Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever ...

Presenting a look at the human mind's capacity while criticizing artificial intelligence, the author makes suggestions about classical and quantum physics and ..

In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating roller-coaster ride through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine.

This book is a fascinating and accessible summary of Roger Penrose's current thinking on those areas of physics in which he feels there are major...

What is consciousness? Some philosophers have contended that ‘qualia’, or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being comprised of ‘occasions of experience’. To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to terms with the physics of space-time -- as is described by Einstein's general theory of relativity -- and its relation to the fundamental theory of (...) matter -- as described by quantum theory. This leads us to employ a new physics of objective reduction: OR which appeals to a form of ‘quantum gravity’ to provide a useful description of fundamental processes at the quantum/classical borderline . Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific ‘objective’ criterion is reached; the coherent system then self-reduces . We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness. OR is taken as an instantaneous event -- the climax of a self-organizing process in fundamental space-time -- and a candidate for a conscious Whitehead-like ‘occasion’ of experience. How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate an OR process with the requisite characteristics to be occurring in cytoskeletal microtubules within the brain's neurons. (shrink)

Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Two of the world's most famous physicists - Stephen Hawking and Roger Penrose - disagree. Here they explain their positions in a work based on six lectures with a final (...) debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. (shrink)

The emperor's new mind (hereafter Emperor) is an attempt to put forward a scientific alternative to the viewpoint of according to which mental activity is merely the acting out of some algorithmic procedure. John Searle and other thinkers have likewise argued that mere calculation does not, of itself, evoke conscious mental attributes, such as understanding or intentionality, but they are still prepared to accept the action the brain, like that of any other physical object, could in principle be simulated by (...) a computer. In Emperor I go further than this and suggest that the outward manifestations ofconscious mental activity cannot even be properly simulated by calculation. To support this view, I use various arguments to show that the results of mathematical insight, in particular, do not seem to be obtained algorithmically. The main thrust ofthis work, however, is to present an overview ofthe present state of physical understanding and to show that an important gap exists at the point where, quantum and classical physics meet, as well as to speculate on how the conscious brain might be taking advantage ofwhatever new physics is needed to fill this gap to achieve its nonalgorithmic effects. (shrink)

Recent developments in quantum theory have focused attention on fundamental questions, in particular on whether it might be necessary to modify quantum mechanics to reconcile quantum gravity and general relativity. This book is based on a conference held in Oxford in the spring of 1984 to discuss quantum gravity. It brings together contributors who examine different aspects of the problem, including the experimental support for quantum mechanics, its strange and apparently paradoxical features, its underlying philosophy, and possible modifications to the (...) theory. (shrink)

What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and best-selling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential (...) in physics, may be leading today's researchers astray in three of the field's most important areas--string theory, quantum mechanics, and cosmology... The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures."--Jacket. (shrink)

This paper argues that the case for “gravitizing” quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change, the very formalism of quantum mechanics. Most particularly, an “Einsteinian”, rather than a “Newtonian” treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass (...) displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author. (shrink)

Grush and Churchland (1995) attempt to address aspects of the proposal that we have been making concerning a possible physical mechanism underlying the phenomenon of consciousness. Unfortunately, they employ arguments that are highly misleading and, in some important respects, factually incorrect. Their article ‘Gaps in Penrose’s Toilings’ is addressed specifically at the writings of one of us (Penrose), but since the particular model they attack is one put forward by both of us (Hameroff and Penrose, 1995; 1996), it is appropriate (...) that we both reply; but since our individual remarks refer to different aspects of their criticism we are commenting on their article separately. The logical arguments discussed by Grush and Churchland, and the related physics are answered in Part l by Penrose, largely by pointing out precisely where these arguments have already been treated in detail in Shadows of the Mind (Penrose, 1994). In Part 2, Hameroff replies to various points on the biological side, showing for example how they have seriously misunderstood what they refer to as ‘physiological evidence’ regarding to effects of the drug colchicine. The reply serves also to discuss aspects of our model ‘orchestrated objective reduction in brain microtubules – Orch OR’ which attempts to deal with the serious problems of consciousness more directly and completely than any previous theory. (shrink)

Gödel appears to have believed strongly that the human mind cannot be explained in terms of any kind of computational physics, but he remained cautious in formulating this belief as a rigorous consequence of his incompleteness theorems. In this chapter, I discuss a modification of standard Gödel-type logical arguments, these appearing to strengthen Gödel’s conclusions, and attempt to provide a persuasive case in support of his standpoint that the actions of the mind must transcend computation. It appears that Gödel did (...) not consider the possibility that the laws of physics might themselves involve noncomputational procedures; accordingly, he found himself driven to the conclusion that mentality must lie beyond the actions of the physical brain. My own arguments, on the other hand, are from the scientific standpoint that the mind is a product of the brain’s physical activity. Accordingly, there must be something in the physical actions of the world that itself transcends computation. We do not appear to find such noncomputational action in the known laws of physics, however, so we must seek it in currently undiscovered laws going beyond presently accepted physical theory. I argue that the only plausibly relevant gap in current understanding lies in a fundamental incompleteness in quantum theory, which reveals itself only with significant mass displacements between quantum states (“Schrödinger’s cats”). I contend that the need for new physics enters when gravitational effects just begin to play a role. In a scheme developed jointly with Stuart Hameroff, this has direct relevance within neuronal microtubules, and I describe this (still speculative) scheme in the following. (shrink)

The singularity theorems of the 1960s showed that Lemaître’s initial symmetry assumptions were not essential for deriving a big-bang origin for a vast multitude of relativistic universe models. Yet the actual universe accords remarkably closely with models of Lemaître’s type. This is a mystery closely related to the form taken by the 2nd law of thermodynamics and is not explained by currently conventional inflationary cosmology. Conformal cyclic cosmology provides another perspective on these issues, one consequence being the necessary initial presence (...) of a dominant scalar material that interacts only gravitationally, but which must ultimately slowly decay away in a novel but perhaps detectable way. According to CCC, our current universe picture provides but one aeon of an unending succession of expanding aeons each having an initial big bang which is the conformal continuation of the remote exponential expansion of its previous aeon. The observational status of CCC is briefly discussed. (shrink)

It is argued, by use of specific examples, that mathematical understanding is something which cannot be modelled in terms of entirely computational procedures. Our conception of a natural number (a non-negative integer: 0, 1, 2, 3,…) is something which goes beyond any formulation in terms of computational rules. Our ability to perceive the properties of natural numbers depends upon our awareness, and represents just one of the many ways in which awareness provides an essential ingredient to our ability to understand. (...) There is no bar to the quality of understanding being the result of natural selection, but only so long as the physical laws contain a non-computational ingredient. (shrink)

For many decades, the proponents of `artificial intelligence' have maintained that computers will soon be able to do everything that a human can do. In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating roller-coaster ride through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine.

Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function "self-collapse"(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum (...) effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, "subjective reduction"( SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. (shrink)

The following is an edited version of Roger Penrose's lecture at the Fifth Mind and Brain Symposium at the Institute of Psychiatry, London, on 29 October 1994, introducing the themes of his recent book Shadows of the Mind. The talk begins by outlining some options for the modelling of the relationship between consciousness and computation, and provides evidence for a model in which it is not possible even in principle to simulate mathematical understanding computationally. It is argued that mathematical understanding (...) is on a continuum with consciousness in general, and that non-computability is a feature of all consciousness. The talk then goes on to outline some of the problems of the relationship between quantum and classical physics and proposes a new theory of `objective reduction' by quantum gravity to bridge the explanatory gap. The talk concludes by examining cytoskeletal microtubules as a possible site for quantum-coherent events in the brain. It is suggested that this might be the physical basis of conscious events. (shrink)

Conformal rescalings of spinors are considered, in which the factor Ω, inε AB ↦Ωε AB, is allowed to be complex. It is argued that such rescalings naturally lead to the presence of torsion in the space-time derivative▽ a. It is further shown that, in standard general relativity, a circularly polarized gravitational wave produces a (nonlocal) rotation effect along rays intersecting it similar to, and apparently consistent with, the local torsion of the Einstein-Cartan-Sciama-Kibble theory. The results of these deliberations are suggestive (...) rather than conclusive. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. The first volume covers the beginnings of a career that is ground-breaking from the outset. Inspired by courses given by Dirac and Bondi, much of the early published (...) work involves linking general relativity with tensor systems. Among his early works is the seminal 1955 paper, 'A Generalized Inverse for Matrices', his previously unpublished PhD and St John's College Fellowship theses, and from 1967, his Adam's Prize-winning essay on the structure of space-time. Add to this his 1965 paper, 'Gravitational collapse and space-time singularities', and the 1967 paper that introduced a remarkable new theory, 'Twistor algebra', and this becomes a truly stellar procession of works on mathematics and cosmology. (shrink)

After 1905, physics would never be the same. In those 12 months, Einstein shattered many cherished scientific beliefs with five great papers that would establish him as the world's leading physicist. On their 100th anniversary, this book brings those papers together in an accessible format.

Professor Sir Roger Penrose is one of the truly original thinkers of our time. He has made several remarkable contributions to science, from quantum physics and theories of human consciousness to relativity theory and observations on the structure of the universe. Unusually for a scientist, some of his ideas have crossed over into the public arena. Now his work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the (...) first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Many important realizations concerning twistor theory occurred during the short period of this third volume, providing a new perspective on the way that mathematical features of the complex (...) geometry of twistor theory relate to actual physical fields. Following on from the nonlinear graviton construction, a twistor construction was found for (anti-)self-dual electromagnetism allowing the general (anti-)self-dual Yang-Mills field to be obtained. It became clear that some features of twistor contour integrals could be understood in terms of holomorphic sheaf cohomology. During this period, the Oxford research group founded the informal publication, Twistor Newsletter. This volume also contains the influential Weyl curvature hypothesis and new forms of Penrose tiles. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Among the new developments that occurred during this period was the introduction of a particular notion of 'quasi-local mass-momentum and angular momentum', the topic of Penrose's Royal Society (...) paper. Many encouraging results were initially obtained but, later, difficulties began to emerge and remain today. Also, an extensive paper (with Eastwood and Wells) gives a thorough account of the relation between twistor cohomology and massless fields. This volume witnesses Penrose's increasing conviction that the puzzling issue of quantum measurement could only be resolved by the appropriate unification of quantum mechanics with general relativity, where that union must involve an actual change in the rules of quantum mechanics as well as in space-time structure. Penrose's first incursions into a possible relation between consciousness and quantum state reduction are also covered here. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Publication of The Emperor's New Mind (OUP 1989) had caused considerable debate and Penrose's responses are included in this volume. Arising from this came the idea that large-scale (...) quantum coherence might exist within the conscious brain, and actual conscious experience would be associated with a reduction of the quantum state. Within this collection, Penrose also proposes that a twistor might usefully be regarded as a source (or 'charge') for a massless field of spin 3/2, suggesting that the twistor space for a Ricci-flat space-time might actually be the space of such possible sources. Towards the end of the volume, Penrose begins to develop a quite different approach to incorporating full general relativity into twistor theory. This period also sees the origin of the Diósi-Penrose proposal. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. This sixth volume describes an actual experiment to measure the length of time that a quantum superposition might last (developing the Diósi-Penrose proposal). It also discusses the significant (...) progress made in relation to incorporating the 'googly' information for a gravitational field into the structure of a curved twistor space. Penrose also covers such things as the geometry of light rays in relation to twistor-space structures, the utility of complex numbers in drawing three-dimensional shapes, and the geometrical representation of different types of musical scales. The turn of the millennium was also an opportunity to reflect on progress in many areas up until that point. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Developing ideas sketched in the first volume, twistor theory is now applied to genuine issues of physics, and there are the beginnings of twistor diagram theory (an analogue (...) of Feynman Diagrams). This collection includes joint papers with Stephen Hawking, and uncovers certain properties of black holes. The idea of cosmic censorship is also first proposed. Along completely different lines, the first methods of aperiodic tiling for the Euclidean plane that come to be known as Penrose tiles are described. This volume also contains Penrose's three prize-winning essays for the Gravity Foundation (two second places with both Ezra Newman and Steven Hawking, and a solo first place for 'The Non-linear graviton'). (shrink)

Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function "self-collapse"(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum (...) effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent massenergy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, "subjective reduction"(SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. Possibilities and probabilities for post-reduction tubulin states are influenced by factors including attachments of microtubule-associated proteins (MAPs) acting as "nodes"which tune and "orchestrate"the quantum oscillations.. (shrink)