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The Integration of Experience, Awareness, and Consciousness into the Relational-Matrix Model I: Experiential Mechanics (by Steven E. Kaufman): Abstract: In Article 2 & 3 of this work, we showed how existence, by forming relationships with itself repetitively and progressively, evolves into a relational structure that functions as the framework of reality. However, what we have described so far as the relational structure of reality, including the differentiation of that relational structure, explains only the fundamental behavior of, and some of the intrinsic relationships within, what we experience and are aware of as physical reality. What we have described so far doesn’t explain why there exists physical experience itself or why there exists an awareness of physical experience. To present a more complete, unified model of reality, it’s necessary to explain not only why physical reality behaves as it does but also, within the context of that same model, explain why we experience physical reality as we do, as well as why we’re aware or conscious of our experience, since experience, awareness, and consciousness are themselves integral parts of our reality. In that same vein, mental and emotional experiences are also integral parts of our reality and so must also be integrated into any model of reality that seeks to account for reality as a whole. The purpose of this article and the next article of this work, then, is to explain within the context of the same unified model of realty that was developed in Articles 2 & 3 of this work, how experience, awareness, and consciousness are all related, and in the process demonstrate that the physical, mental, and emotional experiential realities in which we find ourselves immersed can be understood in terms of a singular or unitary existence existing in relation to itself. Toward that end, we will now begin to explore how evolving existence, by existing in relation to itself at yet another level, becomes aware of physical, mental, and emotional experiences. http://jcer.com/index.php/jcj/article/view/139

The Integration of Experience, Awareness, & Consciousness into the Relational-Matrix Model II: Consciousness and the Awareness of Experience (Steven E. Kaufman): Abstract: We have demonstrated how seemingly separate experiential realities can come to exist within the context of an ultimately indivisible, singular existence, but not why there exists an awareness of experience itself. That is, although we have demonstrated how existence can impactively interact with itself to create the form of any experience, we have yet to explain why there exists an awareness of that experiential form—in other words, why the differentiated area of reality that exists as the experiencer is aware of the form of its impactive-interactive relationship with the surrounding reality. In the following sections, we will explain why an awareness of the experiential boundary exists. In understanding why awareness exists, the nature of consciousness will become apparent.

Consciousness is unlimited, borderless, and undefined, whereas awareness is limited, bordered, and defined. When awareness becomes caught up in experiential reality, mistaking experiential reality for an independently existent reality, it literally becomes un-consciousness, or the opposite of consciousness. Since, for awareness, reality is whatever it experiences it to be, although awareness always remains what it is (i.e., consciousness), what awareness can experience itself to be is another matter entirely. For this reason, awareness can become unaware, can become unconscious of what it is, can become experientially cut off or separated from the consciousness that lies both within and beyond the screen of experience. http://jcer.com/index.php/jcj/article/view/140

The Relational-Matrix Model of Reality I: The Development of the Model (by Steven E. Kaufman): Abstract: In this article, we will describe the behavior of spatial content within the context of a defined spatial construct. This description will leave us with a model of space-time as a dynamic structure. For reasons that will later become clear, we will call this model the relational-matrix model. Once the relational-matrix model has been developed, we will then demonstrate in the next article how the functioning of this dynamic spatial structure can account for certain basic aspects of the nature and behavior of physical reality. Specifically, within the context of the relational-matrix model, we will account for the following aspects of physical reality: (1) the relationship between space and time, including the basis of temporal relativity, as well as the precise nature of time as a function of the dynamic aspect of the spatial structure; (2) the basis of the speed-of-light constant, including why the frequency and wavelength of electromagnetic radiation are inversely related as a function of that constant; (3) the basis of Planck’s constant, including why the energy associated with electromagnetic radiation exists in discrete amounts, or quanta; (4) the nature of gravitation, including why matter and gravitation are always associated and why gravitation is universally attractive; (5) the equivalence of the gravitational and inertial forces; (6) the relationship between electromagnetic radiation and gravitation; (7) the nature of energy; (8) wave/particle duality; and (9) the uncertainty principle. http://jcer.com/index.php/jcj/article/view/137

The Relational-Matrix Model of Reality II: Relating the Model to Space-Time and Physical Reality (by Steven E. Kaufman): Abstract: In this article, we will demonstrate that space-time functions as a dynamic relational structure. The relational-matrix model, as a visualizable representation of the structure of space, will be used to explain, among other things, why the physical relationships that Einstein mathematically described exist. Using the relational-matrix model to explain the behavior of physical reality, we will establish a conceptual basis for understanding how physical reality extends from the structure of space. By the end of this article, we will also have established a conceptual basis for understanding why nothing can truly be separated from anything else—i.e., why nothing can be said to exist independent of all other things. http://jcer.com/index.php/jcj/article/view/138

Surprising Properties of Non-Archimedean Field Extensions of the Real Numbers (by Elemer E. Rosinger): Abstract: This, under the present form, is a replacement that is a two part paper in which the new second part was brought together with my recently posted arxiv paper, upon the suggestion of the arxiv moderators. http://prespacetime.com/index.php/pst/article/view/160

Quantum Foundations: Is Probability Ontological? (by Elemer E. Rosinger): Abstract: It is argued that the Copenhagen Interpretation of Quantum Mechanics, founded ontologically on the concept of probability, may be questionable in view of the fact that within Probability Theory itself the ontological status of the concept of probability has always been, and is still under discussion. http://prespacetime.com/index.php/pst/article/view/161

Leaving the Aristotelean Realm: Some Comments Inspired by the Articles of Elemer E. Rosinger (by Matti Pitkänen): Abstract: In the following I represent some comments on the articles of Elemer Rosinger as a physicist from the point of view of Topological Geometrodynamics. The construction of ultrapower fields (loosely surreals) is associated with physics using the close analogies with gauge theories, gauge invariance, and with the singularities of classical fields. Non-standard numbers are compared with the numbers generated by infinite primes and it is found that the construction of infinite primes, integers, and rationals has a close similarity with construction of the generalized scalars. The construction replaces at the lowest level the index set Ʌ= N of natural numbers with algebraic numbers A, Frechet filter of N with that of A, and R with unit circle S1 represented as complex numbers of unit magnitude. At higher levels of the hierarchy generalized -possibly infinite and infinitesimal- algebraic numbers emerge. This correspondence maps a given set in the dual of Frechet filter of A to a phase factor characterizing infinite rational algebraically so that correspondence is like representation of algebra. The basic difference between two approaches to infinite numbers is that the counterpart of infinitesimals is infinitude of real units with complex number theoretic anatomy: one might loosely say that these real units are exponentials of infinitesimals. http://prespacetime.com/index.php/pst/article/view/162

Space-Time Foam Differential Algebras of Generalized Functions and a Global Cauchy-Kovalevskaia Theorem (by Elemer E. Rosinger): Abstract: The new global version of the Cauchy-Kovalevskaia theorem presented here is a strengthening and extension of the regularity of similar global solutions obtained earlier by the author. Recently the space-time foam differential algebras of generalized functions with dense singularities were introduced. A main motivation for these algebras comes from the so called space-time foam structures in General Relativity, where the set of singularities can be dense. A variety of applications of these algebras have been presented elsewhere, including in de Rham cohomology, Abstract Differential Geometry, Quantum Gravity, etc. Here a global Cauchy-Kovalevskaia theorem is presented for arbitrary analytic nonlinear systems of PDEs. The respective global generalized solutions are analytic on the whole of the domain of the equations considered, except for singularity sets which are closed and nowhere dense, and which upon convenience can be chosen to have zero Lebesgue measure. In view of the severe limitations due to the polynomial type growth conditions in the definition of Colombeau algebras, the class of singularities such algebras can deal with is considerably limited. Consequently, in such algebras one cannot even formulate, let alone obtain, the global version of the Cauchy-Kovalevskaia theorem presented in this paper. http://prespacetime.com/index.php/pst/article/view/157

Brief Lecture Notes on Self-Referential Mathematics and Beyond (by Elemer E. Rosinger): Abstract: Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent Mathematics. http://prespacetime.com/index.php/pst/article/view/158

String Theory: A Mere Prelude to Non-Archimedean Space-Time (by Elemer E. Rosinger): Abstract: It took two millennia after Euclid and until in the early 1880s, when we went beyond the ancient axiom of parallels, and inaugurated geometries of curved spaces. In less than one more century, General Relativity followed. At present, physical thinking is still beheld by the yet deeper and equally ancient Archimedean assumption which entraps us into the limited view of "only one walkable world". In view of that, it is argued with some rather easily accessible mathematical support that Theoretical Physics may at last venture into the Non-Archimedean realms. http://prespacetime.com/index.php/pst/article/view/153

Cosmic Contact to Be, or Not to Be Archimedean (by Elemer E. Rosinger): Abstract: This is a two part paper which discusses various issues of cosmic contact related to what so far appears to be a self-imposed censorship implied by the customary acceptance of the Archimedean assumption on space-time. http://prespacetime.com/index.php/pst/article/view/154

From Reference Frame Relativity to Relativity of MathematicalModels: Relativity Formulas in a Variety of Non-Archimedean Setups (by Elemer E. Rosinger): Abstract: Galilean Relativity and Einstein’s Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance or independence of Laws of Physics with respect to changes of reference frames became a fundamental principle. So far, all of that has only been expressed within one single mathematical model, namely, the traditional one built upon the usual continuum of the field R of real numbers, since complex numbers, finite dimensional Euclidean spaces, or infinite dimensional Hilbert spaces, etc., are built upon the real numbers. Here, following [55], we give one example of how one can go beyond that situation and study what stays the same and what changes in the Laws of Physics, when one models them within an infinitely large variety of algebras of scalars constructed rather naturally. Specifically, it is shown that the Special Relativistic addition of velocities can naturally be considered in any of infinitely many reduced power algebras, each of them containing the usual field of real numbers and which, unlike the latter, are non-Archimedean. The nonstandard reals are but one case of such reduced power algebras, and are as well non-Archimedean. Two surprising and strange effects of such a study of the Special Relativistic addition of velocities are that one can easily go beyond the velocity of light, and rather dually, one can as easily end up frozen in immobility, with zero velocity. Both of these situations, together with many other ones, are as naturally available, as the usual one within real numbers. http://prespacetime.com/index.php/pst/article/view/155

How Far Should the Principle of Relativity Go? (by Elemer E. Rosinger): Abstract: The Principle of Relativity has so far been understood as the covariance of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of one single type of mathematical entities, namely, the scalars given by the usual continuum of the field R of real numbers, or by the usual mathematical structures built upon R, such as the scalars given by the complex numbers C, or the vectors in finite dimensional Euclidean spaces Rn, infinite dimensional Hilbert spaces, etc. This paper argues for progressing deeper and wider in furthering the Principle of Relativity, not by mere covariance with respect to reference frames, but by studying the possible covariance with respect to a large variety of algebras of scalars which extend significantly R or C, variety of scalars in terms of which various theories of Physics can equally well be formulated. First directions in this regard can be found naturally in the simple Mathematics of Special Relativity, the Bell Inequalities in Quantum Mechanics, or in the considerable amount of elementary Mathematics in finite dimensional vector spaces which occurs in Quantum Computation. The large classes of algebras of scalars suggested, which contain R and C as particular cases, have the important feature of typically no longer being Archimedean, see Appendix, a feature which can prove to be valuable when dealing with the so called "infinities" in Physics. The paper has a Comment on the so called "end of time". http://prespacetime.com/index.php/pst/article/view/148

George Boole and the Bell Inequalities (by Elemer E. Rosinger): Abstract: As shown by Pitowsky, the Bell inequalities are related to certain classes of probabilistic inequalities dealt with by George Boole, back in the 1850s. Here a short presentation of this relationship is given. Consequently, the Bell inequalities can be obtained without any assumptions of physical nature, and merely through mathematical argument. http://prespacetime.com/index.php/pst/article/view/149

Which Are the Maximal Ideals? (by Elemer E. Rosinger): Abstract: Ideals of continuous functions which satisfy an off diagonality condition proved to be important connected with the solution of large classes of nonlinear PDEs, and more recently, in General Relativity and Quantum Gravity. Maximal ideals within those which satisfy that off diagonality condition are important since they lead to differential algebras of generalized functions which can handle the largest classes of singularities. The problem of finding such maximal ideals satisfying the off diagonality condition is formulated within some background detail, and commented upon. http://prespacetime.com/index.php/pst/article/view/150

Heisenberg Uncertainty in Reduced Power Algebras (by Elemer E. Rosinger): Abstract: The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far wider frameworks of scalars, namely,within one or the other of the infinitely many reduced power algebras which can replace the usual real numbers R, or complex numbers C. A major advantage of such a re-formulation is, among others, the disappearance of the well known and hard to deal with problem of the so called "infinities in Physics". The use of reduced power algebras also opens up a foundational question about the role, and in fact, about the very meaning and existence, of fundamental constants in Physics, such as Planck’s constant h. A role, meaning, and existence which may, or on the contrary, may not be so objective as to be independent of the scalars used, be they the usual real numbers R, complex numbers C, or scalars given by any of the infinitely many reduced power algebras, algebras which can so easily be constructed and used. http://prespacetime.com/index.php/pst/article/view/151

Crisis of Knowledge at the Beginning of the 21st Century (by Peter Kohut): Abstract: The contemporary crisis of thinking and knowledge is a consequence of positivism and its various branches leading to the extinction of philosophy and refusing to deal with the basic philosophical questions. Positivism became the basis for scientific knowledge replacing Hegelian dialectical rationalism, in which the classical philosophy had achieved its apex. Positivism tried to create the principles for scientific research based on the rules of formal logic and experiment, where the axiomatic approach became a starting point for finding the useful scientific results. Positivism refused to deal with the basic philosophical questions and categories regarding the nature of Being, God and the physical Universe. The way to the truth became “scientific” with many successful and useful discoveries and inventions. The dialectic logic was rejected as speculative, sophistic, metaphysical and useless and replaced by formal logic which together with mathematics and experimental verifications became the basic methods of scientific research mainly in the sphere of theoretical physics. http://scigod.com/index.php/sgj/article/view/103

Basic Cosmic Characteristics (Energy and Force) [by Peter Kohut]: Abstract: The nature of electrostatic and gravitational forces will be derived by using a dialectical logic for finding the basic relations between fundamental physical characteristics of the Universe. http://scigod.com/index.php/sgj/article/view/102

New Proofs for the Existence of God (Part III): The Teleogenical Proof (by Nadeem Haque, Mehran Banaei): Abstract: A synthesis of recent Cosmological and Biological Evidence concretely points to an Intelligence that created this universe that must be independent of this universe. The classical teleological and cosmological arguments have valid components but are not conclusive due to their segmented and non-integrated nature and also because of a logically invalid tactic/strategy used by atheists known as the fallacy of conflation. Also discussed by deconstruction, is the futile attempt at using cloaked language to hide the fact of teleological processes. Epistemologically, it is also shown why the Big Bang is a fact and not a theory. Herein, a complex yet integrated new proof that interweaves all these ideas, called the Teleogenical Proof, is presented that overcomes all the shortcomings of the latter two classical attempted proofs and connects with the Sesamatic proof on the question of infinite regress. http://scigod.com/index.php/sgj/article/view/98

Quantum Entanglement, Its Nature and Manifestations (by Peter Kohut): Abstract: Knowing the mutual interconnection of everything with everything, it is no problem to interpret the interactions between the measuring and quantum systems as any other interactions between two or more systems consisting of elementary quantum dipoles. So, all relations between the measuring apparatus and measured quantum objects are only parts of the universal cosmic network of elementary quantum interactions creating the objective physical reality, independent of a human consciousness. But the observer, as a conscious subject, plays an active and creative role in his communication with the micro-world. http://scigod.com/index.php/sgj/article/view/100

New Proofs for the Existence of God (Part II): The Cosmological Applications of the Sesamatic Proof (by Nadeem Haque, M. Muslim): Abstract: The Sesamatic Proof (aka the Relatiological Proof) for the Existence of God presented in Part I can be applied to three cosmological issues: the Big Bang; the Cyclical Universe and ever-existing matter, to prove the existence of God. http://scigod.com/index.php/sgj/article/view/97

Commentary on Tony Bermanseder’s “Physical Consciousness in a Self-conscious Quantum Universe” (by Michael Cecil): Abstract: This is my brief Commentary on Mr. Bermenseder’s “Physical Consciousness in a Self-conscious Quantum Universe” in this issue of JCER. My point is that any attempt to explain human consciousness which focuses exclusively upon the scientific method for the understanding of consciousness—simply ignoring both the consciousness of the “self” and the origin of the consciousness of the “self” in the ‘movement’ of self-reflection—simply does not fulfill the requirements set out by Thomas Kuhn in The Structure of Scientific Revolutions. http://jcer.com/index.php/jcj/article/view/132

Commentary on David Sahner’s “Human Consciousness and Selfhood” (by Nils J. Nilsson): Abstract: This is my brief Commentary on David Sahner’s “Human Consciousness and Selfhood: Potential Underpinnings and Compatibility with Artificial Complex Systems” in recent issue of JCER. My main point is that if a rich sensorium and extensive experiences are required for consciousness, machines will have, at least, those necessary conditions no less than humans do. http://jcer.com/index.php/jcj/article/view/133