According to orthodox quantum mechanics, state vectors change in two incompatible ways: "deterministically" in accordance with Schroedinger's time-dependent equation, and probabilistically if and only if a measurement is made. It is argued here that the problem of measurement arises because the precise mutually exclusive conditions for these two types of transitions to occur are not specified within orthodox quantum mechanics. Fundamentally, this is due to an inevitable ambiguity in the notion of "meawurement" itself. Hence, if the problem of measurement (...) is to be resolved, a new, fully objective version of quantjm mechanics needs to be developed which does not incorporate the notion of measurement in its basic postuolates at all. (shrink)

This work-in-progress paper consists of four points which relate to the foundations and physical realization of quantum computing. The first point is that the qubit cannot be taken as the basic unit for quantum computing, because not every superposition of bit-strings of length n can be factored into a string of n-qubits. The second point is that the “No-cloning” theorem does not apply to the copying of one quantum register into another register, because the mathematical representation of this copying is (...) the identity operator, which is manifestly linear. The third point is that quantum parallelism is not destroyed only by environmental decoherence. There are two other forms of decoherence, which we call measurement decoherence and internal decoherence, that can also destroy quantum parallelism. The fourth point is that processing the contents of a quantum register “one qubit at a time” destroys entanglement. (shrink)

Building upon Nancy Cartwright's discussion of models in How the Laws of Physics Lie, this paper addresses solid state research in transition metal oxides. Historical analysis reveals that in this domain models function both as the culmination of phenomenology and the commencement of theoretical explanation. Those solid state chemists who concentrate on the description of phenomena pertinent to specific elements or compounds assess models according to different standards than those who seek explanation grounded in approximate applications of the Schroedinger (...) class='Hi'>equation. Accurate accounts of scientific debate in this field must include both perspectives. (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...) former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

Here, S is a sentence—or possibly a smaller or larger unit of meaningful expression for a language—that's written by an author and c is the circumstance in which S is used. R is defined as the language conventions holding between an author and a reader (or better yet, his readership). P, probably the most important part of the equation, is the content of S or, the intended meaning of the author. We assume that the communication between an author and (...) a reader is limited only to written text. Consequently, it is not possible to ask the author about his intention for writing S; that will have to be discovered by a reader. (shrink)

While the philosophers of science discuss the General Relativity, the mathematical physicists do not question it. Therefore, there is a conflict. From the theoretical point view “the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory 's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime (...) setting?”. “The voices of dissent proclaim that Einstein was mistaken over the fundamental ideas of his own theory and that their basic principles are simply incompatible with this theory. Many newer texts make no mention of the principles Einstein listed as fundamental to his theory; they appear as neither axiom nor theorem. At best, they are recalled as ideas of purely historical importance in the theory's formation. The very name General Relativity is now routinely condemned as a misnomer and its use often zealously avoided in favour of, say , Einstein's theory of gravitation What has complicated an easy resolution of the debate are the alterations of Einstein's own position on the foundations of his theory”, (Norton, 1993). Of other hand from the mathematical point view the “General Relativity had been formulated as a messy set of partial differential equations in a single coordinate system. People were so pleased when they found a solution that they didn't care that it probably had no physical significance” (Hawking and Penrose, 1996). So, during a time, the declaration of quantum theorists:“I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.” (Hawking and Penrose, 1996)seemed to solve the problem, but recently achieved with the help of the tightly and collectively synchronized clocks in orbit frontally contradicts fundamental assumptions of the theory of Relativity. These observations are in disagree from predictions of the theory of Relativity. (Hatch, 2004a, 2004b, 2007). The mathematical model was developed first by Grossmann who presented it, in 1913, as the mathematical part of the Entwurf theory, still referred to a curved Minkowski spacetime. Einstein completed the mathematical model, in 1915, formulated for Riemann ́s spacetimes. In this paper, we present as of General Relativity currently remains only the mathematical model, darkened with the results of Hatch and, course, we conclude that a Einstein ́s gravity theory does not exist. (shrink)

1. Schrodinger Equation, fragmentalism, total time T, Euclidean space 2. Does the A-series have the properties of qualia?

Abstract— In this paper, we introduce the definition of triple Aboodh transform, some properties for the transform are presented. Furthermore, several theorems dealing with the properties of the triple Aboodh transform are proved. In addition, we use this transform to solve partial differential equations with integer and non-integer orders.

Many have taken Sellars’s critique of empiricism in “Empiricism and the Philosophy of Mind” (EPM) to be aimed at his teacher C. I. Lewis. But if so, why do the famous arguments of its opening sections carry so little force against Lewis’s views? Understandably, some respond by denying that Lewis’s epistemology is among the positions targeted by Sellars. But this is incorrect. Indeed, Sellars had earlier offered more trenchant (if already familiar) critiques of Lewis’s epistemology. What is original about EPM (...) is that it criticizes empiricist positions like Lewis’s not because of their foundationalism, but because of their psychologism about meaning. Since psychologism turns out to be unacceptable by Lewis’s own lights, EPM has a compelling (if implicit) critique of Lewis to offer after all, one that strikes at the heart of his philosophical system. (shrink)

The problem of measurement in economic models and the possibility of their quantum-mechanical description are considered. It is revealed that the apparent paradox of such a description is associated with a priori requirement of conformity of the model to all the alternatives of free choice of the observer. The measurement of the state of a trader on a stock exchange is formally defined as his responses to the proposals of sale at a fixed price. It is shown that an analogue (...) of Bell's inequalities for this measurement model is violated at the most general assumptions related to the strategy of the trader and requires a quantummechanical description of the dynamics of his condition. In the framework of the theory of weak continuous quantum measurements, the equation of stock price dynamics and the quantum-mechanical generalization of the F. Black and M. Scholes model for pricing options are obtained. The fundamental distinctions between the obtained model and the classical one are discussed. (shrink)

Since its final version and publication in 1916, it is widely reported in several specialized textbooks and research articles that general relativity theory may be reduced to the Newton's gravity theory in the limit of a weak gravitational field and slow motion of the material bodies. In the present paper, the so-called reducibility of Einstein's geodesic and field equations to Newton's equation of motion and Poisson's gravitational potential equation, respectively, is scrutinized and proven to be mathematically, physically and (...) dimensionally wrong and also the geometrization of gravity is not really necessary. (shrink)

Horizontal gene transfer (HGT) has been a paramount mechanism of interest in recent literature addressing the origins of biological evolution. However, research on lightning-triggered electroporation represents the innovative and still insufficiently grasped approach to HGT (Kotnik, 2013). On the other hand, prebiotic synthesis is a fundamental process for chemical evolution. Recently, the effects of volcanic lightning on nitrogen fixation and phosphate reduction have also been considered (NavarroGonzález and Segura, 2004). This paper aims to present a top-down approach to the question (...) of the origin of life on early Earth. By considering the conditions necessary for the emergence of biological and chemical evolution, emphasizing electrostatic discharges, we will attempt to link previous theoretical and experimental research. Furthermore, we will present a recent endeavor at applying the Drake equation to calculating the probability of volcanic lightning impact on the prebiotic synthesis and derive a similar use in estimating the contribution of lightning to HGT (Weaver, 2013). We will also display that choosing a type of probability appropriate for the context of life sciences is not necessarily a quantitative issue. Finally, we will show that significant conceptual constraints, like determining the relevant factors and sources of uncertainty when considering the origin of life on early Earth, are fundamentally philosophical issues. We hope that the results of our research – deriving Drake’s equation in the domain of chemical evolution and considering Bayesian and counterfactual types as potentially more suitable candidates for calculating probabilities in the evolutionary framework – will contribute to developing new discussions in life sciences. (shrink)

The study aimed to identify Design Thinking and its use in NGOs in Gaza Strip. In order to achieve the objectives of the study and to test its hypotheses, the analytical descriptive method was used, relying on the questionnaire as a main tool for data collection. The study society was one of the decision makers in the local NGOs in the Gaza Strip. The study population reached 78 local NGOs in Gaza Strip. The overall inventory of the possible study community (...) was based mainly on the use of the SPSS in processing and analyzing the data obtained through the survey tool. Smart-PLS was also used to construct the structural equation model (SEM) Analyzing the relationship between study variables. The study found that Design Thinking mediates the relationship between the management of process design and decision making with a holistic effect. The study showed the interest of local NGOs in creating a good mental image in the local community. And the ownership of local NGOs to the expertise and technical skills required to implement the projects, and showed the adoption of local NGOs in their activities to meet the needs of the beneficiaries and their wishes, and local NGOs analyze the problem, and causes, through data relevant to the decision, based on reference data for decision-making. The main recommendations of the study are: The need for senior management in the local NGOs in Gaza Strip to adopt the methodology of design thinking because of its impact on the sustainability of the projects, design the technical feasibility study and meet the wishes of the beneficiaries. (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.

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 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.

Is it sensical to ascribe psychological predicates to AI systems like chatbots based on large language models (LLMs)? People have intuitively started ascribing emotions or consciousness to social AI (‘affective artificial agents’), with consequences that range from love to suicide. The philosophical question of whether such ascriptions are warranted is thus very relevant. This paper advances the argument that LLMs instantiate language users in Ludwig Wittgenstein’s sense but that ascribing psychological predicates to these systems remains a functionalist temptation. Social AIs (...) are not full-blown language users, but rather more like Italo Calvino’s literature machines. The ideas of LLMs as Wittgensteinian language users and Calvino’s literature-producing writing machine are combined. This sheds light on the misguided functionalist temptation inherent in moving from equating the two to the ascription of psychological predicates to social AI. Finally, the framework of mortal computation is used to show that social AIs lack the basic autopoiesis needed for narrative façons de parler and their role in the sensemaking of human (inter)action. Such psychological predicate ascriptions could make sense: the transition ‘from quantity to quality’ can take place, but its route lies somewhere between life and death, not between affective artifacts and emotion approximation by literature machines. (shrink)

African cultural values connote core principles and ideals that maintains good, right, fair and just in African societies. This culture is developed over a long period of time, preserved and promoted by all members of a given group or society. Corruption as a phenomenon on the other hand has been variously described as a societal vice. Though research shows that some levels of corruption exist in almost every human society, it is over accommodated in some societies or nations and as (...) such it has notoriously continued to destroy such societies/nations. This is particular to a number of African nations, with Nigeria being among (if not) the worse corrupt nation(s) in the continent. It is not difficult to understand that the value placed on corruption in Nigeria is synonymous to the way cultural values are cherished by people in some nations of the world. In view of this, there is a serious and immediate need to educate the Nigerian public about the consequences of developing a culture of corruption in the country. It seems that some Nigerians take corruption to be a normal way of life, thereby, equating the vice to acceptable cultural values. Today, many Nigerians are not interested in developing and/or preserving amiable cultural values for the nation. Rather, more attention is focus on the promotion of corrupt practices that enables the destruction of even the good cultural values of the nation that were left behind by our forefathers. Therefore, this paper seeks to unmask the importance of developing and preserving good African cultural values that will guarantee unity, patriotism, social cohesion and sustainable development in Nigeria. (shrink)

As is well known, Einstein was dissatisfied with the foundation of quantum theory and sought to find a basis for it that would have satisfied his need for a causal explanation. In this paper this abandoned idea is investigated. It is found that it is mathematically not dead at all. More in particular: a quantum mechanical U(1) gauge invariant Dirac equation can be derived from Einstein's gravity field equations. We ask ourselves what it means for physics, the history of (...) physics and for the actual discussion on foundations. (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)

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)

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)

The concept of sustainable development considers environmental, social and economic issues in general. And the goals of resource conservation and socio-economic development do not contradict each other, but contribute to mutual reinforcement. The purpose of this study is to build and test an economic and mathematical model for the formation of strategies for the behavior of an economic entity with an increase in the impact of negative environmental factors. The proposed strategies and their models are based on the income-expenditure balance (...) equation, which takes into account both quantitative and qualitative characteristics. The constructed models are considered in the state space. The research methodology is based on building models in the form of linear combinations of functions of a homogeneous external impact and various spatial combinations of economic sources (sinks). The study makes it possible to assess the dependence of the amount of resources used for life support on the chosen adaptive strategy. Within the framework of the proposed model, it was found that the criterion for the effectiveness of the applied strategy can be an indicator of satisfaction with the state, the preservation of which, simultaneously with the preservation of the size of resources used, corresponds to the direction of optimization. This approach is consistent with the concept of sustainable development. (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)

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)

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)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

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)

In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular (...) model starting from classical wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations – inertons, carriers of mass and inert properies of matter. We also discuss possible correspondence with Konrad Zuse’s calculating space. (shrink)

It has been known for long time that intuition plays significant role in many professions and human life, including in entrepreneurship, government, and also in detective or law enforcement activities. Even women are known to possess better intuitive feelings or “hunch” compared to men. Despite these examples, such a precognitive interdiction is hardly accepted in established science. In this paper, we discuss briefly the advanced solutions of Maxwell equations, and then make connection between syntropy and precognition from classical perspective. It (...) is our hope that the new proposed method can be verified with experimental data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details. (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.

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. (...) The relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (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)

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)

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.

Cartesian and Western religious and philosophical traditions distinguish the body from the mind, viewing the former as a prison or a burden. The mind (spirit, soul, rationality) is identified as good, while the body is devalued and associated with evil. Some philosophers restored the body's value: humans are not imprisoned spirits, but they are their bodies. Husserl, for example, claims that human beings are not an immaterial substance in a Körper, a physical body, but Leib, a living body that solves (...) within itself the two Cartesian res. Although the Cartesian legacy survives in the Existentialism in the distinction between In-itself (the passive Being) and For-itself (the human, transcendental freedom), the second does not use the object-body as the res cogitans did: "the very nature of the For-itself demands that it be body." Nevertheless, the body plays an ambivalent role, suspended between Körper's passivity and Leib's transcendence. The chapter's focus on Arkham's female characters is not random. Leder notices that "women have consistently been associated with the bodily sphere. They have been linked with nature, sexuality, and the passions, whereas men have been identified with the rational mind. This equation implicitly legitimizes structures of domination." By associating human categories like "lunatics," "savages," or women with the immanence of the body and nature, their transcendentality is denied, and, simultaneously, men's control and domination over them is justified. (shrink)

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...) of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of (...) Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kurucz’s hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details. (shrink)

Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smoryński's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. Let R be a subring of Q with or without 1. By H_{10}(R), we denote the problem of whether there exists an algorithm which for any given Diophantine equation with integer coefficients, can decide (...) whether or not the equation has a solution in R. We prove that a positive solution to H_{10}(R) implies that the set of all Diophantine equations with a finite number of solutions in R is recursively enumerable. We show the converse implication for every infinite set R \subseteq Q such that there exist computable functions \tau_1,\tau_2:N \to Z which satisfy (\forall n \in N \tau_2(n) \neq 0) \wedge ({\frac{\tau_1(n)}{\tau_2(n)}: n \in N}=R). This implication for R=N guarantees that Smoryński's theorem follows from Matiyasevich's theorem. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have a rational solution is not recursive. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have only finitely many rational solutions is not recursively enumerable. These conjectures are equivalent by our results for R=Q. (shrink)

Schröedinger’s question “what is life?” was a real challenge for the scientific community and this still remains as an opened question, because in spite of the important advances in various scientific branches like philosophy, biology, chemistry and physics,, each of them assesses life from its particular point of view to explain the life’ characteristic features, so not a coherent and well structured general model of life was reported. In this paper life is approached from informational perspective, starting from earlier Draganeacu's (...) philosophic concepts, showing that actually life is structured by matter and information. Therefore, it is analyzed carbon-matter properties on the basis of which the living structures are composed, giving rise not only of a considerable number of carbon-based compounds, but serving now beside silicon, as an useful material for micro/nanostructure applications. Such specific properties refers to the high ability of carbon to associate/dissociate in chemical reactions regulated/facilitated by informational (Bit unit) YES/NO bistable mechanisms to form macro/small molecules with complementary properties, reactive info-functional pathways of transduction, relaying, amplification, integration, spreading, modulation, activation and positive/negative feedback reactions, like in the informational microelectronic/microsystems circuits. It is argued that the negentropy invoked earlier in Schrödinger's analysis is a consequence of informational-assisted structuration/organization of the cell and human organism. From the analysis of inter/intra-communication mechanisms in the cell and comparing with the outcomes described by the Informational Model of Human Body, it is deduced that, the living organisms operate on the basis of three main streaming circuits assuring the living functions: (1) the metabolic matter-related circuit; (2) the operative informational circuit; (3) the epigenetic informational circuit for the gradual integration of information in the central informational structure – DNA. It is founded on these bases the Informational Model of the Living Structures, and the Informational System of the Living Structures (ISLS), with similar functions on the entire living scale size, from unitary to multicellular living structures, composed by seven informational systems, namely [CASI (center of acquisition and storing of information), CDC (center of decision and command), IRSS (info-reactive sentient system), MIS (maintenance info-system), GTS (genetic transmission system), IGG (info-genetic generator) and IC (info-connection)]ISLS, and are identified the specific functions of each of them. The living structures operate thus like self-“polarized" bipolar info-matter informational devices by means of the stand-by metabolic matter-related circuit, and react/respond to the external/internal informational stimuli, which modulate their functionality, returning an external reaction signal (“attitude"), for adaptation and survival. (shrink)

From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this (...) endeavor can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

The goal of this paper is to better understand Kant’s conception of philosophy as a “world concept”, which is at the heart of the Architectonic of Pure Reason. This is pursued in two major parts. The first evaluates the textual foundation for reading Kant’s world concept of philosophy as cosmopolitanism and concludes that he most probably never himself equated philosophy as a world concept with any form of cosmopolitanism. The second major part of the paper clarifies this concept of philosophy (...) through the specific role it plays in the argument of the Architectonic. Kant’s unique concept of science is examined and compared with several specific applications of it found elsewhere in Kant’s writings. From this it is concluded that Kant’s intention in the Architectonic was to derive his world concept of philosophy from its logical counterpart, namely the scholastic concept of philosophy, and that its function there is to provide the idea from which the entire structure of Kantian critical metaphysics can be derived. Philosophy as a world concept, it is further argued, is the complete system of critical or Kantian metaphysics in application and the philosopher in this sense is the ideal critical metaphysician who fully realizes its laws through her own understanding and will. (shrink)

We start from previous studies of G.N. Ord and A.S. Deakin showing that both the classical diffusion equation and Schrödinger equation of quantum mechanics have a common stump. Such result is obtained in rigorous terms since it is demonstrated that both diffusion and Schrödinger equations are manifestation of the same mathematical axiomatic set of the Clifford algebra. By using both such ( ) i A S and the i,±1 N algebra, it is evidenced, however, that possibly the two (...) basic equations of the physics cannot be reconciled. 1. (shrink)

In 1916, Johannes Droste independently found an exact (vacuum) solution to the Einstein's (gravitational) field equations in empty space. Droste's solution is quasi-comparable to Schwarzschild's one . Droste published his paper entitled “The field of a single centre in Einstein's theory of gravitation, and the motion of a particle in that fieldˮ. The paper communicated (in the meeting of May 27, 1916) by Prof. H.A. Lorentz, and published in ʻProceedings of the Royal Netherlands Academy of Arts and Science. 19 (1): (...) 197-215 (1917)ʼ. In the present article, the Droste's solution is scrutinized and proven to be invalid purely and simply because the procedure used by Droste is mathematically questionable since he had systematically, deliberately, and without any justification ‒removed the constant coefficient ʻ2ʼ from the differential term (v'w') in Eq.(6) and added the differential term (wv'') to the same Eq.(6) in order to obtain Eq.(7) which was and is his principal objective, that is, the desired solution. Consequently, Eqs.(6,7) had clearly been falsified. (shrink)

Previous research has interlinked alcohol consumption (AC), mental stress (MS), psychotic experiences (PE), and academic performance (AP) of students and psychological behavior of the general population. The current study seems to be the first to consider the joint and partial mediation effects of MS and PE in linking AC to graduates’ job performance in specific areas such as teamwork (TW), communication competence (CC), customer service (CS), and job functions (JF). A virtual cross-section of 3,862 graduates with self-reported cases of having (...) taken alcohol in the past participated in the study. These participants responded to an electronic questionnaire that was mailed to them. The instrument used for data collection had acceptable psychometric properties. The study used the partial least squares structural equation modeling (PLS-SEM) to achieve its objectives. The inner and outer models were all evaluated for quality and goodness of fit. Results showed a significant negative effect of AC and MS on graduates’ job performance in terms of TW, CC, CS, and JF, respectively. AC had a significant positive effect on MS and PE. MS had a significant positive effect on PE. A significant joint mediation effect of MS and PE was found in linking AC to graduates’ TW, CC, and CS, excluding JF. MS partially mediated AC’s paths to all the graduates’ job performance indicators. PE was only a significant partial mediator of the connection between AC to JF, but not TW, CC, and CS. This study’s result can help improve graduates’ work effectiveness and has revealed some negative predictors. Therefore, it is recommended that graduates avoid alcohol or only consume mild quantities of it to enable them to discharge services effectively at the workplace. (shrink)

Unifying physics by describing a variety of interactions – or even all interactions – within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lagrangian. Mie’s main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called (...) solitons), and he clarified the use of variational principles in the context of special relativity. The following brief introduction to Mie’s work has three main objectives. The first is to explain how Mie’s project fit into the contemporary development of the electromagnetic world view. Part of Mie’s project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electromagnetism. Finally, Mie was a vocal critic of other approaches to the problem of gravitation. Mie’s criticisms of Einstein, in particular, bring out the subtlety and novelty of the ideas that Einstein used to guide his development of general relativity. (shrink)