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Finitary Spacetime Sheaves of Quantum Causal Sets: Curving Quantum Causality, paper submitted to the International Journal of Theoretical Physics
, 2000
"... A locally finite, causal and quantal substitute for a locally Minkowskian principal fiber bundle P of modules of Cartan differential forms Ω over a bounded region X of a curved C ∞smooth differential manifold spacetime M with structure group G that of orthochronous Lorentz transformations L +: = SO ..."
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Cited by 19 (15 self)
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A locally finite, causal and quantal substitute for a locally Minkowskian principal fiber bundle P of modules of Cartan differential forms Ω over a bounded region X of a curved C ∞smooth differential manifold spacetime M with structure group G that of orthochronous Lorentz transformations L +: = SO(1,3) ↑, is presented. P is the structure on which classical Lorentzian gravity, regarded as a YangMills type of gauge theory of a sl(2, C)valued connection 1form A, is usually formulated. The mathematical structure employed to model this replacement of P is a principal finitary spacetime sheaf Pn of quantum causal sets Ωn with structure group Gn, which is a finitary version of the group G of local symmetries of General Relativity, and a finitary Lie algebra gnvalued connection 1form An on it, which is a section of its subsheaf Ω 1 n. An is physically interpreted as the dynamical field of a locally finite quantum causality, while its associated curvature Fn, as some sort of ‘finitary Lorentzian quantum gravity.
Computer Learning and the Scientific Method: A Proposed Solution to the Information Theoretical Problem of Meaning
, 1965
"... This discussion outlines and implements the theory of an inductive inference technique that automatically discovers classes among large numbers of input patterns, generates operational definitions of class membership with explicit levels of confidence, creates a continuously updated "selforganized" ..."
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Cited by 9 (3 self)
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This discussion outlines and implements the theory of an inductive inference technique that automatically discovers classes among large numbers of input patterns, generates operational definitions of class membership with explicit levels of confidence, creates a continuously updated "selforganized" coded hierarchical taxonomic classification of patterns, and recognizes to which already discovered class or classes, if any, a new input belongs in an informationtheoretically efficient way. Relationships to the "scientific method" and learning are discussed.
Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Cited by 8 (7 self)
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
Symbols and dynamics in the brain
 BIOSYSTEMS SPECIAL ISSUE ON “PHYSICS AND EVOLUTION OF SYMBOLS AND CODES”
, 2001
"... The work of physicist and theoretical biologist Howard Pattee has focused on the roles that symbols and dynamics play in biological systems. Symbols, as discrete functional switchingstates, are seen at the heart of all biological systems in form of genetic codes, and at the core of all neural syste ..."
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Cited by 7 (2 self)
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The work of physicist and theoretical biologist Howard Pattee has focused on the roles that symbols and dynamics play in biological systems. Symbols, as discrete functional switchingstates, are seen at the heart of all biological systems in form of genetic codes, and at the core of all neural systems in the form of informational mechanisms that switch behavior. They also appear in one form or another in all epistemic systems, from informational processes embedded in primitive organisms to individual human beings to public scientific models. Over its course, Pattee’s work has explored 1) the physical basis of informational functions (dynamical vs. rulebased descriptions, switching mechanisms, memory, symbols), 2) the functional organization of the observer (measurement, computation), 3) the means by which information can be embedded in biological organisms for purposes of selfconstruction and representation (as codes, modeling relations, memory, symbols), and 4) the processes by which new structures and functions can emerge over time. We discuss how these concepts can be applied to a highlevel understanding of the brain. Biological organisms constantly
Are Rindler Quanta Real? Inequivalent Particle Concepts in Quantum Field Theory
, 2000
"... Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the “reality” of particles posed by the possibility of inequivalent quantizations of a classical field th ..."
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Cited by 7 (3 self)
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Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the “reality” of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a particle is, and how a “particle ” will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the very same region of spacetime.
Conventions in Relativity Theory and Quantum Mechanics
, 2002
"... ons. They lie at the very foundations of our world conceptions. Conventions serve as a sort of "scaffolding" from which we construct our scientific worldview. Yet, they are so simple and almost selfevident that they are hardly mentioned and go unreflected. To the author, this unreflectedness and ..."
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Cited by 1 (1 self)
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ons. They lie at the very foundations of our world conceptions. Conventions serve as a sort of "scaffolding" from which we construct our scientific worldview. Yet, they are so simple and almost selfevident that they are hardly mentioned and go unreflected. To the author, this unreflectedness and unawareness of conventionality appears to be the biggest problem related to conventions, especially if they are mistakenly considered as physical "facts" which are empirically testable. This confusion between assumption and observational, operational fact seems to be one of the biggest impediments for progressive research programs, in particular if they suggest postulates which are based on conventions different from the existing ones. In what follows we shall mainly review and discuss conventions in the two dominating theories of the 20th century: quantum mechanics and relativity theory. 2. CONVENTIONALITY OF THE CONSTANCY OF THE CHARACTERISTIC SPEED Sup
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"... Earlier work on modular arithmetic of k − ary representations of length L of the natural numbers in quantum mechanics is extended here to k − ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators ..."
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Earlier work on modular arithmetic of k − ary representations of length L of the natural numbers in quantum mechanics is extended here to k − ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators using creation and annihilation operators for bosons and fermions are defined. Emphasis is on definitions and properties of operators corresponding to the basic operations whose properties are given by the axioms for each type of number. The importance of the requirement of efficient implementability for physical models of the axioms is emphasized. Based on this, successor operations for each value of j corresponding to +k j−1 are defined. It follows from the efficient implementability of these successors, which is the case for all computers, that implementation of the addition and multiplication operators, which are defined in terms of polynomially many iterations of the successors, should be efficient. This is not the case for definitions based on just the successor for j = 1. This is the only successor defined in the usual axioms of arithmetic.