\/i\u003e \u003cbr\u003e\u003cbr\u003e“This is his magnum opus, the culmination of an already stellar career and a comprehensive summary of the current state of physics and cosmology. It should be read by anyone entering the field and referenced by everyone working in it.” —\u003ci\u003eThe New York Sun\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“Extremely comprehensive. . . . \u003ci\u003eThe Road to Reality\u003c\/i\u003e unscores the fact that Penrose is one of the world’s most original thinkers.” —\u003ci\u003eTucson Citizen\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“What a joy it is to read a book that doesn't simplify, doesn't dodge the difficult questions, and doesn't always pretend to have answers. . . . Penrose’s appetite is heroic, his knowledge encyclopedic, his modesty a reminder that not all physicists claim to be able to explain the world in 250 pages.”\u003cbr\u003e—\u003ci\u003eThe  Times \u003c\/i\u003e(London)\u003cbr\u003e\u003cbr\u003e“For physics fans, the high point of the year will undoubtedly be \u003ci\u003eThe Road to Reality.\u003c\/i\u003e”\u003cbr\u003e—\u003ci\u003eThe Guardian\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“A truly remarkable book...Penrose does much to reveal the beauty and subtlety that connects nature and the human imagination, demonstrating that the quest to understand the reality of our physical world, and the extent and limits of our mental capacities, is an awesome, never-ending journey rather than a one-way cul-de-sac.”—\u003ci\u003eLondon Sunday Times\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“Penrose’s work is genuinely magnificent, and the most stimulating book I have read in a long time.”—\u003ci\u003eScotland on Sunday\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e“Science needs more people like Penrose, willing and able to point out the flaws in fashionable models from a position of authority and to signpost alternative roads to follow.”—\u003ci\u003eThe Independent\u003c\/i\u003e\u003cb\u003eRoger Penrose \u003c\/b\u003eis Emeritus Rouse Ball Professor of Mathematics at Oxford University. He has received a number of prizes and awards, including the 2020 Nobel Prize in Physics for his work on black hole formation, as well as the 1988 Wolf Prize for physics, which he shared with Stephen Hawking for their joint contribution to our understanding of the universe. His books include \u003ci\u003eCycles of Time\u003c\/i\u003e, \u003ci\u003eThe Road to Reality\u003c\/i\u003e, \u003ci\u003eThe Nature of Space and Time\u003c\/i\u003e, which he wrote with Hawking, and \u003ci\u003eThe Emperor’s New Mind\u003c\/i\u003e. He has lectured extensively at universities throughout America. He lives in Oxford.\u003cb\u003ePrologue\u003cbr\u003e\u003c\/b\u003e\u003cbr\u003eAm-tep was the King’s chief craftsman, an artist of consummate skills. It was night, and he lay sleeping on his workshop couch, tired after a handsomely productive evening’s work. But his sleep was restless – perhaps from an intangible tension that had seemed to be in the air. Indeed, he was not certain that he was asleep at all when it happened. Daytime had come – quite suddenly – when his bones told him that surely it must still be night.\u003cbr\u003e\u003cbr\u003eHe stood up abruptly. Something was odd. The dawn’s light could not be in the north; yet the red light shone alarmingly through his broad window that looked out northwards over the sea. He moved to the window and stared out, incredulous in amazement. The Sun had never before risen in the north! In his dazed state, it took him a few moments to realize that this could not possibly be the Sun. It was a distant shaft of a deep fiery red light that beamed vertically upwards from the water into the heavens.\u003cbr\u003e\u003cbr\u003eAs he stood there, a dark cloud became apparent at the head of the beam, giving the whole structure the appearance of a distant giant parasol, glowing evilly, with a smoky flaming staff. The parasol’s hood began to spread and darken – a daemon from the underworld. The night had been clear, but now the stars disappeared one by one, swallowed up behind this advancing monstrous creature from Hell.\u003cbr\u003e\u003cbr\u003eThough terror must have been his natural reaction, he did not move, transfixed for several minutes by the scene’s perfect symmetry and awesome beauty. But then the terrible cloud began to bend slightly to the east, caught up by the prevailing winds. Perhaps he gained some comfort from this and the spell was momentarily broken. But apprehension at once returned to him as he seemed to sense a strange disturbance in the ground beneath, accompanied by ominous-sounding rumblings of a nature quite unfamiliar to him. He began to wonder what it was that could have caused this fury. Never before had he witnessed a God’s anger of such magnitude.\u003cbr\u003e\u003cbr\u003eHis first reaction was to blame himself for the design on the sacrificial cup that he had just completed – he had worried about it at the time. Had his depiction of the Bull-God not been sufficiently fearsome? Had that god been offended? But the absurdity of this thought soon struck him. The fury he had just witnessed could not have been the result of such a trivial action, and was surely not aimed at him specifically. But he knew that there would be trouble at the Great Palace. The Priest-King would waste no time in attempting to appease this Daemon-God. There would be sacrifices. The traditional offerings of fruits or even animals would not suffice to pacify an anger of this magnitude. The sacrifices would have to be human.\u003cbr\u003e\u003cbr\u003eQuite suddenly, and to his utter surprise, he was blown backwards across the room by an impulsive blast of air followed by a violent wind. The noise was so extreme that he was momentarily deafened. Many of his beautifully adorned pots were whisked from their shelves and smashed to pieces against the wall behind. As he lay on the floor in a far corner of the room where he had been swept away by the blast, he began to recover his senses, and saw that the room was in turmoil. He was horrified to see one of his favourite great urns shattered to small pieces, and the wonderfully detailed designs, which he had so carefully crafted, reduced to nothing.\u003cbr\u003e\u003cbr\u003eAm-tep arose unsteadily from the floor and after a while again approached the window, this time with considerable trepidation, to re-examine that terrible scene across the sea. Now he thought he saw a disturbance, illuminated by that far-off furnace, coming towards him. This appeared to be a vast trough in the water, moving rapidly towards the shore, followed by a cliff-like wall of wave. He again became transfixed, watching the approaching wave begin to acquire gigantic proportions. Eventually the disturbance reached the shore and the sea immediately before him drained away, leaving many ships stranded on the newly formed beach. Then the cliff-wave entered the vacated region and struck with a terrible violence. Without exception the ships were shattered, and many nearby houses instantly destroyed. Though the water rose to great heights in the air before him, his own house was spared, for it sat on high ground a good way from the sea.\u003cbr\u003e\u003cbr\u003eThe Great Palace too was spared. But Am-tep feared that worse might come, and he was right – though he knew not how right he was. He did know, however, that no ordinary human sacrifice of a slave could now be sufficient. Something more would be needed to pacify the tempestuous anger of this terrible God. His thoughts turned to his sons and daughters, and to his newly born grandson. Even they might not be safe.\u003cbr\u003e\u003cbr\u003eAm-tep had been right to fear new human sacrifices. A young girl and a youth of good birth had been soon apprehended and taken to a nearby temple, high on the slopes of a mountain. The ensuing ritual was well under way when yet another catastrophe struck. The ground shook with devastating violence, whence the temple roof fell in, instantly killing all the priests and their intended sacrificial victims. As it happened, they would lie there in mid-ritual – entombed for over three-and-a-half millennia!\u003cbr\u003e\u003cbr\u003eThe devastation was frightful, but not final. Many on the island where Am-tep and his people lived survived the terrible earthquake, though the Great Palace was itself almost totally destroyed. Much would be rebuilt over the years. Even the Palace would recover much of its original splendour, constructed on the ruins of the old. Yet Am-tep had vowed to leave the island. His world had now changed irreparably.\u003cbr\u003e\u003cbr\u003eIn the world he knew, there had been a thousand years of peace, prosperity, and culture where the Earth-Goddess had reigned. Wonderful art had been allowed to flourish. There was much trade with neighbouring lands. The magnificent Great Palace was a huge luxurious labyrinth, a virtual city in itself, adorned by superb frescoes of animals and flowers. There was running water, excellent drainage, and flushed sewers. War was almost unknown and defences unnecessary. Now, Am-tep perceived the Earth-Goddess overthrown by a Being with entirely different values.\u003cbr\u003e\u003cbr\u003eIt was some years before Am-tep actually left the island, accompanied by his surviving family, on a ship rebuilt by his youngest son, who was a skilled carpenter and seaman. Am-tep’s grandson had developed into an alert child, with an interest in everything in the world around. The voyage took some days, but the weather had been supremely calm. One clear night, Am-tep was explaining to his grandson about the patterns in the stars, when an odd thought overtook him: \u003ci\u003eThe patterns of stars had been disturbed not one iota from what they were before the Catastrophe of the emergence of the terrible daemon.\u003cbr\u003e\u003c\/i\u003e\u003cbr\u003eAm-tep knew these patterns well, for he had a keen artist’s eye. Surely, he thought, those tiny candles of light in the sky should have been blown at least a little from their positions by the violence of that night, just as his pots had been smashed and his great urn shattered. The Moon also had kept her face, just as before, and her route across the star-filled heavens had changed not one whit, as far as Am-tep could tell. For many moons after the Catastrophe, the skies had appeared different. There had been darkness and strange clouds, and the Moon and Sun had sometimes worn unusual colours. But this had now passed, and their motions seemed utterly undisturbed. The tiny stars, likewise, had been quite unmoved.\u003cbr\u003e\u003cbr\u003eIf the heavens had shown such little concern for the Catastrophe, having a stature far greater even than that terrible Daemon, Am-tep reasoned, why should the forces controlling the Daemon itself show concern for what the little people on the island had been doing, with their foolish rituals and human sacrifice? He felt embarrassed by his \u003ci\u003eown\u003c\/i\u003e foolish thoughts at the time, that the daemon might be concerned by the mere patterns on his pots.\u003cbr\u003e\u003cbr\u003eYet Am-tep was still troubled by the question ‘why?’ What deep forces control the behaviour of the world, and why do they sometimes burst forth in violent and seemingly incomprehensible ways? He shared his questions with his grandson, but there were no answers.\u003cbr\u003e. . .\u003cbr\u003e\u003cbr\u003eA century passed by, and then a millennium, and still there were no answers. \u003cbr\u003e. . .\u003cbr\u003e\u003cbr\u003eAmphos the craftsman had lived all his life in the same small town as his father and his father before him, and his father’s father before that. He made his living constructing beautifully decorated gold bracelets, earrings, ceremonial cups, and other fine products of his artistic skills. Such work had been the family trade for some forty generations – a line unbroken since Am-tep had settled there eleven hundred years before.\u003cbr\u003e\u003cbr\u003eBut it was not just artistic skills that had been passed down from generation to generation. Am-tep’s questions troubled Amphos just as they had troubled Am-tep earlier. The great story of the Catastrophe that destroyed an ancient peaceful civilization had been handed down from father to son. Am-tep’s perception of the Catastrophe had also survived with his descendants. Amphos, too, understood that the heavens had a magnitude and stature so great as to be quite unconcerned by that terrible event. Nevertheless, the event had had a catastrophic effect on the little people with their cities and their human sacrifices and insignificant religious rituals. Thus, by comparison, the event itself must have been the result of enormous forces quite unconcerned by those trivial actions of human beings. Yet the nature of those forces was as unknown in Amphos’s day as it was to Am-tep.\u003cbr\u003e\u003cbr\u003eAmphos had studied the structure of plants, insects and other small animals, and crystalline rocks. His keen eye for observation had served him well in his decorative designs. He took an interest in agriculture and was fascinated by the growth of wheat and other plants from grain. But none of this told him ‘why?’, and he felt unsatisfied. He believed that there was indeed reason underlying Nature’s patterns, but he was in no way equipped to unravel those reasons.\u003cbr\u003e\u003cbr\u003eOne clear night, Amphos looked up at the heavens, and tried to make out from the patterns of stars the shapes of those heroes and heroines who formed constellations in the sky. To his humble artist’s eye, those shapes made poor resemblances. He could himself have arranged the stars far more convincingly. He puzzled over why the gods had not organized the stars in a more appropriate way? As they were, the arrangements seemed more like scattered grains randomly sowed by a farmer, rather than the deliberate design of a god. Then an odd thought overtook him: \u003ci\u003eDo not seek for reasons in the specific patterns of stars, or of other scattered arrangements of objects; look, instead, for a deeper universal order in the way that things behave.\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003eAmphos reasoned that we find order, after all, not in the patterns that scattered seeds form when they fall to the ground, but in the miraculous way that each of those seeds develops into a living plant having a superb structure, similar in great detail to one another. We would not try to seek the meaning in the precise arrangement of seeds sprinkled on the soil; yet, there must be meaning in the hidden mystery of the inner forces controlling the growth of each seed individually, so that each one follows essentially the same wonderful course. Nature’s laws must indeed have a superbly organized precision for this to be possible.\u003cbr\u003e\u003cbr\u003eAmphos became convinced that without precision in the underlying laws, there could be no order in the world, whereas much order is indeed perceived in the way that things behave. Moreover, there must be precision in our ways of thinking about these matters if we are not to be led seriously astray.\u003cbr\u003e\u003cbr\u003eIt so happened that word had reached Amphos of a sage who lived in another part of the land, and whose beliefs appeared to be in sympathy with those of Amphos. According to this sage, one could not rely on the teachings and traditions of the past. To be certain of one’s beliefs, it was necessary to form precise conclusions by the use of unchallengeable reason. The nature of this precision had to be mathematical – ultimately dependent on the notion of \u003ci\u003enumber\u003c\/i\u003e and its application to geometric forms. Accordingly, it must be number and geometry, not myth and superstition, that governed the behaviour of the world.\u003cbr\u003e\u003cbr\u003eAs Am-tep had done a century and a millennium before, Amphos took to the sea. He found his way to the city of Croton, where the sage and his brotherhood of 571 wise men and 28 wise women were in search of truth. After some time, Amphos was accepted into the brotherhood. The name of the sage was \u003ci\u003ePythagoras\u003c\/i\u003e.","brand":"Vintage","offers":[{"title":"Default Title","offer_id":46301725556965,"sku":"NP9780679776314","price":29.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780679776314.jpg?v=1767741265","url":"https:\/\/k12savings.com\/es\/products\/the-road-to-reality-isbn-9780679776314","provider":"K12savings","version":"1.0","type":"link"}