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Moments of meaning and wholeness have become so rare within our culture that we have had to invented special words to describe them, such as synchronicity or epiphany. The psychologist Abraham Maslow also referred to what he called "peak experiences". Yet, to some peoples, life is always lived at this level and it is to these Indigenous people, with their feeling of a direct relationship to nature, that we turn for our first map.

In the words of Chief Seattle (Seathl) of the Swamish people, "every space, every humming bee, every part of the Earth" is sacred. Writing in the mid nineteenth century, he explained, "We are part of the Earth and the Earth is part of us. The fragrant flowers are our sisters. The reindeer, the horse, the great eagle are our brothers. The rocky heights, the foamy crests of waves in the river, the sap of meadow flowers, the body heat of the pony--and of human beings--all belong to the same family."

To the Native person, everything is alive, and it is possible to talk to animals, trees and even rocks. The idea of Jung's "meaningful connection" or "acausal connecting principle" becomes a lived experience, rather than some theoretical idea. But to many of us, with our rational conception of the nature, the possibility of communicating with inanimate matter would be dismissed as being totally out of the question. Communication, as we see it, must always involve some sort of interaction in which a signal, involving matter or energy, passes from one location to an other. How then could a rock speak? And how could a tree listen?

But suppose that there are other ways of being, ways in which communication becomes communion, a direct and unmediated presence? To the North American forest and woodland dwellers this is called "skanagoah" and is the electrifying awareness of unity and balance felt in nature. When there is no separation to be bridged it becomes possible to talk to the rocks and trees and to hear their inner voices; indeed, it becomes possible to experience the authenticity of all things. In the words of another native elder: "We have to understand the nature. That is why we have to talk to them. We don't pray to them, we talk to them because they breath the same air we do. We are put here with them. We are also a part of the plant life. We are always growing, we have to have strong roots. " (Colorado 1988)

The North American continent must have appeared boundless to the early settlers who arrived from Europe. Yet already, to Chief Seattle, writing in the mid nineteenth century, the implications of the White Man's separation from nature were crystal clear: "To him, one piece of land is much like another...The Earth is not his friend but his enemy, and when he has conquered it, he moves on...His hunger will eat the Earth bare and leave only a desert."

It is my suggestion that despite society's prevailing sense of separation and alienation, it is still possible to capture that earlier sense of wholeness. Indeed if we go back far enough we are all, in a sense, Indigenous people and our childhoods were flooded with a similar intensity. The search for a new physics and a new scientific vision may also help to heal the wounds divided us from nature and reanimate our lives and society.

In undertaking this journey towards a new vision we are going to be guided by maps. In fact we must reject one set of maps, those of Newtonian science, for another which will be called non-unitary physics. But what exactly is a map? It is, in a sense, a true synchronicity for it is a symbol of the connection between physical events in the external world and the inner life of a person or group. To view a map in this way may seem a little strange at first but we have to remember that the road maps we use to find our way in the city represent only one very restricted example taken form the whole world of maps. Maps, to many people, are sacred objects in themselves, indeed in some societies there is an absolute taboo resulting in death against the wrong person looking at certain maps.

There are maps consisting of sticks and small stones that are used by the Micronesians in their canoe journeys between the Pacific islands. There are the marks and paintings of the Hopi which represent their journeys across the length and breath of the Americas, and their arrival on this continent via a series of stepping stones placed across the Pacific waters. There are the Maori great houses or marae whose architecture and very physical arrangements are maps of the cosmos and representations of the human body.

There are Navaho sand paintings which are so sacred that they must be destroyed after use. These latter paintings are synchronicities in that the maps themselves are sources of power. In healing, for example, the sick person journeys into the map itself by carefully walking inside its patterns and thereby regaining harmony with the cosmos.

There are the beautiful maps made by the Australian aborigines that represent the tracks taken by The Ancestors during the period of The Dreaming in which the continent and all its features were laid down. Such maps represent the intersection and celebration of many, many layers of meaning and function. In one sense they are representations of the geography and topography of a certain area and an expression of the relationship of society to the landscape. They are also a cosmology and a history of a whole people and their land. But these maps are also a walk through life for each individual Aborigine who is on a journey from that first quickening within the womb to his or her the moment of death. Every point in the landscape corresponds to part of a dream track on the map, and each region of that map has its own song lines that must be sung and one journeys. Finally, as death approaches, it is important that each person should take a journey in order to arrive at that special region of the landscape made sacred by the Ancestor who was responsible for his or her first breath of life. And so, through the great journeyings with the map, the harmony of the universe, the landscape and the individual is maintained.

Many Native Americans speak of having "a map in the head", of being able to trace their way through the landscape even to the point of recreating the great journeys of their grandfathers and grandmothers. On one level such maps contain the memories and locations of hunting trails and the passage of game. But they are more than this, for the map is a celebration; it is a story; it is a knowledge of the land in all its seasons; the history of the tribe, and knowledge of its sacred places. The map is the wind in the trees and the voice of the rocks. The map in the head comes into being as the child sits around the fire listening to the stories and songs of the elders. It is colored and enriched by ceremonies and journeys. The map expresses the feeling of oneness with plants and animals, it points to the path taken by the tribe, and each person's journey through life.

In the Native map there is no sharp distinction between space and time, or between the sacred and the everyday. If the flesh of the Buffalo or Caribu is good medicine then the act of eating that flesh is to make a direct connection with the creative center of the earth. Everything in the map is, at one and the same time, both sacred and practical. Time and the space within this map are infinitely rich for each region has its own quality and value, and to move through the landscape is to enter into a story and a song. Within such a map there can be no separation, no distancing, no objectivizing of the external, no sense of the other.

The gulf that exists between our Western topographical representations of certain features of the landscape and the maps of the Native American is beautifully illustrated by an incident related in Hugh Brody's "Maps and Dreams'. Government hearings on a proposed pipe line in northern British Columbia were being held and one day the commission visited a Native community. Various official presentations were given, maps were displayed by company engineers and there were even topographical maps on which had been drawn the Native's hunting tracks and trap lines. So far the enquiry had been grounded in Western society's vision of landscape, ownership and of what they took a map to mean. But then, as the meeting was about to close, people arrived carrying a sacred bundle which was carefully unwrapped to display a dream map.

This dream map expressed the whole meaning of that group's relationship to the landscape and to their own past. Indeed it went further, for it was also a map used to guide the dead to the other world. As a true synchronicity, this map united heaven and earth, past and present, human and landscape, the world of dreams and the world of physical events.

According to the account given by Hugh Brody, the deeper significance of this map was lost on the members of the hearing who, after admiring it, began to pack up and leave. But, protested the Native people, having shown you the map it is now necessary that there should be a period of drumming and singing. The hearing members waited politely for one round of drumming and then left in their bus. The Natives continued long into the day. Clearly the worlds represented by these two sorts of map could not be further apart.

The idea of a map, in its much wider sense, will therefore be used both as a metaphor and as an actual device for journeying through the ideas within this book. For just as their are Indigenous maps drawn on sand, bark, stone and skins so too there are maps of science created in the medium of numbers and abstract mathematics. As just as the native map represents a vision of the cosmos, so too, enfolded within the maps of science are the values that our society holds about nature and ourselves.

It is my contention that the maps drawn by science are no longer satisfying to us. They do not bind us together and make us whole. Instead they fragment our experience and reduce the landscape to an object. They are maps of alienation. We must therefore seek to reanimate the maps of science and restore a sense of value and meaning to them.

New Maps for Old

Maps, symbols, mandalas and other symbolic works are used all over the world to express the link between the inner and the outer, between the self and the world, the individual and the environment. Such maps enrich us and bind us together. As we have seen, they are synchronicities, patterns of meaning and connection between the mental, spiritual and material worlds. But in our society one set of maps, the maps of science, have become the most powerful of all devices, overshadowing all other earlier maps and reducing them to the status of myths, legends and "primitive" representations. The maps of science have reached a high degree of abstraction and sophistication, but on the way they lost their sacred quality and their power to bind us to the world. Indeed the maps of Newtonian science fragment the world around us rather than make it whole.

If we are to develop a new physics, a new ethics and a new vision of the universe then it is first necessary to examine the maps of science and discover where they went wrong. Within this chapter we will explore the very powerful ideas of Cartesian coordinates and with their help construct a special sort of map called phase space.

In order to reach this phase space map we will move over a series of stepping stones, earlier maps which trace the path from the sacred to the abstract, from the qualitative to the quantative.

Maps and Perspectives.

Although life in the Middle Ages was far from ideal there was certainly an aspect of wholeness to it and a sense that each person had a special place within society. Meister Eckhardt referred to this as the "good life", an existence in which the quality of one's life came from inner peace rather than from exterior cravings for goods, possessions, money and progress. In that period the secular was not fragmented from the sacred, neither was art divided from craft.

Evidence of this can be seen in many beautifully worked objects, from illuminated manuscripts and carvings in bone and ivory, to great cathedrals and paintings. When we look into these objects we sense the same feeling for unity that is present in Indigenous maps.

A painting from the life of a saint is both the telling of a story and a religious celebration. Time and space are unified in such a painting, for the saint may be portrayed as being at several different points in his or her life and in physically different locations. Yet all these different elements in time and space are woven into a single tapestry.

When color is used, for example, it is not intended to be purely realistic but has a symbolic quality, as have the various shapes and objects in the painting. The painting is rich with shapes and symbols and, for those who know the tradition of its alphabet, it can be read like a book. The painting is an integration of the sacred and the secular. In one corner a small dog is playing and a peasant lies heavily asleep with an empty wine skin at his feet. Yet, nearby, a miracle is taking place, or God is looking down from heaven. Within the painting, each form is authentic in itself and exists in its own space. Everyday objects are executed with as much passion as Christ on the cross. Each object, each part of the scene, has its own truth and the whole is integrated together in a marvelous way.

One senses, in such a painting, how immediate and ever present was the sacred. This is even made manifest in the way space itself is treated within, say, a crucifixion. The scene is simultaneously presented from many different viewpoints. One looks in silence into the face of Christ, jostles with the crowd at the foot of the cross, examines with microscopic clarity a clump of grass, stares down at the vast panorama below, looks up at the Madonna and hovers above the earth in the company of God and His angels. The whole effect is almost cinematographic, for it evokes the sense that many different camera angles that have been edited together. It is like a montage in which close up, establishing shot and medium shot are intercut.

The same thing can also be found within Persian miniatures, where each object exists within its own radiant space and takes on its own authentic form. By enfolding many different orders of space within the one painting, by integrating the bliss of heaven with the immediacy of a blade of grass, these early paintings become the outward expression of the integrated inner live of society.

But this was to undergo a radical and sudden change. With the flowering of the Renaissance this vision of a unified society in which each person had a special place was replaced by the individual as supreme arbiter and measure of all things. Rather than a person being a harmonious image of the cosmos, expressed in the Medieval philosophy of "As above so below", the motto of the new age became "Man is the Measure of All things".

The human individual had become the crown of creation, and individual human reason was the final court of appeal. The sacred was separated from the secular, and art from craft. In turn, the maps of art were transformed to express this new vision. In place of an integrated whole in which many different spaces are enfolded together one has the single, dominant vision of the great artist. It is in this moment, I believe, that we can actually see the shift from the old world to the new. And as the new paintings develop ( these new maps of the world) so does our distancing from nature begin.

This change was made technically possible by the development of perspective the architect and sculptor Filippo Brunelleschi(1377-1446). Perspective is an invention of human reason whereby space is portrayed from a single viewpoint. In a sense, perspective makes a painting more "realistic". But it also imposes two new things; it makes space the dominant theme in a painting, and it distorts the forms and structures of objects in order to fit them into this dominant vision. For perspective is indeed a distortion, it is a falsehood, a denial of the essential indwelling of each object in favour of a single-minded, obsessive vision. Is it not too far fetched perhaps to see the dominance of science over nature as foretold in the dominance of perspective.

By portraying a scene, a crucifixion perhaps, from a single viewpoint everything must now be pressed into service. Because a single, unique vision of space has triumphed, there can be no sacred, no personal, no indwelling space of things; there is simply a mathematical gloss placed over all objects - in more technical terms, the laws of projective geometry. A vase, a landscape, a human face must all be stretched and compressed, distorted to fit the demands of perspective.

Not only has the artist, in a sense, abstracted himself from being within nature, but abstract relationships in space have become the dominant quality. And, with this move, something of the quality of things has vanished. From now on our maps will begin to place their emphasis on what can be compared, measured and quantified rather than what can be experienced and given interior value.

The development of perspective allowed artists to unify a painting not though its symbolic elements, or use of shape and color, but through space itself, by presenting the scene from a single viewpoint. But in doing this it was necessary to distort natural shapes and forms. The image that comes to mind is that of stretching nature on a grid. And so by focussing on spatial relationships and measurements and forcing nature to conform to an abstract plan one begins to loose contact with the more subtle clues and promptings of the natural world.

Grids and Racks.

The idea that natural forms must be stretched on a grid and forced to conform to the single, viewpoint of perspective in fact expresses very well just how perspective drawings were once made.

An by Albrecht Durer (1471-1528) portrays a perspective grid, the device by which an artist could take the most complex scene and cause it to conform to mathematical law of perspective geometry. Perspective is based upon a study of optics and the laws by which the rays of light reflected from a scene enter the pupil of the eye. By drawing upon these laws an artist can, using a grid of strings, project a scene onto a piece of paper and obtain its perspective correctly.

It is ironic that just as art was stretching the forms of nature on the grid of perspective so too Elizabethan philosopher and statesman, Francis Bacon (1561-1626) asked that the natural world be stretched on the grid of science. It was Bacon who first sought to present the ideal methodology of science in his book Novum Organum. Bacon argued that nature should be "bound into service" and placed on the rack and "examined" until she revealed the correct answers to our questions. (The use of the female form for nature was no accident.)

The image of a grid represents another step in our journey from the richly integrated and directly experienced maps of nature towards the more abstract and quantative maps of science. Already we see that Durer's perspective grid presents the vision of the one-eyed man. It is a vision that is passive and objective, in which the eye does not scan the scene, the head is incapable of movement, the artist's body does not walk into the scene and the hand will not touch and explore.

This autistic, monocular vision of the world is nowhere better displayed than in the frontispiece to one of the classics of nineteenth century thought, Ernst Mach's Analysis of Sensations and the Relation of the Physical and the Psychical. (Footnote: Die Analyse der Empfindungen und dan Verhaltnis des Physischen zum Psychischen first appeared in 1886 under a slightly different title and in four subsequent editions underwent important modifications and expansions.) Mach (1838-1916) was both a physicist, philosopher and psychiologist whose writings deeply influenced the young Albert Einstein, and also led to developments in the philosophical movement called positivism. In the opinion of the psychiatrist Thomas Szasz Mach also contributed to the development of Sigmund Freud's throught. While at the University of Prague Mach conducted studies in experimental psychology and proposed that scientific enquiry always begins with physiological "sensations." These sense sensations are, according to Mach, the raw material out of which scientists construct their maps of nature. The best scientific theories, in his opinion, are those that take the shortest logical path between immediate sensation and theoretical conclusions. For a time Mach's proposal became the ideal to which scientific theories aspired. Einstein himself grappled with Mach's notions and, in the end, showed that rather than being the end point in a short logical chain from sensation, a good theory should actually determine and point to the important observables within the world.

At the time Mach's vision of science attracted a considerable following amongst scientists of a philosophical bent. But at the illustration below indicates, this view is singularly passive. The scientist sits in his armchair and surveys the world--or rather the sensations of the world impinge onto his eye. The eye, monocular vision, has become the sole window into the universe, indeed it almost appears as if Mach, the scientist, were hiding behind this eye, an homoncule within the skull looking out from that protected position. Science becomes the ultimate spectator, rather than a participator in the richness of nature.

Cartesian Coordinates

The way perspective tends to objectify and quantify the world leads to one of the most far reaching and productive inventions of all science--the coordinate system. It is thanks to Cartesian coordinates that everything from superstrings and the theory of relativity, to map references and the tracking of satellites has been made possible. Cartesian coordinates were one of the first inventions of modern science and remain at its forefront today for they have successfully survived every scientific revolution.

The philosopher and mathematician Rene Descartes may be best known for his maxim "Cogito ergo sum" (I think therefore I am), his system of philosophy, the famous Cartesian split between mind and body, and the Newtonian-Cartesian system of science. But, in fact, one of his more remarkable inventions was a mathematical system of coordinates whereby any point in space can be rationally represented, and every material object associated with a set of numbers that become its dynamical essence.

A Cartesian coordinate grid looks identical to the perspective grid of Durer's etching. In both cases an arrangement of parallel lines and intersections act to define the position of an object in space. In Descartes' case, however, this grid was abstract and mathematical. Imagine that a grid is laid down upon your kitchen floor. The effect will be somewhat like a system of tiles and it is possible to define the position of, say, a tennis ball by indicating which tile the ball is standing on - five tiles up from a corner and three tiles to the left. By treating the tiles as a coordinate grid and counting along the two walls it is possible to describe its position of the ball in terms of two numbers, called its x and y coordinates.

This Cartesian grid, along with its coordinate system, becomes the new, objective, scientific way of portraying space and the grid is nothing less that the mathematical projection of that grid of strings portrayed by Durer. It was, in fact, Descarte's goal to fully quantify the universe and he took the first step in this direction by first quantifying space. Descartes coordinate grid has since become one of the most powerful inventions in all of science for Cartesian coordinates now become the measure of all things.

Since a point anywhere is space is defined once its three coordinates have been given, Descartes was able to demonstrated a perfect correspondence between real objects in space and mathematical points on an abstract coordinate grid. From this juncture onwards the universe could be quantified and objectified. But while the Map in the Mind for a Native Person, or a medieval painting, is rich and filled with all the qualities of space, time and ritual, the map of science has become abstract and objectified. Everything is number. From now on science becomes trapped and isolated like Durer's artist behind his perspective grid of Ernst Mach's passive all seeing eye.

In the hands of a genius like Newton, Decartes' coordinate system was to become to a dominating force in science and led to the establishment of one of the most versatile maps used in science--phase space. Thanks to this ability to reduce all change to mathematical operations on coordinates in phase space, our modern age became convinced of its ability to exert prediction and control. And, as the map of science gained in its power, the synchronicities and direct correspondences of older maps became diluted.

(End of Extract)

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