<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>The Emperor's New Mind (Penrose (Roger)) - Theo Todman's Book Collection (Book-Paper Abstracts)</title> <link href="../../../TheosStyle.css" rel="stylesheet" type="text/css"><link rel="shortcut icon" href="../../../TT_ICO.png" /> </head> <a name="Top"></a> <BODY> <div id="header"> <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; &copy; Theo Todman, 2018</li><LI><FONT COLOR = "800080">Mauve</FONT>: Text by correspondent(s) or other author(s); &copy; the author(s)</li></OL> </center> <BR><HR><BR><center> <TABLE class = "Bridge" WIDTH=950> <TR><TD WIDTH="30%">&copy; Theo Todman, June 2007 - August 2018.</TD> <TD WIDTH="40%">Please address any comments on this page to <A HREF="mailto:theo@theotodman.com">theo@theotodman.com</A>.</TD> <TD WIDTH="30%">File output: <time datetime="2018-08-02T02:21" pubdate>02/08/2018 02:21:55</time> <br><A HREF="../../../Notes/Notes_10/Notes_1010.htm">Website Maintenance Dashboard</A> </TD></TR><TD WIDTH="30%"><A HREF="#Top">Return to Top of this Page</A></TD> <TD WIDTH="40%"><A HREF="../../../Notes/Notes_11/Notes_1140.htm">Return to Theo Todman's Philosophy Page</A></TD> <TD WIDTH="30%"><A HREF="../../../index.htm">Return to Theo Todman's Home Page</A></TD> </TR></TABLE></CENTER><HR> </BODY> </HTML>