The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...) explains the distinction and why it has proved to be one of the great organizing themes of mathematics. (shrink)

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We also argue that discrete (...) representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

In this field questions arise which are certainly difficult; but as I listened last time to members of the group, I felt that the main difficulty perhaps lay in determining precisely what questions we are trying to answer. I have the conviction that if we could only say clearly what the questions are, the answers to them might not appear so elusive. So I have begun with a simple list of questions about discretion which in one form or another (...) were, as it seemed to me, expressed by the group last time. I may indeed have omitted something and inserted something useless: if so, no doubt I shall be informed of this later. The central questions then seem to me to be the following: 1. What is discretion, or what is the exercise of discretion? 2. Under what conditions and why do we in fact accept or tolerate discretion in a legal system? 3. Must we accept discretion or tolerate discretion, and if so, why? 4. What values does the use of discretion menace, and what values does it maintain or promote? 5. What can be done to maximize the beneficial operation of the use of discretion and to minimize any harm that it does? (shrink)

The use of the model of discrete/quantized space sets the focus on mathematics instead of physics. It benefits the interpretation of observed and measured phenomena at the cosmological scale size. It is an approach that simplifies the problems around the understanding of the properties of the basic quantum fields.

Leibniz argues against Descartes’s conception of material substance based on considerations of unity. I examine a key premise of Leibniz’s argument, what I call the Plurality Thesis—the claim that matter (i.e. extension alone) is a plurality of parts. More specifically, I engage an objection to the Plurality Thesis stemming from what I call Material Monism—the claim that the physical world is a single material substance. I argue that Leibniz can productively engage this objection based on his view that matter is (...) discrete. The discreteness of matter provides two aspects of support for the Plurality Thesis. First, it indicates that the parts of matter do not share boundaries and are, therefore, independent in an important sense. Second, it indicates that the parts of matter are determinate and are, therefore, ontologically prior to the wholes they compose. (shrink)

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote Principia (...) Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)

Recently there is some new interest in understanding the physical reality behind the formalism of quantum mechanics. This paper relates the known “quantum mysteries” of QM with the properties of the underlying structure of discrete space. DOI: 10.5281/zenodo.5236617.

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

This paper addresses the issues related to designing and estimating the strength of solid-alloy elements in the deforming broaches of significant diameter (exceeding 150 mm) for the developed process of discrete broaching. The tool limit condition was assessed based on two strength criteria: the specific potential energy of shape change and the maximum tangent stresses. Numerical modeling using the finite element method has made it possible to derive the distribution of equivalent stresses in the tool elements and the contact stresses (...) at the surface of the contact between a solid-alloy insert and the body, which enabled the analysis of tool strength under loading. The simulation was performed under a single normal load, which ensured the versatility of the calculation for any contact pressure values. We have derived formulae to calculate the acceptable contact pressure depending on unit load. The effect of the insert protrusion height over the body on the strength of tool elements has been established. We have derived engineering dependences that determine the required magnitude of insert protrusion over the body depending on the ultimate load. An example of calculating the strength of a prefabricated deforming element in the machining of a sleeve made from gray modified cast iron of hardness HB230 has been considered. Our calculations have shown that the deforming element designed for the new technological process corresponds to the conditions of strength, provided the ratio h1/h=0.15 is maintained (where h1 is the insert height above the body, h is the insert height). The results obtained could be used in engineering calculations when designing the prefabricated tool for discrete deformation, as well as to assess the strength of prefabricated tools, such as cutters, core drills, reamers, when refining external loads. (shrink)

This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of these theories and CCQM for a realist view of the quantum realm.

In this paper, we have tried to prove the lack of discretion by providing a logical and philosophical connection between the fundamental concept of a function in mathematics and one of Einstein's most exceptional relativity results, namely, the relativity of simultaneity. Then, by providing real examples of social experiences and philosophical interpretations of them, we propose another proof for lack of discretion.

The ancient Greek philosopher Parmenides reasoned that observable reality is created by an underlying reality. However, an invisible underlying creating reality suggests that we cannot determine its existence with the help of experimental physics. This paper describes an experiment to measure absolute motion that will show that Parmenides concept about an underlying reality is correct. This in spite of Albert Einstein’s theory of special relativity that is founded on the assumption that it is impossible to detect the absolute motion of (...) objects. (shrink)

According to Discrete Emotion Theory, a number of emotions are distinguishable on the basis of neural, physiological, behavioral and expressive features. Critics of this view emphasize the variability and context-sensitivity of emotions. This paper discusses some of these criticisms, and argues that they do not undermine the claim that emotions are discrete. This paper also presents some works in dynamical affective science, and argues that to conceive of discrete emotions as self-organizing and softly assembled patterns of various processes accounts more (...) naturally than traditional Discrete Emotion Theory for the variability and context-sensitivity of emotions. (shrink)

The concept of discrete space can be termed as “the ex­ternal mathematical reality hypothesis”. The concept was already known among the ancient Greek philosophers (≈ 500 BC). Unfortunately the phenomenological point of view has dominated science during more than 2000 years and it is only recently that the concept of discrete space gets “tangible” attention again in philosophy and theoretical physics. Although the model de­scribes the existence of the universal conservation laws, constants and principles in a convincing way, the re­lation (...) between phenomenological reality and the geo­metrical description of discrete space is difficult to ima­gine for everyone who is only familiar with phenomeno­logical reality. The purpose of this paper is to describe some easy to imagine properties of discrete space. DOI: 10.5281/zenodo.5498120. (shrink)

While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment? – from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. To elucidate our (...) propositions, in the last section we will discuss some implications of discrete cellular-space model in several areas of interest: (a) cell biology, (b) cellular computing, (c) Maxwell equations, (d) low energy fusion, and (e) cosmology modelling. (shrink)

We give a new argument supporting a gravitational role in quantum collapse. It is demonstrated that the discreteness of space-time, which results from the proper combination of quantum theory and general relativity, may inevitably result in the dynamical collapse of thewave function. Moreover, the minimum size of discrete space-time yields a plausible collapse criterion consistent with experiments. By assuming that the source to collapse the wave function is the inherent random motion of particles described by the wave function, we further (...) propose a concrete model of wavefunction collapse in the discrete space-time. It is shown that the model is consistent with the existing experiments and macroscopic experiences. (shrink)

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I (...) believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time. (shrink)

We analyze the possible implications of spacetime discreteness for the special and general relativity and quantum theory. It is argued that the existence of a minimum size of spacetime may explain the invariance of the speed of light in special relativity and Einstein’s equivalence principle in general relativity. Moreover, the discreteness of spacetime may also result in the collapse of the wave function in quantum mechanics, which may provide a possible solution to the quantum measurement problem. These interesting results might (...) have some important implications for a complete theory of quantum gravity. (shrink)

In this brief introduction, I shall rather reflect, from a biographer’s viewpoint, on the significance of Discretion for our understanding of the trajectory of Hart’s ideas and on the significance of his year at Harvard. I shall then move on to consider the intriguing question of why Hart did not subsequently publish or build on some of the key insights in the paper itself. Here I highlight the fact that, almost uniquely in Hart’s work, Discretion features a notable (...) emphasis on the significance of institutional factors in our understanding of the nature of legal decisionmaking; and I argue that Hart’s failure fully to develop this insight in the essay, or to build on it in his subsequent work, derives from the fact that such a development would have necessitated a diversion from the philosophical issues that were his core intellectual concern, and moreover would have presented certain dangers to his conception of legal positivism. I shall conclude by considering what contribution the essay makes to our overall interpretation and evaluation of Hart’s legal philosophy. (shrink)

Paper about the origin of the wave-particle duality.

The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. The author (...) notes that the appearance of writing, symbolic language and the depiction of the picture of the world through mathematics, led us into the sphere of discrete mathematical mathematics. (shrink)

A recently proposed model of sensory processing suggests that perceptual experience is updated in discrete steps. We show that the data advanced to support discrete perception are in fact compatible with a continuous account of perception. Physiological and psychophysical constraints, moreover, as well as our awake-primate imaging data, imply that human neuronal networks cannot support discrete updates of perceptual content at the maximal update rates consistent with phenomenology. A more comprehensive approach to understanding the physiology of perception (and experience at (...) large) is therefore called for, and we briefly outline our take on the problem. (shrink)

There are reports about human experiences of time that are not in line with Einstein’s theory of Special relativity and not in line with the rate of change of the electromagnetic field at the smallest scale size. Some psychological reports describe human experiences about the metric of time that defy physical reality as we know it. These reports question the reliability of our understanding of time.

As far as we know the scientific search for the nature of reality in Europe started about 2500 years ago in ancient Greek. It was the ancient Greek philosopher Parmenides who reasoned that observable reality is created by an underlying reality. There are indications that the ancient Greek concept of the atom was (also) related to the proposed units of the structure of the underlying creating reality of Parmenides. However, an invisible underlying creating reality suggests that we cannot determine its (...) existence with the help of experimental physics. This paper describes an experiment that will show that Parmenides concept about an underlying reality is correct. (shrink)

The increasing use of opioid treatment agreements has prompted debate within the medical community about ethical challenges with respect to their implementation. The focus of debate is usually on the efficacy of OTAs at reducing opioid misuse, how OTAs may undermine trust between physicians and patients and the potential coercive nature of requiring patients to sign such agreements as a condition for receiving pain care. An important consideration missing from these conversations is the potential for racial bias in the current (...) way that OTAs are incorporated into clinical practice and in the amount of physician discretion that current opioid guidelines support. While the use of OTAs has become mandatory in some states for certain classes of patients, physicians are still afforded great leeway in how these OTAs are implemented in clinical practice and how their terms should be enforced. This paper uses the guidelines provided for OTA implementation by the states of Indiana and Pennsylvania as case studies in order to argue that giving physicians certain kinds of discretion may exacerbate racial health disparities. This problem cannot simply be addressed by minimising physician discretion in general, but rather by providing mechanisms to hold physicians accountable for how they treat patients on long-term opioid therapy to ensure that such treatment is equitable. There are no data in this work. (shrink)

Special issue in honour of Landon Rabern. This special issue of Discrete Mathematics is dedicated to his memory, as a tribute to his many research achievements. It contains 10 new articles written by his collaborators, friends, and colleagues that showcase his interests.

This paper presents a theoretical study of the binary oppositions underlying the mechanisms of natural computation understood as dynamical processes on natural information morphologies. Of special interest are the oppositions of discrete vs. continuous, structure vs. process, and differentiation vs. integration. The framework used is that of computing nature, where all natural processes at different levels of organisation are computations over informational structures. The interactions at different levels of granularity/organisation in nature, and the character of the phenomena that unfold through (...) those interactions, are modeled from the perspective of an observing agent. This brings us to the movement from binary oppositions to dynamic networks built upon mutually related binary oppositions, where each node has several properties. (shrink)

Street-level bureaucrats are a fundamental part of the implementation process of any policy. This study provides an examination of the factors that shape the behavior of street-level bureaucrats at the frontlines of policy implementation. This study investigates how rebelliousness generates an impact on the discretion of street-level bureaucrats and to what extent client meaningfulness plays a moderating factor. It utilizes a survey questionnaire distributed among inspectors of the Department of Labor in the Ministry of Human Resources of Malaysia (n=241). (...) The result of this study demonstrates that rebelliousness has a negative relationship with discretion, and client meaningfulness has a direct positive correlation with discretion. However, the relationship between rebelliousness and discretion is stronger with a high level of client meaningfulness. The objective of this study is to examine street-level bureaucrat behavior through the lens of Lipsky's theory which will provide an answer to the broad question of the factors that contribute to the existence of an imperfect implementation process. This study sheds light on the importance of client meaningfulness in moderating the behavior of street-level bureaucrats while interacting with inspectees. The novelty of this study is by highlighting two main constructs that are likely contributing to the implementation process by directly and indirectly impacting bureaucrats’ discretion: rebelliousness, and client meaningfulness. (shrink)

This report presents the results of a research project which examined how Polish administrative courts exercise discretionary powers when deciding cases related to business activity. When a business enterprise asks the court to review actions taken by administration, judges decide whether an administrative body has used its powers in accordance with the law. The law in this case includes both the relevant statutory regulations but also more general principles originating from other sources, such as the Constitution or European Union law. (...) It is generally accepted that in such cases courts have discretion, i.e. are able to select legal standards on which to base their judgments and to decide how to apply such standards to the case at hand. This does not mean, of course, that administrative court judges can do what they please. But, within some well-established boundaries, they can select from among various rules and principles those legal standards which apply to the case before them, interpret their meaning, and assess their importance. We aim to understand this process. (shrink)

In this essay I argue that art is able to open a new window on to reality only when art can transcend reason and the confines of language. Moreover, both logic and language have their limitations when used as tools for the creation of meaning and that art helps us overcome these inadequacies in the way it transcends — or even transgresses — the absolutes that underpin our “rational” view of the world. Lastly, the violation of the strictures of logic (...) by art is also emblematic of art’s heightened awareness of certain unique features of reality — in particular, its dynamic and fluid nature — which are not normally readily visible to a mind tied to thinking in terms only of binary truth values. (shrink)

Among the many problems facing u.s. immigration law is a crisis of discretion and judicial deference. Through two recently passed laws, the United States Congress and the President have seriously limited judicial review o f discretionary immigration decisions o f the Board ofImmigration Appeals. This Article focuses on this preclusion of judicial review of discretionary agency decisions. The Article begins with an examination ofdiscretion from a theoretical perspective, and goes on to examine areas o f immigration law in which (...) discretion was traditionally most imponant. That examination is followed by a discussion of immigration-law scholarship and critique. The Article concludes that what is needed in U.S. immigration law is greater restraint, and calls on the Judiciary to provide more oversight regarding discretionary agency decisions. (shrink)

The explanation of the existence of quantum transfer in vacuum space around celestial bodies under influence of gravitational vectors./.

Regulatory enforcement is a multifaceted phenomenon that revolves around the concept of discretion of Street-Level Bureaucrats (SLBs). Discretion can be defined as the ability to freely decide how to deliver services to the clients/public. Regulations are enforced by the decisions made by bureaucrats when they interact with clients. By combining street-level bureaucracy and responsive regulation theories, this study is set to examine how different factors shape the discretion of street-level bureaucrats. This study is built on available literature (...) pertaining to SLBs and policy implementation to provide a comprehensive understanding of regulation enforcement in Malaysia. SLBs are the Labor Inspectors responsible for the enforcement of minimum wage in Malaysia. The study’s main contribution is examining how personal characteristics, internal organizational factors, and a multidimensional enforcement style shape the discretion of bureaucrats in Malaysia. The study’s main finding highlights that Labor Inspectors in Malaysia demonstrate a range of enforcement style dimensions when enforcing the minimum wage. The novelty of this thesis highlights two primary constructs; willingness to implement and client meaningfulness, and their importance in shaping policy implementation and its effect on street-level bureaucrats' behavior. These constructs are also likely contributing to the imperfect enforcement of the minimum wage policy. Furthermore, this study demonstrates that enforcement style consists of three dimensions; legal, facilitation, and accommodation. Finally, this study's empirical finding highlights that street-level bureaucrats' discretion is influenced by various factors that ultimately define the enforcement process. (shrink)

Our universe shows to be local and non-local. The concept is confusing because in daily live we are not aware of the non-locality of our universe. Actually, in daily live local reality seems to be quite orderly and understandable. But we don’t know why everything is in motion and all our theories in physics are still approximations of physical reality. At least that is what they supposed to be.

In 2001, three non-Aboriginal men in their twenties were charged with the sexual assault of a twelve year old Aboriginal girl in rural Saskatchewan. Legal proceedings lasted almost seven years and included two preliminary hearings, two jury trials, two retrials with juries, and appeals to the provincial appeal court and the Supreme Court of Canada. One accused was convicted. The case raises questions about the administration of justice in sexual assault cases in Saskatchewan. Based on observation and analysis of the (...) record, this paper: (1) examines relationships between legal errors dealing with availability of the defence of “belief in consent” and interpretation of the “all reasonable steps” provision, the need for retrials, and apprehended race-gender-age bias and discrimination; and 2) proposes incremental and systemic remedies to address the weaknesses in police, prosecutorial and judicial policy and practice highlighted by this case. (shrink)

This study considers the problem of using approximate way for realizing the neural supervisor for nonlinear multivariable systems. The Nonlinear Autoregressive-Moving Average (NARMA) model is an exact transformation of the input-output behavior of finite-dimensional nonlinear discrete time dynamical organization in a hoodlum of the equilibrium state. However, it is not convenient for intention of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate technique are used for realizing the neural supervisor to (...) overcome computational complexity. In this study, we introduce two classes of ideal which are approximations to the NARMA model and which are linear in the control input, namely NARMA-L1 and NARMA-L2. The latter fact substantially simplifies both the theoretical breakdown as well as the practical request of the controller. Extensive imitation studies have shown that the neural controller designed using the proposed approximate models perform very well and in dozens situation even better than an approximate controller designed using the exact NARMA Model. In view of their mathematical tractability as well as their fate in simulation studies, a matter is made in this study that such approximate input-output paragon warrants a detailed study in their own right. (shrink)

One of the oldest questions in science and philosophy is whether reality is fundamentally discrete, or fundamentally continuous. In this short essay I show that this question should first be classified into two main categories. 1) Intrinsic existence, 2) Behavioral existence. I show that the first category should be continuous by definition, while the second category could probably be either continuous or discrete.

The ancient Greek philosophers – like Parmenides – reasoned that observable reality cannot exist by itself. It has to be a creation of an underlying reality. An all-in­clusive existence that has a structure because observable reality shows structure at every scale size. Although observable reality is involved in a continuous transformation too. If our concept about the relation between phenomenological reality and the creating underlying reality is correct, the unification of the properties of phenomenological reality is part of an enveloping (...) mathematical model. DOI: 10.5281/zenodo.5457368. (shrink)

This Essay analyzes an essay by H. L. A. Hart about discretion that has never before been published, and has often been considered lost. Hart, one of the most significant legal philosophers of the twentieth century, wrote the essay at Harvard Law School in November 1956, shortly after he arrived as a visiting professor. In the essay, Hart argued that discretion is a special mode of reasoned, constrained decisionmaking that occupies a middle ground between arbitrary choice and determinate (...) rule application. Hart believed that discretion, soundly exercised, provides a principled way of coping with legal indeterminacy that is fully consistent with the rule of law. This Essay situates Hart’s paper – Discretion – in historical and intellectual context, interprets its main arguments, and assesses its significance in jurisprudential history. In the context of Hart’s work, Discretion is notable because it sketches a theory of legal reasoning in depth, with vivid examples. In the context of jurisprudential history, Discretion is significant because it sheds new light on long-overlooked historical and theoretical connections between Hart’s work and the Legal Process School, the American jurisprudential movement dominant at Harvard during Hart’s year as a visiting professor. Hart’s Discretion is part of our jurisprudential heritage, advancing our understanding of legal philosophy and its history. (shrink)

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

The proposed existence of relative time and the curvature of space – both combined into the concept of spacetime – influences the search for an adequate theoretical model that can describe the structure of space in an accurate way. The aim of building space is to develop a quantum theory of gravitation. This paper investigate the theoretical problems that have their origin in the concepts that are at the basis of phenomenological physics.

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...) that ignorance of their nature is profound. (shrink)

The literature acknowledges a distinction between immoral, amoral and moral management. This paper makes a case for the employee (at any level) as a moral agent, even though the paper begins by highlighting a body of evidence which suggests that individual moral agency is sacrificed at work and is compromised in deference to other pressures. This leads to a discussion about the notion of discretion and an examination of a separate, contrary body of literature which indicates that some individuals (...) in corporations may use their discretion to behave in a socially entrepreneurial manner. My underlying assumption is that CSR isn’t solely driven by economics and that it may also be championed as a result of a personal morality, inspired by employees’ own socially oriented personal values. A conceptual framework is put forward and it is suggested that individuals may be categorized as Active or Frustrated Corporate Social Entrepreneurs; Conformists or Apathetics, distinguished by their individualistic or collectivist personal values. In a discussion of the nature of values, this paper highlights how values may act as drivers of our behavior and pays particular attention to the values of the entrepreneur, thereby linking the existing debate on moral agency with the field of corporate social responsibility. (shrink)

Big Bang and the actual state of the universe; not information; entropic time is wrong; not discrete computation; 1-d topologies; QBism reconsidered; not Boltzmann brains; A-theories; the Big Bang and A-theories; not Boltzmann brains again.

Let a "smooth experience" be an experience with perfectly gradual changes in phenomenal character. Consider, as examples, your visual experience of a blue sky or your auditory experience of a rising pitch. Do the phenomenal characters of smooth experiences have continuous or discrete structures? If we appeal merely to introspection, then it may seem that we should think that smooth experiences are continuous. This paper (1) uses formal tools to clarify what it means to say that an experience is continuous (...) or discrete, and (2) develops a discrete model of the phenomenal characters of smooth experiences. As a result, I'll argue that introspection leaves open whether smooth experiences are continuous or discrete. Yet I’ll also argue—perhaps surprisingly—that the discrete theory may better fit our introspective evidence. (shrink)

This paper argues that all of the standard theories about the divisions of space and time can benefit from, and may need to rely on, parsimony considerations. More specifically, whether spacetime is discrete, gunky or pointy, there are wildly unparsimonious rivals to standard accounts that need to be resisted by proponents of those accounts, and only parsimony considerations offer a natural way of doing that resisting. Furthermore, quantitative parsimony considerations appear to be needed in many of these cases.

Being able to ask others to do things, and thereby giving them reasons to do those things, is a prominent feature of our interpersonal lives. In this paper, I discuss the distinctive normative status of requests – what makes them different from commands and demands. I argue for a theory of this normative phenomenon which explains the sense in which the reasons presented in requests are a matter of discretion. This discretionary quality, I argue, is something that other theories (...) cannot accommodate, though it is a significant aspect of the relations that people stand in to one another, and the kinds of practical reasons that flow from those relations. (shrink)

An ideal constructor produces geometry from scratch, modelled through the bottom-up assembly of a graph-like lattice within a space that is defined, bootstrap-wise, by that lattice. Construction becomes the problem of assembling a homogeneous lattice in three-dimensional space; that becomes the problem of resolving geometrical frustration in quasicrystalline structure; achieved by reconceiving the lattice as a dynamical system. The resulting construction is presented as the introductory model sufficient to motivate the formal argument that it is a fundamental structure; based on (...) which, it is proposed that where mathematics’ numbers conventionally correspond to dimensionless points on the stateless number line, numbers more fundamentally correspond to an ordering of discrete objects constructed within the stateful number lattice. A second observation is that this fundamental lattice structure is helically configured with fractal character, which, as it relates to the geometry underlying spacetime, has relevance to questions in physics, particularly those involving wave-particle duality. (shrink)