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Preface

Our technical capabilities are increasing at an enormous and unprecedented rate. In contrast our spirituality and values are developing much more slowly. This has created a perilous time and often empty culture. We need a broadly accepted spirituality that gives purpose and meaning beyond the necessities of daily existence. Our scientific understanding has undermined many conventional approaches to spirituality at the very time we most need to strengthen these capacities.

We need to develop our values and spirituality at a pace comparable to the rapid technical achievements that empower us. For our technical prowess does not produce the wisdom needed to use that power. This book explores a path to accomplish this through a reintegration of our spiritual and scientific understanding.

Historically science could only progress by splitting off from philosophical, spiritual and religious traditions that were burdened with false assumptions about the physical world. Science succeeded by focusing on understanding what was observed and developing techniques to test that understanding. Science seeks the simplest possible models to explain observations and relies increasingly on mathematics as a source of those models. Today the hard sciences such as physics depend entirely on abstract mathematical models.

As science has become more mathematical and abstract it has created an opening to reconnect with values and meaning. For the ultimate content of mathematics is the empty set or nothing at all. Mathematics describes only structure or how complex entities are constructed out of simpler ones. For example the number one is defined as the set containing the empty set. The number two is the set containing zero (the empty set) and one. All mathematical objects are defined in this way using the relationship of set membership. The empty set is the only primitive object not constructed as a set of simpler objects.

This high level of abstraction forces all assumptions about structure to be explicit. There are no inherent properties. There are only properties explicitly constructed with the relationship of set membership. Making all assumptions explicit avoids attributing logical necessity to implicit assumptions such as the parallel postulate in Euclidean Geometry.1But reducing everything to structure makes it clear that something profoundly important is missing from our mathematically based scientific understanding. In fact everything that has intrinsic value is missing.

For these abstractions are explicitly free of meaning and value. This contrast with older metaphysics such as the one based on earth, air, fire and water. These each had an inherent nature and through that nature gave meaning and value to the objects that were constructed from them.

The physical world is permeated with meaning through conscious experience. Making love or dying a painful death have intrinsic value. Every conscious moment of every sentient beings' existence has positive or negative intrinsic value.

Connecting physical structure with conscious experience is the starting point for integrating science and spirituality. In doing so we do not seek an explanation for consciousness. Science ultimately explains nothing. The fundamental laws of science are the simplest known description of a wide range of phenomena. Science makes no claims to explain why those descriptions are correct. The power of science comes from the ability to model and thus to manipulate a wide range of phenomena using relatively simple descriptive laws.

The nature of existence is a deep and profound mystery that cannot be solved. For any explanation depends on assumptions which themselves must be explained in an endless regress. At best on can develop the simplest possible assumptions consistent with what we know to be true as science has done with its assumptions about physical structure.

The simplest possible assumption about consciousness is that all physical structure exists as direct conscious experience. The essence and totality of the existence of physical structure is immediate conscious experience. Any other assumption must distinguish between conscious and unconscious structures in a way that adds unnecessary complexity. An embryo, fetus and then infant develop into a conscious being in a continuous process. An adult conscious mind gradually fades into an amorphous simplicity through Alzheimer's disease.

There is no need to assume the existence of anything but consciousness. Space-time does not exist in space-time. It exists in conscious experience. At first statements like this seem absurd. We have an innate sense of the objective reality of the external physical world. Equating everything to immediate awareness is not denial of objective reality. It puts that reality in a wider context.

Once we recognize the continuity of consciousness from the human mind to the simplest physical structure there is no need to assume anything but structured conscious experience exists. One can raise many questions about and objections to this assumption. We lay the ground work for the assumption in Chapter 1. We develop the assumption and deal with some possible objections in Chapter 2.

This assumption allows us to reconnect the abstract structure of science with meaning. In a sense this connection is trivial. Physical structures that are painful have negative value and those that are joyful have positive value. (We are talking about intrinsic value. Any experience can be positive because of what it leads to or how it helps someone change.)

The connection becomes nontrivial when we focus on the evolution of structure and thus the evolution of consciousness. Using our mathematical understanding of structure we can begin to understand the boundary conditions that are necessary for the creative evolution of a conscious universe. The universe is creative beyond understanding. Reproducing molecules have evolved to human beings with extraordinarily wonderful and terrible conscious experience. Mathematics suggests that we are at an infinitesimal fragment of the creative evolution that is possible.

Historically we have seen ourselves as the center of the universe and the center of creation. Science has repeatedly dethroned us from such positions. We may be at the leading edge of evolution on one small planet but we are not its end point or ultimate achievement. We like the life we have evolved from are a stepping stone to an ever expanding consciousness.

We choose to call this creatively evolving consciousness God. We are the eyes of God with the power to create the world through our ability to understand and change biological evolution and our developing capacity to create artificial intelligence.

Evolution has become conscious of itself and is acquiring an understanding of its own structure. This is a dangerous but inevitable situation. We are encroaching on the power of God. But God is not an other worldly being. She is the creative process of evolving consciousness. We are the highest level of God's consciousness on this planet. We are not so much encroaching on God as we are God becoming conscious of her work and starting to consciously direct that work.

We make a second simplest possible assumption. We assume that all consciousness and thus all physical structure is finite. Each moment of our experience is a finite irreducible gestalt. We exist in a vast and possibly potentially infinite universe of creatively evolving but always finite conscious experience.

Our second assumption restores the earlier mathematical idea that infinity is a limit that can never be reached. In our framework this means each conscious experience has a finite structure. The totality of all conscious experiences may be infinite but there is no single infinite gestalt experience. In the language of mathematics there is no completed infinite totality.

Mathematics is a key to understanding the framework of the creative process. Through Gödel's Incompleteness Theorem (see Section 3.8) we know that the creative evolution of structure can never be captured in finite form. It is an open ended ever expanding process. There is a hierarchy of mathematical truth that characterizes levels of abstraction or self reflection such as the self reflection that is a defining characteristic of human consciousness. Gödel proved that this hierarchy cannot be finitely described[16]. However it can be fully developed by exploring an every increasing number of paths without selecting a best or correct path as biological evolution has done in creating the human mathematical mind.

This is not the view of most mathematicians. Gödel's result was and remains a shock to the mathematical community that sees mathematical truth as the one absolute certainty in a confusing world. Many mathematicians believe intuition about infinite sets borders on the mystical. By asserting the existence of complex infinite sets one can indirectly define levels in the hierarchy of mathematical truth that are difficult to approach in other ways. This suggests to some that mathematical intuition can transcend the limits Gödel's theorem imposes on any single path approach to extending mathematics. In Chapters 3 and 4 we describe the structure of the mathematical hierarchy of self reflecting structures and possible approaches to extending it. We argue that there are more powerful approaches to exploring mathematical truth that have no need to transcend the limits of Gödel's theorem with mystical intuition.

Chapters 3 and 4 develop in an intuitive and semi-formal way the basics of formal set theory. This is done in terms of properties of logically determined sequence of events in a potentially infinite universe. Computer programs serve as an effective model of such processes. Developing mathematics in this way makes it more concrete and intuitive. Section 3.8 contains a sketch of a proof of a limited version Gödel's Incompleteness Theorem called the Halting Problem. Chapter 4 speculates about extending mathematics in light of Gödel's result.

The assumption that everything is finite has implications for physics. In Chapters 5 and 6 we explore the possibility that discrete as opposed to continuous models might be needed to explain physical reality as Einstein came to suspect near the end of his life[21]. Chapter 5 gives a brief overview of the two theories, relativity and quantum mechanics, that a discrete model must account for.

Chapter 6 discusses the problems of combining relativity and quantum mechanics. General relativity and quantum mechanics are incompatible when one attempts to combine them at small distances. This is a powerful suggestion that space and time are grainy or digital and that a radically different class of models is called for when we approach the scale of digital space-time.

The path to a new theory may lie in reconciling quantum randomness, absolute conservation laws and locality. Einstein first called attention to these issues in 1935[15]. This has led through the work of Bell and others to practical experiments that could provide the data essential to developing a more complete and perhaps digital theory. Up to this point the experimental results remain consistent with quantum mechanics although experts agree that there are two loopholes, detection efficiency and timing, that have yet to be simultaneously addressed in a single experiment. We describe many of the relevant experiments and explain why we suspect a conclusive experiment will differ with the predictions of quantum mechanics in Section 6.6.

Think of the evolution of consciousness on our planet from the first molecules that reproduced through single celled creatures and the hierarchy of animal life to human consciousness. Understanding the structure of that process does nothing to touch the profound mystery of human experience. One can only gasp in dumbfounded wonder at the miracle of it. Yet connecting this process with the hierarchies of mathematics suggests that this is the merest hint of a shadow of what will be. The connection between mathematics and creativity is explored in Chapter [*].

Creativity is inherently risky with inevitable disappointment and failure. No matter where we are in the evolutionary process we can never assume we are on the right path. We must always recognize the need to give autonomy to other paths. Infectious disease is a lower form of life that has exercised its autonomy in a way that has created enormous evil. We are conquering this problem. We can repeatedly reach evolutionary levels that allow us to eliminate some lower level sources of evil. However we cannot eliminate the struggle between lower and higher levels without limiting the creative process. Understanding the mathematical structure of evolution can help us understand and deal with evil in a way that does not violate creativity. This is a subject of Chapter [*].

Spiritual instincts connect our individual existence to a wider sense of self. This starts with our family and can expand to include our local community, our country, all of humanity, other species, all of life and ultimately the creative process itself. How we see ourselves is largely a matter of conscious choice. We are of course individuals with an individual destiny. But we are also part of a creative process. Our genes and our instincts are very much a product of and designed to support that creative process. Excessive focus on our individual existence does violence to this deeper sense of self. The development of a deeper sense of self is a subject of Chapter [*].

Our assumptions imply there is no immaterial soul. On the contrary we see all matter as soul stuff. Our consciousness is not connected to some essence that can be divorced from our physical structure. We are the consciousness embodied in our bodies. There is no magic moment when a soul enters our body at the beginning of life nor leaves us in death. There is a continual transformation of consciousness. We are not separate from the physical world around us but a part of the universal flow of consciousness. We are the universe becoming conscious of itself. We are the eyes of God with the power to create the world. Many spiritual traditions intuitively see this. By reintegrating essence to science we can move beyond intuition to understanding. The spiritual implications are explored in Chapter [*].

But understanding is not enough. One must feel a connection with the physical universe. One must feel that one is the universe becoming conscious of itself. Our values come from feeling. Values will determine if we continue the open ended exploration of consciousness that has created us.

Often in spite of ourselves our instincts push us in the right direction. They are doing so blindly and unconsciously and thus can take terrible detours. In contemporary Western culture we value some instincts and devalue others in a way that is very dangerous. But evolution is working with the wisdom of eons. It can afford to take its time. The danger is that our technological prowess is advancing far beyond our wisdom to use it. That is why it is so important to understand the fundamental basis of the creative human instincts. It is one of many essential paths to the wisdom we need to use our rapidly expanding power.

The goals of this book are extraordinarily ambitious. Yet our assumptions are simple and conservative. Some of the ambition stems from the simplicity. The assumptions are less complex then the prevailing paradigms in mathematics and physics.

Our most ambitions goal is the development of an objective spirituality with a base in mathematics and physics and implications for those fields. Philosophical considerations have always guided science. When these were dogmatic views postulated by vested interests they were obstacles to the growth of an objective science. When the philosophy stems in part from our scientific understanding it has the potential to contribute to the scientific enterprise.

Many recognize the need to reintegrate science and spirituality. For some the vague interpretations of quantum mechanics are fertile ground for spirituality. Quantum mechanical models describe the evolution of probabilities but never actualize those probabilities to create events. Metaphysical interpretations are needed to connect the mathematics to experimental observations. Many physicists believe that classical mathematics and logic are inadequate to deal with the quantum domain.

We see no problems with classical logic either in contemporary physics or in integrating spirituality with science. Like Einstein we think the vagueness in existing theory is due to the limitations of the existing theory that will in time be overcome. For us the way to integrate science and spirituality is by pushing science and mathematics to their limit where they self destruct as ultimate paradigms. For that leads to the empty set symbolic of the essence that is absent. The one thing we know with absolute certainty is the essence in our own conscious awareness. A science that does not include this indisputable reality is deficient.

This book is largely about connections between disparate existing ideas. It does not follow a logical deductive path. It starts in many places and leads many places to paint a picture of reality that is consistent with what we know, internally coherent and extraordinary in its implications. Our two fundamental assumptions are a crossroads where these paths meet and diverge. There are many reasons for adopting these assumptions and many implications of them. The journey across this terrain is more intuitive than intellectual but it is an intuition firmly rooted in intellect.

Western academia knows how to develop and foster intellect but not intuition. Those in the creative arts are more aware of what intuition is and how it can be developed. This is ironic since many of the greatest scientists such as the physicists Einstein, Bohr and Feynman were more intuitive geniuses than intellectual ones.

Intuition is a pattern recognition process. It senses when many pieces fit together to form a coherent whole not unlike facial recognition in which many features combine to form the face of someone familiar. Intuition was crucial in creating this book and is crucial in comprehending it. Intuitive talent is becoming increasingly important. Intuition has always led the way in creating the new idea or seeing the new possibility that intellect could develop. As we have mastered the territory that is well defined enough for intellect to deal with more of the major issues we confront fall outside of that domain. Intuition is the subject of Chapter [*].

The unlimited potential for evolution in a potentially infinite universe does not exist on our planet. Its future is limited in time and resources and thus creative potential. If we avoid self destruction on a massive scale we will almost certainly within this millennium begin to travel between the stars. We will do so on unmanned ships equipped with our knowledge and with biological material and machines that are capable of colonizing planets on which life could not develop spontaneously. We will reproduce and evolve not as individuals but as entire worlds. We will probably evolve as a combination of biological and manufactured components. Over time the manufacturing processes and biological processes may merge as the former become more subtle and efficient and the latter are more controlled and directed. The goal is the never ending expansion of conscious experience. We will grow more capable of pleasure, happiness, joy and ecstasy. The goal is the never ending journey of God becoming ever more deeply conscious of herself in her unbounded glory. That is the subject of Chapter [*].


Completed second draft of this book

PDF version of this book
next up previous contents
Next: Structure and essence Up: whatth Previous: List of Tables   Contents


Mountain Math Software
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Email comments to: webmaster@mtnmath.com