This paper aims to construct a new formula that generates a generalized version of congruent numbers based on a generalized version of Pythagorean triples. Here, an elliptic curve equation is constructed from the derived generalized version of Pythagorean triples and congruent numbers and gives some new results.

Data security is, protecting data from ill- conceived get to, utilize, introduction, intrusion, change, examination, recording or destruction. Cloud computing is a sort of Internet-based computing that grants conjoint PC handling resources and information to PCs what's more, different gadgets according to necessity. It is a model that empowers universal, on-request access to a mutual pool of configurable computing resources. At present, security has been viewed as one of the best issues in the improvement of Cloud Computing. The key issue (...) in effective execution of Cloud Computing is to adequately deal with the security in the cloud applications. This paper talks about the part of cryptography in cloud computing to improve the data security. The expectation here is to get bits of knowledge another security approach with the usage of cryptography to secure information at cloud data centers. (shrink)

The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it from (...) the pre-Socratics to the Pythagoreans). Husserl’s phenomenology and Heidegger’s derivative “fundamental ontology” as well as his later doctrine after the “turn” are the starting point of the research as established and well known approaches relative to the newly introduced conception of ontomathematics, even more so that Husserl himself started criticizing his “Philosophy of arithmetic” as too naturalistic and psychological turning to “Logical investigations” and the foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as a relation of locality and nonlocality, respectively as a motion from nonlocality to locality if both are physically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from the pre-Socratics' “Logos” or Heideger’s “Language” (after the “turn”) to the Pythagoreans “Numbers” or “Arithmetics” as an inherent and fundamental philosophical doctrine. Then, a leap to contemporary physics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’s opposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowing for the “creation from nothing” instead of the quasi-scientific myth of the “Big Bang”. Furthermore, ontomathematics needs another interpretation of arithmetic, propositional logic and set theory in the foundations of mathematics, where the latter two ones are both identified with Boolean algebra, and the former is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it after doubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of the foundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where the latter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newly introduced substance of quantum information being physically dimensionless and generalizing classical information measured in bits. The substance of information, whether classical or quantum, visualizes the way of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic and Hilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics to the Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity, is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectless choice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by Michel Foucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as the philosophy of locality ends the study. (shrink)

The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or “complimentary” (...) to its model. The historical reality by itself can be seen as mathematical if one considers it in Hegel’s manner as a specific interpretation of the totality being in a permanent self-movement due to being just the totality, i.e. by means of the “speculative dialectics” of history, however realized as a theory both mathematical and empirical and thus falsifiable as by logical contradictions within itself as emprical discrepancies to facts. Not less, a Husserlian kind of “historical phenomenology” is possible along with Hegel’s historical dialectics sharing the postulate of the totality (and thus, that of transcendentalism). One would be to suggest the transcendental counterpart: an “eternal”, i.e. atemporal and aspatial history to the usual, descriptive temporal history, and equating the real course of history as with its alternative, actually happened branches of the regions of the world as with only imaginable, counterfactual histories. That universal and transcendental history is properly mathematical by itself, even in a neo-Pythagorean model. It is only represented on the temporal screen of the standard historiography as a discrete series of unique events. An analogy to the readings of the apparatus in quantum mechanics can be useful. Even more, that analogy is considered rigorously and logically as implied by the mathematical transcendental history and sharing with it the same quantity of information as an invariant to all possible alternative or counterfactual histories. One can involve the hypothetical external viewpoint to history (as if outside of history or from “God’s viewpoint to it), to which all alternative or counterfactual histories can be granted as a class of equivalence sharing the same information (i.e. the number choices, but realized in different sequence or adding redundant ones in each branch) being similar and even mathematically isomorphic to Feynman trajectories in quantum mechanics. Particularly, a fundamental law of mathematical history, the law of least choice of the real historical pathway is deducible from the same approach. Its counterpart in physics is the well-known and confirmed law of least action as far as the quantity of action corresponds equivocally to the quantity of information or that of number elementary historical choices. (shrink)

This essay is a contribution to the historical phenomenology of science, taking as its point of departure Husserl’s later philosophy of science and Jacob Klein’s seminal work on the emergence of the symbolic conception of number in European mathematics during the late sixteenth and seventeenth centuries. Sinceneither Husserl nor Klein applied their ideas to actual theories of modern mathematical physics, this essay attempts to do so through a case study of the conceptof “spacetime.” In §1, I sketch Klein’s account of (...) the emergence of the symbolic conception of number, beginning with Vieta in the late sixteenth century. In §2,through a series of historical illustrations, I show how the principal impediment to assimilating the new symbolic algebra to mathematical physics, namely, thedimensionless character of symbolic number, is overcome via the translation of the traditional language of ratio and proportion into the symbolic language of equations. In §§3–4, I critically examine the concept of “Minkowski spacetime,” specifically, the purported analogy between the Pythagorean distance formula and the Minkowski “spacetime interval.” Finally, in §5, I address the question of whether the concept of Minkowski spacetime is, as generally assumed, indispensable to Einstein’s general theory of relativity. (shrink)

A set D subset of V(G) is a dominating set of a graph G if for all x ϵ V(G)\D, for some y ϵ D such that xy ϵ E(G). A dominating set D subset of V(G) is called a connected dominating set of a graph G if the subgraph <D> induced by D is connected. A connected domination number of G, denoted by γ_c(G), is the minimum cardinality of a connected dominating set D. The triple repetition sequence denoted by (...) {S_n:n ϵ Z+} is a sequence of positive integers which is repeated thrice, i.e., {S_n}={1,1,1,2,2,2,3,3,3, ...}. In this paper, we construct a combinatorial explicit formula for the triple repetition sequence of connected domination numbers of a triangular grid graph. (shrink)

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).

In the twenty-fourth aporia of Theophrastus' Metaphysics, there appears an important, if ‘bafflingly elliptical’, ascription to Plato and the ‘Pythagoreans’ of a theory of reduction to the first principles via ‘imitation’. Very little attention has been paid to the idea of Platonic and ‘Pythagorean’ reduction through the operation of ‘imitation’ as presented by Theophrastus in his Metaphysics. This article interrogates the concepts of ‘reduction’ and ‘imitation’ as described in the extant fragments of Theophrastus’ writings – with special attention to (...) his Metaphysics – in an attempt to make sense of how, precisely, Theophrastus characterizes the metaphysical systems of Plato and the ‘Pythagoreans’. A fuller examination of Aporia 24 produces important new understandings of the nature of the Early Academy in the mid fourth century B.C.E. Specifically, by ascribing the concept of reduction via ‘imitation’ to Plato and the ‘Pythagoreans’, Theophrastus is actually describing theories about the structure of the universe held by an important Platonist competitor and the contemporary head of the Academy in Athens, Xenocrates of Chalcedon (396/5–314/13 B.C.E.), who (a) took it upon himself to establish a Platonic doctrine that could be associated with his master’s writings and (b) coordinated that doctrine with the philosophical precepts of the Pythagoreans. As a consequence, we are prompted to question Aristotle’s famous ascription of a theory of ‘imitation’ to the metaphysics of the genuine contemporary or recently deceased Pythagoreans (such as Philolaus of Croton or Archytas of Tarentum) and consider how Xenocrates’ writings on Plato and the ‘Pythagoreans’ might be informing both Theophrastus’ and Aristotle’s descriptions of the Platonic and Pythagorean philosophical system(s). (shrink)

India dropped its target of 500 GW of renewable energy capacity fossil fuel sources by 2030. Its responsibilities the United Nations Framework Convention Climate Change [UNFCCC],and reducing radiations by one billion tonnes by the end of the decade at the COP26 conference, held in Glasgow in November 2022. Researchers are continually searching for inexhaustible and reasonable energy sources. Solar energy is one of the greenest sources of energy and is also one of the cleanest. The most important factor in using (...) solar energy is the location of the solar power plant. The main objective of this study is to find the best location for a new solar power plant in a specific region called Bundelkhand region of Uttar Pradesh in India. Here we offer an extension of ELECTRE III method as two-phase Pythagorean neutrosophic elimination and choice translating reality PN-ELECTRE-III) method to adapt with fuzzy, ambiguous, unsure, and indeterminate criteria. The Pythagorean neutrosophic numbers [PNNs] used by the group decision support system of PN-ELECTRE III to measure performance of the alternatives. The options are entirely outclassed in the subsequent stage in view of the past stage's evaluations of them. By defining PNN we describe the technique of indifference threshold functions, preference treshold and veto threshold functions, which provide a more stable basis to drop outranking relations. By calculating the concordance credibility, discordance credibility and net credibility degrees of each alternative, the ranking module of the PN-ELECTRE III approach is made simpler. In order to confirm the applicability of the strategy suggested in this paper, the location selection problem for solar plants is finaly solved. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive (...) evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

Notoriously, the Einstein equations of general relativity have solutions in which closed timelike curves occur. On these curves time loops back onto itself, which has exotic consequences: for example, traveling back into one's own past becomes possible. However, in order to make time travel stories consistent constraints have to be satisfied, which prevents seemingly ordinary and plausible processes from occurring. This, and several other "unphysical" features, have motivated many authors to exclude solutions with CTCs from consideration, e.g. by conjecturing a (...) chronology protection law. In this contribution we shall investigate the nature of one particular class of exotic consequences of CTCs, namely those involving unexpected cases of indeterminism or determinism. Indeterminism arises even against the backdrop of the usual deterministic physical theories when CTCs do not cross spacelike hypersurfaces outside of a limited CTC-region|such hypersurfaces fail to be Cauchy surfaces. We shall compare this CTC-indeterminism with four other types of indeterminism that have been discussed in the philosophy of physics literature: quantum indeterminism, the indeterminism of the hole argument, non-uniqueness of solutions of differential equations and lack of predictability due to insuffcient data. By contrast, a certain kind of determinism appears to arise when an indeterministic theory is applied on a CTC: things cannot be different from what they already were. Again we shall make comparisons, this time with other cases of determination in physics. We shall argue that on further consideration both this indeterminism and determinism on CTCs turn out to possess analogues in other, familiar areas of physics. CTC- indeterminism is close to the epistemological indeterminism we know from statistical physics, while the "fixedness" typical of CTC-determinism is pervasive in physics. CTC- determinism and CTC-indeterminism therefore do not provide incontrovertible grounds for rejecting CTCs as conceptually inadmissible. (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)

General Introduction: In [1] a Calculus of Qualia (CQ) was proposed. The key idea is that, for example, blackness is radically different than █. The former term, “blackness” refers to or is about a quale, whereas the latter term, “█” instantiates a quale in the reader’s mind and is non-referential; it does not even refer to itself. The meaning and behavior of these terms is radically different. All of philosophy, from Plato through Descartes through Chalmers, including hieroglyphics and emojis, used (...) referential terms up until CQ. This paper in this series of papers address equations vs. qualations (which contain non-referential terms), proofs, and logic. An example of an equation is x+2=4, which uses exclusively referential terms, even if some of them are numbers. A Qualation is like an equation except it uses actual non-referential terms (qualia), like █ ≠ ▲, and can be clearly non-trivial, like ¬((█ ≠ ▲) ∧ (▲ ≠ ■) → (█ ≠ ■)). (see below). This has implications for assertions, proofs, truth, etc. Incompleteness and truth are addressed in a different paper in this series. (shrink)

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.

This paper explores the physical and metaphysical implications of time travel, focusing on the possibility of changing the past, through a comparative analysis of David Lewis' modal realism and Everett's many-worlds interpretation of quantum mechanics. The existence of closed timelike curves (CTCs) in certain solutions to Einstein's field equations provides a theoretical basis for the possibility of backwards time travel, but this leads to a range of paradoxes, most notably the grandfather paradox. David Lewis argues that time travel must maintain (...) consistency and that the past cannot be changed, even if time travel were possible. His view is supported by his modal realism, which posits the existence of a plurality of possible worlds. In contrast, Everett's many-worlds interpretation, which holds that quantum mechanics describes a multiverse of branching realities, might seem to allow for the possibility of multiple, inconsistent histories. By examining these two ontological frameworks, this paper aims to shed light on the paradoxes of time travel and to explore whether the many-worlds interpretation provides a more satisfactory resolution to these paradoxes than Lewis' modal realism. It is argued that while Lewis' view provides a coherent model for maintaining consistency in time travel, Everett's interpretation may offer a more physically grounded and philosophically compelling account of the metaphysics of time travel. The paper concludes by suggesting that the many-worlds interpretation, by locating the branching of timelines within the structure of quantum mechanics itself, may provide a more promising framework for understanding the possibility and implications of time travel than Lewis' modal realism. However, significant questions remain about the nature of personal identity and free will in a branching multiverse. This comparative analysis aims to contribute to the ongoing debate about the metaphysical possibility of time travel and to highlight the value of engaging with interpretations of quantum mechanics in this context. Keywords: time travel, closed timelike curves, modal realism, many-worlds interpretation, grandfather paradox, metaphysics of time. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

This contribution aims to explore the historical predecessors of the Five Percenter model of self-realization, as popularized by Hip Hop artists such as Supreme Team, Rakim Allah, Brand Nubian, Wu-Tang Clan, or Sunz of Man. As compared to frequent considerations of the phenomenon as a creative mythological background for a socio-political struggle, Five Percenter teachings shall be discussed as contemporary interpretations of historical models of self-realization in various philosophical, religious, and esoteric systems. By putting the coded system of the tenfold (...) Supreme Mathematics as one of its core teachings in context with the Pythagorean Tetractys, an arrangement of ten points in four lines, the commonalities between the sequence and concepts attributed to the respective numbers will be demonstrated. (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)

Reading tough books to achieve excellent marks, perform well in class, and gain attention from teachers and parents is less likely to drive students. Students used to evaluate their language learning requirements, define the abilities they wished to develop, pick effective study techniques, and set aside gadgets when studying. They also used to read the question before looking for hints in the relevant content, extract the essential lines that convey the major ideas, concentrate on titles, names, numbers, quotations, or instances, (...) and comprehend the overall context to infer an option. The survey discovered that most of the time, students utilized it to determine the progress of their learning and create learning objectives. It was also found that there was a link between the exogenous variables and the academic performance of students. (shrink)

This book deals with Colombeau solutions to Einstein field equations in general relativity: Gravitational singularities, distributional SAdS BH spacetime-induced vacuum dominance. This book covers key areas of Colombeau nonlinear generalized functions, distributional Riemannian, geometry, distributional schwarzschild geometry, Schwarzschild singularity, Schwarzschild horizon, smooth regularization, nonsmooth regularization, quantum fields, curved spacetime, vacuum fluctuations, vacuum dominance etc. This book contains various materials suitable for students, researchers and academicians of this area.

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)

The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter. Implications to time-dependent Schrodinger wave equation and uncertainty (...) principle are hinted. (shrink)

A. Accident 1. We call an accident (συμβεβηκὸς) that which attaches to something and can be truly asserted, but neither of necessity nor usually.’ (Met. , Δ, 1025a14-16) 2. Whenever an accident attaches to a subject, it attaches to it not because it is that subject (μὴ διότι τοδὶ ἧν). (Met., Δ, 1025a21-24) 3. ‘There is no definite cause for an accident, but a chance cause, i.e. an indefinite one.’ (Met., Δ, 1025a24-25) 4. ‘The accident has happened or exists, -not (...) in virtue of itself, however, but of something else. (Met., Δ, 1025a28-29) 5. ‘What attaches to each thing in virtue of itself but is not in its substance is an accident.’ (Met., Δ, 1025a30-32) 6. ‘An accident is something which, though it is … neither a definition nor a property nor a genus, yet belongs to the thing.’ (To., I, 5, 102b4-) 7. An accident is ‘something which may either belong or not belong to any one and the self-same thing, as (e.g.) being seated may belong or not belong to some self-same thing.’ (To., I, 5, 102b4-) 8. ‘There is nothing to prevent an accident from becoming a temporary or relative property … [and] there is nothing to prevent an accident from becoming both a relative and a temporary property; but a property absolutely it will never be.’ Aristotle’s example is ‘being seated.’ That it is a temporary property is evident. It is also a relative property to those who are not seating when he is the only person sitting. Therefore, it is a temporary and also a relative property. 9. ‘In the case of accidents and in no other it is possible for something to be true in a certain respect and not universally’ and ‘there is nothing to prevent an attribute belonging in part’ so that it is open to dispute accidents e.g. being white or just about a man because he might be white or just in part only. Thus, ‘conversion is not a necessary process in the case of accidents.’ (To., B, 1, 109a9-) B. Essential versus accidental Aristotle distinguishes between two senses of being (τὸ ὄν): accidental sense (κατὰ συμβεβηκός) and essential sense (καθ᾿ αὑτό). The accidental sense happens when something is said to be another thing while there is in fact a third thing which is both of them. Thus, being the first thing is not by itself the second thing. a) Aristotle speaks of three ways in which one thing is said in an accidental sense to be another. (Met., Δ, 1017a8-22) i) When both the subject and the predicate are accidents of a third thing and it is in fact the third thing which ‘is’ by its own. Thus, when it is said e.g. that ‘The just is musical’ it is said accidentally because it is in fact a third thing, Socrates for example, which is just and musical. (Met., Δ, 1017a13-19) ii) When that to which the attribute belongs is. The example of this must be ‘the man is musical’ because it is in fact the man which is. iii) When the subject which has as an attribute that of which it is itself predicated, itself is. The example of this must be Aristotle’s third example: ‘The musical is man.’ b) Aristotle rejects the essential sense to categories: ‘Those things are said in their own right to be that are indicated by the figures of predication; for the senses of ‘being’ are just as many as these figures.’ (Met., Δ, 1017a22-24) Aristotle does not give us any example of the essential sense. Daniel W. Graham suggests that while essential predication is of the logical form of ‘S is P,’ the logical form of the accidental predication is ‘S has P.’ Although he concedes that the is/has contrast is not Aristotle’s, for which he thinks Aristotle prefers ‘said of’/’in’ terminology, he points to the discussion of ‘have’ in Cat. 15 as an evidence of its potential value for an analysis of predication. Kirwan analyses the distinction of essential and accidental predicate as such: while essential predicates ‘are identical with the subjects of which they are predicated; other predications are true in virtue of the fact that two distinct items, e.g. a substance and a quality, ‘coincide.’ Herman Weidemann believes ‘what divides a predicative statement which predicates essentially from a predicative statement which predicates accidentally is the fact that the former does- whereas the latter does not- answer the question what its subject cannot fail to be without ceasing to exist, as the somewhat its subject goes on existing, no matter what happens to be true of it during its existence, or, what kind of things its subject must be in order to be identifiable as one and the same object as long as it exists.’ C. Essential 1. Either the formula or the name of the subject of an essential attribute is involved in it. For example, animal is involved in female but not in white. (Met., Z, 1030b23-26) 2. Essential attributes, combined together, form a unity. Thus, e.g. animal and biped form a unity because they are both essential of man. (OI., II, 11, 21a14-16) 3. Aristotle distinguishes between two kinds of essential attributes (PsA., A, 4, 73a34-b3; 22, 84a12-17): a) Those attributes that belong to their subject as elements in its essential nature as e.g. line belongs to triangle or point to line. Here the very being of triangle is composed of line or that of line is composed of points: line is contained in the formula of triangle and point in that of line. b) Those attributes whose subjects are contained in their own defining formula as e.g. straight is an essential attribute of line because line is part of the defining formula of straight or odd belongs to number because number is part of the defining formula of odd. Every attribute that is related in neither of these two ways to its subject, it is not an essential but an accidental attribute. (PsA., A, 4, 73b3-5) 4. That attribute which is not predicated of a subject other than itself is an essential attribute. A substance cannot be predicated of anything but itself and is, thus, essential. (PsA., A, 4, 73b5-10) 5. A thing consequently co-stated with anything is essential. For example, if a beast dies when its throat is being cut, its death is also essentially connected with the cutting because the cutting was the cause of death, not death a coincidence of cutting. (PsA., A, 4, 73b10-15) 6. Essential attributes in both of this sense, either in the sense that their subjects are contained in them or in the sense that they are contained in their subjects, are necessary as well as consequently co-stated with their subjects. The reason is that it is impossible for them to inhere in their subjects either simply or in the qualified sense (that one or other of a pair of opposites must inhere in the subject as e.g. one of straight or curve must be necessarily predicable of a line or one of odd or even of number). (PsA., A, 4, 73b16-21; 6, 74b5-12; B, 96b1-5) 7. Only those attributes that are within a genus are essential and possessed by their respective subjects as such and, thus, are necessary. Thereupon, both the conclusion and the premises of demonstrations which produce scientific knowledge are essential. (PsA., A, 6, 75a28-31) Therefore, ‘the extreme and the middle terms must be drawn from the same genus; otherwise, as predicated, they will not be essential and will thus be accidents.’ (PsA., A, 6, 75b10-12) Also, the theorems of a science can be demonstrated by means of another science only when they are related as subordinate to superior. (PsA., A, 6, 75b13-) 8. Our knowledge of the connexion of an attribute with a subject is essential only when ‘we know that connexion through the middle term in virtue of which it inheres (καθ᾿ὃ ὑπἀρχει), and as an inference from basic premises essential and ‘appropriate’ to the subject.’ The essential belonging of the middle to the minor has a necessary connexion with its belonging to the same genus of the major and minor: ‘If that middle term also belongs essentially to the minor, the middle must belong to the same genus as the major and minor terms (ἀνάγκη τὸ μέσον ἐν τῇ αὐτῇ συγγενείᾳ εἶναι). (PsA., A, 9, 76a4-9) 9. In an essential predication, the predicate is signified of a subject identical with itself or with a species of itself. Since only predicates which signify substance signify that the subject is identical with the predicate or with a species of the predicate, predicates signifying substance are essentially predicated and any other predicate is accidental or coincidental. Thus, while animal is essentially predicated of man because man is identical with a species of animal, white is accidentally predicated of man because man is neither identical with white nor a species of it. (PsA., A, 22, 83a24-32) Weidemann discusses the confusion between essential predications and statements of identity. He warns that the expression ‘(to be) just what a man is’ (analogous to the Greek phrase ‘(εἶναι) ὃπερ ἀνθρώπον) ought not to be confused with the expression ‘just what it is for a man to be,’ which renders the phrase τὸ ὃπερ ἀνθρώπῳ εἶναι’ (1007a22, 23, 27-28); a confusion Kirwan discusses. 10. ‘Demonstration proves the inherence of essential attributes in things.’ (PsA., A, 22, 84a11-12) 11. ‘Nothing which does not happen to belong to the genus is essentially the genus; e.g. a white man is not essentially a color.’ Thus, while justice falls within the genus, a just man does not. (To., Γ, 1, ^116a24-) 12. There is no syllogism of essence (ti esti). Nevertheless, we come to know ti esti through a demonstration. (93b15-20; cf. 93b25-28) D. Accidental 1. An accidental attribute cannot be predicated of a subject universally. Thus, we cannot say ‘Every man is musical.’ The reason is that ‘universal attributes belong to things in virtue of their nature.’ Therefore, accidental predicates are predicated only of the individuals. (Met., Δ, 1017b33-1018a2) 2. An accidental is a mere name. (Met., E, 1026b13-) 3. An accidental is obviously akin to non-being. (Met., E, 1026b21) 4. ‘That which is neither always nor for the most part we call accidental.’ (Met., E, 1026b27-33) 5. The matter (ὕλη) is the cause of the accidental because it is matter which is capable of being otherwise than as it for the most part is. (Met., E, 1027a13-16) In fact, there is cause or principle of the incidental of the same kind as there are of the essential because if there were, everything would be of necessity. (Met., K, 1065a6-8) The causes of accidental are unordered and indefinite. (Met., K, 1065a25-26) 6. Since all science is either of that which is always or of that which is for the most part, there is no science of the accidental. (Met., E, 1027a19-24; K, 1064b30-1065a6) Therefore, since an accident may also not inhere and, thus, it is impossible to prove its inherence as a necessary conclusion, there is no demonstrative knowledge of accidents. (PsA., A, 6, 75a18-23) 7. The accidental is not necessary but indeterminate. (Met., K, 1065a24-26) 8. The co-positing of a subject and a predicate which are accidental either to the same subject or to one another, whiteness and being musical for instance, does not form a unity. (OI, II, 11, 21a7-14) 9. Negative predicates, i.e. predicates including a ‘not,’ are accidental predicates. Thus, if good be an essential predicate of a subject, ‘not bad’ cannot be essential but is accidental. (OI., II, 14, 23b15-20) 10. Every attribute which does not belong to its subject in either of two senses of essential attribute (cf. PsA., A, 4, 73a34-b3), namely, belonging to their subjects as an element of its formula or their subjects belonging to them as an element of them, is an accidental attribute. (PsA., A, 4, 73b3-5) 11. Those attributes that are predicated of a subject other than themselves are accidental attributes. Thus, everything except substance is an accidental in this sense. (PsA., A, 4, 73b5-10) 12. A thing not consequentially connected with anything is accidental. For example, in ‘while he was walking it lightened,’ the lightening was not due to his walking but was a coincidence. (PsA., A, 4, 73b10-15) 13. Those attributes that are not within a genus are accidental attributes. (PsA., A, 6, 75a28-31) Therefore, the extreme and middle terms that are not drawn from the same genus are accidents. (PsA., A, 6, 75b10-12) Moreover, to apply an attribute to subjects in different genera afford knowledge of the attribute, only as inhering accidentally, not as belonging to its subject as such.’ (PsA., A, 9, 75b38-76a3) . (shrink)

Two main cognitive theories predict that people find refuting evidence that falsifies their theorising difficult, if not impossible to consider, even though such reasoning may be pivotal to grounding their everyday thoughts in reality (i.e., Poletiek, 1996; Klayman & Ha, 1987). In the classic 2-4-6 number sequence task devised by psychologists to test such reasoning skills in a simulated environment – people fail the test more often than not. In the 2-4-6 task participants try to discover what rule the number (...) triple 2-4-6 conforms to. The rule is ‘ascending numbers’, but it is tricky to discover this rule. Participants tend to generate hypotheses with the properties of the 2-4-6 triple, for example, ‘even numbers ascending in twos’. They must search for evidence to test whether their hypothesis is the rule. But experimental evidence has shown that they tend to generate confirming triples that they expect to be consistent with their hypothesis rather than inconsistent falsifying triples. Counter to the two main hypothesis testing theories this paper demonstrates that falsification is possible in five 2-4-6 task experiments when participants consider an Imaginary Participant’s hypothesis. Experiment 1 and 2 show that competition with an opponent hypothesis tester facilitates falsification. Experiments 3 to 5 show that the consideration of an alternative hypothesis helps this falsification of hypotheses lead to rule discovery. The implications of the results for theories of hypothesis testing and reasoning are discussed. (shrink)

The flame displacement speed is one of the major characteristics in turbulent premixed flames. The flame displacement speed is experimentally obtained from the displacement normal to the flame surface, while it is numerically evaluated by the transport equation of the flame surface. The flame displacement speeds obtained both experimentally and numerically cannot be compared directly because their definitions are different. In this study, two kinds of experimental flame displacement speeds—involving the mean inflow velocity and the local flow velocity—were simulated using (...) the DNS data with the different Lewis numbers, and were compared with the numerical flame displacement speed. The simulated experimental flame displacement speed involving the mean inflow velocity had no correlation with the numerical flame displacement speed, while the simulated displacement speed involving the local flow velocity had a clear correlation with the numerical displacement speed in the cases of higher Lewis number than unity. The correlation coefficient of the simulated displacement speed involving the local flow velocity with the numerical displacement speed had a maximum value on the isosurface of the reaction progress variable with the maximum temperature gradient where the dilation effect of the flame is strongest. (shrink)

Sir Roger Penrose and prof. Stuart Hameroff had substantiated a theory that a human brain performs quantum computations. Logically, a question comes what information does then the brain compute and what is the result of such a quantum computing? To answer this, it is tempting to exploit isomorphism between complex hermitian 2 × 2 matrices and R4, more specifically a real vector representation of qubit states. P Arrighi proposed that "qubit states may be viewed as spatio-temporal objects, or indeed as (...) four-vectors of a Minkowski space-time." Under Orch OR theory assumptions, a very large number of entangled qubits is involved in a massive and highly complex computing task. What does this gigantic quantum computing machinery produce as the final outcome of its coordinated computations? The answer is obvious - it is the physical world as we see it, or the so called an external, to the human brain, reality (Minkowski space). Accordingly, underlying Orch OR brain computing concept is a mathematical connection between a qubit (qm) and relativity (Minkowski space). It is a connection between our mind, or the consciousness, and a physical reality the way we see it as the result of quantum computations of our brain. Does this mean that a physical reality as we see it, is being internally quantum computed and represented to us as a Minkowski space? That is, can a physical classical world be viewed as the result of our internal measurement leading to collapse of the quantum computed wave function? This abstract omits this question as irrelevant to the subject matter of a paper. The most important question is the aforementioned mathematical connection between quantum mechanics and relativity, it is a foundation which proves that Orch OR theory is correct. I propose that enormous quantum computing power in human brain does produce the Minkowski space, a representation of the physical reality. Mathematically, it is done by integrating, or encoding, the information about external physical world, into a qubit wave function vectors. I believe that probability distribution functions of pairs of fermions and bosons serve as the hidden variables encoding information about external world, into a qubit wave function vectors. They are hidden for two reasons. First is that these variables are not obvious as an intrinsic part of a qubit equation defining human brain quantum computing. Traditional way of thinking does not easily accommodate these variables into a qubit equation. The second reason they are hidden is because Einstein was desperately looking for them to make quantum mechanics complete. Simply, Sir Roger Penrose and prof. Stuart Hameroff had made a breakthrough that will have a very far reaching implications, including but not limited to Einstein hidden variables discovery. Quantum mechanics and relativity can be easily unified should indeed these variables be encoded into qubit as the carriers of information of the classical physical world. (shrink)

Abstract: In this research, an Artificial Neural Network (ANN) model was developed and tested to predict effect of oxygen consumption of thylakoid membranes (chloroplasts) from spinach after inhibition. A number of factors were identified that may affect of oxygen consumption of thylakoid membranes from spinach. Factors such as curve, herbicide, dose, among others, as input variables for the ANN model. A model based on multi-layer concept topology was developed and trained using the data from some inhibition of photosynthesis in (...) farms. The evaluation of testing the dataset shows that the ANN model is capable of correctly predicting the effect of oxygen consumption of thylakoid membranes (chloroplasts) from spinach after inhibition with 100% accuracy. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

According to the standard interpretation of Einstein’s field equations, gravity consists of mass-energy curving spacetime, and an additional physical force or entity—denoted by Λ (the ‘cosmological constant’)—is responsible for the Universe’s metric-expansion. Although General Relativity’s direct predictions have been systematically confirmed, the dominant cosmological model thought to follow from it—the ΛCDM (Lambda cold dark matter) model of the Universe’s history and composition—faces considerable challenges, including various observational anomalies and experimental failures to detect dark matter, dark energy, or inflation-field candidates. This (...) paper shows that Einstein’s Equivalence Principle entails two possible physical interpretations of General Relativity’s field equations. Although the field equations facially appear to support the standard interpretation—that gravity consists of mass-energy curving spacetime—the field equations can be equivalently understood as holding that gravitational effects instead result from mass-energy accelerating the metric-expansion of a second-order spacetime fabric superimposed upon an absolute, first-order Euclidean space, resulting in the observational appearance of spacetime curvature. This alternative interpretation of relativity is shown to be empirically equivalent to the standard interpretation of relativity, albeit with a changing value for Λ (which is similar to how Λ is understood in the conception of Λ as ‘quintessence’, but in this case takes Λ to be gravity). The reconceptualization is then shown to potentially resolve major observational anomalies for the ΛCDM model, including recent observations conflicting with ΛCDM predictions, as well as failures to directly detect dark matter, dark energy, and inflation field/particle candidates. (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

A number of papers have applied the CNI model of moral judgments to investigate deontological and consequentialist response tendencies (Gawronski et al., 2017). A controversy has emerged concerning the methodological assumptions of the CNI model (Baron & Goodwin, 2020, 2021; Gawronski et al. 2020). In this paper, we contribute to this debate by extending the CNI paradigm with a skip option. This allows us to test an invariance assumption that the CNI model shares with prominent process-dissociation models in cognitive and (...) social psychology (Klauer et al., 2015). Like for these models, the present experiments found violations of the invariance assumption for the CNI model. In Experiment 2, we replicate these results and selectively influence the new parameter for the skip option. In addition, structural equation modeling reveals that previous findings for the relationship between gender and the CNI parameters are completely mediated by the association of gender with primary psychopathy. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations (...) of energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, i.e. (...) geodesics are obtained from the principle of least action for mechanics, electrodynamics and quantum mechanics. The arrow of time, associated with the expansion of the Universe, identifies with grand dispersal of energy when high-energy densities transform by various mechanisms to lower densities in energy and eventually to ever-diluting electromagnetic radiation. Likewise, time in a quantum system takes an increment forwards in the detection-associated dissipative transformation when the stationary-state system begins to evolve pictured as the wave function collapse. The energy dispersal is understood to underlie causality so that an energy gradient is a cause and the resulting energy flow is an effect. The account on causality by the concepts of physics does not imply determinism; on the contrary, evolution of space–time as a causal chain of events is non-deterministic. (shrink)

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon for this purpose (...) are the differential calculus and the theory of dynamical systems, and Galois’ theory of polynomial equations. For the purposes of this paper I will only treat the first of these, which is based on the idea that the singularities of vector fields determine the local trajectories of solution curves, or their ‘topological behaviour’. These singularities can be described in terms of the given mathematical problematic, that is for example, how to solve two divergent series in the same field, and in terms of the solutions, as the trajectories of the solution curves to the problem. What actually counts as a solution to a problem is determined by the specific characteristics of the problem itself, typically by the singularities of this problem and the way in which they are distributed in a system. Deleuze understands the differential calculus essentially as a ‘calculus of problems’, and the theory of dynamical systems as the qualitative and topological theory of problems, which, when connected together, are determinative of the complex logic of different/ciation. (DR 209). Deleuze develops the concept of a problematic idea from the differential calculus, and following Lautman considers the concept of genesis in mathematics to ‘play the role of model ... with respect to all other domains of incarnation’. While Lautman explicated the philosophical logic of the actualization of ideas within the framework of mathematics, Deleuze (along with Guattari) follows Lautman’s suggestion and explicates the operation of this logic within the framework of a multiplicity of domains, including for example philosophy, science and art in What is Philosophy?, and the variety of domains which characterise the plateaus in A Thousand Plateaus. While for Lautman, a mathematical problem is resolved by the development of a new mathematical theory, for Deleuze, it is the construction of a concept that offers a solution to a philosophical problem; even if this newly constructed concept is characteristic of, or modelled on the new mathematical theory. (shrink)

The sequential patterns of the sixty-four hexagrams in the Yijing, variously known as I Ching (the Book of Changes) are structured to embrace the universe of possibilities, scenarios and probabilities. Each hexagram equates to each moment in space-time. With the arrow of time, a string of hexagrams represent a string of moments. A probability curve can be formed from the string of hexagrams. Physicists call this mathematical entity a wave function which is constantly changing and proliferating. A wave function (...) is mathematical representation of all possibilities that can happen to an observed entity when it interacts with an observer. The form of the wave function can be calculated by the Schrodinger wave equation for any part of the range of moments. The string of hexagrams deal with probabilities. Physicists deal mainly with two wave forms and functions – dynamic wave that follows the Schrodinger wave equation and the second phenomenon is the “collapse of the wave function” which is abrupt and discontinuous. Which part of the wave collapses is a matter of probability and chance. The wave transition from the first to the second is call the quantum jump. This exhibited phenomenon is very similar to how the hexagram in the Yijing. When unobserved, the sequential formation of the hexagrams, moment by moment, form a probability wave but when it is observed, it abruptly collapses. It is the abrupt collapse of all the development aspects of the wave function except the one that actualizes and that particular hexagram is therefore the mathematical representation of the observed entity. What spurs all the changes is the energy that flows through the system and all the interacting waves are interconnected and interdependent and they form the energy fields. Emphasis is on the stringed hexagrams, each possesses a sophisticated mathematical structure, suggesting at the same time that it would hold great significance as an integral part of the whole of the wave or energy field. The subject of this paper is on the quantum- informational theoretical framework of Yijing. (shrink)

This paper attempts to demonstrate that the conviction about the harmony and order of the world was a fundamental metaphysical principle of the Pythagoreans. This harmony and order were primarily sought in the structures of arithmetics, yet following the discovery of incommensurable magnitudes (irrational numbers, as we now call them), the Pythagoreans began to see geometrical structure as a fundamental part of the world. On the example of the Pythagoreans’ metaphysics and science, the paper shows the mutual relations between metaphysics (...) and science. It demonstrates— on the one hand—the necessity of the first as a guide for the latter, and—on the other—how our scientific research can change its basic metaphysical principles when these are found to be inappropriate. The paper also tries to show the need for a realistic approach in our scientific research by means of the same example of the Pythagoreans, that is, the need to discern something which is below the surface appearance. (shrink)

We compare the medieval projects of commentaries and disputations with the modern projects of formal ontology and of mathematics.

The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after (...) measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question. Number and being (by the meditation of time), the natural and artificial turn out to be not more than different hypostases of a single common essence. This implies some kind of neo-Pythagorean ontology making related mathematics, physics, and technics immediately, by an explicit mathematical structure. (shrink)

The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...) geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and (...) mass ratios suggest some further foundational interpretations of quantum electrodynamics. (shrink)

The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden (...) ratio. The Kepler triangle, with its golden ratio proportions, is also a Pythagorean triangle. Combining classical harmonic proportions derived from Kepler’s triangle with quartic equations determine an approximate value for the fine-structure constant that is the same as that found in our previous work with the golden ratio geometry of the hydrogen atom. These results make further progress toward an understanding of the golden ratio as the basis for the fine-structure constant. (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)

There are two problems Analytical Geometry with facing anyone who studies this discipline: define the nature of the locus represented by the general equation 2do degree in two or three variables: That curve represents the plane? What surface is in space? These two problems are posed and solved by applying the study of matrices and spectral theory.

In this paper I discuss how Borges uses his ideas on selfhood to explore the “central problem of literature” that Andre Maurois highlighted and how in the process projects to the reader his idea of reality. I argue also that the self that Borges tries to present in his work may nevertheless not be always congruent with the self he may have wanted to convey. This is because his quest is influenced by a number of factors, not least the (...) fact that the self-creation process is affected by our interplay with the external world. (shrink)

New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods described in this paper are able to work (...) with the exact values of the derivatives, instead of their approximations. (shrink)

The latest draft (posted 05/14/22) of this short, concise work of proof, theory, and metatheory provides summary meta-proofs and verification of the work and results presented in the Theory and Metatheory of Atemporal Primacy and Riemann, Metatheory, and Proof. In this version, several new and revised definitions of terms were added to subsection SS.1; and many corrected equations, theorems, metatheorems, proofs, and explanations are included in the main text. The body of the text is approximately 18 pages, with 3 sections; (...) 1, an Introduction (with a 108 page listing of key terms & definitions), sect. 2, the Results, sect. 3, Discussion (commentary & predictions), and sect. 4, Works Cited. As much as possible, the style is intended for readability and understanding by very bright children (with some interest & knowledge of maths, etc.) and very interested nonprofessionals. The results of this project also enable upgrades of number theory, set theory, proof theory, metamathematics, the foundations of science, and quantum mechanics theory (etc.). (shrink)

This paper examines the relation between Pythagorean and Heraclitean political views. I argue that for Pythagoras, Heraclitus, and Archytas the cosmological and musical notions of harmony (ἁρμονία) and the related notion of concord (ὁμόνοια) have an intrinsic political significance. These thinkers variously reflect upon political harmony and concord, and agree that a crucial condition for it is law (νόμος), which according to Pythagoras and Heraclitus has a divine origin. I begin with the Heraclitean fragments 22 B51, 54, 72, and (...) 114 DK, in which social and political reflection is connected with the theory of the harmony of opposites. In the case of Pythagoras and early Pythagoreanism, the intense, albeit indirect political influence in Magna Graecia—as transmitted by Iamblichus and Porphyry—offers evidence for social and political ideas determined by a reflection on the cosmological role of harmony and number. Finally, Archytas’ political application of rational calculation in fragment 47 B3 DK, which aims at producing concord by establishing the just measures of wealth in the city, together with the testimony on Archytas’ intense and fruitful political activity, can be taken as confirmation that the thinker’s wider cosmological views were indeed intertwined with his political reflection and action. (shrink)