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David BohmIntroduction to and articles on David Bohm, Karl Pribram, Basil Hiley and David Peat 1.) Introduction 2.) Information, quantum theory & the brain - Basil Hiley 3.) Brain & Mathematics - Karl Pribram 4.) Mind, Matter & Active Information - Paavo Pylkkanen 5.) Consciousness in Bohm's Ontology - Paavo Pylkkanen 6.) Are our spaces made of words? - Jonathan Edwards Introduction: David Bohm & the Implicate Order David Bohm took the view that quantum theory and relativity contradicted one another, and that this contradiction implied that there existed a more fundamental level in the physical universe. He claimed that both quantum theory and relativity pointed towards this deeper theory. This more fundamental level was supposed to represent an undivided wholeness and an implicate order, from which arose the explicate order of the universe as we actually experience it. The explicate order is seen as a particular case of the implicate order. The implicate order applies both to matter and consciousness, and it can therefore explain the relationship between these two apparently different things. Mind and matter are here seen as related projections into our explicate order from the underlying reality of the implicate order. Bohm claims that when we look at the extension of matter and separation of its parts in space, we can see nothing in these concepts that helps us with understanding consciousness. Bohm compares this problem to Descartes discussion of the difference between mind and matter. Descartes to some extent relied on God to resolve the gap. Bohm says that since Descartes time the idea of introducing God into the equation has been let drop, but he argues that as a result conventional modern thinking has no way left to it for bridging the gap between matter and consciousness. In Bohm’s scheme there is an unbroken wholeness at the fundamental level of the universe, in which consciousness is not separated from matter. Bohm’s view of consciousness is closely connected to Karl Pribram’s hologaphic conception of the brain (27-9). Pribram sees sight and the other senses as lenses, without which the universe would appear as a hologram. Pribram thinks that information is recorded all over the brain, and that this information is enfolded into a whole, also in the manner of a hologram, although it is suggested that the physical function involved is more complicated than a hologram. In Pribram’s scheme, it is suggested that the different memories are connected by association and manipulated by logical thought. If the brain is also attending to sensory data, all of these facets are proposed to fuse together in an overall experience or unanalysable whole. This is suggested to be closer to the essence of consciousness than the mere excitation of neurons. In trying to arrive at a description of consciousness, Bohm discusses the experience of listening to music. He thinks that the sense of movement and change that constitutes the experience of the music relies on notes both from the immediate past and the present being held in the brain at the same time. Bohm does not view the notes from the immediate past as memories but as active transformations of what came earlier. He proposes that a given moment can cover an extended duration, as opposed to the more conventional ‘now’ concept of something instantaneous. The moment is proposed to have extension in time and space, but the amount of this extension is not precisely defined. One moment gives rise to the next, with content that was implicate in the immediate past becoming explicate in the present. The sense of movement in music is the result of the intermingling of transformations. Bohm likens these transformations to the emergence of consciousness from the implicate order. He thinks that in listening to music people are directly perceiving the implicate order. The order is thought to be active and to flow into emotional and physical responses. Bohm also discusses the problem of time, the concept of ‘now’ and the difficulty of distinguishing ‘now’ from the immediate past, which no longer exists. In classical physics this problem is overcome via the calculus, with its concept of ‘the limit’, which is effectively a zero change in time or space. This is successful for calculating the movement of material objects in classical physics, which comprises the explicate order. However, it is not applicable to quantum theory in which movement is not seen as continuous. In the implicate order intermingled elements are present together, and processes are the outcome of what is enfolded in the implicate order. In this structure, there is a flow between experience and logical thought that is considered by Bohm to hold out the possibility of a bridge between matter and consciousness. Bohm also advances the idea of overall necessity driving short-term brain processes. Thus it is proposed that an ensemble of elements enfolded in the brain will constitute the next development of thought, and that these elements are bound by an overall necessity that brings them together, and also determines the next moment in consciousness. Bohm relates movement to the implicate order; for movement, we can also read change or flow or the coherence of our perception of a piece of music over a short period of time. Evidence for this is claimed to derive from studies of infants (30. Piaget, 1956), who have to learn about space and time, which are seen as part of the explicate order, but appear to have a hard-wired understanding of movement that is implicate. Bohm’s view is that the movement and flow of the implicate order are hard-wired into human brains, in the same way that Chomsky asserts that grammar is hard- wired into the human brain, but that by way of contrast, the classical space and time of the explicate order are something that has to be learnt by experience. Basil Hiley Birbeck College Information, quantum theory and the brain In Globus, G., Pribram, H. & Vitiello, G. Eds. Brain and Being John Benjamins Basil Hiley was the long-term associate of David Bohm, and is a continuing exponent of many of his ideas. In this paper, Hiley argues that the Bohmian notion of active information introduced in relation to quantum phenomena can also be applied to classical signalling. This is suggested to have relevance to concept of meaning as opposed to mere information. Hiley queries whether the word ‘information’ that is widely used in science including neuroscience always carries the same meaning. Bohm and Hiley were interested in so-called active information that drives physical processes and leaves no choice as to whether they are implemented or not. This is distinct from a mere list of data or instructions or a way of viewing entropy. Active information has been used in a number of papers relative to the mind/matter relationship (Hiley 1995a&b, 2001) (Hiley & Pylkkänen 1997, 2001)(1-5). The colloquial understanding of information is that it is data from which meaning can be extracted by an intelligent entity. Hiley regards it as a fundamental question as to whether information has objective significance devoid of the subjective involvement. Verbal communication is seen as a particular problem, where meaning is translated into sound waves and then back into meaning. Hiley relates this meaning to the agency of the speaker and the agency of the listener. He relates this inseparable link to Bohr’s notion of the indivisibility of the quantum action, which cannot distinguish between the system under observation and the means of observation. Bohm believed that a quantum potential could be extracted from Schrödinger’s equation and that this quantum potential could act as an information potential. In transmitting a signal there is a trade off between the duration of the pulse and the frequency. There is an ambiguity in the signal that is similar to the uncertainty in quantum mechanics. The two concepts are said to employ different aspects of the same mathematical structure. Hiley refers to the two-slit experiment, where the potential is claimed to cover the whole experimental arrangement. The quantum information changes in relation to any change in the experimental arrangement, and this is related to information entering the brain and changing the arrangement of its parts. Within the brain Bohm thought that meaning was in the process itself. Bohm proposed that there were two sides or two poles to the brain, the manifest and relatively stable material side and the subtle mind-like side. The manifest side is classical physics, while the subtle side is the quantum level that produces the classical level. Thus the mind cannot be separated from matter. The ambiguity or uncertainty of the quantum comes through in the ambiguity attached to meaning. The quantum is seen as a pool of information shared by entangled particles. When the potential or pool vanishes, the classical world emerges. Hiley also agrees that this system could operate in terms of quantum fields. The main weakness of this description seems to be the lack of detail as to how the quantum mechanism would operate in the brain, and the lack of distinction between information which does not by itself imply consciousness and consciousness itself. The emergence of meaning could be thought to imply consciousness but this important point is not at all developed. References:- (1) Hiley, B. (1995a) The Bohm Interpretation of Quantum Mechanics In Laurikainen, K. et al Foundation of Modern Physics, pp. 99-118 Editions Frontiers (2) Hiley, B. (1995b) The Implicate Order and the relationship between mind and matter (3) Hiley, B. (2001) The Bohm Inerpretation and the Mind Matter Relationship In Dubois, D. Ed. Computing Anticipatory Systems (4) Hiley, B. & Pylkkänen, P. (1997) Active information and cognitive science in Pylkkänen, P. et al eds. Brain, mind and physics (5) Hiley, B. & Pylkkänen, P. (2001) The Mind in a quantum framework In Pylkkänen, P. & Vaden eds. Dimensions of Conscious Experience John Benjamins Binz, E. et al (2003) A unifying structure of signal theory, holography and quantum information theory Journal of Applied Math and Comp, 11, pp. 1-57 Bohm, D. (1994) A new notion of the relationship between the physical and the mental Psycoscience,1, 6-26 Bohm, D., Hiley, B. & Stuart, A. (1970) On a new mode of description in physics International Journal of Theoretical Physics, 3, pp. 171-183 Bohm, D. & Hiley, B. (1981) Quantum algebraic approach to a generalised space Found. Phys., pp. 179-203 Bohm, D. & Hiley, B. (1983) Relativistic phase space In A. van der Merwe Ed, Old and new questions in physics and theoretical biology, pp. 67-76 Plenum Bohm, D. & Hiley, B. (1987) An Ontological Basis for Quantum Theory: I Phys. Rep., 144, pp. 323-348 Bohm, D., Hiley, B., Kaloyerou, P. (1987) An Ontological Basis for Quantum Theory: II Phys. Rep., 144, pp. 349-375 Bohm, D. & Hiley, B. (1993) The Undivided Universe Routledge Cushing, J. (1994) Quantum Mechanics Chicago University Press Gabor, D. (1946) Theory of Communication Journal Inst. Elect. Engineers, 93, pp. 429-41 Hiley, B. (1971) A Note on discreteness In T. Bastin Ed. Quantum Theory and Beyond, pp. 181-190 Cambridge University Press Hiley, B. (1997) Information and quantum theory In Fedoric, A. & Marcer, P. eds. The Outer Limits of Computing, pp. 25-42, University of Greenwich Press Hiley, B. (2003) Phase space descriptions of quantum phenomena Holland, P. (1988) Causal interpretation of Fermi fields Phys. Lett., 128A, pp. 9-18 Moyal, J. (1949) Quantum mechanics as a statistical theory Proceedings of the Cambridge Philosophical Society, 45, pp. 99-123 Thom, R. (1975) Structural stability and morphogenesis Benjamin Vitiello, G. (2001) My Double Unveiled John Benjamins Wheeler, J. (1990) Information, physics, quantum In Zurek, W. ed. Complexity, Entropy and the Physics of Information, pp. 3-28 Addison-Wesley Wigner, E. (1972) Time-energy uncertainty relation In Salem, A. & Wolf, E. eds. Aspects of Quantum Theory Cambridge University Press Wigner, E. (1932) Quantum correction for thermodynamic equilibrium Phys. Rev., 40, pp. 749-759 Karl Pribram Georgetown University Brain and mathematics In Globus, G., Pribram, H. & Vitiello, G. Eds. Brain and Being John Benjamins Pribram stresses that the same mathematical formulations apply to a variety of databases, including brain processes, information, thermodynamics and quantum physics. The relationships can be portrayed by the Fourier transformation. The similarity implies that neural processes are based on relations between quantum events, or that quantum rules can be applied to some macroscopic features. Pribram discusses two articles by another quantum mind theorist, Henry Stapp (Stapp, 1997a & b) (1-2) . Stapp took the view that the brain process was a search process for satisfactory responses conditioned by earlier experience. He envisages a point moving in a well that blocks out those brain states that are not good solutions, while not blocking out those that are good solutions. Classical solutions to this don’t work in the chaotic conditions of the brain. However, Stapp points out thay quantum solutions will work, because they can explore a superposition of all solutions. Pribram notes that a number of publications have reported that quantum coherence characterises the oscillation of ions in neural ion channels. Pribram relates the 'double' suggested by Vitiello, which comprises the external world and the internal, so-called tilda copy. Pribram also refers to George Chapline, who suggested that quantum theory presented a method for solving pattern recognition problems, and that this could be a model for the type of distributing information processing carried out in the brain. References:- Adey, W. (1987) The modulation of brain tissue functions In Adelman, G. Ed. The International Encyclopaedia of Neuroscience Barrett, T. (1993) Is quantum physics a branch of sampling theory? In Corrmier-Delanous, C. et al Eds. Ecueilsen Microphysique Fondation Louis DeBroglie Bohm, D. (1973) Indication of a new order in physics Foundations of Physics, 3, 139-168 Bohm, D. & Hiley, B. (1993) The Undivided Universe Routledge Bohr, N. (1961) Atomic Physics and Human Knowledge Science Editions Chapline, G. (1999) Is theoretical physics the same thing as mathematics? Physical Reports, 315, pp. 95-105 Chapline, G. (2002) Entangled states, holography and quantum surfaces Chaos, Solitons and Fractals, 14, 809-816 DeValois, R. & Devalois, K. (1988) Spatial Vision In Oxford Psychology Series Oxford University Press Fourier, J. (1807) Sine and cosine series for an arbitrary function In Joseph Fourier MIT Press Gabor, D. (1948) A new microscopic principle Nature, 161, pp. 777-778 Hameroff, S. & Penrose, R. (1995) Orchestrated reduction of quantum coherence in brain microtubules In King, J.& Pribram, K. eds. Is the brain too important to be left to specialists to study? Lawrence Erlbaum Hebb, D. (1949) The Organisation of Behaviour Wiley Hiley, B. (1996) Mind and Matter In Pribram, K. & King, J. Eds. Learning as Self Organisation Lawrence Relbaum Hiley, B. (2001) Towards a dynamics of moments In Bowden, K. Ed. Correlations, 23, pp.104-134 Lashley, K. (1942) The problem of cerebral organisation in vision In Biological Symposia, pp. 327-349 Moyal, J. (1949) Quantum mechanics as statitical theory Proceedings of the Cambridge Philosophical Society, 45, 99-123 Pribram, K. (1959) On the neurology of thinking Behavioural Science, 4, 265-287 Pribram, K. (1971) Languages of the Brain Prentice-Hall Pribram, K. (1982) Brain mechanisms In Clynes, M. Ed. Music, Mind and Brain, pp. 21-35 Plenum Press Pribram, K. (1991) Brain and Perception Lawrence Erlbaum Pribram, K. & Bradley, H. (1998) The Brain, the Me and the I In Ferrari, M. & Sternberg, J. Eds. Self-Awareness, pp. 273-307 The Guildford Press Pribram, K. (2004) Consciousness reassessed Journal of Mind and Matter Shannon, C. & Weaver, W. (1949) The mathematical theory of communications The University of Illinois Press Smolin, Lee (2004) Atoms of space and time Scientific American, vol. 290 Stapp, H. (1972/97) The Copenhagen Interpretation American Journal of Physics, 40 (8), 1098-1116 Vitiello, G. (2001) My Double Unveiled John Benjamins Wigner, E. (1967) Symmetries and reflections Indiana University Press Wigner, E. (1972) Time-energy uncertainty relation In Salam, A. & Woolf, P. Eds. Aspects of Quantum Theory Mind, Matter & Active Information: The Relevance of David Bohm’s Interpretation of Quantum Theory to Cognitive Science Paavo Pylkkänen Reports of the Dept. of Philosophy, University of Helsinki In this paper, Pylkkänen’s manages to clarify Bohm’s sometimes nebulous description of active information and its role in both quantum theory and Bohm’s own mind-matter theory. The mind-matter theory advanced by Bohm in 1990 proposed that information at the mental level reached, via a series of levels, the quantum particles of the brain, and could from there influence the movement of the body. Working in the opposite direction, perception is conceived to begin at the quantum level, and work its way upwards. Neither Bohm nor the author suggest detailed mechanisms for how this process would be accomplished in the brain. This is in marked contrast to some other quantum consciousness theories, such as Orch OR, QBD or the work of Gustav Bernroider. If Bohm’s scheme were substantiated, it would mean that existing modern physics allowed mental states to be causally efficacious. This is the reverse of much modern thinking in consciousness studies, where the notion that consciousness cannot be causally efficacious is validated by an appeal to physics. Active information The author’s analysis concentrates on Bohm’s 1990 paper, ‘A new theory of the relation of mind and matter’, published in Philosophical Psychology. In his approach to quantum theory in this paper, Bohm regards an electron as an inseparable union of a particle and a field, as distinct from the more conventional view that it is either a wave or a particle, but never both at the same time. The field, in Bohm’s view, may be regarded as containing active information similar in function to the information found at the macroscopic level. This idea is suggested to unite mind and matter, and to break away from any concept of dualism. Active information is viewed as organising the movement of quantum particles, and Bohm sees this organisation as analogous to the way in which he thinks that consciousness guides the body. Bohm advanced the idea of quantum wholeness or the participation of one thing in another, to replace the idea of either reducing mind to matter or visa versa. At the same time, he rejected the idea of consciousness as an epiphenomenon or by-product that could have no causal effect. A key notion for Bohm was the concept of the implicate order, originally developed when he was trying to understand the relationship between quantum theory and relativity. Quantum theory and relativity as presently understood are not compatible. The implicate order was suggested to be a more fundamental level from which they both arose, and the existence of which would resolve the conflict between them. in the implicate order the whole universe is enfolded in everything and everything is enfolded in the whole universe. This is Bohm’s version of quantum wholeness. Our own experience comprises an explicate or unfolded order, which arises from the implicate order, and which is also seen in classical physics. Reality Bohm, in common with some other physicists, stresses that reality is comprised of processes rather than things. Matter is not a permanent thing because, unlike energy, it can be created and destroyed. Quantum particles can be destroyed in collisions with anti-particles, with their energy being converted into light quanta. Matter is merely bound energy and can be returned to energy. The universe should be viewed not as a collection of things but as a series of interacting processes. Bohm’s concept of the implicate order is an attempt to express this idea of interlocking processes. The explicate order of the world as we experience it emerges or unfolds from this interlocking process. The implicate order is also seen as the basis for understanding the mind and the relationship between mind and matter. Both mind and matter are conceived as processes rather than things, so the conventional mind-matter problem, with matter as a thing, but mind not, is dissolved. However, Bohm admits that all this is vague and lacking even a suggested mechanism, as to how either mind or matter arise from the implicate order, or how they relate to one another. However, he suggests that understanding quantum theory will go a long way towards understanding the implicate order. It is stressed that given that the scientific world view is physicalist, the widespread disagreements over the interpretation of quantum theory, a theory that is fundamental to our understanding of the physical world, means that in fact there is a lack of any clear world view in the core scientific community. Bohm, in collaboration with Basil Hiley, emphasised a number of problems in quantum theory, notably, the wave particle duality of the quanta and the need to assume something like a wave function collapse, when a measurement is made, or an interaction with the environment occurs, the problem of non-local influences on quantum properties and the lack of a clear picture of the underlying reality of energy and matter. For most of the 20th century the Copenhagen interpretation, deriving from Neils Bohr, was the quantum orthodoxy. Bohr’s proposal was that the quanta were only mathematical abstractions allowing a prediction of the possible results of experiments. Nothing could be said about the individual quanta. Bohm, however, questioned this view. He proposed that the quanta had a well defined existence, but were accompanied by a quantum field, quantum wave or quantum potential. Given this assumption, it might be possible to dispose of the problems arising in quantum theory. The orthodox view is that the quantum wave is a probability wave, indicating the probability of a particle being found in a particular position, but for Bohm the wave had a real existence, although it still satisfies Schrödinger’s equation. Non-locality In particular, Bohm tried to resolve the non-locality problem, in which quantum theory shows that measurement or decoherence of one quantum particle can instantaneously effect the quantum properties of a distant particle, that is out of range of a signal travelling at the speed of light. Bohm suggested that the concept of active information would allow us to understand non-locality, with the form of the quantum wave shaping the state of the particle. The quantum potential may be seen as a common pool of information or possibly as a configuration of spacetime. The state of a many-body quantum system involves the whole system and cannot be reduced to its individual parts. Superconductivity Bohm suggested that the activity of the common pool might be apparent in superconductivity. With superconductivity, the wave states of electrons are locked in phase, and are able to move together without encountering resistance. He viewed this ability as a non-local property that might derive from the existence of active information, instructing the particles to move in phase, much as music instructs ballet dancers to move in phase. Such active information is also viewed as a possible bridge between mind and matter. Active information can be viewed as the underlying reality, both physical and mental, from which both mind and matter emerge. Mind is viewed as a function of a primary, fundamental or given level of the universe. In this scheme, it is no longer a problem for mind to influence matter. Pylkkänen criticises the active information concept as inadequate in some respects, in that it does not distinguish between the conscious mind and presumably non-conscious processes such as the non-local relationships between quanta. In defence of what is obviously a very speculative theory, Bohm says that the whole point of science is to begin with some assumptions, and see if you can explain a wide range of phenomena from a few assumptions. This statement is an important confirmation of how the scientific process can be initiated, in contrast to some of the criticisms of quantum consciousness theories. Thus commentators such as Patricia Churchland have seemed to suggest theories such as those of Penrose and Hameroff are ridiculous because they make as yet unsubstantiated hypothesises. But such hypothesis are essential to the development of science. Consciousness in Bohm’s Ontology Paavo Pylkkännen University of Skövde, Sweden Bohm’s views on both quantum theory and consciousness changed over the course of his life, making it difficult to specify his exact views. Bohm proposed that a quantum particle was accompanied by a field or quantum potential that Bohm proposed as the central feature of his version of quantum theory. This is sometimes referred to as a ‘hidden variable’ or ‘pilot wave’ theory. In contrast to Neils Bohr and his Copenhagen interpretation, Bohm thought that the quantum level was real rather than a mathematical abstraction. For Bohm classical physics, with its separate objects and processes, was real but not fundamental. Bohr is seen as belonging to a Kantian tradition, in which the mind constructs the world, and nothing is actually known about the external world. He is close to the positivists in this respect. Scientific realists such as Bohm are opposed to the Kantian view. Bohm denied criticisms that he was trying to put back the determinism in physics, which had been removed by the advent of quantum theory. He argued that determinism and indeterminism were two sides of the processes of nature. Determinism and indeterminism were seen complimentary to one another, and as applicable to separate and limited domains. In his 1957 book, ‘Causality and Chance in Modern Physics’ Bohm took the view that the universe was infinite in a qualitative as well as a quantitative sense, which view is deemed to leave room for the existence of consciousness in the physical world. Bohm’s version of quantum theory became more relevant to consciousness, when a later reformulation of his ideas led to the proposal that the wave aspect of a quanta was what he called ‘active information’ that could shape the state of a particle. He suggested that this active information was a manifestation of the implicate order which was suggested to underlie both classical and quantum physics, and to resolve their incompatibility. The logical reasoning of the human mind is here equated to the classical level of physics, and like the classical level it is seen as not the whole or even the most fundamental part of the mind. Are our spaces made of words? Jonathan Edwards University College London Journal of Consciousness Studies, 15, No. 1, 2008, pp. 63-83 The author’s concept of consciousness appears to be closely aligned to the ideas of David Bohm. Edwards proposes that the elements of the universe are best viewed as dynamic processes that transfer and in some cases experience ‘pure’ or ‘active information, when they interact with one another. He accepts the conventional view that what we experience is a model produced by our brain, rather than the external world as it actually is. He refers to evidence (1. Smythies, 2003) that our spatial experience is based on models or maps that are based on selected aspects of the external world. In contrast to a lot of mainstream consciousness studies, Edwards takes the view that there is something in the brain that has access to already-interpreted information, such as the mapping of external events, memory and emotional responses. In fact, in his own words, he is bringing the homunculus back into the mind, in defiance of the rulings of Dennett. Edwards concept of the homunculus is something receiving inputs, not from the external world, but from internal maps and information. The brain is seen as having maps in many areas, and he takes the view that there is probably no single place in the brain where everything comes together. Edwards sees the interaction of fundamental as the type of event that produces active information. As an example of this, radio waves being diffracted by buildings are seen as an indivisible process distributed in spacetime. Nothing pushes or pulls. The process just happens according to the fundamental law. It is a pattern of probabilities that something will occur, and as such represents pure information, or what Bohm and Hiley called active information. Edwards goes from the idea of pure or active information to the suggestion that human subjectivity is itself a fundamental process. He looks for something in the brain that could be regarded as such a fundamental process. Modern physics suggests the oscillation of quanta as a fundamental process. He sees the best candidates for this as being an elastic phonons in the dendritic trees of neurons with a wave length close to the distance between synapses, and coupled to the electrical potential across the cell membrane. A recent study of neuronal membrane excitation (2. Heimburg & Jackson, 2005) suggests that this is dependent on coupling to an elastic wave for the propagation of the action potential. The author suggests that anaesthetics decouple the elastic wave and in doing this remove consciousness. In this model, consciousness in the form of the elastic wave, is seen as crucial to neuronal function. Edwards admits that while this may serve as a theory of consciousness, it still does not actually solve the binding problem. We may be conscious of a circle, and we may be conscious of blue, but how do these two qualia become integrated into a blue circle? Edwards suggests that this integration may be similar to the integration of a series of words into an overall meaning. Unfortunately, this process is also not properly understood. One suggestion is that there is a pattern of electrical perturbations in the dendrites that is a code for producing an integrated experience. It is suggested that this would involve phonons in the neuronal dendrites. In summary, the active information in the brain forms the basis of the appearance of the world to us in our subjective experience. The exchange of active information in the brain is determined by fundamental processes, which can be observed to be governed by the laws of physics. The fundamental process may handle bits of the active information in an analogous manner to the way that words are handled in a language. References:- 1.) Smythies, J. (2003) - Space, time & consciousness - Journal of Consciousness Studies, 10, (3), pp. 47-56 2.) Heimburg, T. & Jackson, A. (2005) - On soliton propagation in biomembranes and nerves - Proceedings of National Academy of Science USA, 102, pp. 9790-5 |
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