Shadows of the Mind Quotes

“If, as I believe, the Godel argument is consequently forcing us into an acceptance of some form of viewpoint C, the we shall also have to come to terms with some of its other implications. We shall find ourselves driven towards a Platonic viewpoint of things. According to Plato, mathematical concepts and mathematical truths inhabit an actual world of their own that is timeless and without physical location. Plato's world is an ideal world of perfect forms, distinct from the physical world, but in terms of which the physical world must be understood. It also lies beyond our imperfect mental constructions; yet, our minds do have some direct access to this Platonic realm through an 'awareness' of mathematical forms, and our ability to reason about them. We shall find that whilst our Platonic perceptions can be aided on occasion by computation, they are not limited by computation. It is this potential for the 'awareness' of mathematical concepts involved in this Platonic access that gives the mind a power beyond what can ever be achieved by a device dependent solely upon computation for its action.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Awareness, I take to be one aspect-the passive aspect-of the phenomenon of consciousness. Consciousness has an active aspect also, namely the feeling of free will.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“It will be one of my purposes, in later arguments, to show that there is indeed an aspect of 'genuine understanding' that cannot be properly simulated in any computational way whatever. Consequently, there must indeed be a distinction between genuine intelligence and any attempt at a proper computational simulation of it.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“It would seem that it is in some kind of combination of top-down and bottom-up organization that we must expect to find the most successful AI systems.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Technology provides the potential, by use of well-produced books, film, television, and interactive computer-controlled systems of various kinds. These, and other developments, provide many opportunities for expanding our minds-or else for deadening them. The human mind is capable of vastly more than it is often given the chance to achieve. Sadly, these opportunities are all to frequently squandered, and the minds of neither young nor old are provided the openings that they undoubtedly deserve.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Support for the Platonic viewpoint (as opposed to the formalist one) was an important part of Godel's initial motivations. On the other hand, the arguments from Godel's theorem serve to illustrate the deeply mysterious nature of our mathematical perceptions. We do not just 'calculate' in order to form these perceptions, but something else is profoundly involved-something that would be impossible without the very conscious awareness that is, after all, what the world of perceptions is all about.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Does awareness play some kind of role as a 'bridge' to a world of Platonic absolutes.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“It is even harder to predict the possibility (or the timescale) for building a device whose action depends on a physical theory that we do not even know at present. Such a theory would be needed, I am claiming, before we could understand the physics underlying a non-computably acting device-'non-computably', that is, in the Turing-machine-inaccessible sense that I have been using in this book. According to my own arguments, in order to build such a device we should first need to find the appropriate physical (OR) theory of quantum-state reduction-and it is very hard to know how far we are from such a theory-before we could begin to contemplate its construction. It is also possible that the specific nature of that OR theory might itself provide an unexpected complexion on the very task at hand.

At least, I suppose that we should need to find the theory first, if we are to construct such a non-computational device. But conceivably not: in actual practice, it has often been the case that surprising new physical effects have been discovered many years before their theoretical explanation. A good example was superconductivity, which was originally observed experimentally (by Heike Kammerlingh Onnes in 1911) nearly 50 years before the full quantum-theoretic explanation was eventually found, by Bardeen, Cooper, and Schrieffer in 1957. Moreover, high-temperature superconductivity was discovered in 1986, cf. Shent et al. (1988), also without prior good reason to believe in it on purely theoretical grounds.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“In view of the anomalous relation that consciousness has to the very physical notion of time, as was described at the beginning of this section, it seems to me to be at least possible that there is no such clear-cut 'time' at which a conscious event must occur.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“One appears to conclude from these experiments that: (i) the conscious act of 'free will' is a pure illusion, having been, in some sense, already preprogrammed in the preceding unconscious activity of the brain; or (ii) there is a possible 'last-minute' role for the will, so that it can sometimes (but not usually) reverse the decision that had been unconsciously building up for a second or so before; or (iii) the subject actually consciously wills the finger-flexing at the earlier time of a second or so before the flexing takes place, but mistakenly perceives, in a consistent way, that the conscious act occurs at the much later time, just before the finger is indeed flexed.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“As a final point, it should be remarked that it is precisely the potential tilting of the light cones in Einstein's general relativity (cf. 4.4) that gives us the non-computable effects that Deutsch points out. Once the light cones are allowed to tilt at all, even by the minute amounts that occur with Einstein's theory in ordinary circumstances, then there is the potential possibility for them to tilt to such a degree that closed timelike lines will be the result. This potential possibility need only play a role as a counterfactual, according to quantum theory, for it to have an actual effect!”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“If we now consider what it means to perform a quantum computation in such a situation, we apparently come to the conclusion that non-computable operations can be performed! This arises from the fact that in the space-time geometries with closed timelike lines, a Turing-machine operation can feed on to its own output, running around indefinitely, if necessary, so that the answer to the question 'does that computation ever stop' has an actual influence on the final result of the quantum computation. Deutsch comes to the conclusion that in his quantum gravity scheme, quantum oracle machines are possible. As far as I can make out, his arguments would apply just as well to higher-order oracle machines also.

Of course, many readers may feel that all this should be taken with an appropriate amount of salt. Indeed, there is no real suggestion that the scheme provides us with a consistent (or even plausible) theory of quantum gravity. Nonetheless, the ideas are logical within their own framework and are suggestively interesting-and it seems quite reasonable to me that when the appropriate scheme for quantum gravity is eventually found, then some important vestiges of Deutsch's proposal will indeed survive.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Though it indeed seems reasonable to rule out space-time geometries with closed timelike lines as descriptions of the classical universe, a case can be made that they should not be ruled out as potential occurrences that could be involved in a quantum superposition.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“There is another point that should be made, however, and this is that it need not be the case that human mathematical understanding is in principle as powerful as any oracle machine at all. As noted above, the conclusion G does not necessarily imply that human insight is powerful enough, in principle, to solve each instance of the halting problem. Thus, we need not necessarily conclude that the physical laws that we seek reach, in principle, beyond every computable level of of oracle machine (or even reach the first order). We need only seek something that is not equivalent to any specific oracle machine (including also the zeroth-order machines, which are Turing machines). Physical laws could perhaps lead to something that is just different.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Nevertheless, the Geroch-Hartle work does indicate the clear possibility that non-computability may have a genuine role in whatever quantum gravity theory finally emerges as being physically correct.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“In a particular approach to quantum gravity, Robert Geroch and James Hartle (1986) found themselves confronted with a computationally unsolvable problem, namely the topological equivalence problem for 4-manifolds. Basically, their approach involved the questions of deciding when two four-dimensional spaces are 'the same', from the topological point of view (i.e. when it is possible to deform one of them continuously until it coincides with the other, where the deformation does not allow tearing or gluing the spaces in any way). In Fig. 7.14, this is illustrated in the two-dimensional case, where we see that the surface of a ball is different. In two dimensions, the topological equivalence problem is computationally solvable, but it was shown by A.A. Markov in 1958 that there is not algorithm for solving this problem in the four-dimensional case. In fact, what is shown effectively demonstrates that if there were such an algorithm, then one could convert that algorithm into another algorithm which could solve the halting problem, i.e. it could decide whether or not a Turing-machine action will stop. Since, as we have seen in 2.5, there is no such algorithm, it follows that there cannot be any algorithm for solving the equivalence problem for 4-manifolds either.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“In the present chapter, we tried to pinpoint the place in the brain where quantum action might be important to classical behaviour, and have apparently been driven to consider that it is through the cytoskeletal control of synaptic connections that this quantum/classical interface exerts its fundamental influence on the brain's behaviour.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Think of the superposed state of a lump in two different locations as being like an unstable nucleus that decays, after a characteristic 'half-life' timescale, into something else more unstable. In the case of the superposed lump locations we likewise think of an unstable quantum state which decays, after a characteristic lifetime (given, roughly on average, by the reciprocal of the gravitational energy of separation), to a state where the lump is in one location or the other-representing two possible decay modes.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“A point that should be emphasized is that the energy that the energy that defines the lifetime of the superposed state is an energy difference, and not the total, (mass-) energy that is involved in the situation as a whole. Thus, for a lump that is quite large but does not move very much-and supposing that it is also crystalline, so that its individual atoms do not get randomly displaced-quantum superpositions could be maintained for a long time. The lump could be much larger than the water droplets considered above. There could also be other very much larger masses in the vicinity, provided that they do not get significantly entangled with the superposed state we are concerned with. (These considerations would be important for solid-state devices, such as gravitational wave detectors, that use coherently oscillating solid-perhaps crystalline-bodies.)”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Once there is a sufficient disturbance in the environment, according to the present ideas, reduction will rapidly actually take place in that environment-and it would be accompanied by reduction in any 'measuring apparatus' with which that environment is entangled. Nothing could reverse that reduction and enable the original entangled state to be resurrected, even imagining enormous advances in technology. Accordingly, there is no contradiction with the measuring apparatus actually registering either YES or NO-as in the present picture it would indeed do.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“In general, when we consider an object in a superposition of two spatially displaced states, we simply ask for the energy that it would take to effect this displacement, considering only the gravitational interaction between the two. The reciprocal of this energy measures a kind of 'half-life' for the superposed state. The larger this energy, the shorter would be the time that the superposed state could persist.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“The point is that we really have no conception of how to consider linear superpositions of states when the states themselves involve different space-time geometries. A fundamental difficulty with 'standard theory' is that when the geometries become significantly different from each other, we have no absolute means of identifying a point in one geometry with any particular point in the other-the two geometries are strictly separate spaces-so the very idea that one could form a superposition of the matter states within these two separate spaces becomes profoundly obscure.

Now, we should ask when are two geometries to be considered as actually 'significantly different' from one another? It is here, in effect, that the Planck scale of 10^-33 cm comes in. The argument would roughly be that the scale of the difference between these geometries has to be, in an appropriate sense, something like 10^-33 cm or more for reduction to take place. We might, for example, attempt to imagine (Fig. 6.5) that these two geometries are trying to be forced into coincidence, but when the measure of the difference becomes too large, on this kind of scale, reduction R takes place-so, rather than the superposition involved in U being maintained, Nature must choose one geometry or the other.

What kind of scale of mass or of distance moved would such a tiny change in geometry correspond to? In fact, owing to the smallness of gravitational effects, this turns out to be quite large, and not at all unreasonable as a demarcation line between the quantum and classical levels. In order to get a feeling for such matters, it will be useful to say something about absolute (or Planckian) units.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Applying the standard U-procedures of quantum mechanics, we find that the photon's state, after it has encountered the mirror, would consist of two parts in two very different locations. One of these parts then becomes entangled with the device and finally with the lump, so we have a quantum state which involves a linear superposition of two quite different positions for the lump. Now the lump will have its gravitational field, which must also be involved in this superposition. Thus, the state involves a superposition of two different gravitational fields. According to Einstein's theory, this implies that we have two different space-time geometries superposed! The question is: is there a point at which the two geometries become sufficiently different from each other that the rules of quantum mechanics must change, and rather than forcing the different geometries into superposition, Nature chooses between one or the other of them and actually effects some kind of reduction procedure resembling R?”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“There are strong reasons for suspecting that the modification of quantum theory that will be needed, if some form of R is to be made into a real physical process, must involve the effects of gravity in a serious way. Some of these reasons have to do with the fact that the very framework of standard quantum theory fits most uncomfortably with the curved-space notions that Einstein's theory of gravity demands. Even such concepts as energy and time-basic to the very procedures of quantum theory-cannot, in a completely general gravitational context, be precisely defined consistently with the normal requirements of standard quantum theory. Recall, also, the light-cone 'tilting' effect (4.4) that is unique the physical phenomenon of gravity. One might expect, accordingly, that some modification of the basic principles of quantum theory might arise as a feature of its (eventual) appropriate union with Einstein's general relativity.

Yet most physicists seem reluctant to accept the possibility that it might be the quantum theory that requires modification for such a union to be successful. Instead, they argue, Einstein's theory itself should be modified. They may point, quite correctly, to the fact that classical general relativity has its own problems, since it leads to space-time singularities, such as are encountered in black holes and the big bang, where curvatures mount to infinity and the very notions of space and time cease to have validity (see ENM, Chapter 7). I do not myself doubt that general relativity must itself be modified when it is appropriately unified with quantum theory. And this will indeed be important for the understanding of what actually takes place in those regions that we presently describe as 'singularities'. But it does not absolve quantum theory from a need for change. We saw in 4.5 taht general relativity is an extraordinarily accurate theory-no less accurate than is quantum theory itself. Most of the physical insights that underlie Einstein's theory will surely survive, not less than will most of those of quantum theory, when the appropriate union that moulds these two great theories together is finally found.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“In the GRW scheme, however, an object as large as a cat, which would involve some 10^27 nuclear particles, would almost instantaneously have one of its particles 'hit' by a Gaussian function (as in Fig. 6.2), and since this particle's state would be entangled with the other particles in the cat, the reduction of that particle would 'drag' the others with it, causing the entire cat to find itself in the state of either life or death. In this way, the X-mystery of Schrodinger's cat-and of the measurement problem in general-is resolved.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“I believe that the problem of quantum measurement should be faced and solved well before we can expect to make any real headway with the issue of consciousness in terms of physical action-and that the measurement problem must be solved in entirely physical terms. Once we are in possession of a satisfactory solution, then we may be in a better position to move towards some kind of answer to the question of consciousness. It is my view that solving the quantum measurement problem is a prerequisite for an understanding of mind and not at all that they are the same problem. The problem of mind is a much more difficult problem than the measurement problem!”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Perhaps Cardano's curious combination of a mystical and a scientifically rational personality allowed him to catch these first glimmerings of what developed to be one of the most powerful of mathematical conceptions. In later years, through the work of Bombelli, Coates, Euler, Wessel, Argand, Gauss, Cauchy, Weierstrass, Riemann, Levi, Lewy, and many others, the theory of complex numbers has flowered into one of the most elegant and universally applicable of mathematical structures. But not until the advent of the quantum theory, in the first quarter of this century, was a strange and all-pervasive role for complex numbers revealed at the very foundational structure of the actual physical world in which we live-nor had their profound link with probabilities been perceived before this. Even Cardano could have had no inkling of a mysterious underlying connection between his two greatest contributions to mathematics-a link that forms the very basis of the material universe at its smallest scales.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“However, in other circumstances, such as with PSR 1913 + 16, the situation is very different, and gravitational radiation from the system indeed has a significant role to play. Here, Einstein's theory provides a firm prediction of the detailed nature of the gravitational radiation that the system ought to be emitting, and of the energy that should be carried away. This loss of energy should result in a slow spiralling inwards of the two neutron stars, and a corresponding speeding up of their orbital rotation period. Joseph Taylor and Russell Hulse first observed this binary pulsar at the enormous Aricebo radio telescope in Puerto Rico in 1974. Since that time, the rotation period has been closely monitored by Taylor and his colleagues, and the speed-up is in precise agreement with the expectations of general relativity (cf. Fig. 4.11). For this work, Hulse and Taylor were awarded the 1993 Nobel Prize for Physics. In fact, as the years have rolled by, the accumulation of data from this system has provided a stronger and stronger confirmation of Einstein's theory. Indeed, if we now take the system as a whole and compare it with the behaviour that is computed from Einstein's theory as a whole-from the Newtonian aspects of the orbits, through the corrections to these orbits from standard general relativity effects, right up to the effects on the orbits due to loss of energy in gravitational radiation-we find that the theory is confirmed overall to an error of no more than about 10^-14. This makes Einstein's general relativity, in this particular sense, the most accurately tested theory known to science!”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“May we expect that there is something corresponding to be learnt with regard to the phenomenon of consciousness? If so, it would not be mass that would need to be large for the phenomenon to become apparent-at least not only mass-but some kind of delicate physical organization. According to the arguments put forward in Part I, such organization would have to have found a way of making use of some hidden non-computational ingredient already present in the behaviour of ordinary matter-an ingredient that, like the light-cone tilting of general relativity, would have totally escaped attention had that attention been confined to the study of the behaviour of tiny particles.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Yet despite the fact that gravity is different from other physical forces, there is a profound harmony integrating gravity with all of the rest of physics. Einstein's theory is not something foreign to the other laws, but it presents them in a different light. (This is particularly so for the laws of conservation of energy, momentum, and angular momentum.) This integration of Einstein's gravity with the rest of physics goes some way to explaining the irony that Newton's gravity had provided a paradigm for the rest of physics despite the fact, as Einstein later showed, that gravity is actually different from the rest of physics! Above all, Einstein taught us not to get too complacent in believing, at any stage of our understanding, that we have, as yet, necessarily found the appropriate physical viewpoint.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness