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Unifying Mysticism and Mathematics to Realize Love, Peace, Wholeness, and the Truth Prologue, Chapters 1–3, and Epilogue Unifying Mysticism and Mathematics To Realize Love, Peace, Wholeness, and the Truth Paul Hague Unifying Mysticism and Mathematics To Realize Love, Peace, Wholeness, and the Truth Paul Hague Paragonian Publications Svenshögen, Sweden Published by: Paragonian Publications Hällungevägen 60 SE-444 97 Svenshögen Sweden Web: mysticalpragmatics.net, paulhague.net Email: paul at mysticalpragmatics.net The most up-to-date, searchable version of this book will be available at: http://mysticalpragmatics.net/documents/unifying_mysticism_mathematics.pdf In the Mystical Society and Age of Light, there will be no copyright on books because everything created in the relativistic world of form is a gift of God. There is thus no separate entity in the Universe who can be said to have written this, or, indeed, any other book. However, this understanding is not yet accepted by society at large. So we feel obliged to copyright this book in the conventional manner. © 2019 Paul Hague First edition, 2019 ISBN: 978-91-975176-9-0, 91-975176-9-0 Typeset in Adobe Caslon 12/15 The image on the front cover is a symbol of Indra’s Net of Jewels or Pearls in Huayan Buddhism, visualized as a dewy spider’s web in which every dewdrop contains the reflection of the light emanating from all the other dewdrops, like nodes in a mathematical graph. Contents Having shown how the business modelling methods used by information systems architects have evolved into Integral Relational Logic, this edition of my final book uses this commonsensical science of thought and consciousness to map the entire number system, from Zero to Transfinity. As these correspond to Shūnyāta ‘Emptiness’ and Satchitānanda ‘Bliss of Absolute Truth and Consciousness’, this third chapter of Unifying Mysticism and Mathematics marks the culmination of my life’s work to heal the cultural psychic split between science and spirituality. Even though this book now feels complete, as it is, I plan to spend the first few months of 2019 writing the two remaining chapters I have sketched out. The first on ‘Sequences and Series’ will describe many beautiful formations that emerge naturally when we view mathematics as a generative science of patterns and relationships, often seen in the natural world around us. The fifth chapter, on ‘Universal Algebra’, goes beyond the number system, describing some of the mathematical abstractions that have now evolved into Integral Relational Logic: the Cosmic Context, Gnostic Foundation, and coordinating framework for all knowledge, which I call Panosophy or the Unified Relationships Theory, better known as the elusive Theory of Everything. This January-2019 edition also includes a 14-page Epilogue on how I currently view the great existential crisis that humanity faces at the moment and how we could perhaps resolve it, realizing that the Divine Essence we all share is Love. Prologue ...................................................................................................................... vii 1. Business Modelling .................................................................................................... 1 Managing data as a corporate resource ................................................................................................... 4 The meaning of meaning ........................................................................................................................ 8 Awakening Self-reflective Intelligence ................................................................................................. 11 Function of information systems architect ............................................................................................ 14 Modelling our rapidly changing world .................................................................................................. 20 2. Integral Relational Logic .......................................................................................... 34 Starting afresh at the very beginning .................................................................................................... 36 Building meaningful relationships ........................................................................................................ 47 Unifying opposites ................................................................................................................................ 63 Transcending the categories ................................................................................................................. 72 The Unified Relationships Theory ....................................................................................................... 78 3. From Zero to Transfinity ......................................................................................... 87 Growth of number types ....................................................................................................................... 87 Growth of numerical operators ........................................................................................................... 123 The infinitesimal calculus ................................................................................................................... 133 Infinity of infinities ............................................................................................................................. 166 4. Sequences and Series .............................................................................................. 175 Finite series ......................................................................................................................................... 175 Infinite series ...................................................................................................................................... 179 Spatial dimensions .............................................................................................................................. 184 5. Universal Algebra .................................................................................................. 185 Abstract algebra of groups, rings, and fields ....................................................................................... 185 Linear algebra and vector space .......................................................................................................... 202 Boolean algebra to quantum computation .......................................................................................... 202 Epilogue .................................................................................................................... 203 References ................................................................................................................. 217 For humanity Prologue his book marks the glorious culmination of my lifelong quest to realize Love, Peace, Wholeness, and the Truth, which I set out to bring to light as a seven-year-old in 1949. For having been born T near London in the middle of the Second World War, I could see that we humans would never be able to live in love, peace, and harmony with each other unless we could end the long-running war between science and religion, arising from a deep wound in the cultural and collective psyche. Healing this wound in my own personal psyche has meant making radical changes to the concepts of God and the Universe, which I introjected into consciousness in childhood from the culture into which I was born. For just as I was beginning to think for myself, I could see that it did not make sense to say that God—as the Supreme Being—should reside somewhere in outer space, as indicated by the first words of the Lord’s Prayer in the Anglican Book of Common Prayer, established in 1662, as the result of the English Reformation: “Our Father, which art in heaven, …” The concepts of God and Universe provide the overall context for religion and science, respectively, yet they are incompatible with each other. And as we need a context to form concepts—as mental images of the world we live in—without an overall context for all our learning, we have no way of determining what is true or false. As a consequence, I learned almost nothing during my formal education. It was only after the age of thirty-eight that I began to make sense of my experiences and the world that I live in, as an autodidact. As I have discovered through seventy years of questioning the fundamental assumptions of Western civilization and forty years of profound self-inquiry, the discordant concepts of God and the Universe can only be reconciled by plunging into the Nondual, mystical foundations of mathematics, recognizing Consciousness as Ultimate Reality and that none of us is ever separate from any other being, including the Supreme Being, for an instant. I have come to this realization as the result of a life-changing death and rebirth process I went through in the spring of 1980. When working in an innovative marketing job for IBM in London, having some influence in Europe, I realized that the global economy is inherently unstable and that my children were not being educated to live in the world that would exist when they came to be bringing up children of their own, as my daughter, at least, is doing. What triggered me to abandon my family and business career in search of Wholeness and the Truth was an apocalyptic awakening that I experienced at 11:30 on Sunday 27th April 1980, as I was strolling across Wimbledon Common to the pub for lunch. Puzzling about what is causing technologists
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