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Non-locality in Nature and Cognition

F. David Peat

A text only version of this essay is available to download.

Abstract

An exploration of the meaning of non-locality is made in physics and thought. It is suggested that non-local correlations may play an essential role within the nature.

Introduction

The prime mover of the Copenhagen Interpretation of Quantum Theory, Neils Bohr, took pains to stress the essential wholeness of quantum phenomena. As a direct result of the indivisibility of the quantum of action, each experiment or observation of the quantum domain must be taken as an unanalyzable whole. Bohr's interpretation of the quantum theory had the effect of introducing a radically new idea into science, for up to that time it had been natural to define material bodies in terms of their properties and, in particular, their locations in space. Their behavior was then described in terms of the various forces operating between them which caused them to move or change their states. But now Bohr was denying the validity of this whole approach for, at the quantum mechanical level, he argued, bodies in interaction form a single, indissoluble whole.

More recently this quantum holism has been underscored by the various experimental tests of Bell's Theorem.1 In essence they indicate that two quantum particles--initially in interaction but now well separated in space must be represented by a single inseparable state. This notion of this inherent inseparability has led a number of authors to argue that a basic non-locality is essential to a quantum theoretical description of nature.

Is this non-locality something that can be added to conventional quantum mechanics or is a radically different approach required? Is it possible to develop a description of non-separability within a purely local theory, or does non-locality represent a complementary form of description to that of locality? Could it be that the concept of space is far richer than physics has hitherto supposed, so that it contains a whole series of properties? And would this imply that physics should move to some deeper theory in which both locality and non-locality emerge as limiting forms?

This essay is an attempt to explore, in very general terms, such a complementary description and to ask what may be meant by non-locality, not only in quantum physics, but very generally in other forms of thought and activity. Its aim is to open up the discussion of non-locality, to allow for other complementary views of space, time and causality, and to call for a formal development of new concepts. For, it is suggested, non-locality may indeed play a significant role in mind and nature.

Locality

For well over two hundred years locality has been fundamental to our way of looking at the physical world. Indeed it is so deeply ingrained in scientific thinking that a non-local form of interaction appears, in Einstein's words, as "spooky".2

A local description gives central position to the concepts of location and separation in space. Bodies are defined in terms of their spatial position and the trajectories they make. In turn, this description is founded upon the idea of a continuous manifold--a coordinate grid created out of dimensionless space (or space-time) points. Moreover, this manifold is supposed to exist prior to bodies and fields. Indeed it has an important ontological significance for, since the time of Clifford and Einstein there have been theoretical attempts to build fields and matter out of its geometry. A continuous space-time therefore becomes the ground out of which the entire physical world is to be built.

To reject locality would therefore be to throw away the full potential of this underlying manifold. In addition, physicists would be forced to abandon a whole range of rich and powerful mathematics. This latter action would, in itself, involve a major revolution in science. But the idea of locality goes even deeper for it pervades the whole of physics in an almost subliminal way. Indeed even the attempt to discuss non-locality runs into difficulties with the very language we speak. Terms like space, distance, location and separation have all become colored by several hundred years of thinking about space in a particular way. There does not even exist a word to describe the concept we are now exploring--except in terms of the negation of "locality". Locality has become so deeply ingrained in the thinking of physicists that it now seems impossible to abandon it. Nevertheless, in the next section I will argue that non-locality is in many ways a more natural way of looking at the world and is certainly not alien to our deepest thinking.

Despite the authority inherent in the locality of space-time, evidence is accumulating that it is an inappropriate way to describe quantum theory. Neils Bohr has called for a holistic approach to quantum phenomena, while Pauli and others felt that conventional concepts of space and time are inadequate for a quantum description. Current discussions of Bell's Theorem suggest that we may be forced to entertain complementary non-local descriptions-- although it may also be possible to develop purely local theories which forbid separability of certain quantum states.

To this must be added the notion of global quantum states. The wave function for a superconductor, and other condensed states, is defined over macrosopic dimensions. This suggests that a more natural description may involve what could be called a global rather than a local mathematics.

Elsewhere I have argued3 that quantum theory is characterized by the importance given to the overall form of the wave function, and this form is essentially a property of the whole system. An example of this would be the Pauli Exclusion Principle that demands an overall symmetry for a wave function that extends over all space. It is this global form, or symmetry, that plays a role in deriving Bell's correlations, for it dictates that the wave function cannot be spit into a simple product of independent terms associated with different locations in space. A global form, I have argued, is a general requirement of which the Bell theorem is only one example.

While Schrodinger's wave mechanics and quantum field theory are formulated using local mathematics based on an underlying continuous manifold of space-time points, there are powerful arguments suggesting that such a manifold can not have an actual physical existence. The energy content of small regions approaching the Planck length is so high as to break down space-time structure into regions of extremely high curvature or even into a space-time "foam". Clearly the notion of dimensionless points is incompatible with quantum theory. Does the answer lie in some modification of our current approach, such as replacing space-time points by extended objects like strings-- or is some more radical departure needed?

Non-locality

Bohm and Hiley4 have pointed out that physicists feel such a degree of revulsion towards non-locality that "they would prefer not to consider the idea even as a possibility". However, I would argue that, despite this prejudice, the idea of non-locality is perfectly natural and pervades much of our thinking. While it is certainly true that in the past locality and causality have been enormously useful in physics this does necessarily rule out any other approach, or even the possibility that space may be described in a number of different, complementary ways. The human mind is perfectly capable of accommodating different and even paradoxical viewpoints together.

Inseparability, an oceanic sense, a feeling of oneness with all nature and a direct communion with others are given high value in all cultures. Poets and mystics have attempted to explore in words and image their feeling of immediate contact with all things. Such a sense of connection appears to lie outside the confines of space and time and resonates deeply with our experience of the world. Indeed, I would argue that the cluster of concepts surrounding non-locality have much to do with the operation of the mind and brain. We can begin to see this by considering how the world is dealt with in art and literature.

Much of the world's art is concerned with a non-local representation of space. Early paintings were able to integrate may different viewpoints or "perspectives" of the same event. In a painting of the life of a saint, for example, this enfoldement or overlaying took place not only in space but also in time, for events occurring at different periods are presented together. Even during the Renaissance, paintings of the crucifixion combine together what could be called "divine" and "secular" space. A painting is more concerned with relationship than with absolute location. Its integrating force comes more from color, movement, thrust, gesture and shape rather than from position within some background "scientific" space. Pictorial space, in this view is particularly rich, it varies in its properties from place to place so that the viewer becomes a participator within the scene rather than an external observer.5

Such paintings treat space in a more profoundly different yet entirely natural way than is suggested by a "realistic painting" in which, generally speaking, space is portrayed from single viewpoint. This latter view had its origin in the development of perspective during the early Renaissance. The end result in hands of a painter like David, working in the late eighteenth century, is a sort of snapshot or "tableau" in which motion and change is frozen in a single instant of time and presented from the unique perspective of the artist, the objective viewer of the scene. In this way a purely local view of space had been born. Space becomes the supreme arbiter, the ground out of which relationship and structure is born. Yet it is a space defined from only one viewpoint which dominates the painting. It is not difficult to see the origin of this new objectivity in the rise of the individual, for it also heralds the appearance of the concerto, the novel and the diarist. Moreover it is persuasive to trace a development from perspective, through the perspective grid used by painters such as Durer to the coordinate grid of Descartes and our modern theory of local space.

In our own century painting has returned to the non-local order. Mainly as a result of Cezanne, space became richer, with many different perspectives and viewpoints being overlaid together. In Cezanne a sinvle fixed space does not dominate the painting. Rather each form has its own order and the whole is integrated together in a strikingly truthful way. Space emerges out of much deeper considerations and is the expression of the whole painting. Painting has escaped the seduction of a particular narrow world view and returned to its earlier and more natural way of experiencing the world--an experience that is essentially complementary.

Research on visual perception confirms this view for it suggests that our knowledge of the world is built out of complementary movements. What we see is the result of a complicated collection of processes involving eye movements and the relevation of different aspects of a scene--edges, colors, moving planes,etc.-- which are then processed independently in different parts of the visual cortex. The building of space, through neurological processing is complementary. All this suggests that space is never experienced as prior, or in any way divorced from events and occurrences. The notion of space as being the ground or backdrop out of which geometrical relationships and the world is built is alien to the very way we experience the world. Rather the notion of space is something that emerges out of a deeper and more complex experience and is essentially inseparable from other aspects of this experience.

Not only visual perception but also thought itself has a similar complex, overlaid quality which demands complementary viewpoints, including what could be loosely termed "non-local". It is true that certain aspects of thought have a relatively "causal" or "mechanical" order. An example of this would be the experience of a "train of thought" in which one thought appears to follow immediately on the other, the whole being triggered by some word or memory. Yet in their other aspects our experiences of the world enfold and overlap, they blossom and unfold out of each other rather than following in any linear causal fashion. A thought may seem to grow out of the center of another thought and to embrace other, more distant thoughts and feelings.

A musical phrase is not apprehended as a sequence of notes but as a whole melody--indeed if it is played too slowly its shape becomes meaningless. Likewise an entire poem or a piece of music may appear to its creator all of a piece: it is a single, undivided whole and only later unfolded in a linear fashion. Clearly such experiences call for a global description. Moreover at the physiological level it appears that physical memory itself is not localized within any one region of the brain (although memories may be processed within the hippocampus) but involves some sort of non-local distribution.

Memory itself can be triggered by a word, a fleeting taste or smell which evokes a whole world of experience. This whole aspect of memory has been thoroughly researched and discussed by the writer Marcel Proust. Moreover Proust has described the experience of space. He evokes a sense of many different locations being overlaid and interpenetrating one another.

While it would be possible to go into thought, experience and perception at much greater length these few brief examples do suggest that our experience of space, events and processes cannot be described by any single viewpoint, rather some form of complementarity is demanded which would include some sort of non-locality as one of its aspects.

Communication

Communication, I would suggest, is a paradigm case which cries out for a non-local description. The image of distinct, localized bodies in interaction pervades not only communications theory but systems theory, linguistics, psychology, physics and discussions of the mind-body question. This common view is essentially dualistic with the bodies, or systems, being treated as distinct from the interaction, signal or message that passes between them. In physics material bodies are passive and are acted on by an interaction. In communications theory a message passes, like cargo on a train, between transmitter and receiver where it is decoded.

In essence this whole approach to communication sustains the mechanistic view of the world with its causality, separability, locality and the absolute distinction between matter and information. Yet this entire view is totally at odds with our experience. Separability is only a limiting case of something more general -- a whole dynamic movement of meaning between two participants.

The prevalent notion of communication is also at odds with the spirit of quantum theory for the indivisibility of the quantum of action means that there can be no separation, no analysis, between transmitter and receiver since the entire system must be treated as an inseparable whole. This essential inseparability has been confirmed by the many experimental tests of Bell's Theorem and, more recently, by the development of what has been called a quantum communication device, in which a receiver and transmitter are linked by a weak beam of coherent light. Any attempt to interfere or modify this quantum communication results in an uncontrollable disruption of the whole system.

Communication or interaction at the quantum level operates as an unified whole, but this wholeness is not confined to quantum phenomena is also an essential characteristic of human communication. In any dialogue between two people the meaning cannot be associated exclusively with either participant, neither does it reside in the worlds that flow between them. Rather this meaning arises out of the whole activity of the discussion--indeed it goes further for the meaning unfolds out of the context in which the discussion takes place and out of the whole social structure in which language is used. In this sense meaning could be said to be "non-local", or rather to depend upon an extended context that cannot be localized within either participant. While a local analysis in terms of "transmitter", "receiver" and "code" may be of some limited use it cannot capture the whole essence of the dialogue.

Ford and I6 have drawn attention to this analogy between human communication and the quantum wholeness of observer and observed. The recent linguistic theory of "mental spaces"7, for example, stresses the essentially creative nature of communication. The listener is not a passive object acted on by the message, or a simple decoder of syntax and semantics. Listening and talking are creative acts in which whole mental spaces are built in a highly active way. A single word or phrase can trigger the creative construction of some new "mental space" so that meaning is constantly flowing backward and forward between the two speakers. The meaning of the word is, like a quantum, indivisible and belongs neither to speaker or listener but to the whole creative act of communication.

Not only should communication demand an new holistic treatment but it also denies the absolute distinction between message and object. Meaning unfolds within thought, the meaning of a word resonates throughout the body giving rise to thoughts, emotions, feelings, physiological changes, fresh arrangements of the muscles, changes in heart beat and breathing and the disposition to further verbal action. Meaning, therefore, is neither exclusively mental, nor physical, but both. The word is an abstract concept--a sign-- but is also soundwaves, thought and physical activity within the body, it is inseparably all of these things. I would also suggest that this image of the wholeness of communication and the inseparability of the signifier and the signified can be applied metaphorically to the natural world. Communication becomes physical interaction between material objects, and the movement of meaning though society or the human body.

Mathematical Forms

In the previous sections we have argued that non-locality and inseparability are generally more characteristic of the way we experience the world than locality and what could be termed linear causality. In the section following this one we shall speculate that non-locality plays a pervasive role in the physical universe. But before doing so we shall enquire as to what sort of mathematical descriptions of this non-locality exist.

David Bohm and his co-workers8 have demonstrated how it is possible to develop a quantum physics of non-separability using an underlying local mathematics. Bohm's curious quantum potential is determined by the wave function for the whole system, ideally by the wave function for the entire universe. It acts on a quantum particle in such a way that its effect is not determined by the size of the potential but rather by its form. But this means that distant objects can still exert a strong effect on the particle--in essence the motion of the particle is determined by the whole experimental situation including the orientations of quite distant objects.

In this sense the behavior of each part of the system is determined by the whole. Bohm's quantum potential implies that quantum states are basically inseparable and it allows for the non-local correlations of Bell's Theorem, and the sort of quantum wholeness stressed by Bohr. Nevertheless the potential itself, and indeed the wave function, is described locally using the familiar mathematics of differential equations and a continuous manifold. This suggests that the physical manifestation of wholeness and inseparability can be produced out of a purely local substratum.

Similar images arise in non-local systems. A vortex is an expression of the non-linearity of a fast flowing river. It has the appearance of an isolated object for it is located in a well defined region of space, persists for a given time and may even appear to interact with other objects in the river. Nevertheless the vortex has, in a deeper sense, a non-local origin for it arises out of the movement of the whole river. The vortex is a particular example of the more general case of solitons which act as if they were ordinary material bodies and even may appear to interact with each other yet which have a common origin in some underlying non-local ground. At one level the soliton, the vortex and, indeed, two communicating systems have a local, causal description--at another they become one with the ground that gives birth to them.

While the quantum potential and the soliton can be discussed using purely local mathematics, on the other hand David Bohm has provided a powerful non-local metaphor for such systems that he calls the Implicate (or enfolded) Order.9 What we take for reality, Bohm argues, are surface phenomena, explicate forms that have temporarily unfolded out of an underlying implicate order. Within this deeper order forms are enfolded within each other so systems which may be well separated in the Explicate Order are contained within each other in the Implicate Order. Within the Implicate Order one form can be both interior and exterior to another.

In a superficial sense the Implicate and Explicate Orders could be seen as dual forms related by an integral transform. Yet Bohm gives the Implicate Order a much deeper status and suggests that it is the ground out of which reality emerges. Indeed there may be a whole hierarchy of implicate orders, each more subtle than the other. The Implicate Order therefore provides a powerful image of a general sort of non-locality which may apply not only to a discussion of the material world but also to the activity of mind. However this approach still remains to be developed mathematically.

The duality between local and non-local forms is to some extent displayed in projective geometry where an extended object, like a line may be dual to a point, or a line dual to a plane. Roger Penrose has developed a particularly powerful treatment of non-local forms in his Twistor Theory.10 In this case space is built not out of points but from extended objects called twistors. A space-time point now becomes a complex object, generated by the congruence of twistors. But, as Penrose points out, this is exactly the experience of space given to us by elementary particle physics for tiny regions of space are probed by elementary particles shooting in from different directions. Indeed the smaller the region to be explored, the higher the energy that must be used and the larger the elementary particle accelerators employed. In this sense small regions of space-time have a complementary, global aspect.

In Penrose's twistor description the properties of space are particularly rich and may be contrasted with the usual approach to geometry in which space-time points are featureless and primitive. Penrose's twistor mathematics is a powerful starting point for the non-local discussion of fields and gravity. Penrose also holds out the hope that the quantum measurement problem, i.e. the so-called "collapse of the wave function", the curious double slit experiment and Bell's correlations may be discussed in a basically non-local way.

Speculations

By seriously considering the ideas of non-locality, not only in the quantum theory but in a much wider context, it may be possible to develop a conception of nature that integrates more deeply with our own perception, thought and experience. Moreover, it may lead to a much deeper understanding of nature. Non-locality is not simply a matter of substituting, for the continuous manifold of space, some new mathematical formalism. It is intimately connected with the whole notion of causality, force and interaction, and with the definition of material bodies. Indeed to contemplate non-locality is to entertain a radically different conception of the universe.

We have noted, for example, how existing treatments of communication are intimately tied to notions of separability and causality. Yet to consider the alternative viewpoint, in which the meaning of a dialogue emerges out of the whole context, and which takes account of the basic wholeness of the activity, may be remarkably fruitful. Indeed it may help in understanding the relationship between mind and body, mind and matter, for the communicator and the communicated would no longer be considered as distinct.

One approach would be to explore the possibility of non-locality in physics, beginning at the quantum level. In the previous section we met Penrose's twistors. It was the original aim of that research project to derive space-time as a limit or approximation to the underlying global twistor space. A local space-time may turn out to be simply a limit that appears at a certain scale of distance. Or, as Penrose believes, manifestations of non-locality are present at all scales. We could speculate, for example, that what we term "space" has a rich complementary structure so that, just as "wave" or "particle" are manifestations within different experimental contexts so that locality or non-locality may also be context dependent. Indeed space itself may not be a single concept but involve a richly enfolded structure.

In his general theory of relativity Einstein gave the image of local co-ordinate patches which join up to generate a curved space-time. By contrast, the image of non-locality calls for something closer to an overlaying of transparencies as is the case with a color photograph to be printed in a book. Each region of space would then be generated by a superposition of non-local forms. But it could also be the case that space-time is even richer than this, involving both the overlaying of non-local regions and the overlapping of local co-ordinate patches. In this respect the structure of space would evoke the structures used by the brain for its visual information processing, these involve both specific localized regions within the visual cortex together with a delocalization of visual information.

Of course it may not necessarily be the case that space and time together form an inseparable space-time. Neither may time itself be represented by a single dimension--a line that is perpendicular to those of space. Moreover it may not be possible to derive space-time (or space and time) as an independently existing substratum but rather its complex properties may appear in conjunction with those of material process. In another paper11 I have suggested that certain structures emerge spontaneously out of quantum systems. These structures would include both material systems and space-time and would appear at a certain limit of complexity. The universe in that view has an essential non-unitary, or creative, nature so that new forms are constantly being thrown out. An opposing tendency is, by virtue of their overall form, for old structures to persist as a sort of "habit", or inheritance from earlier forms. In other words, new forms appear spontaneously and are then sustained so that unitary mappings appear as special cases of more general non-unitary operations. One aspect of this process would be the appearance of the familiar space-time structure together with the symmetries associated with the elementary particles and forces. However this particular approach assumes the general ideas of quantum theory, which is itself tied up with pre-existing notions of space and time, so clearly something more radical is required.

Essentially the goal is to derive the properties of space-time out of some deeper theory. It is often suggested that, in doing so, the properties of space-time would be modified in some way to allow for a successful integration of quantum theory and general relativity. But must quantum theory necessarily be the starting point for such a program? The meaning of the quantum theory is in many respects unclear and its formulation, in terms of a local space-time, incompatible with this program. Clearly some more radical approach is needed. But what would be the features of such an approach? One could speculate that at least the ideas of wholeness and the overall importance of the "form" of a description would be carried over from quantum theory.

And is it possible to attempt a radically different treatment of space, or space-time, without, at the same time, including a new description of matter and fields. Indeed is it possible to separate space-time from process? And what, indeed would be the status of physical law? Is law external to and imposed upon material process to give it direction and form? Or does physical law exist prior to space and time, or is it also something which evolves and exists only within a prescribed context? In fact there are no end of speculations and theoretical starting points possible. What seems to be required at this time are new and deeper philosophical ideas. These ideas may then act as the impetus for a new approach in physics, one in which locality, quantum theory and general relativity would have validity only within certain contexts.

Finally one could point to the need to make a thorough experimental investigation of non-locality and non-separability. Some experiments have already been carried out on the non-classical correlations predicted by Bell's Theorem. But these have yet to distinguish between non-separability brought about by something like Bohm's quantum potential and a true non-locality which transcends any local space-time description. T. D. Lee has also pointed out the need to probe space-time properties in quantum theory.12 His suggestion is to carry out "vacuum engineering", that is, rather than always focussing on small spatial regions experiments should be devised which explore coherent phenomena and the distribution of energy over large spatial volumes. In the following sections the possibility of non-local correlations being manifested in sensitive and chaotic systems and in neutral nets is also discussed.

The whole subject of non-locality in physics could be compared, by way of illustration, with that of non-linearity. For two hundred years physics was able to explain a wide range of phenomena using only linear theories and by explaining nonlinear effects in terms of a linearized perturbation theory. But the success of this program lay not so much in the power of linearization but rather in that physicists simply did not give much attention to non-linear phenomena and tended to focus on the considerably simpler linear systems. Today, however, with the help of modern mathematical techniques and computer modeling, it has become possible to treat a variety of non-linear systems. For example, solitons and other non-linear effects abound in solid state physics where, a decade or so ago, almost the entire field was described in terms of linear approximations.

Today linearity is viewed as a special case of non-linearity that holds only under certain limiting conditions. While, in the past, physicists saw linear systems all around them, today they deal in non-linearity. It may also be possible that locality and certain forms of causality will one day be seen as limiting cases of a more general non-local holism, for our current paradigms of physics may be blinding us to different ways of seeing.

Yet locality has served physics well, which implies that our hypothetical underlying non-local effects must be extremely subtle. So where should we look for them? Supposing that true non-locality is present quite generally in the universe: how would it manifest itself? I suggest that the most promising place to look is in these extraordinarily sensitive non-linear systems that are termed "chaotic". Systems which suffer constant iteration and in which every tiny region is contingent upon all others are known to behave in extremely complicated ways. Their dynamics are characterized by fractal behavior--in which endless levels of detail are found at finer and finer scales. But "chaos" may be a poor term to describe such systems for it is not so much that they are "random", "anarchic", or "orderless" as that they have an extremely complex and subtle order.

These systems are so extraordinarily sensitive that the smallest perturbation has an uncontrollable and unpredictable effect upon their dynamics. These are the ideal systems in which to study non-local effects for their behavior could well be controlled by the global correlation of vanishingly small effects. Attempting to control such systems locally proves useless: on the other hand global, or non-local description and control may be entirely appropriate. The global co-ordination of boundary conditions, for example, could act to guide, in a very general way, the overall form of the system.

Information which is distributed globally as boundary conditions or very delicate non-local perturbations would be hidden within the apparent chaos of a sensitive system. Attention to individual regions of space would not be sufficient to display this non-local influence. What is required is some new, global description of these systems.

A simple image will illustrate this point. Local disturbances propagate through a system and are normally assumed to dissipate themselves, becoming lost in the random fluctuations of the medium. But in a world in which events are correlated non-locally what may appear to be a vanishingly small random fluctuation may in fact be the manifestation of a global order. Extremely small perturbations, when correlated non-locally could, for example, have the effect of initiating an inwardly moving wave of disturbance which then interferes co-operatively and gives rise to a large local disturbance. This is the reversal of what is normally assumed, in which an effect spreads out and is dissipated. I am therefore suggesting that local events in such systems can have a non-local origin. More generally I propose that sensitive dynamical systems may be guided by non-local effects and are best understood using a non-local description. The possibility of non-local control in chaotic and sensitive systems is far-reaching.

There are a wide variety of systems in nature that have the characteristics of "chaos", or rather of complex, non-local order. In such systems rather than causes producing effects of a similar magnitude it may be more a matter of very tiny, but globally coordinated causes having a wide range of global effects. The size of the cause is no longer related to the magnitude of the effect, what is important is the overall form of that cause. Moreover what appear as "random fluctuations" may be highly significant aspects of global behavior. Life forms a particularly important subset of these globally complex systems. It may be valuable to consider its processes from a non-local perspective. Life "rides the wave" and lives on a delicate knife edge between order and chaos. Some form of non-local correlation of dynamics is, I would suggest, characteristic of living systems.

Other aspects of non-locality could be the appearance of similar structures or dynamical patterns at widely differing scales of space, time and energy throughout the universe. In the case of a non-local description it may be possible for direct connections to exist between the large and the small scale . Moreover the existence of very delicate, but globally correlated effects, could have a major influence over the form of a system. It is certainly true that many patterns recur throughout the animate and inanimate world. In some cases they are clearly due to a balance of certain natural local forces, in others, however, they may be the manifestation of gentle non-local promptings. Indeed it may be possible that even the large scale structure of the universe, with all its puzzles (such as the so-called Great Wall), could be partially influenced by weak non-local forces.

One of the most complex and sensitive systems in nature is the human brain and again I would suggest that a significant part of its activity takes place in a non-local fashion. In the brain activity appears to sweep in from all over the cortex, focus in a particular area then move out again. Electrical activity, which is admittedly only a part of the brain's total function, appears to involve a constant transformation between the local and the global. Again it would be interesting to consider the possibility that the brain is both generating and responding to certain non-local signals which give form to its otherwise locally determined electrical activity

A particular example would be memory which does not appear to have any fixed location within the brain: rather a name, a particular texture, taste or smell will evoke a whole complex of sensations--memories of places, conversations, faces, smells, tastes, sounds and so on. Suppose that memories are encoded non-locally so that a particular recollection is not totally determined by the sensitivity of groups of synapses but arises through a non-local correlation of the activity of whole sections of the cortex. A particular memory will be enfolded with many others and its particular presentation in consciousness would be the result both of the overall form of the particular memory-trigger and the creativity of the human mind. In this way a memory would not be an isolated fact but a whole spectrum of sensations, feelings and encoded events that are enfolded together. (The holonomic theory of memory (of Pribram and others13) involves information that is distributed by analogy to a hologram. But here something more radically non-local is being proposed.)

Memory storage. of course, need not consist solely of the electrochemical sensitivities associated with synapses but may also take the form of subtle, non-local coordination of neurochemical reactions and even of muscular-skeletal dispositions and, indeed, the activity of the whole body. In turn, memories flow into thought and action, the whole spectrum moving out into the wider context of society and communication.

Research and theoretical modeling that is based upon locality, and on the absolute separation between meaning and material process in the brain, is clearly not going to reveal this more subtle level of the non-local activity of matter/meaning. The suggestion being made in this essay is that it may be useful to entertain at least the possibility of discussing and investigating the brain in different ways. One immediate practical approach would be to consider the theoretical implications of non-locality in neural-net processing. Computer simulations of such neural nets, and actual nets themselves, have become quite fashionable at the moment. In one sense a neural net could be said to be global in its approach to information processing. Yet its foundation is local, with activity being determined by the state of each node.

Suppose however that the sensitivity of nodes is correlated in a non-local fashion, would this, for example, enable the net to operate in what could be called a non-algorithmic fashion? What advantages would such non-local correlations have for an information-processing device? Clearly this would represent a theoretical step to what could be termed a quantum-computer in which the state of the computer is determined by the whole system. In such a hypothetical computer distant parts may be correlated and it may not be possible to split up its activity into separable parts, for the overall form of the computer's wave function would determine its activity. (Of course under certain conditions a sort of limited separability would be possible as is the case with molecules which can, to a certain degree of approximation, be treated as independent. However, this very separability and relative independence is a function of the form of the overall system.) Of course a quantum computer is not a brain. Nevertheless a theoretical investigation of the implications of non-locality may suggest new ways of investigating and thinking about the brain.

What is being proposed in this essay is that the mind, the brain and the universe can be looked upon in a radically different light. The notion of non-locality brings with it a new attitude to separability, to material bodies and force, and to the distinction between information and material process. In essence what I am suggesting is that a more subtle level operates within the universe.14 The existence of this level has been hinted at by recent quantum mechanical experiments and, more directly, by our own experience. There are a number of inroads into its investigation, a discussion of non-locality being only one of them. In summary therefore, the essay proposes that non-locality operates throughout the universe and not simply at the quantum level. Non-locality could be considered as a complementary description to that of locality, as part of a general nexus of new ideas, or as the starting point of a radically new approach to science.

References

1. Recent discussions of Bell's Theorem and its experimental verification include: Kafatos, Menas (ed.) (1989) Bell's Theorem, Quantum Theory and Conceptions of the Universe, Kulwer Academic Publishers, Dortrecht and Cushing, James. T and McMullin, Ernan (eds.) (1989) Philosophical Consequences of Quantum Theory, University of Notre Dame Press, Indiana.
2. Born, M (ed) (1971) The Born-Einstein Letters, Macmillan Publishers, London.
3. Peat, F. David (1989) 'Bell's Theorem: Form and Information in Quantum Theory' in Kafatos, Menas (1989) Bell's Theorem, Quantum Theory and Conceptions of the Universe, Kulwer Academic Publishers, Dortrecht; and 'Non-locality: Bell's Theorem, Condensed States and the Form of the Wave Function' (1990) (unpublished)
4. Bohm, D and Hiley, B.J. (1989) 'Non-Locality and Locality in the Stocastic Interpretation of Quantum Mechanics', Physics Reports, 172 (3), 93-122.
5. Peat, F. David ( October 1989) 'I've Got a Map in My Head', Paper given at the Smithsonian Museum conference on Patterns in the Universe. To be published in a conference proceedings edited by Kafatos, Menas. See also Bohm, David and Peat, F. David (1987) Science, Order and Creativity, Bantam Books, New York.
6. Ford, Alan, J and Peat, F. David (1988) 'The Role of Language in Science', Foundations of Physics, 18, 1233-1242.
7. Fauconnier, G, (1985), Mental Spaces: Aspects of meaning construction in natural language, M.I.T. Press, Cambridge.
8. Bohm, David, Hiley, B.J. and Kaloyerou, P.N. (1987) 'An Ontological Basis for the Quantum Theory' (Parts I. and II.) Physics Reports, 6, 323-374.
9. Bohm, David (1980) Wholeness and the Implicate Order, Routledge and Kegan Paul, London.
10. Penrose, R. and Rindler, W. (1987) Spinors and Space Time (volume 2), Cambridge University Press, Cambridge.
11. Peat, F. David, (1988) 'Time, Structure and Objectivity in Quantum Theory', Foundations of Physics, 18, 1213-1231.
12. Lee, T. D. Particle Physics and Introduction to Field Theory, pp 824-828, Harwood Academic Publishers, Chur.
13. Pribram, K.H., Nuwer, M. and Baron, R. (1974) 'The holographic hypothesis of memory structure in brain function and perception' in Atkinson, R.C., Krantz, D.H., Luce, R.C. and Suppes, P. (eds.), Contemporary Developments in Mathematical Phychology, W. H. Freeman, San Francisco.
14. See also Peat, F. David (1989) 'Gentle Action for a Harmonious World', Edges: New Planetary Patterns (Toronto), 2 (3), 8-46.

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