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From the empty set to God

Conscious experience has an intrinsic nature. The experience of the color blue has an irreducible reality that cannot be analyzed into constituent parts. In the technical language of philosophy it is a `quale'. (The plural of quale is qualia.) It feels like something to experience blue.

What is the connection between the structure of physical reality and the intrinsic nature in immediate experience. There is no way to answer this question from science or mathematics. Through those disciplines we can understand a great deal about the structure of conscious experience. For example we know a great deal about optical illusions from studying the structure of the eye and the neural network that connects the eye to the brain. But this provides no clues as to why the experience of a blue sky is as it is.

One approach to such questions is to look for the simplest assumption consistent with what we experience. This is the approach used for fundamental laws of physics like Einstein's Special Theory of Relativity. The fundamental equations of this theory are known as the Lorentz Transformation because they were invented by Hendrik Lorentz not Albert Einstein. Einstein showed how these equations could be derived from very simple assumptions that had wider implications. The most famous of these is the equation $E=mc^2$.

The simplest assumption about conscious experience leads to a very old intuitive idea. Immediate experience in some form is universal in all that exists. This assumes there is nothing special about the matter in our brain that seems to embody conscious experience. In thinking about this many years ago I went further in the search for simplicity. I assumed that structured conscious experience is all that exists. There is no need for ``physical stuff'' of which external reality is constructed and ``soul stuff'' that embodies our consciousness. Everything is soul stuff.

The essence and totality of the existence of physical structure is immediate awareness in some form. Qualia are universal in all that exists. Simpler brains have simpler experiences. This can be extrapolated all the way down to inanimate matter. Immediate awareness in some form is all that exists. Once one can explain the structure of conscious experience, including the experience of the external world, there is nothing remaining that requires explanation. The physical world is the transformation of conscious experience and nothing but the transformation of conscious experience.

This assumption, which is part of the Totality Axiom of Section 4.1, came to me in an advanced philosophy course. My focus at the time was on mathematics and especially physics. If all that exists is the abstract structure of mathematics made real as immediate awareness, then physics at its core must be discrete and not continuous. For consciousness is finite. We seem to experience continuity in vision but that is an illusion created by the brain. Our eye detects light as discrete pixels just as a video camera does. It is only subsequent processing in the brain that groups these pixels and creates the illusion of continuous structures like lines.

This philosophical speculation and the observations that complex computers and all of mathematics are built up from simple discrete structures had a powerful impact on me. I became preoccupied with the idea that discrete models might be the solution to some of the paradoxical aspects of quantum mechanics. I entered graduate school in computer science because I felt the background research needed could qualify as computer science long before, and whether or not, it led to new physics. A thesis adviser agreed to sponsor me on this line of research, but I was not making enough progress and had to find a different topic.

I eventually completed a conventional thesis in computer science, but the pull of these other ideas was overwhelming. Since I was not able to make progress on creating new physics I started focusing on the mathematical implications of these ideas. If there were no infinite structures what was the immense and important body of mathematics based on these structures about?

Mathematics defines an extraordinary rich hierarchy of objects or structures. These are characterized by the mathematical language needed to define them. Some of these have obvious interpretations in a discrete universe of the sort I was considering. For example we have already discussed functions that can be defined by a precise set of mechanical instructions or a Universal Turing Machine. These are called recursive functions. Such functions can be though of as properties of the particular computer program that can generate the function.

I came to see how most sequences of integers, that can be defined mathematically, can be treated as properties of computer programs. To understand this one most know that one can assign a unique integer to every possible computer program. This is called Gödel numbering and it is explained in Section 5.8. One example of a set that is not recursive is the set of Gödel numbers of computers that halt. (Today computer programs do not literally halt the computer, but they did so in the early days of computing. Today programs return control to an operating system like Linux or Windows.)

If a computer program halts it does so in some finite time. To say that it never halts is a statement about an infinite sequence of events. But those events can all be generated by a computer. They are the sequence of instructions the program executes. Thus they have meaning in a universe they may exist forever but is finite in each moment of its existence. Such a universe is said to be potentially infinite.

Statements about infinite sequences of events enumerated by a computer are absolutely true or false. They are completely determined by the program or rules for generating the events. Yet there is no general way to determine if such a statement is true or false. This was proved by Kurt Gödel with his Incompleteness Theorem (see Section 5.8) in the 1930's.

One can generalize the question of whether a computer halts by asking if a computer will have an infinite number of outputs if it runs forever. By generalizing and iterating this property it was possible to treat most mathematically definable infinite sequences of integers as properties of computer programs that were meaningful in a finite but potentially infinite universe. I suspect that it is only mathematics that can be interpreted in this way that has an absolute meaning. There are mathematical questions like the Continuum Hypothesis discussed in Section 5.7 that cannot be interpreted in this way. Those questions are a little like the parallel postulate. They are not true or false in any absolute sense. Instead they may be true, false or undecidable in a particular formal mathematical system.

As far as I know this is a unique approach to mathematical truth. My insight about a computer program having an infinite number of outputs as a way to define many nonrecursive sets was not new. It had been anticipated in the $U$ quantifier discussed in Section 6.1. I found this approach to mathematics compelling. It suggested that mathematics was in a sense an experimental science that dealt with properties that were not determined by a particular event but were determined by an infinite sequence of events that you can program a computer to generate.

These ideas totally engrossed me, but seem to have little interest for others. There seemed to be no place for me and the energy that moved me. Carl Jung's Psychological Types[32] helped me to gain some perspective on myself. In the language of Jungian theory I am an introverted thinking type. But my most powerful function is my intuition. It was my intuition that was always pushing me off on tangents or making connections that others did not see or did not think were important. These insights helped me make sense out of my chaotic life.

Jung's emphasis on the creative nature of psychic development was especially appealing to me. It connected with my mathematical understanding and my life experience. For me, the creative nature of the universe has always been its most astounding and appealing feature.

I was raised a Catholic but rejected that and every other conventional religion as a college sophomore. But the rituals of the Catholic Church instilled a profound sense of the spiritual that never left me. My idea that consciousness was the essence and totality of all the exists implied a unity between the spiritual and physical. I began to connect ideas from other religious traditions, especially Buddhism, with the sense of spirituality that was emerging from these ideas.

I was born on August 6, 1945, the day the atom bomb was first used to destroy human life. One might say I was born with a sense that our science could get out of hand and destroy us. The immense cruelty that permeated the twentieth century, as I lived through half of it and learned about it all, amplified my concern. I became aware of and concerned about the disparity between the steady growth of science and technology and the chaotic development of spirituality and values. To me the reason for the disparity was clear. The objective guidance of experiments allowed science to make steady progress. This contrasted with philosophy, religion, spirituality and values which remain permeated with prejudice and superstition. Scientists are able to reach agreement about any issues that can be investigated experimentally. Philosophers, theologians and ethicists can reach agreement about almost nothing.

The world faces a long list of potential dangers from human activity. At their core is this disconnect between the steady progress of science and the random walk that characterizes the development of spirituality and values. As the discrepancy between these grow the danger grows. Thus the most important motivation for and biggest ambition of this book is to point the way for starting to repair the split between science and meaning.

The unified view that emerges from this work is that of God as the unbounded evolutions of consciousness. This evolution is a physical process. We can measure it and characterize it mathematically. Its core and essence is experiential. We are the evolution of consciousness that is God. Why this is true is a mystery beyond explanation. But if we try to understand the reality we experience and to give the simplest possible description of what existence is, then this is the vision that emerges. That is the journey that this book is intended to take you on.


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