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<title>The Emperor's New Mind (Penrose (Roger)) - Theo Todman's Book Collection (Book-Paper Abstracts)</title>
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<HR><H1>Theo Todman's Book Collection (Book-Paper Abstracts)</H1></div>
<hr><CENTER><TABLE class = "Bridge" WIDTH=950><tr><td colspan =3><A HREF = "../BookSummary_135.htm">The Emperor's New Mind</A></td></tr><tr><td colspan =3><A HREF = "../../../Authors/P/Author_Penrose (Roger).htm">Penrose (Roger)</a></td></tr><tr><td colspan =3>This Page provides (where held) the <b>Abstract</b> of the above <b>Book</b> and those of all the <b>Papers</b> contained in it.</td></tr><tr><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td><td><A HREF = "../BookCitings_135.htm">Books / Papers Citing this Book</A></td><td><A HREF = "../BooksToNotes_135.htm">Notes Citing this Book</A></td></tr></tr></TABLE></CENTER><hr>
<P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><B>BOOK ABSTRACT: </B><BR><BR><U>Foreword by Martin Gardner</U> (Full Text)<FONT COLOR = "800080"><ol type="1"><li>Many great mathematicians and physicists find it difficult, if not impossible, to write a book that non-professionals can understand. Until this year one might have supposed that Roger Penrose, one of the world's most knowledgeable and creative mathematical physicists, belonged to such a class. Those of us who had read his non-technical articles and lectures knew better. Even so, it came as a delightful surprise to find that Penrose had taken time off from his labours to produce a marvellous book for informed laymen. It is a book that I believe will become a classic.</li><li>Although Penrose's chapters range widely over relativity theory, quantum mechanics, and cosmology, their central concern is what philosophers call the mind body problem'. For decades now the proponents of strong Al' (Artificial Intelligence) have tried to persuade us that it is only a matter of a century or two (some have lowered the time to fifty years!) until electronic computers will be doing everything a human mind can do. Stimulated by science fiction read in their youth, and convinced that our minds are simply computers made of meat' (as Marvin Minsky once put it), they take for granted that pleasure and pain, the appreciation of beauty and humour, consciousness, and free will are capacities that will emerge naturally when electronic robots become sufficiently complex in their algorithmic behaviour.</li><li>Some philosophers of science (notably John Searle, whose notorious Chinese room <a name="1"></a><A HREF="../../../Notes/Notes_0/Notes_32.htm">thought experiment</A><SUP>1</SUP> is discussed in depth by Penrose), strongly disagree. To them a computer is not essentially different from mechanical calculators that operate with wheels, levers, or anything that transmits signals. (One can base a computer on rolling marbles or water moving through pipes.) Because electricity travels through wires faster than other forms of energy (except light) it can twiddle symbols more rapidly than mechanical calculators, and therefore handle tasks of enormous complexity. But does an electrical computer understand' what it is doing in a way that is superior to the understanding' of an abacus? Computers now play grandmaster chess. Do they 'understand' the game any better than a tick-tack-toe machine that a group of computer hackers once constructed with tinker toys?</li><li>Penrose's book is the most powerful attack yet written on strong Al. Objections have been raised in past centuries to the reductionist claim that a mind is a machine operated by known laws of physics, but Penrose's offensive is more persuasive because it draws on information not available to earlier writers. The book reveals Penrose to be more than a mathematical physicist. He is also a philosopher of first rank, unafraid to grapple with problems that contemporary philosophers tend to dismiss as meaningless.</li><li>Penrose also has the courage to affirm, contrary to a growing denial by a small group of physicists, a robust realism. Not only is the universe out there', but mathematical truth also has its own mysterious independence and timelessness. Like Newton and Einstein, Penrose has a profound sense of humility and awe toward both the physical world and the Platonic realm of pure mathematics. The distinguished number theorist Paul Erdos likes to speak of God's book' in which all the best proofs are recorded. Mathematicians are occasionally allowed to glimpse part of a page. When a physicist or a mathematician experiences a sudden aha' insight, Penrose believes, it is more than just something 'conjured up by complicated calculation'. It is mind making contact for a moment with objective truth. Could it be, he wonders, that Plato's world and the physical world (which physicists have now dissolved into mathematics) are really one and the same?</li><li>Many pages in Penrose's book are devoted to a famous fractal-like structure called the Mandelbrot set after Benoit Mandelbrot who discovered it. Although self-similar in a statistical sense as portions of it are enlarged, its infinitely convoluted pattern keeps changing in unpredictable ways. Penrose finds it incomprehensible (as do I) that anyone could suppose that this exotic structure is not as much out there' as Mount Everest is, subject to exploration in the way a jungle is explored.</li><li>Penrose is one of an increasingly large band of physicists who think Einstein was not being stubborn or muddle-headed when he said his little finger' told him that quantum mechanics is incomplete. To support this contention, Penrose takes you on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, the bewildering paradoxes of quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, the structure of the brain, and scores of other topics at the heart of current speculations. Are dogs and cats conscious' of themselves? Is it possible in theory for a matter-transmission machine to translocate a person from here to there the way astronauts are beamed up and down in television's <I>Star Trek</I> series? What is the survival value that evolution found in producing consciousness? Is there a level beyond quantum mechanics in which the direction of time and the distinction between right and left are firmly embedded? Are the laws of quantum mechanics, perhaps even deeper laws, essential for the operation of a mind?</li><li>To the last two questions Penrose answers yes. His famous theory of twistors' abstract geometrical objects which operate in a higher-dimensional complex space that underlies space-time is too technical for inclusion in this book. They are Penrose's efforts over two decades to probe a region deeper than the fields and particles of quantum mechanics. In his fourfold classification of theories as superb, useful, tentative, and misguided, Penrose modestly puts twistor theory in the tentative class, along with superstrings and other grand unification schemes now hotly debated.</li><li>Since 1973 Penrose has been the Rouse Ball Professor of Mathematics at Oxford University. The title is appropriate because W. W. Rouse Ball not only was a noted mathematician, he was also an amateur magician with such an ardent interest in recreational mathematics that he wrote the classic English work on this field, <I>Mathematical Recreations and Essays</I>. Penrose shares Ball's enthusiasm for play. In his youth he discovered an impossible object' called a tribar'. (An impossible object is a drawing of a solid figure that cannot exist because it embodies self-contradictory elements.) He and his father Lionel, a geneticist, turned the tribar into the Penrose Staircase, a structure that Maurits Escher used in two well-known lithographs: <I>Ascending and Descending</I>, and <I>Waterfall</I>. One day when Penrose was lying in bed, in what he called a fit of madness', he visualized an impossible object in four-dimensional space. It is something, he said, that a four-space creature, if it came upon it, would exclaim My God, what's that?'</li><li>During the 1960s, when Penrose worked on cosmology with his friend Stephen Hawking, he made what is perhaps his best known discovery. If relativity theory holds all the way down', there must be a singularity in every black hole where the laws of physics no longer apply. Even this achievement has been eclipsed in recent years by Penrose's construction of two shapes that tile the plane, in the manner of an Escher tessellation, but which can tile it only in a non-periodic way. (You can read about these amazing shapes in my book <I>Penrose Tiles to Trapdoor Ciphers</I>.) Penrose invented them, or rather discovered them, without any expectation they would be useful. To everybody's astonishment it turned out that three-dimensional forms of his tiles may underlie a strange new kind of matter. Studying these 'quasicrystals' is now one of the most active research areas in crystallography. It is also the most dramatic instance in modern times of how playful mathematics can have unanticipated applications.</li><li>Penrose's achievements in mathematics and physics and I have touched on only a small fraction spring from a lifelong sense of wonder toward the mystery and beauty of being. His little finger tells him that the human mind is more than just a collection of tiny wires and switches. The Adam of his prologue and epilogue is partly a symbol of the dawn of consciousness in the slow evolution of sentient life. To me he is also Penrose the child sitting in the third row, a distance back from the leaders of Al - who dares to suggest that the emperors of strong AI have no clothes. Many of Penrose's opinions are infused with humour, but this one is no laughing matter. </li></ol></FONT><BR><U>Contents</U><FONT COLOR = "800080"><ol type="1">Prologue 1<li>Can A Computer Have A Mind? 3<ul type="disc"><li>Introduction 3</li><li>The Turing test 6</li><li>Artificial intelligence 14</li><li>An Al approach to pleasure' and pain' 17</li><li>Strong Al and Searle's Chinese room 21</li><li>Hardware and software 30</li></ul></li><li>Algorithms And Turing Machines 40<ul type="disc"><li>Background to the algorithm concept 40</li><li>Turing's concept 46</li><li>Binary coding of numerical data 56</li><li>The Church-Turing Thesis 61</li><li>Numbers other than natural numbers 65</li><li>The universal Turing machine 67</li><li>The insolubility of Hilbert's problem 75</li><li>How to outdo an algorithm 83</li><li>Church's lambda calculus 86</li></ul></li><li>Mathematics And Reality 98<ul type="disc"><li>The land of Tor'Bled-Nam 98</li><li>Real numbers 105</li><li>How many real numbers are there? 108</li><li> Reality' of real numbers 112</li><li>Complex numbers 114</li><li>Construction of the Mandelbrot set 120</li><li>Platonic reality of mathematical concepts? 123</li></ul></li><li>Truth, Proof, And Insight 129<ul type="disc"><li>Hilbert's programme for mathematics 129</li><li>Formal mathematical systems 133</li><li>Godel's theorem 138</li><li>Mathematical insight 141</li><li>Platonism or intuitionism? 146</li><li>Godel-type theorems from Turing's result 151</li><li>Recursively enumerable sets 155</li><li>Is the Mandelbrot set recursive? 161</li><li>Some examples of non-recursive mathematics 168</li><li>Is the Mandelbrot set like non-recursive mathematics? 177</li><li>Complexity theory 181</li><li>Complexity and computability in physical things 188</li></ul></li><li>The Classical World 193<ul type="disc"><li>The status of physical theory 193</li><li>Euclidean geometry 202</li><li>The dynamics of Galileo and Newton 209</li><li>The mechanistic world of Newtonian dynamics 217</li><li>Is life in the billiard-ball world computable? 220</li><li>Hamiltonian mechanics 225</li><li>Phase space 228</li><li>Maxwell's electromagnetic theory 238</li><li>Computability and the wave equation 243</li><li>The Lorentz equation of motion; runaway particles 244</li><li>The special relativity of Einstein and Poincare 248</li><li>Einstein's general relativity 261</li><li>Relativistic <a name="2"></a><A HREF="../../../Notes/Notes_0/Notes_39.htm">causality</A><SUP>2</SUP> and determinism 273</li><li>Computability in classical physics: where do we stand? 278</li><li>Mass, matter, and reality 280</li></ul></li><li>Quantum Magic And Quantum Mystery 291<ul type="disc"><li>Do philosophers need quantum theory? 291</li><li>Problems with classical theory 295</li><li>The beginnings of quantum theory 297</li><li>The two-slit experiment 299</li><li>Probability amplitudes 306</li><li>The quantum state of a particle 314</li><li>The uncertainty principle 321</li><li>The evolution procedures U and R 323</li><li>Particles in two places at once? 325</li><li>Hilbert space 332</li><li>Measurements 336</li><li>Spin and the Riemann sphere of states 341</li><li>Objectivity and measurability of quantum states 346</li><li>Copying a quantum state 348</li><li>Photon spin 349</li><li>Objects with large spin 353</li><li>Many-particle systems 355</li><li>The paradox' of Einstein, Podolsky, and Rosen 361</li><li>Experiments with photons: a problem for relativity? 369</li><li>Schrodinger's equation; Dirac's equation 372</li><li>Quantum field theory 374</li><li>Schrodinger's cat 375</li><li>Various attitudes in existing quantum theory 379</li><li>Where does all this leave us? 383</li></ul></li><li>Cosmology And The Arrow Of Time 391<ul type="disc"><li>The flow of time 391</li><li>The inexorable increase of entropy 394</li><li>What is entropy? 400</li><li>The second law in action 407</li><li>The origin of low entropy in the universe 411</li><li>Cosmology and the big bang 417</li><li>The primordial fireball 423</li><li>Does the big bang explain the second law? 426</li><li>Black holes 427</li><li>The structure of space-time singularities 435</li><li>How special was the big bang? 440</li></ul></li><li>In Search Of Quantum Gravity 450<ul type="disc"><li>Why quantum gravity? 450</li><li>What lies behind the Weyl curvature hypothesis? 453</li><li>Time-asymmetry in state-vector reduction 458 </li><li>Hawking's box: a link with the Weyl curvature hypothesis? 465</li><li>When does the state-vector reduce? 475</li></ul></li><li>Real Brains And Model Brains 483<ul type="disc"><li>What are brains actually like? 483</li><li>Where is the seat of consciousness? 492</li><li>Split-brain experiments 496</li><li>Blindsight 499</li><li>Information processing in the visual cortex 500</li><li>How do nerve signals work? 502</li><li>Computer models 507</li><li>Brain plasticity 512</li><li>Parallel computers and the oneness' of consciousness 514</li><li>Is there a role for quantum mechanics in brain activity? 516</li><li>Quantum computers 518</li><li>Beyond quantum theory? 520</li></ul></li><li>Where Lies The Physics Of Mind? 523<ul type="disc"><li>What are minds for? 523</li><li>What does consciousness actually do? 529</li><li>Natural selection of algorithms? 534</li><li>The non-algorithmic nature of mathematical insight 538</li><li>Inspiration, insight, and originality 541</li><li>Non-verbality of thought 548</li><li>Animal consciousness? 550</li><li>Contact with Plato's world 552</li><li>A view of physical reality 555</li><li>Determinism and strong determinism 558</li><li>The anthropic principle 560</li><li>Tilings and quasicrystals 562</li><li>Possible relevance to brain plasticity 566</li><li>The time-delays of consciousness 568</li><li>The strange role of time in conscious perception 573</li><li>Conclusion: a child's view 578</li></ul></li><li>Epilogue 583</li></ol> </FONT></P>
<a name="ColourConventions"></a><hr><br><B><U>Text Colour Conventions</U> (see <A HREF="../../../Notes/Notes_10/Notes_1025.htm">disclaimer</a>)</B><OL TYPE="1"><LI><FONT COLOR = "0000FF">Blue</FONT>: Text by me; © Theo Todman, 2018</li><LI><FONT COLOR = "800080">Mauve</FONT>: Text by correspondent(s) or other author(s); © the author(s)</li></OL>
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