Roger Penrose > Quotes

“We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.”
― Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe

“No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.”
― Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe

“... Even an aardvarks think their offspring are beautiful”
― Roger Penrose

“To make this condition mathematically clearer, it is convenient to assert it in the form that the space-time can be continued smoothly, as a conformal manifold, a little way prior to the hypersurface . To before the Big Bang? Surely not: the Big Bang is supposed to represent the beginning of all things, so there can be no ‘before’. Never fear—this is just a mathematical trick. The extension is not supposed to have any physical meaning! Or might it …?”
― Roger Penrose, Cycles of Time: An Extraordinary New View of the Universe

“There are considerable mysteries surrounding the strange values that Nature's actual particles have for their mass and charge. For example, there is the unexplained 'fine structure constant' ... governing the strength of electromagnetic interactions, ....”
― Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe

“The final conclusion of all this is rather alarming. For it suggests that we must seek a non-computable physical theory that reaches beyond every computable level of oracle machines (and perhaps beyond).”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“If we try to make general inferences about the theoretical possibility of a reliable computational model of the brain, we ought indeed to come to terms with the mysteries of quantum theory.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“A scientific world-view which does not profoundly come to terms with the problem of conscious minds can have no serious pretensions of completeness.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Consciousness is the phenomenon whereby the universe's very existence is made known.”
― Roger Penrose

“These are deep issues, and we are yet very far from explanations. I would argue that no clear answers will come forward unless the interrelating features of all these worlds are seen to come into play. No one of these issues will be resolved in isolation from the others. I have referred to three worlds and the mysteries that relate them one to another. No doubt there are not really three worlds but one, the true nature of which we do not even glimpse at present.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“What is it that we can do with conscious thought that cannot be done unconsciously? The problem is made more elusive by the fact that anything that we do seem originally to require consciousness for appears also to be able to be learnt and then later carried out unconsciously (perhaps by the cerebellum”
― Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics

“All I would myself ask for would be that our perceptive interrogator should really feel convinced, from the nature of the computer’s replies, that there is a conscious presence underlying these replies”
― Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics

“I argue that the phenomenon of consciousness cannot be accommodated within the framework of present-day physical theory.”
― Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics

“Objective mathematical notions must be thought of as timeless entities and are not to be regarded as being conjured into existence at the moment that they are first humanly perceived.”
― Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe

“What the Second Law indeed states, roughly speaking, is that things are getting more ‘random’ all the time.”
― Roger Penrose, Cycles of Time: An Extraordinary New View of the Universe

“However, in 1930 (published in 1931), Godel produced his bombshell, which eventually showed that the formalists' dream was unattainable! He demonstrated that there could be no formal system F, whatever, that is both consistent (in a certain 'strong' sense that I shall describe in the next section) and complete-so long as F is taken to be powerful enough to contain a formulation of the statements of ordinary arithmetic together with standard logic. Thus, Godel's theorem would apply to systems F for which arithmetical statements such as Lagrange's theorem and Goldbach's conjecture, as described in 2.3, could be formulated as mathematical statements.”
― Roger Penrose

“A point that should be emphasized is 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

“There are completely deterministic universe models, with clear-cut rules of evolution, that are impossible to simulate computationally.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“What Godel and Rosser showed is that the consistency of a (sufficiently extensive) formal system is something that lies outside the power of the formal system itself to establish.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“The reason that I have concentrated on non-computability, in my arguments, rather than on complexity, is simply that it is only with the former that I have been able to see how to make the necessary strong statements. It may well be that in the working lives of most mathematicians, non-computability issues play, if anything, only a very small part. But that is not the point at issue. I am trying to show that (mathematical) understanding is something that lies beyond computation, and the Godel (-Turing) argument is one of the few handles that we have on that issue. It is quite probable that our mathematical insights and understandings are often used to achieve things that could in principle also be achieved computationally-but where blind computation without much insight may turn out to be so inefficient that it is unworkable (cf. 3.26). However, these matters are much more difficult to address than the non-computability issue.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“How is that perceiving beings can arise from out of the physical world, and how is that mentality is able seemingly to 'create' mathematical concepts out of some kind of mental model.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“The algorithm has some kind of disembodied ‘existence’ which is quite apart from any realization of that algorithm in physical terms.”
― Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics

“Mathematical truth is not determined arbitrarily by the rules of some 'man-made' formal system, but has an absolute nature, and lies beyond any such system of specifiable rules.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“My own view is that to understand quantum nonlocality we shall require a radical new theory. This new theory will not just be a slight modification of quantum mechanics but something as different from standard quantum mechanics as general relativity is from Newtonian gravity. It would have to be something which has a completely different conceptual framework.”
― Roger Penrose, The Large, the Small and the Human Mind

“It is in mathematics that our thinking processes have their purest form.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone”
― Roger Penrose

“We cannot say, in familiar everyday terms, what it 'means' for an electron to be in a state of superposition of two places at once, with complex-number weighting factors w and z. We must, for the moment, simply accept that this is indeed the kind of description that we have to adopt for quantum-level systems. Such superpositions constitute an important part of the actual construction of our microworld, as has now been revealed to us by Nature. It is just a fact that we appear to find that the quantum-level world actually behaves in this unfamiliar and mysterious way. The descriptions are perfectly clear cut-and they provide us with a micro-world that evolves according to a description that is indeed mathematically precise and, moreover, completely deterministic!”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Moreover, the slightest ‘mutation’ of an algorithm (say a slight change in a Turing machine specification, or in its input tape) would tend to render it totally useless, and it is hard to see how actual improvements in algorithms could ever arise in this random way. (Even deliberate improvements are difficult without ‘meanings’ being available.”
― Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics

“The perceiving of mathematical truth can be achieved in very many different ways. There can be little doubt that whatever detailed physical activity it is that takes place when a person perceives the truth of some mathematical statement, this physical activity must differ very substantially from individual to individual, even though they are perceiving precisely the same mathematical truth. Thus, if mathematicians just use computational algorithms to form their unassailable mathematical truth judgments, these very algorithms are likely to differ in their detailed construction, from individual to individual. Yet, in some clear sense, the algorithms would have to be equivalent to one another.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“Somehow, consciousness is needed in order to handle situations where we have to form new judgements, and where the rules have not been laid down beforehand.”
― Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics