Socioeconomic inequalities are functions not only of intrinsic differences between persons or groups, but also of the dynamics of their interactions. Inequalities can arise and become stabilized if there are advantages (such as generalized wealth including “human capital”) which are self-enhancing, whereas depletion of limiting resources is widely distributed. A recent theory of biological pattern formation has been generalized, adapted and applied to deal with this process. Applications include models for the non-Gaussian distribution of personal income and wealth, for overall (...) economic growth in relation to inequalities and for effects of uncoupling strategies between developing and developed countries. Note added after publication: The equations (14) for the model of the income distribution, with its characteristic non-Gaussian extension towards higher incomes (fig.4), are closely related to the Fokker-Planck equation that is widely applied in many fields of physics. (shrink)

This paper offers a solution to the problem of time by proposing that if the universe is time-like, stationary, and bounded, then it can be divided into static temporal gradations or contours. This led to the establishment of an energy diffusion flux (EDF) equation from which the Planck and Hubble times were derived. It was found that time becomes unimportant after applying Gauss's Law on EDF when searching for the characteristic length of the universe א. Additionally, an uncertainty (...) rule that may limit our simultaneous knowledge about the scope of space and the masses it contains was discovered. The paper concludes that if the universe is stationary and bounded, then it did not have a beginning compared to a vast, probably timeless background. Its appearance of having a beginning is because the information is largely conveyed through optics. (shrink)

In the article, with the help of various models, the thesis on the fundamental nature of the field form of matter in physics is considered. In the first chapter a model of special relativity is constructed, on the basis of which the priority of the massless form of matter is revealed. In the second chapter, a field model of inert and heavy mass is constructed and on this basis the mechanism of inertia and gravity of weighty bodies is revealed. In (...) the third chapter, the example of geons shows the fundamental nature of a massless form of matter on the Planck scale. The three-dimensionality of the observable space is substantiated. In the fourth chapter, we consider a variant of solving the problem of singularities in general relativity using the example of multidimensional spaces. The last chapter examines the author's approach to quantum gravity. Quantization of the gravitational radius of black holes is predicted. The conclusions do not contradict the main thesis of the article on the fundamental nature of the massless form of matter. We emphasize the qualitative nature of the presentation of the material in the article. (shrink)

Albert Einstein's bold assertion of the form-invariance of the equation of a spherical light wave with respect to inertial frames of reference became, in the space of six years, the preferred foundation of his theory of relativity. Early on, however, Einstein's universal light-sphere invariance was challenged on epistemological grounds by Henri Poincaré, who promoted an alternative demonstration of the foundations of relativity theory based on the notion of a light-ellipsoid. Drawing in part on archival sources, this paper shows how (...) an informal, international group of physicists, mathematicians, and engineers, including Einstein, Paul Langevin, Poincaré, Hermann Minkowski, Ebenezer Cunningham, Harry Bateman, Otto Berg, Max Planck, Max Laue, A. A. Robb, and Ludwig Silberstein, employed figures of light during the formative years of relativity theory in their discovery of the salient features of the relativistic worldview. (shrink)

Albert Einstein’s bold assertion of the form invariance of the equation of a spherical light wave with respect to inertial frames of reference became, in the space of 6 years, the preferred foundation of his theory of relativity. Early on, however, Einstein’s universal light-sphere invariance was challenged on epistemological grounds by Henri Poincaré, who promoted an alternative demonstration of the foundations of relativity theory based on the notion of a light ellipsoid. A third figure of light, Hermann Minkowski’s lightcone (...) also provided a new means of envisioning the foundations of relativity. Drawing in part on archival sources, this paper shows how an informal, international group of physicists, mathematicians, and engineers, including Einstein, Paul Langevin, Poincaré, Hermann Minkowski, Ebenezer Cunningham, Harry Bateman, Otto Berg, Max Planck, Max von Laue, A. A. Robb, and Ludwig Silberstein, employed figures of light during the formative years of relativity theory in their discovery of the salient features of the relativistic worldview. (shrink)

According to the BSM- Supergravitation Unified Theory (BSM-SG), the energy is indispensable feature of matter, while the matter possesses hierarchical levels of organization from a simple to complex forms, with appearance of fields at some levels. Therefore, the energy also follows these levels. At the fundamental level, where the primary energy source exists, the matter is in its primordial form, where two super-dense fundamental particles (FP) exist in a classical pure empty space (not a physical vacuum). They are associated with (...) the Planck scale parameters of frequency and distance and interact by Supergravitational forces. These forces are inverse proportional to the cube of distance at pure empty space and they are based on frequency interactions. Since the two FPs have different intrinsic frequencies, the SG forces appear different for interactions between the like and unlike FPs and may change the sign. This primordial form of matter exists in the super-heavy black holes located in the center of each well formed galaxy. The next upper level of matter organization includes the underlying structure of the physical vacuum, called a Cosmic Lattice, and the structure of elementary particles. They have common substructure elements obtained by specific crystallization process preceding the formation of the observable galaxies. The Cosmic Lattice, forming a space known as a physical vacuum, is responsible for the existence and propagation of the physical fields: electrical, magnetic, Newtonian gravity and inertia. The energy of physical vacuum is in two forms: Static (enormous) and Dynamic (weak). The Static energy is directly related to the Newtonian mass by the Einstein equation E = mc^2 and it is a primary source of the nuclear energy. The Dynamic energy is responsible for the existence of the electric and magnetic fields, the constant speed of light and the quantum mechanical properties of the physical vacuum. The next upper energy level is the dynamical energy of excited atoms and molecules. At this level a hidden energy wells exit, such as the internal energy of the electron and the internal energy of atoms with more than one electron. The next upper energy level is at some organic molecules and particularly in the biomolecules that contain ring atomic structures. In such a structure, some quantum states are not emitted immediately, but rotating in the ring. While in organic molecules the energy stored in such a ring is released by a chemical process, in the long chain molecule of proteins in the living organism the stored energy can be released simultaneously by triggering. A huge number of atomic rings are contained in the DNA strands. The release of the energy stored in DNA, for example, is an avalanche process that causes an emission of entangled photons possessing a strong penetrating capability. A sequence of entangled photons emitted by DNA should carry the genetic information encoded by the cordons. This mechanism, predicted in BSM-SG theory, is very important for intercommunication between the cells of the living organism. The next upper level of energy organization may exist in the brain. The brain is an organ of a most abundant number of atomic rings, while its tissue environment might permit complex energy interactions. The human brain contains billions of atomic rings. The next hypothetical upper level of energy organization is an information field, physically existed outside, but connected with the living brain. It corresponds to a specific field known as aura, while the possibility of its existence is still not accepted by the main stream science. The problem is that this field could not be detected by the currently existing technical means used for EM communications. The BSM-SG predicts that this field might differ from the EM field we use for communication, but it is a subject of a further theoretical development that must be supported by experiments using specifically designed technical means. According to the BSM-SG theory, the energy conversion from the primary energy source to the complex levels of matter and field organization is a permanent syntropic process based on complex resonance interactions. (shrink)

A simple solution to the problem of time is proposed by postulating that if the Universe is time-like, stationary, and bounded then it could be divided into static temporal gradations or contours. Hence, an energy diffusion flux (EDF) equation was established from which the Planck and the Hubble times have been derived. It is then found that time is unimportant after applying Gauss's Law on EDF when looking for a characteristic length of the Universe א. An uncertainty rule (...) was also found that may limit our simultaneous information between the scope of looking into space and the masses that it comprises. The paper concludes that if the Universe was in a stationary state and bounded, then, it did not begin to exist when compared to a vast and, probably, timeless Background. It appears to begin to exist because the information is largely mediated by optics. Thus, time is more epistemological in nature rather than ontological because of the limit that light imposes against instantaneous access to information. For this reason, the beginninglessness of the Universe should not preclude one from saying that the Universe does have a cause. (shrink)

In the standard model of cosmology, λCDM, were introduced to explain the anomalies of the orbital velocities of galaxies in clusters highest according estimated by General Relativity the dark matter and the accelerated expansion of the universe the dark energy. The model λCDM is based in the equations of the General Relativity that of the total mass-energy of the universe assigns 4.9% to matter (including only baryonic matter), 26.8%, to dark matter and 68.3% to dark energy adjusted according observed in (...) Planck mission, therefore, excluding bosonic matter (quantum vacuum). However, the composition of dark matter and dark energy are unknown. Due to that it lacks of a correct physical theory of gravity since General Relativity is only their powerful equations, which in their applications, their results are interpreted arbitrarily. Properties as curvature, viscous fluid, dragging frame and gravity action are attributed mistakenly to the spacetime by the materialist substantivalism, the most credible philosophical interpretation that complements the General Relativity, caused by its absence of physical definition of spacetime and static gravitational field as immaterial, but which violates, the conception of gravity as an effect of coordinates of the generalization of the inertial motion to the accelerated motion and, in particular, the description of the metric tensor of gravity as a geometric field. These properties are really of the quantum vacuum, the main existence form of the matter. In this paper we propose that the quantum vacuum is the source of dark matter and dark energy, therefore, the components of the quantum vacuum are of them. Both are opposite effects of the quantum vacuum that when gravitationally interacts with the cosmic structures, the vacuum it curves and when such interaction tends to cease by declination of the formation of these structures, occurring since near five milliard of years ago, vacuum it maintains quasi plane, since it interacts gravitationally very weakly with itself, accelerating expansion of the universe. (shrink)

A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, (...) the latter is that of quantum mechanics and information. Ciclicity in the manner of Nicolas Cusanus (Nicolas of Cusa) is complemented as a fundamental and definitive property of any totality, e.g. physically, that of the universe. It has to contain its externality within it somehow being namely the totality. This implies a seemingly paradoxical (in fact, only to common sense rather logically and mathematically) viewpoint for the universe to be repesented within it as each one quant of action according to the fundamental Planck constant. That approach implies the unification of gravity and entanglement correspondiing to the former or latter class of reference frames. An invariance, more general than Einstein's general covariance is to be involved as to both classes of reference frames unifying them. Its essence is the unification of the discrete and cotnitinuous (smooth). That idea underlies implicitly quantum mechanics for Bohr's principle that it study the system of quantum microscopic entities and the macroscopic apparatus desribed uniformly by the smmoth equations of classical physics. (shrink)

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum in-variance (...) designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious in-variance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained. Quantum in-variance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum in-variance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. The non-locality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum in-variance. Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics. (shrink)

Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated (...) to a well-ordered set after measurement and thus requires the axiom of choice. Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. (shrink)

When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the universe – the home of life – and how did it originate?”, “How can time travel be removed from fantasy and (...) science fiction, to be made scientific and practical?”, and “How can the proposed young age of genus Homo be made to actually be reasonable – when simply stating it would be solid ground for instant rejection and dismissal?” The result is that the article also talks about subjects like Artificial Intelligence, General Relativity, and cosmology. -/- From where did life originate? God? Evolution? Panspermia? If the tendency of humans and scientists to regard undiscovered science as pseudoscience can be overcome, Einstein gave another alternative to consider when he introduced General Relativity. Time isn’t linear – progressing in a straight line from past to present to future. That assumption ignores Relativity which states that space AND TIME are curved. Where did life and the genetic code come from? Can the answer build AI? -/- The first question can be answered by the section of this article titled SETI, Evolution, and Time which says life (possibly multicellular and intelligent) and the genetic code came from humans acquiring knowledge of these things over the centuries, then applying that knowledge – via terraforming, accumulation of raw materials like amino acids and nucleic acids, genetic engineering - to a time in the past when life didn’t exist. From that origin, life evolved through innumerable mutations and adaptations, with humans once again acquiring knowledge of it in cyclic (nonlinear) time. -/- The second question is answered by saying artificial intelligence (AI) as the product of life is only half of the equation. The other half refers to Relativity’s curved space-time and violation of the notion that time always travels from past to future. We have always lived in an artificially intelligent, non-probabilistic universe where everything in time and space is connected into one thing by quantum entanglement – making the brain and genes products of binary-digit activity or artificial intelligence (life is not merely dependent on biology’s “lock and key” mechanisms but also possesses AI). -/- The earliest documented representative of the genus Homo is Homo habilis, which evolved around 2.8 million years ago. Scientists used to believe there was a straight line from H. habilis to us, Homo sapiens. This article will use the “advanced” waves loved by Physics Nobel laureate Richard Feynman, view the history of science through the lens of Conic Sections applied to Relativity’s curved space-time, and incorporate the necessity of so-called imaginary time * – popularized by Prof. Stephen Hawking. While the evolutionary proposals are more in agreement with this early straight line than with modern theories, Albert Einstein’s General Relativity is used to transform the straight line into a curved line, ultimately concluding that Homo habilis (H. habilis) originated only (and unbelievably, as far as today’s science and technology is concerned) ~250,000 years ago. Other branches and dead ends of Homo – e.g. Neanderthals – are the result of mutations and adaptations, with the resultant modifications to anatomy and physiology. The surprisingly young age of H. habilis allows nearly 200,000 years for habilis, or one of its descendants, to reach Australia … if this country’s indigenous Aboriginal population did, as claimed, reach this “island continent” 60,000 years ago. -/- * The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, is a failure of classical physics to predict observed phenomena: it can be shown that a blackbody - a hypothetical perfect absorber and radiator of energy - would release an infinite amount of energy, contradicting the principles of conservation of energy and indicating that a new model for the behaviour of blackbodies was needed. At the start of the 20th century, physicist Max Planck derived the correct solution by making some strange (for the time) assumptions. In particular, Planck assumed that electromagnetic radiation can only be emitted or absorbed in discrete packets, called quanta. Albert Einstein postulated that Planck's quanta were real physical particles (what we now call photons), not just a mathematical fiction. From there, Einstein developed his explanation of the photoelectric effect (when quanta or photons of light shine on certain metals, electrons are released and can form an electric current). So it appears entirely possible that another supposed mathematical trickery (imaginary time and the y-axis of Wick rotation) will find practical application in the future. -/- The article includes mathematical references to cosmology (spoiler alert – you’ll read about things like Vector-Tensor-Scalar Geometry, topology, the “eternal present”, Einstein’s Unified Field, the inverse-square law, and there being no Big Bang and no multiverse - but there will also be no equations). -/- The other subheadings in this essay are – -/- NONLINEAR TIME AND ELECTRICAL ENGINEERING (about a 2009 electrical engineering experiment at America’s Yale University, and cosmic wormholes) -/- BITS AND TOPOLOGY (base-2 maths aka Binary digiTS, Mobius strips, and figure-8 Klein bottles) -/- WICK ROTATION, CAUSALITY, AND UNITING TIME (do past, present and future co-exist in an “eternal present”?) -/- DIGITAL BRAIN, DIGITAL UNIVERSE (if the brain and the universe are ultimately composed of binary digits, we'll someday be able to do the same things with the brain and universe that we now do with computers) -/- PROPOSAL: HUMAN AND ANIMAL INSTINCTS ARE THE RESULT OF THE UNIVERSE BEING UNIFIED BY BINARY DIGITS (AND TOPOLOGY) (If everything in the universe is ultimately composed of electronic BITS, then the universe must possess Artificial Intelligence - some prefer the term Cosmic Consciousness) -/- INFORMATION THEORY CONQUERS A RED GIANT (preserving Earth by keeping the Sun near today’s level of activity forever). (shrink)

This paper centers on the implicit metaphysics beyond the Theory of Relativity and the Principle of Indeterminacy – two revolutionary theories that have changed 20th Century Physics – using the perspective of Husserlian Transcedental Phenomenology. Albert Einstein (1879-1955) and Werner Heisenberg (1901-1976) abolished the theoretical framework of Classical (Galilean- Newtonian) physics that has been complemented, strengthened by Cartesian metaphysics. Rene Descartes (1596- 1850) introduced a separation between subject and object (as two different and self- enclosed substances) while Galileo and Newton (...) did the “mathematization” of the world. Newtonian physics, however, had an inexplicable postulate of absolute space and absolute time – a kind of geometrical framework, independent of all matter, for the explication of locality and acceleration. Thus, Cartesian modern metaphysics and Galilean- Newtonian physics go hand in hand, resulting to socio- ethical problems, materialism and environmental destruction. Einstein got rid of the Newtonian absolutes and was able to provide a new foundation for our notions of space and time: the four (4) dimensional space- time; simultaneity and the constancy of velocity of light, and the relativity of all systems of reference. Heisenberg, following the theory of quanta of Max Planck, told us of our inability to know sub- atomic phenomena and thus, blurring the line between the Cartesian separation of object and subject, hence, initiating the crisis of the foundations of Classical Physics. But the real crisis, according to Edmund Husserl (1859-1930) is that Modern (Classical) Science had “idealized” the world, severing nature from what he calls the Lebenswelt (life- world), the world that is simply there even before it has been reduced to mere mathematical- logical equations. Husserl thus, aims to establish a new science that returns to the “pre- scientific” and “non- mathematized” world of rich and complex phenomena: phenomena as they “appear to human consciousness”. To overcome the Cartesian equation of subject vs. object (man versus environment), Husserl brackets the external reality of Newtonian Science (epoché = to put in brackets, to suspend judgment) and emphasizes (1) the meaning of “world” different from the “world” of Classical Physics, (2) the intentionality of consciousness (L. in + tendere = to tend towards, to be essentially related to or connected to) which means that even before any scientific- logical description of the external reality, there is always a relation already between consciousness and an external reality. The world is the equiprimordial existence of consciousness and of external reality. My paper aims to look at this new science of the pre- idealized phenomena started by Husserl (a science of phenomena as they appear to conscious, human, lived experience, hence he calls it phenomenology), centering on the life- world and the intentionality of consciousness, as providing a new way of looking at ourselves and the world, in short, as providing a new metaphysics (as an antidote to Cartesian metaphysics) that grounds the revolutionary findings of Einstein and Heisenberg. The environmental destruction, technocracy, socio- ethical problems in the modern world are all rooted in this Galilean- Newtonian- Cartesian interpretation of the relationship between humans and the world after the crumbling of European Medieval Ages. Friedrich Nietzsche (1844-1900) comments that the modern world is going toward a nihilism (L. nihil = nothingness) at the turn of the century. Now, after two World Wars and the dropping of Atomic bomb, the capitalism and imperialism on the one hand, and on the other hand the poverty, hunger of the non- industrialized countries alongside destruction of nature (i.e., global warming), Nietzsche might be correct: unless humanity changes the way it looks at humanity and the kosmos. The works of Einstein, Heisenberg and Husserl seem to be pointing the way for us humans to escape nihilism by a “great existential transformation.” What these thinkers of post- modernity (after Cartesian/ Newtonian/ Galilean modernity) point to are: a) a new therapeutic way of looking at ourselves and our world (metaphysics) and b) a new and corrective notion of “rationality” (different from the objectivist, mathematico- logical way of thinking). This paper is divided into four parts: 1) A summary of Classical Physics and a short history of Quantum Theory 2) Einstein’s Special and General Relativity and Heisenberg’s Indeterminacy Principle 3) Husserl’s discussion of the Crisis of Europe, the life- world and intentionality of consciousness 4) A Metaphysics of Relativity and Indeterminacy and a Corrective notion of Rationality in Husserl’s Phenomenology . (shrink)

In the standard model of cosmology, λCDM, were introduced to explain the anomalies of the orbital velocities of galaxies in clusters highest according estimated by General Relativity the dark matter and the accelerated expansion of the universe the dark energy. The model λCDM is based in the equations of the General Relativity that of the total mass-energy of the universe assigns 4.9% to matter (including only baryonic matter), 26.8%, to dark matter and 68.3% to dark energy adjusted according observed in (...) Planck mission, therefore, excluding bosonic matter (quantum vacuum). However, the composition of dark matter and dark energy are unknown. Due to that it lacks of a correct physical theory of gravity since General Relativity is only their powerful equations, which in their applications, their results are interpreted arbitrarily. Properties as curvature, viscous fluid, dragging frame and gravity action are attributed mistakenly to the spacetime by the materialist substantivalism, the most credible philosophical interpretation that complements the General Relativity, caused by its absence of physical definition of spacetime and static gravitational field as immaterial, but which violates, the conception of gravity as an effect of coordinates of the generalization of the inertial motion to the accelerated motion and, in particular, the description of the metric tensor of gravity as a geometric field. These properties are really of the quantum vacuum, the main existence form of the matter. In this paper we propose that the quantum vacuum is the source of dark matter and dark energy, therefore, the components of the quantum vacuum are of them. Both are opposite effects of the quantum vacuum that when gravitationally interacts with the cosmic structures, the vacuum it curves and when such interaction tends to cease by declination of the formation of these structures, occurring since near five milliard of years ago, vacuum it maintains quasi plane, since it interacts gravitationally very weakly with itself, accelerating expansion of the universe. (shrink)

In this paper, we make a proposal for addressing the cosmological constant problem. Our approach will be based on a reinterpretation of two non-standard de Sitter solutions given by the Einstein vacuum equations with Λ>0. As a first result, we derive an uncertainty principle for both variants of the de Sitter space (Theorem). Subsequently, a decomposition of the cosmological constant in a pair of time-dependent pieces is introduced (Corollary). The time-dependence of the corresponding energy and dark energy density is discussed (...) and especially matched at the Planck scale. Furthermore, we show that for every instant of cosmic time this approach can be revealed in terms of a Schwarzschild-Anti-de Sitter cosmology with Λ>0. The corresponding field equations are provided. (shrink)

Defined are gravitational formulas in terms of Planck units and units of $\hbar c$. Mass is not assigned as a constant property but is instead treated as a discrete event defined by units of Planck mass with gravity as an interaction between these units, the gravitational orbit as the sum of these mass-mass interactions and the gravitational coupling constant as a measure of the frequency of these interactions and not the magnitude of the gravitational force itself. Each particle (...) that is in the mass-state (defined by a unit of Planck mass) per unit of Planck time is directly linked to every other particle also in the mass-state by a discrete unit of $m_P v^2 r = \hbar c$, the velocity of a gravitational orbit is summed from these individual $v^2$. As this approach presumes a digital time, it is suitable for use in programming Simulation Hypothesis models. As this link is responsible for the particle-particle interaction it is analogous to the graviton. Orbital angular momentum of the planetary orbits derives from the sum of the planet-sun particle-particle orbital angular momentum irrespective of the angular momentum of the sun itself and the rotational angular momentum of a planet includes particle-particle rotational angular momentum. (shrink)

The Simulation Hypothesis proposes that all of reality, including the earth and the universe, is in fact an artificial simulation, analogous to a computer simulation, and as such our reality is an illusion. In this essay I describe a method for programming mass, length, time and charge (MLTA) as geometrical objects derived from the formula for a virtual electron; $f_e = 4\pi^2r^3$ ($r = 2^6 3 \pi^2 \alpha \Omega^5$) where the fine structure constant $\alpha$ = 137.03599... and $\Omega$ = 2.00713494... (...) are mathematical constants and the MLTA geometries are; M = (1), T = ($2\pi$), L = ($2\pi^2\Omega^2$), A = ($4\pi \Omega)^3/\alpha$. As objects they are independent of any set of units and also of any numbering system, terrestrial or alien. As the geometries are interrelated according to $f_e$, we can replace designations such as ($kg, m, s, A$) with a rule set; mass = $u^{15}$, length = $u^{-13}$, time = $u^{-30}$, ampere = $u^{3}$. The formula $f_e$ is unit-less ($u^0$) and combines these geometries in the following ratio M$^9$T$^{11}$/L$^{15}$ and (AL)$^3$/T, as such these ratio are unit-less. To translate MLTA to their respective SI Planck units requires an additional 2 unit-dependent scalars. We may thereby derive the CODATA 2014 physical constants via the 2 (fixed) mathematical constants ($\alpha, \Omega$), 2 dimensioned scalars and the rule set $u$. As all constants can be defined geometrically, the least precise constants ($G, h, e, m_e, k_B$...) can also be solved via the most precise ($c, \mu_0, R_\infty, \alpha$), numerical precision then limited by the precision of the fine structure constant $\alpha$. (shrink)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

Abstract to Equations, Qualia, and Qualations -/- With regard to consciousness, we could write an equation B = black. But it is possible to rewrite this using a quale, namely, B = █. This latter equation might be called a ‘qualation’. It has the same meaning regardless of the physiology that apprehends it. This article argues a whole theory of qualations could be developed. Further, to a Dualist, it could be that a materialist is convinced by materialist arguments (...) involving the first equation, but it is unimaginable how this could ever be for a qualation. In view of the strong association of qualia with McTaggart’s A-series (future/present/past) a few notes on time are included. (shrink)

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be (...) verified with observation data. (shrink)

This study aimed to construct structural equation model of students’ competence in mathematics through selected students profile variables. The structural model revealed interesting influence of the profile variables to the competency in mathematics. It can be conveyed that better mother’s work status, higher educational level expected to complete, more confident and did not repeat kinder, have better competency in mathematics. The four variables that directly influenced the competence variables were also influenced with other profile variables such as family background. (...) The family background and confidence level consistently had the highest total effect and indirect effect to the competence in mathematics. Hence, this model can serve as a guide in making programs in the classroom or curriculum in mathematics. (shrink)

I give concise derivations of Price's equation and the criteria for kin and group selection, prove that kin and group selection are equivalent, and discuss the controversies about altruism.

Science begins with mystery. What causes lightning? How did this mold stop bacterial growth? Why do we age? Arguably, the two greatest mysteries are the cosmos and consciousness—the vast world out there and the vibrant world within. Scientists captivated by one can be called to study the other, seduced by the thought that these mysteries are connected. Science writer George Musser’s book Putting Ourselves Back in the Equation reviews their progress: Can physics unlock the mystery of consciousness? Does consciousness (...) underlie fundamental physics? (shrink)

This is an English translation of Waldenfels' German essay: Equality and inequality are basic elements of law, justice and politics. Equality integrates each of us into a common sphere by distributing rights, duties and chances among us. Equality turns into mere indifference as far as we get overintegrated into social orders. When differences are fading away experience loses its relief and individuals lose their face. Our critical reflections start from the inevitable paradox of making equal what is not equal. In (...) various ways they refer to Nietzsche’s concept of order, to Marx’s analysis of money, to Lévinas’s ethics of the Other, and to novelists like Dostoevsky and Musil. Our critique turns against two extremes, on the one hand against any sort of normalism fixed on functioning orders, on the other hand against any sort of anomalism dreaming of mere events and permanent ruptures. Responsive phenomenology shows how we are confronted with extraordinary events. Those deviate from the ordinary and transgress its borders, without leaving the normality of our everyday world behind. The process of equalizing moves between the ordinary and the extraordinary. What makes the difference and resists mere indifference are creative responses which are to be invented again and again. (shrink)

A *qualation* does not contain merely references to qualia, but contains actual qualia. There are many differences to equations. Qualations are irreducibly 1st-person and are required for the statement of a hard problem.

The biochemistry of geotropism in plants and gravisensing in e.g. cyanobacteria or paramacia is still not well understood today [1]. Perhaps there are more ways than one for organisms to sense gravity. The two best known relatively old explanations for gravity sensing are sensing through the redistribution of cellular starch statoliths and sensing through redistribution of auxin. The starch containing statoliths in a gravity field produce pressure on the endoplasmic reticulum of the cell. This enables the cell to sense direction. (...) Alternatively, there is the redistribution of auxin under the action of gravity. This is known as the Cholodny-Went hypothesis [2], [3]. The latter redistribution coincides with a redistribution of electrical charge in the cell. With the present study the aim is to add a mathematical unified field explanation to gravisensing. (shrink)

It is shown that the heuristic "derivation" of the Schrödinger equation in quantum mechanics textbooks can be turned into a real derivation by resorting to spacetime translation invariance and relativistic invariance.

The objective of the study was to develop a structural model that explores the relationship between Mathematics Performance and students’ self-regulated learning skills, grit, and expectancy-value towards science, technology, engineering and mathematics (STEM). The research collected survey data from 664 senior high school students from 17 STEM high schools, and conducted a covariance-based structural equation modeling (SEM) analysis. The results of the SEM analysis indicate that the Re-specified Self-Regulated Learning Skill – Expectancy-Value towards STEM – Grit – Mathematics Performance (...) (Re-specified SRL-EV-GR-MP) model is the most parsimonious fit, offering the best empirical support for the theoretical model of the study. The research findings suggest that the mathematics performance of senior high school students in STEM curriculum is attributed to their high expectancies for success and perceived values of the STEM tasks, high grit, and high self-regulated learning skills. Moreover, the research also observed evidence of mediating and moderating grit effects in the concurrent effects of expectancy-values towards STEM and self-regulated learning skills towards students’ mathematics performance. (shrink)

Following a hypothesis by Marciak-Kozlowska, 2011, we consider one-dimensional Schumann wave transfer phenomena. Numerical solution of that equation was obtained by the help of Mathematica.

An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. Each of (...) these two equations is generally-covariant, transforms the wave function as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense. (shrink)

There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer (...) is able to work numerically with finite, infinite, and infinitesimal numbers giving so the possibility to use different infinitesimals numerically and, in particular, to take advantage of infinitesimal values of h. To show the potential of the new framework a number of results is established. It is proved that the Infinity Computer is able to calculate derivatives of the solution y(x) and to reconstruct its Taylor expansion of a desired order numerically without finding the respective derivatives analytically (or symbolically) by the successive derivation of the ODE as it is usually done when the Taylor method is applied. Methods using approximations of derivatives obtained thanks to infinitesimals are discussed and a technique for an automatic control of rounding errors is introduced. Numerical examples are given. (shrink)

The Simulation Hypothesis proposes that all of reality is in fact an artificial simulation, analogous to a computer simulation. Outlined here is a method for programming relativistic mass, space and time at the Planck level as applicable for use in Planck Universe-as-a-Simulation Hypothesis. For the virtual universe the model uses a 4-axis hyper-sphere that expands in incremental steps (the simulation clock-rate). Virtual particles that oscillate between an electric wave-state and a mass point-state are mapped within this hyper-sphere, the (...) oscillation driven by this expansion. Particles are assigned an N-S axis which determines the direction in which they are pulled along by the expansion, thus an independent particle motion may be dispensed with. Only in the mass point-state do particles have fixed hyper-sphere co-ordinates. The rate of expansion translates to the speed of light and so in terms of the hyper-sphere co-ordinates all particles (and objects) travel at the speed of light, time (as the clock-rate) and velocity (as the rate of expansion) are therefore constant, however photons, as the means of information exchange, are restricted to lateral movement across the hyper-sphere thus giving the appearance of a 3-D space. Lorentz formulas are used to translate between this 3-D space and the hyper-sphere co-ordinates, relativity resembling the mathematics of perspective. (shrink)

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields (...) to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details. (shrink)

Inspired by “One Note Samba,” a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology (BECC). Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also discuss shortly possible link with our previous paper, where we describe Newtonian Universe with Vortex in terms of Ermakov equation.

Outlined here is a simulation hypothesis approach that uses an expanding (the simulation clock-rate measured in units of Planck time) 4-axis hyper-sphere and mathematical particles that oscillate between an electric wave-state and a mass (unit of Planck mass per unit of Planck time) point-state. Particles are assigned a spin axis which determines the direction in which they are pulled by this (hyper-sphere pilot wave) expansion, thus all particles travel at, and only at, the velocity of expansion (the (...) origin of $c$), however only the particle point-state has definable co-ordinates within the hyper-sphere. Photons are the mechanism of information exchange, as they lack a mass state they can only travel laterally (in hypersphere co-ordinate terms) between particles and so this hypersphere expansion cannot be directly observed, relativity then becomes the mathematics of perspective translating between the absolute (hypersphere) and the relative motion (3D space) co-ordinate systems. A discrete `pixel' lattice geometry is assigned as the gravitational space. Units of $\hbar c$ `physically' link particles into orbital pairs. As these are direct particle to particle links, a gravitational force between macro objects is not required, the gravitational orbit as the sum of these individual orbiting pairs. A 14.6 billion year old hyper-sphere (the sum of Planck black-hole units) has similar parameters to the cosmic microwave background. The Casimir force is a measure of the background radiation density. (shrink)

The study's general objective is to determine the students' stance on the most appropriate model of writing skills, using Structural Equation Modeling (SEM) as a basic design in the relationship of self-regulated learning strategies, communicative learning strategies, learning grammatical strategies, and writing skills. This study used a mixed-method sequential explanatory design, in which quantitative design is more widely used than qualitative Creswell, J., & Creswell, D. (2017). The researcher used the stratified random sampling technique for selecting respondents and, by (...) using the Raosoft sample size calculator, identified 390 respondents using a four-part questionnaire to collect data. Purposive sampling is the method for determining participants in a qualitative design using a guided questionnaire to obtain data from In-Depth Interviews and Focus Group Discussions. Model 5 was the best-fitting model for writing skills, showing significant correlations with the exogenous variables: self-regulated learning strategies, communicative learning strategies, learning grammatical strategies, and writing skills as endogenous variables. Both the exogenous and endogenous variables obtained a high level of overall description, meaning that students often practiced strategies to cultivate writing skills. The participants' stance on the most appropriate model is essential for tertiary students to have different strategies for developing writing skills. It is necessary to reach the full description of the highest level by using different strategies to build writing skills. (shrink)

In a rather old paper, Mario Liu described a hydrodynamic Maxwell equations. While he also discussed potential implications of these new approaches to superconductors, such a discussion of electrodynamics of superconductors is made only after Tajmar’s paper. Therefore, in this paper we present for the first time a derivation of fluidic Maxwell-Proca equations. The name of fluidic Maxwell-Proca is proposed because the equations were based on modifying Maxwell-Proca and Hirsch’s theory of electrodynamics of superconductor. It is hoped that this paper (...) may stimulate further investigations and experiments in superconductor. It may be expected to have some impact to cosmology modeling too, for instance we consider a hypothetical argument that photon mass can be origin of gravitation. Then, after combining with the so-called chiral modification of Maxwell equations (after Spröessig), then we consider chiral Maxwell-Proca equations as possible alternative of gravitation theory. Such a hypothesis has never considered in literature to the best of our knowledge. (shrink)

Arguments for the effectiveness, and even the indispensability, of mathematics in scientific explanation rely on the claim that mathematics is an effective or even a necessary component in successful scientific predictions and explanations. Well-known accounts of successful mathematical explanation in physical science appeals to scientists’ ability to solve equations directly in key domains. But there are spectacular physical theories, including general relativity and fluid dynamics, in which the equations of the theory cannot be solved directly in target domains, and yet (...) scientists and mathematicians do effective work there (McLarty 2023, Elder 2023). Building on extant accounts of structural scientific explanation (Bokulich 2011, Leng 2021), I argue that philosophical accounts of the role of equations in scientific explanation need not rely on scientists’ ability to solve equations independently of their understanding of the empirical or experimental context. For instance, the process of formulating solutions to equations can involve significant appeal to information about experimental contexts (Curiel 2010) or of physically similar systems (Sterrett 2023). Working from a close analysis of work in fluid mechanics by Martin Bazant and Keith Moffatt (2005), I propose an account of heuristic structural explanation in mathematics (Einstein 1921, Pincock 2021), which explains how physical explanations can be constructed even in domains where basic equations cannot be solved directly. (shrink)

We propose to simplify the problem of the unified theory of Quantum-Gravity through dealing first with the simple case of non-relativistic equations of Gravity and Quantum Mechanics. We show that unification of the two non-relativistic formalisms can be achieved through the joined classical and Quantum postulate that every natural body is composed of N identical final particles. This includes the current 'elementary' particles of the standard model such as quarks, photons, gluons, etc. Furthermore, we show that this opens a new (...) route toward a Generalized Equation of Quantum-Gravity that takes the effects of both of velocity and acceleration into account. (shrink)

In recent years, there are a number of proposals to consider collision-based soliton computer based on certain chemical reactions, namely Belousov-Zhabotinsky reaction, which leads to soliton solutions of coupled Nonlinear Schroedinger equations. They are called Manakov System. But it seems to us that such a soliton computer model can also be based on solitary wave solution of Maxwell-Dirac equation, which reduces to Choquard equation. And soliton solution of Choquard equation has been investigated by many researchers, therefore it (...) seems more profound from physics perspective. However, we consider both schemes of soliton computer are equally possible. More researches are needed to verify our proposition. (shrink)

An ongoing mystery in sensory science is how sensation magnitude F(I), such as loudness, increases with increasing stimulus intensity I. No credible, direct experimental measures exist. Nonetheless, F(I) can be inferred algebraically. Differences in sensation have empirical (but non-quantifiable) minimum sizes called just-noticeable sensation differences, ∆F, which correspond to empirically-measurable just-noticeable intensity differences, ∆I. The ∆Is presumably cumulate from an empirical stimulus-detection threshold I_th up to the intensity of interest, I. Likewise, corresponding ∆Fs cumulate from the sensation at the stimulus-detection (...) threshold, F(I_th ), up to F(I). Regarding the ∆Is, however, it is unlikely that all of them will be known experimentally; the procedures are too lengthy. The customary approach, then, is to find ∆I at a few widely-spaced intensities, and then use those ∆Is to interpolate all ∆Is using some smooth continuous function. The most popular of those functions is Weber’s Law, ∆I⁄I=K. But that is often not even a credible approximation to the data. However, there are other equations for ∆I⁄I. Any such equation for ∆I⁄I can be combined with any equation for ∆F, through calculus, to altogether obtain F(I). Here, two assumptions for ∆F are considered: ∆F=B (Fechner’s Law) and (∆F⁄F)=g (Ekman’s Law). The respective integrals involve lower bounds I_th and F(I_th ). This stands in broad contrast to the literature, which heavily favors non-bounded integrals. We, hence, obtain 24 new, alternative equations for sensation magnitude F(I) (12 equations for (∆I⁄I) × 2 equations for ∆F). (shrink)

In physics there are different opinions about the conceptual interpretation of Einstein’s famous equation that describes the equivalence between mass and energy. It is understandable that the equation has different interpretations because of the different points of view to interpret phenomenological reality. This paper is about the meaning of the equation in relation to the general concept of quantum field theory. In other words, reality is created by the underlying structure of the basic quantum fields.

Recent studies tend to explain the importance of communication in the organisation as well as prescribing the most commonly practised techniques adopted by school managers. Studies on financial management are quite limited with the available ones suggesting that poor financial management is a source of conflict between school leaders and host communities. Little seems to be known on the connection between principals’ communication patterns and funds’ management as predictors of school-community relationship. This study builds on existing studies and appears to (...) be the first to assess the linkages between principals’ communication patterns, fund management practices and school- community relationship based on empirical rather than subjective data. A structural modelling approach was adopted to examine the nexus using quantitative primary data obtained from a random sample of 2108 respondents. A questionnaire which was designed and validated by the researchers served as the data collection device. Collected data were subjected to Exploratory and Confirmatory Factor Analyses, as well as Multiple Regression Analysis. Findings revealed various significant communication, funds management and school-community relationship practices that are available for adoption. However, it was found that the extent to which principals utilised such practices were below expected minimum standards. It was also found that there were no significant partial and composite effects of principals’ communication and funds management practices on school-community relationship (SCR). Based on these results, relevant theoretical, policy and practical implications are discussed. (shrink)

This note briefly discusses the observation of elapsed time in a flat universe while exploring the argument of past-eternal time versus emergent time in cosmology. A flat universe with an incomplete past forever has a finite age. Despite an infinite number of Planck time coordinates independent of phenomena and endless expansion, a flat universe never develops an age with an infinite number of Planck times. This observation indicates the impossibility of infinitely elapsed time in the future or past, (...) which limits acceptable scientific models of cosmology. (shrink)

In this paper we study the connection between the use of evaluative language and the building of both personal and social identities, from the perspective of Dynamical System Theory. We primarily discuss two issues: 1) The use of evaluation ) as a means to the construction of both individual and group identities, thus exploring how the connection between linguistic choices and social identities is shaped by interactional needs for stancetaking. In order to illustrate this connection, we examine examples of the (...) use of evaluative language in a web social network, and we analyze some of the discourse elements showing ways of positioning that act as catalysts for the emergence of a multifactorial dynamic system of identities. 2) The consideration of Dynamical System Theory as a theoretical framework for the modeling of language and identity. Although originally a mathematical theory, DST has been adopted by cognitive science as a valid framework for the study of cognitive phenomena, on the grounds that natural cognition is a dynamical phenomenon. Within the realm of linguistics and pragmatics, this study is to a certain degree in line with some recent studies such as Gibbs, Geeraerts, Kristiansen and Peirsman, or Moreno Fernández. Thus, we herein focus on how linguistic evaluation intervenes in the intricate dynamical system of identity, and even though we do not engage in complex mathematical disquisition, we argue that the idea and philosophical foundation underlying DST can lead us towards the ‘integration’ of the complex equation of identity construction, and that consequently the field has great potential for further research. (shrink)

The mass-energy relationship does not derive logically from Special Relativity, since it is not a function of relative velocity. It might be a function of acceleration. ‘Mass’ is re-examined as a stand-alone concept.

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The study was underpinned by Skemp’s relational and instrumental understanding, and Kilpatrick, Swafford and Findel’s conceptual and procedural understanding to gain the insights into (...) Grade 11 learners’ understanding of the roots of quadratic equations. A case study design was espoused to answer the main research questions of this study. A written test was administered to 42 learners, and eight learners were purposively sampled to participate in a clinical interview based on their responses to the test. The findings of this study revealed that learners find it difficult to describe the roots, determine the other root when one root is given, to solve quadratic equations written in standard form, to represent the roots to determine the value of unknown variable(s), and to execute the reversal process using the given roots to find the equation. (shrink)