Toc: The Emperor's New Mind......Page p0003.djvucopyright......Page p0004.djvuForeword......Page p0005.djvuon reading mathematical equations......Page p0008.djvuAcknowledgements & Dedication......Page p0009.djvuFigure acknowledgements......Page p0010.djvuContents......Page p0011.djvuPrologue......Page p1.djvuIntroduction......Page p3.djvuThe Turing test......Page p5.djvuArtificial intelligence......Page p11.djvuAn AI approach to 'pleasure' and 'pain'......Page p14.djvuStrong AI and Searle's Chinese room......Page p17.djvuHardware and software......Page p23.djvuBackground to the algorithm concept......Page p30.djvuTuring's concept......Page p35.djvuBinary coding of numerical data......Page p42.djvuThe Church-Turing Thesis......Page p47.djvuNumbers other than natural numbers......Page p49.djvuThe universal Turing machine......Page p51.djvuThe insolubility of Hilbert's problem......Page p57.djvuHow to outdo an algorithm......Page p64.djvuChurch's lambda calculus......Page p66.djvuThe land of Tor'Bled-Nam......Page p74.djvuReal numbers......Page p80.djvuHow many real numbers are there?......Page p82.djvu'Reality' of real numbers......Page p86.djvuComplex numbers......Page p87.djvuConstruction of the Mandelbrot set......Page p92.djvuPlatonic reality of mathematical concepts?......Page p94.djvuHilbert's programme for mathematics......Page p99.djvuFormal mathematical systems......Page p102.djvuGödel's theorem......Page p105.djvuMathematical insight......Page p108.djvuPlatonism or intuitionism?......Page p112.djvuGödel-type theorems from Turing's result......Page p116.djvuRecursively enumerable sets......Page p118.djvuIs the Mandelbrot set recurslye?......Page p124.djvuSome examples of non-recursive mathematics......Page p129.djvuIs the Mandelbrot set like non-recursive mathematics?......Page p138.djvuComplexity theory......Page p140.djvuComplexity and computability in physical things......Page p145.djvuThe status of physical theory......Page p149.djvuEuclidean geometry......Page p156.djvuThe dynamics of Galileo and Newton......Page p162.djvuThe mechanistic world of Newtonian dynamics......Page p167.djvuIs life in the billiard-ball world computable?......Page p170.djvuHamiltonian mechanics......Page p174.djvuPhase space......Page p176.djvuMaxwell's electromagnetic theory......Page p184.djvuComputability and the wave equation......Page p187.djvuThe Lorentz equation of motion; runaway particles......Page p188.djvuThe special relativity of Einstein and Poincare......Page p191.djvuEinstein's general relativity......Page p202.djvuRelativistic causality and determinism......Page p211.djvuComputability in classical physics: where do we stand?......Page p216.djvu