CONTENTS -- Preface -- About Pierre -- List of Contributors -- Unital Homogeneous Polynomial Operators on Hilbert Space -- 1. Introduction -- 2. Unital homogeneous polynomial operators on a Hilbert space -- 2.1. Context -- 2.2. Unital homogeneous polynomial operators -- 3. Unital polynomial operators on a Hilbert space -- 4. Composition of homogenous unital operators -- 5. The unital system on a Hilbert space -- 6. Equations involving unital homogeneous polynomial operators -- 6.1. Fredholm equations with unital homogeneous polynomial operators -- 6.2. Characteristic equations with unital homogeneous polynomial operators -- Concluding Remarks -- References -- Brief Biography -- Towards a Generalised Combinatorial Hierarchy -- Introduction -- Motivation -- The Classical Hierarchy -- Generalising to Groups -- Generalising to Categories -- Combining the Automorphisms -- Conclusions -- Dedication -- Acknowledgements -- References -- Brief Biography -- Quantum Cosmology and Special Mersenne Primes -- Introduction -- Preliminaries -- Elementary Leptons and Quarks as 3-Quc Composites -- Electromagnetism-Gravity Unification and Huge-Prime Inflation Specification -- The Macroscopic Spacetime Scale of Life and Consciousness -- Conclusion -- Acknowledgment -- References -- BiEntropy - the Measurement and Algebras of Order and Disorder in Finite Binary Strings -- 1. Introduction -- 2. Historical Background -- 3. Tacit Understanding of Binary Order and Disorder -- 4. Shannon Entropy and Binary Derivatives -- 4.1. Shannon Entropy -- 4.2. Binary Derivatives and Periodicity -- 5. BiEntropy -- 6. BiEntropy of the 2, 4, and 8-bit Strings -- 6.1. The 2-Bit Strings -- 6.2. The 4-Bit Strings -- 6.3. The 8-Bit Strings -- 7. Empirical Testing of BiEntropy -- 7.1. The Prime Numbers -- 7.2. Human Vision -- 7.3. Random Number Generation -- 7.4. Cryptography.

8. Algebras of BiEntropy -- 8.1. Bit-String Algebra -- 8.2. Concatenation -- 8.3. Negation -- 8.4. Addition -- 8.5. Multiplication -- 8.6. Summary and Future Development of the Algebras -- 9. Summary -- Acknowledgements -- References -- Brief Biography -- Constraints Theory Brief -- 1. Purpose -- 2. The Archetype -- 3. The Identities -- 4. Quantization:- The Rules -- 5. Quantization Of The Identities -- 6. When The First Constraint Holds -- 7. When The First Two Constraints Hold -- 8. Hamilton's Equations and the Space C -- 9. The Riemannian Space C' -- 10. Electromagnetism -- 11. Curvature of C, the GTE and the KE -- 12. Newtonian Gravity, GR and Constraints Theory -- 13. The KE -- Acknowledgements -- References -- An Elegance First Approach to Looking for the Universe in Finite Geometry -- Mathematical Structures -- Sensory experience and Mathematical Structure -- Graphics feedback -- First Story - Sets -- Structure - Finite Well formed Sets, Lists, Alphabets, Words and Vectors -- The space of all mappings from one structure to another -- Cataloging all algebraic structures on a very short alphabet -- From sets via bitstrings to vector spaces over F2 -- Second Story - Vector spaces over F2 -- From vectors to finite fields -- Classifying finite fields by characteristic modulo 4 -- Our Numbers -- My conjecture -- The number of directions, Professor DeVogelaere, and Trig functions -- Generators -- Our Polynomials -- The Tree of Catalan-Mersenne Trinomials -- Awe -- Third Story - The tree of even fields modulo Catalan-Mersenne trinomials -- Double fields -- Fourth Story - The Tree of Double Fields of the Catalan-Mersenne trinomials -- Fifth Story - Tree with projective lines over odd fields of the Catalan-Mersenne trinomials, with traditional names for operators.

Sixth Story - With matrices of cartesian products of projective lines over the odd fields of the trinomials, with standard names for operators -- Seventh Story - With matrices of projective lines over F1272 and FL2 -- Calculating views in finite spaces -- Finite Vector Spaces and Projective Spaces -- Distance, wavelength, energy and photons -- Over extensions of Fp -- If the universe does not involve any infinite sets -- A Challenge -- Cosmic implications of many diverse explorers viewing a variety of geometries -- We never know who else found it -- Aknowlegements -- My Quest -- About me -- Favorite Sources -- Boolean Geometry and Non-boolean Change -- 0. Introduction -- 1. Illogic, Pre-logic and Logic -- 2. Boolean Logic -- 2.1. Boolean algebras -- 2.2. Boolean logics -- 2.3. Projections -- 2.4. The Boolean lattice -- 2.5. The Boolean graph -- 2.6. Probability -- 2.7. Sublogics, factors and independence -- 3. Boolean Geometry -- 3.1. Boole space -- 3.2. Geometric invariants -- 3.3. Independence -- Brief Biography -- Speculation on Consciousness as Relative Existence -- 1. Constructing systems that are to support consciousness -- 2. `Existence-for-others' and how Dualism arises -- 3. Summary -- References -- A Management View of ANPA (East) 1979 to 2012 -- 1. Introduction -- 2. Executive Summary -- The Formative Years from ANPA 01 to ANPA 09 -- The Growth Years from ANPA 10 to ANPA 18 -- The Philosophical Years from ANPA 19 to ANPA 24 -- The Mature Years from ANPA 25 to ANPA 32 -- 3. The Formation of ANPA -- Preface to Proceedings of ANPA 07 (1985) -- Combinatorial Hierarchy (CH) -- Statement of Purpose -- Organization -- 4. Analysis Using ANPA Proceedings -- Proceedings Covers -- Tables of Content -- Method of Analysis -- Classification -- 5. Some Results from the Analysis Using ANPA Proceedings.

6. Distribution of Papers by the Ten Most Prolific Authors -- Brief Biography -- Critical Stability of Few-body Systems -- 1. Introduction -- 2. Relativistic three-body system with zero-range interaction -- 2.1. Equation -- 2.2. Results -- 3. Two-fermion system with Yukawa interaction -- 3.1. States with J = 0 -- 3.2. Asymptotical behavior of the kernels -- 3.3. The cutoff dependence of the binding energy -- 3.4. States with J = 1 -- 3.5. Numerical results -- 3.6. Positronium -- 4. Conclusions -- References -- Non-Commutative Worlds and Classical Constraints -- 1. Introduction -- 2. Quantum Mechanics - The Square Root of Minus One is a Clock -- 2.1. The Wave Function in Quantum Mechanics and The Square Root of Minus One -- 2.2. Time Series and Discrete Physics -- 2.3. Simplicity and the Heisenberg Commutator -- 3. Review of Non-Commutative Worlds -- 4. Non-commutative Electromagnetism and Gauge Theory -- 4.1. Generalized Feynman Dyson Derivation -- 4.2. Discrete Thoughts -- 5. Constraints - Classical Physics and General Relativity -- 6. On the Algebra of Constraints -- 6.1. Algebra of Constraints -- References -- Brief Biography -- Report on ANPA to the ANPA Advisory Board, 2008 -- 1. Introduction -- 2. The Parker-Rhodes Construction -- 3. The Identification Problem -- 4. Physics and Algebra -- 5. Process Generation of a New CH -- 6. The Fine Structure Constant -- 7. The Construction of Space and Time -- 8. Relation to Non-relativistic Quantum Mechanics -- 9. Relation to High Energy Particle Theory -- 10. Conclusion -- Brief Biography -- Reflections on Fundamentals and Foundations of Physics -- 1. Introduction -- 1.0.1. Relativistic few-particle scattering theory -- 1.0.2. Dark energy and cosmological fluctuations -- 1.0.3. Scientific eschatology -- 2. Fundamentals of Microscopic Physics -- 2.0.4. Combinatorial input to dynamics.

2.1. Fixed particle number relativistic scattering theory -- 2.1.1. Faddeev's formulation of scattering theory -- 2.1.2. The Efimov effect -- 2.2. Inclusion of particle-antiparticle symmetries -- 2.3. Compton scattering -- 2.3.1. Quantum dis-entanglement of classical sources and sinks -- 3. Cosmological Scale and Dark Energy -- 3.1. Motivation -- 3.1.1. Jones' Microcosmology -- 3.1.2. Dyson-Noyes-Jones Anomaly -- 3.2. Coherent Gravitating Matter -- 3.3. Correspondence with the Cosmological Constant -- 3.4. Gravitating massive scalar particle -- 3.5. Subsequent thermal expansion -- 3.6. De-coherence from Dark Energy -- 3.6.1. Dark energy -- 3.6.2. Rate of Expansion during De-Coherence -- 3.6.3. Fluctuations -- 4. Scientific Eschatology -- 4.1. Dyson's "Time without end" -- 4.2. Late Time de Sitter Universes -- 4.2.1. Are societal strategies futile? -- 4.3. Is the "Cosmological Constant" Really Constant? -- 5. Conclusions and Discussion -- References -- Brief Biography -- Ordering Operators -- Preface -- I. Introduction -- II. Conceptual Beginnings -- III. Physical Motivations -- A. Problems with the Computational Apparatus -- B. Conicts Between Ontology and Epistemology -- IV. Ordering Operators -- A. Graph Representation -- B. Properties and Objects -- C. Metrics and Probability -- D. Composition via Tensor Product -- V. Correspondences to Physics -- A. General Considerations -- B. Feynman's Discrete Path Integrals -- C. Interpretation of Tensor Calculus -- VI. Conclusion -- References -- Brief Biography -- Information, Entropy, and the Combinatorial Hierarchy: Calculations -- Introduction -- 1. Information Content and Kind -- 2. Non-Shannon information -- 3. Cosmological Evolution -- 4. The Combinatorial Hierarchy -- References -- Brief Biographies -- Spacetime, Dirac and Bit-Strings -- Introduction.

Prolog: Spacetime, the Unit Imaginary and Discrete Origins.