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Shadows of the MindShadows of the Mind Roger Penrose ‘Shadows of the Mind’ is Roger Penrose's second book on consciousness. The early part of the book is largely taken up by his response to the numerous criticism of his first consciousness book, 'The 'Emperor's New Mind' (ENM). However, the late chapters of the book introduce new concepts bring us to the fully developed Orch OR model of quantum consciousness. This involves, firstly, a proposal for a new version of the collapse of the wave function, which links it to fundamental spacetime geometry, and, secondly, suggestions as to how such a process could be physically instantiated in the brain. Responses to Criticisms of 'The Emperor's New Mind Penrose discusses at length some of the criticisms aimed at his first book. In this, he had argued that Gödel's theorem showed that human mathematicians used some form of understanding that was not based on any algorithm, when they were able to grasp the truth of statements that could not be proved using the axioms of a formal statement. His critics had suggested that while mathematicians could do this, they were in fact using a knowable algorithm present in their brains when they did it. Penrose contests this, arguing that all possible algorithms are defeated by the Gödel problem. In respect to arguments as to whether computers could be programmed to deal with Godel propositions, Penrose accepts that a computer could be instructed as to the non-stopping property of Turing's halting problem. Here, a proposition that goes beyond the original axioms of the system is put into a computation. However, this proposition is not part of the orginal formal system, but instead relies on the computer being fed with human insights so as to break out of the difficulty. So the situation becomes circular, with the apparently non-algorithmic insights required to supplement the functioning of the computer. Penrose
further discusses the suggestion of an unknowable algorithm that
enables mathematicians to perceive the truth of statements. He argues
that there is no escape in any kind of computer or human development
from the knowability of algorithms. An unknowable algorithm means an
algorithm, whose specification could not be achieved. But any algorithm
is in principle knowable, because it depends on the natural numbers,
which are knowable, and it is possible to specify natural numbers that
are larger than any number needed to specify the algorithmic action of
an organism such as a human and a human brain. In the later chapters, Penrose develops the idea of a form of wave function collapse not involving the conventional concepts of measurement or interaction with the environment. He is discussing the situation where quanta remain isolated from their environment, so that there is nothing in the conventional theory to bring about a wave function collapse. He suggests that as a result of the evolution of the Schrodinger wave, the superpositions of the quanta grow further apart. According to Penrose's interpretation of general relativity, each superposition of the quanta is conceived to have its own spacetime geometry. When the superpositions reach a point where they are separated by the Planck length (10^-35 metres) they become unstable, and the wave function collapses, giving a choice of one or other of the possible space-time geometries for the particle. This form of wave function collapse is proposed to exist in addition to the more conventional forms of collapse. The significance of this for the study of consciousness is that, in contrast to the conventional idea of wave function collapse, this form of collapse is suggested to be non-random, and instead driven by a non-computable function at the most fundamental level of spacetime. Penrose suggests that there is a non-computational aspect to the structure of spacetime itself. In support of this, he points out that when the physicists Geroch and Hartle studied quantum gravity, they found that there was no algorithm for solving certain problems involving superpositions of four dimensional space-time. Earlier the mathematician A. Markov had shown there was no algorithm for such a problem, and that if such an algorithm did exist, it could solve the Turing halting, for which it had already been shown that there was no algorithm. The possibly non-computable nature of the structure of four-dimensional space-time is deemed to open up the possibility that wave function collapses in the brain could give the mind access to this non-computable feature of fundamental space-time. Penrose
says that with a mathematical robot, it would not be practical to
encode all the possible insights of mathematicians. The robot would
have to learn certain truths by studying the environment, which in its
turn is assumed to be based on algorithms. But to be a creative
mathematician, the robot will need a concept of unassailable truth,
that a concept that some things are obviously true. This involves the
mathematical robot having to perceive that a formal system 'H' implies
the truth of its Gödel proposition, and at the same time perceiving
that the Gödel proposition cannot be proved by the formal system 'H'.
It would perceive that the truth of the proposition follows from the
soundness of the formal system, but the fact that the proposition
cannot be proved by the axioms also derives from the formal system.
This would involve a contradiction for the robot, since it would have
to believe something outside the formal system that encapsulated its
beliefs. The significance of this for the study of consciousness is that, in contrast to the conventional idea of wave function collapse, this form of collapse is suggested to be non-random, and instead driven by a non-computable function at the most fundamental level of spacetime. Penrose suggests that there is a non-computational aspect to the structure of spacetime itself. In support of this, he points out that when the physicists Geroch and Hartle studied quantum gravity, they found that there was no algorithm for solving certain problems involving superpositions of four dimensional space-time. Earlier the mathematician A. Markov had shown there was no algorithm for such a problem, and that if such an algorithm did exist, it could solve the Turing halting, for which it had already been shown that there was no algorithm. The possibly non-computable nature of the structure of four-dimensional space-time is deemed to open up the possibility that wave function collapses in the brain could give the mind access to this non-computable feature of fundamental space-time. Penrose also looks at the possibility that so-called closed timelike lines could provide a basis for non-computable processing. This idea has also been developed by David Deutsch. Kurt Gödel (separately from his famous theorem) had been the first to propose that general relativity theoretically allowed closed timelike lines. A closed timelike line could arise around a very massive object, if the continous tilting of a light cone in line with a very strong gravitational field meant that an individual, whose world-line lay within the light cone eventually came back to the point where they started, meaning in this case the point in time, i.e. a point in their past. Penrose thinks that the potential for paradox would prevent this happening in the macroscopic world, but that it would be feasible for it to happen at the quantum level. This area is speculative even by the standards of consciousness theory, but the suggestion appears to be that a quantum computing device circling on a closed timelike line could carry out repeated calculations which it could bring back to a computer lieing in its own past, which might derive some 'insights' from the repeated future calculations. In the later stages of the book, Penrose begins to look at how quantum activity could be instantiated in the brain. The idea that there might be quantum activity in biological tissue was poineered by the phycisist, Fröhlich in the mid 20th century, who argued for quantum coherent activity in biological tissues as a result of metabolic energy. He and others have argued that some form of quantum ordering was required to maintain the orderly sequence of chemical reactions necessary to living organisms. Metabolic energy and dielectric properties are argued to be sufficiently pronounced quantum coherence to arise, and these could come in the macroscopic form of Bose-Einstein condensates. There is some evidence now for the oscillations in tissues predicted by Fröhlich. In the later stages of the book, Penrose begins to look at how quantum activity could be instantiated in the brain. The idea that there might be quantum activity in biological tissue was poineered by the phycisist, Fröhlich in the mid 20th century, who argued for quantum coherent activity in biological tissues as a result of metabolic energy. He and others have argued that some form of quantum ordering was required to maintain the orderly sequence of chemical reactions necessary to living organisms. Metabolic energy and dielectric properties are argued to be sufficiently pronounced quantum coherence to arise, and these could come in the macroscopic form of Bose-Einstein condensates. There is some evidence now for the oscillations in tissues predicted by Fröhlich. Penrose considers microtubules as a plausible site for the control of sophisticated activity in organisms. Single cell creatures are seen to navigate and perform other functions without the aid of a brain or a nervous system. The cytoskeleton is believed to be responsible for their capabilities, and microtubules are the most important component of the cytoskeleton. The cytoskeleton can be viewed as analogous to the cell's own nervous system. Penrose discusses the structure of the microtubules. Each microtubule is former out of subunits of the protein tubulin. Each subunit is a dimer of an alpha and beta tubulin. The microtubule is a long tubular structure, and the tubulins are organised into an hexagonal lattice. Each tubulin dimer has two different configurations or conformations. The switching of configurations is thought to correspond to different electric polarisations of the dimer, resulting from the movement of an electron positioned at the junction of the alpha and beta tubulins. Stuart Hameroff, who cooperated with Penrose on the development of the Orch OR theory that emerges in 'Shadows in the Mind', had suggested that signals could be passed along the microtubules as waves of polarisation of the tubulin dimers. Each dimer would be influenced by the polarisation of six of its neighbours, giving rise to effective rules for the conformation of the tubulins, which in turn makes them suitable for the transmission of signals. The microtubules are closely related to the synapses, carrying neurotransmitter molecules to them, and possibly altering their strength as a result. They are also involved in the growth of nerve endings and guiding them towards other cells. They are indirectly connected to dendritic spines, the growth and degeneration of which is an important factor in the plasticity of the brain. Penrose thinks that these structures point to much greater computing power in the brain than had previosuly been realised if as he thinks the tubulin dimers are computational units. However, Penrose is not satisfied with the proposition of increased computing power. The whole argument from the Godel theorem says in effect that no matter how great the computing power, you will get no closer to solving the problem of consciousness. Penrose holds to the argument that the brain must manifest some non-computational property, and that anything that is non-computational will be the result of quantum coherent activity, because this is the only aspect of the universe in which non-computational activity can arise. Because of their influence over the activity of cells and because of their structural suitability for signalling and information processing, microtubules are considered the most likley site for such non-computational activity. Penrose discusses both the plausibility of quantum activity in microtubules, and the type of quantum activity that might be useful for the production of consciousness. This is against the background of the fact that quantum states would normally be expected to decohere in the environment of the brain. Frohlich had argued that metabolic energy and the dieletric properties of biological tissue would be sufficient to maintain quantum coherence at body temperatures. However, the Penrose/Hameroff model places more emphasis on the idea that the microtubules themselves could shield quantum coherence. This is suggested to arise mainly from the ordering of water close to the surface of the microtubules. The structure of the microtubules is also suggested to be favourable for the formation of macroscopic quantum coherence known as Bose-Einstein condensates. Penrose further suggests that the quantum coherent state could extend between microtubules and also between neurons, thus creating a macroscopic quantum structure across a significant area of the brain. It is further suggested that when this macroscopic quantum state undergoes wave function collapse, this will involve the objective reduction (OR), which would connect the microtubules to the non-computational aspect of fundamental spacetime. Numerous articles, mainly published after 'Shadows in the Mind' go into the proposed physical structures in the brain in greater detail, and some of these are reviewed under Penrose & Hameroff sections 3-6. |
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