Author(s): Roger Penrose
Publisher: Penguin Books
Year: 1991
Language: English
Pages: 480
The Emperor's New Mind......Page p0003.djvu
copyright......Page p0004.djvu
Foreword......Page p0005.djvu
on reading mathematical equations......Page p0008.djvu
Acknowledgements & Dedication......Page p0009.djvu
Figure acknowledgements......Page p0010.djvu
Contents......Page p0011.djvu
Prologue......Page p1.djvu
Introduction......Page p3.djvu
The Turing test......Page p5.djvu
Artificial intelligence......Page p11.djvu
An AI approach to 'pleasure' and 'pain'......Page p14.djvu
Strong AI and Searle's Chinese room......Page p17.djvu
Hardware and software......Page p23.djvu
Background to the algorithm concept......Page p30.djvu
Turing's concept......Page p35.djvu
Binary coding of numerical data......Page p42.djvu
The Church-Turing Thesis......Page p47.djvu
Numbers other than natural numbers......Page p49.djvu
The universal Turing machine......Page p51.djvu
The insolubility of Hilbert's problem......Page p57.djvu
How to outdo an algorithm......Page p64.djvu
Church's lambda calculus......Page p66.djvu
The land of Tor'Bled-Nam......Page p74.djvu
Real numbers......Page p80.djvu
How many real numbers are there?......Page p82.djvu
'Reality' of real numbers......Page p86.djvu
Complex numbers......Page p87.djvu
Construction of the Mandelbrot set......Page p92.djvu
Platonic reality of mathematical concepts?......Page p94.djvu
Hilbert's programme for mathematics......Page p99.djvu
Formal mathematical systems......Page p102.djvu
Gödel's theorem......Page p105.djvu
Mathematical insight......Page p108.djvu
Platonism or intuitionism?......Page p112.djvu
Gödel-type theorems from Turing's result......Page p116.djvu
Recursively enumerable sets......Page p118.djvu
Is the Mandelbrot set recurslye?......Page p124.djvu
Some examples of non-recursive mathematics......Page p129.djvu
Is the Mandelbrot set like non-recursive mathematics?......Page p138.djvu
Complexity theory......Page p140.djvu
Complexity and computability in physical things......Page p145.djvu
The status of physical theory......Page p149.djvu
Euclidean geometry......Page p156.djvu
The dynamics of Galileo and Newton......Page p162.djvu
The mechanistic world of Newtonian dynamics......Page p167.djvu
Is life in the billiard-ball world computable?......Page p170.djvu
Hamiltonian mechanics......Page p174.djvu
Phase space......Page p176.djvu
Maxwell's electromagnetic theory......Page p184.djvu
Computability and the wave equation......Page p187.djvu
The Lorentz equation of motion; runaway particles......Page p188.djvu
The special relativity of Einstein and Poincare......Page p191.djvu
Einstein's general relativity......Page p202.djvu
Relativistic causality and determinism......Page p211.djvu
Computability in classical physics: where do we stand?......Page p216.djvu
Mass, matter, and reality......Page p217.djvu
Do philosophers need quantum theory?......Page p225.djvu
Problems with classical theory......Page p228.djvu
The beginnings of quantum theory......Page p230.djvu
The two-slit experiment......Page p231.djvu
Probability amplitudes......Page p236.djvu
The quantum state of a particle......Page p243.djvu
The uncertainty principle......Page p248.djvu
The evolution procedures U and R......Page p250.djvu
Particles in two places at once?......Page p251.djvu
Hilbert space......Page p257.djvu
Measurements......Page p260.djvu
Spin and the Riemann sphere of states......Page p264.djvu
Objectivity and measurability of quantum states......Page p268.djvu
Copying a quantum state......Page p269.djvu
Photon spin......Page p270.djvu
Objects with large spin......Page p273.djvu
Many-particle systems......Page p275.djvu
The 'paradox' of Einstein, Podolsky, and Rosen......Page p279.djvu
Experiments with photons: a problem for relativity?......Page p286.djvu
Schrödinger's equation; Dirac's equation......Page p288.djvu
Quantum field theory......Page p289.djvu
Schrödinger's cat......Page p290.djvu
Various attitudes in existing quantum theory......Page p293.djvu
Where does all this leave us?......Page p296.djvu
The flow of time......Page p302.djvu
The inexorable increase of entropy......Page p304.djvu
What is entropy?......Page p309.djvu
The second law in action......Page p314.djvu
The origin of low entropy in the universe......Page p317.djvu
Cosmology and the big bang......Page p322.djvu
The primordial fireball......Page p326.djvu
Does the big bang explain the second law?......Page p328.djvu
Black holes......Page p330.djvu
The structure of space-time singularities......Page p335.djvu
How special was the big bang?......Page p339.djvu
Why quantum gravity?......Page p348.djvu
What lies behind the Weyl curvature hypothesis?......Page p350.djvu
Time-asymmetry in state-vector reduction......Page p354.djvu
Hawking's box: a link with the Weyl curvature hypothesis?......Page p359.djvu
When does the state-vector reduce?......Page p367.djvu
What are brains actually like?......Page p374.djvu
Where is the seat of consciousness?......Page p381.djvu
Split-brain experiments......Page p384.djvu
Blindsight......Page p386.djvu
Information processing in the visual cortex......Page p387.djvu
How do nerve signals work?......Page p389.djvu
Computer models......Page p392.djvu
Brain plasticity......Page p396.djvu
Parallel computers and the 'oneness' of consciousness......Page p398.djvu
Is there a role for quantum mechanics in brain activity?......Page p400.djvu
Quantum computers......Page p401.djvu
Beyond quantum theory?......Page p402.djvu
What are minds for?......Page p405.djvu
What does consciousness actually do?......Page p409.djvu
Natural selection of algorithms?......Page p414.djvu
The non-algorithmic nature of mathematical insight......Page p416.djvu
Inspiration, insight, and originality......Page p418.djvu
Non-verbality of thought......Page p423.djvu
Animal consciousness?......Page p425.djvu
Contact with Plato's world......Page p427.djvu
A view of physical reality......Page p429.djvu
Determinism and strong determinism......Page p431.djvu
The anthropic principle......Page p433.djvu
Tilings and quasicrystals......Page p434.djvu
Possible relevance to brain plasticity......Page p438.djvu
The time-delays of consciousness......Page p439.djvu
The strange role of time in conscious perception......Page p443.djvu
Conclusion: a child's view......Page p447.djvu
Epilogue......Page p451.djvu
References......Page p452.djvu
Index......Page p461.djvu
