All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (i.e. all its non-empty clopen subspaces are homeomorphic), with the trivial exception of locally compact spaces. In fact, we obtain a more general result on the uniqueness of zero-dimensional homogeneous spaces which generate a given Wadge class. This extends work of van Engelen (who obtained the corresponding results for Borel spaces), complements a result of (...) van Douwen, and gives partial answers to questions of Terada and Medvedev. (shrink)

ABSTRACTThe emergence of dimensional analysis in the early nineteenth century involved a redefinition of the pre-existing concepts of homogeneity and dimensions, which entailed a shift from a qualitative to a quantitative conception of these notions. Prior to the nineteenth century, these concepts had been used as criteria to assess the soundness of operations and relations between geometrical quantities. Notably, the terms in such relations were required to be homogeneous, which meant that they needed to have the same geometrical (...) dimensions. The latter reflected the nature of the quantities in question, such as volume vs area. As natural philosophy came to encompass non-geometrical quantities, the need arose to generalize the concept of homogeneity. In 1822, Jean Baptiste Fourier consequently redefined it to be the condition an equation must satisfy in order to remain valid under a change of units, and the ‘dimension' correspondingly became the power of a conversion factor. When these innovations eventually found an echo in France and Great Britain, in the second half of the century, tensions arose between the former, qualitative understanding of dimensions as reflecting the nature of physical quantities, and the new, quantitative conception based on unit conversion and measurement. The emergence of dimensional analysis thus provides a case study of how existing rules and concepts can find themselves redefined in the context of wider conceptual changes; in the present case this redefinition involved a generalization, but also a shift in meaning which led to conceptual tensions. (shrink)

The one-dimensional case of the homogeneous Hamilton–Jacobi and Bernoulli equations St $${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0em}\!\lower0.7ex\hbox{$2$}}$$ S x 2 =0, where S(x, t) is Hamilton's principal function of a free particle and also Bernoulli's momentum potential of a perfect liquid, is considered. Non-elementary solutions are looked for in terms of odd power series in t with x-dependent coefficients and even power series in x with t-dependent coefficients. In both cases, and depending upon initial conditions, unexpected regularities are observed in (...) the terms of these expansions and this suggests that S(x, t) should be written as a product of the elementary solution x2/(2t) and a function f=f(φ) where φ=φ(x, |t|) owing to the symmetry property which is that S(x, −t)=−S(x, t). Requiring that this Ansatz satisfies the said equation and choosing the simplest realization of φ(x, |t|)=φ0 |t/t0|κ (x/x 0)λ≥0 with κ, λ∈ ℝ results in a soluble ordinary differential equation, of first order in u=ln φ and quadratic in f. This ODE has two fixed points: f=1, obviously, and f=0, a new fixed point which is often called “trivial.” The phase plane (fu, f) consists of a family of parabolas, all of which pass through the two fixed points. Explicit solutions of the general case are given close to these fixed points. A one-parameter family of solution is found to emerge from the “trivial” fixed point with non-trivial initial values S(x, 0). Detailed analyses of these findings will be reported elsewhere, bearing in mind that Bernoulli's equation has to be supplemented by the continuity equation satisfied by the density of the liquid. (shrink)

It is shown that the admissible solutions of the continuity and Bernoulli or Burgers' equations of a perfect one-dimensional liquid are conditioned by a relation established in 1949–1950 by Pauli, Morette, and Van Hove, apparently, overlooked so far, which, in our case, stipulates that the mass density is proportional to the second derivative of the velocity potential. Positivity of the density implies convexity of the potential, i.e., smooth solutions, no shock. Non-elementary and symmetric solutions of the above equations are (...) given in analytical and numerical form. Analytically, these solutions are derived from the original Ansatz proposed in Ref. 1 and from the ensuing operations which show that they represent a particular case of the general implicit solutions of Burgers' equation. Numerically and with the help of an ad hoc computer program, these solutions are simulated for a variety of initial conditions called “compatible” if they satisfy the Morette–Van Hove formula and “anti-compatible” if the sign of the initial velocity field is reversed. In the latter case, singular behaviour is observed. Part of the theoretical development presented here is rephrased in the context of the Hopf–Lax formula whose domain of applicability for the solution of the Cauchy problem of the homogeneous Hamilton–Jacobi equation has recently been enlarged. (shrink)

Some arguments, based on the possible spontaneous violation of the cosmological principle (represented by the observed large-scale structures of galaxies), on the Cartan geometry of simple spinors, and on the Fock formulation of hydrogen atom wave equation in momentum space, are presented in favor of the hypothesis that space-time and momentum space should be both conformally compactified and should both originate from the two four-dimensional homogeneous spaces of the conformai group, both isomorphic (S 3 ×S 1)/Z 2 and correlated (...) by conformal inversion, but should not necessarily be identified with them. Within this framework, the possible common origin for the SO(4) symmetry underlying the geometrical structure of the Universe, of Kepler orbits, and of the H atom is discussed. One of the consequences of the proposed hypothesis could be that any quantum field theory should be naturally free from both infrared and ultraviolet divergences. But then physical spaces defined as those where physical phenomena may be best described through some set of fields, could be different from those homogeneous spaces. A simple, exactly soluble, toy model, valid for a two-dimensional spacetime, is presented where the conjectured conformally compactified homogeneous spaces are both isomorphic to (S 1 ×S 1)/Z 2,while the possible physical spaces could be two finite lattices which are dual since Fourier transforms, represented by finite, discrete, sums, may be well defined on them. (shrink)

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed (...) phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered. (shrink)

We prove a partition theorem for analytic sets, namely, if X is an analytic set in a Polish space and [X]n = K0 ∪ K1 with K0 open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect K0-homogeneous subset or X is a countable union of K1-homogeneous subsets. We also prove a partition theorem for analytic sets in the three-dimensional case. Finally, we give some applications of the theorems.

In the homogeneous case of one-dimensional objects, we show that any relation that is positive and homothetic can be represented by a ratio-scale and a unique and constant biasing factor. This factor may favor or disfavor the preference for an object over another. In the first case, preferences are complete but not transitive and an object may be preferred even when its value is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it (...) may not be sufficient for an object to have a greater value to be preferred. In this manner, the biasing factor reflects the extent to which preferences may depart from a maximization process. (shrink)

It is an old idea, lately out of fashion but now experiencing a revival, that quantum mechanics may best be understood, not as a physical theory with a problematic probabilistic interpretation, but as something closer to a probability calculus per se. However, from this angle, the rather special C *-algebraic apparatus of quantum probability theory stands in need of further motivation. One would like to find additional principles, having clear physical and/or probabilistic content, on the basis of which this apparatus (...) can be reconstructed. In this paper, I explore one route to such a derivation of finite-dimensional quantum mechanics, by means of a set of strong, but probabilistically intelligible, axioms. Stated very informally, these require that systems appear completely classical as restricted to a single measurement, that different measurements, and likewise different pure states, be equivalent (up to the action of a compact group of symmetries), and that every state be the marginal of a bipartite non-signaling state perfectly correlating two measurements. This much yields a mathematical representation of (basic, discrete) measurements as orthonormal subsets of, and states, by vectors in, an ordered real Hilbert space – in the quantum case, the space of Hermitian operators, with its usual tracial inner product. One final postulate (a simple minimization principle, still in need of a clear interpretation) forces the positive cone of this space to be homogeneous and self-dual and hence, to be the state space of a formally real Jordan algebra. From here, the route to the standard framework of finite-dimensional quantum mechanics is quite short. (shrink)

A simple interpretation of quantity calculus is given. Quantities are described as two-place functions from objects, states or processes (or some combination of them) into numbers that satisfy the mutual measurability property. Quantity calculus is based on a notational simplification of the concept of quantity. A key element of the simplification is that we consider units to be intentionally unspecified numbers that are measures of exactly specified objects, states or processes. This interpretation of quantity calculus combines all the advantages of (...) calculating with numerical values (since the values of quantities are numbers, we can do with them everything we do with numbers) and all the advantages of calculating with standardly conceived quantities (calculus is invariant to the choice of units and has built-in dimensional analysis). This also shows that the standard metaphysics and mathematics of quantities and their magnitudes is not needed for quantity calculus. At the end of the article, arguments are given that the concept of quantity as defined here is a pivotal concept in understanding the quantitative approach to nature. As an application of this interpretation of quantity calculus, an easy proof of dimensional homogeneity of physical laws is given. (shrink)

This chapter concerns dimensions as the term is used in the physical sciences today. Some key points made are: Quantities of the same kind have the same dimension; but that two quantities have the same dimension does not necessarily mean they are of the same kind. The dimension of a quantity is not determined for a single quantity in isolation, but relative to a system of quantities and the relations that hold between them. Dimensions, units, and quantities are distinct notions. (...) In this article, I explain how dimensions, units, and quantities are involved in the design of coherent systems of units; the account involves the equations of physics. When the use of a coherent system of units can be presumed, dimensional analysis is a powerful logico-mathematical method for deriving equations and relations in physics, and for parameterizing equations in terms of dimensionless parameters, which allows identifying physically similar systems. The source of the information yielded by dimensional analysis is not yet well understood in philosophy of physics. This chapter aims to reveal the role of dimensions not only in applications of dimensional analysis to obtain information by involving the principle of dimensional homogeneity, but to the role of dimensions in encoding information about physical relationships in the language of dimensions, specifically via the feature of coherence of a system of units. Philosophers of mathematics and philosophers of science have been concerned to address the question of the effectiveness of mathematics in science. It is argued here that no philosophical analysis of the question of the applicability of mathematics to science is complete without including dimensions and dimensional analysis in the picture. (shrink)

This paper shows that, in Newtonian mechanics, unstable three-dimensional rigid bodies must exist. Laraudogoitia recently provided examples of one- and two-dimensional homogeneous unstable rigid bodies, conjecturing the instability would persist for three-dimensional bodies in four-dimensional space. My result proves that, if one admits non homogeneous balls or hollow spheres, then the conjecture is true without having to resort to tetra-dimensionality. Furthermore, I show that instability also holds for at least certain simple classes of elastic bodies. Altogether, (...) the laws of classical dynamics actually lead to the existence of unstable material bodies belonging to the three types of entities accepted therein: point particles, rigid bodies and continuous deformable bodies. A whole range of forms of indeterminism which, until now, has not been considered in the literature. I end with a new conjecture on the connection existing between all these forms of instability and the dimensionality of space. (shrink)

The generative and governing "idea" of radical modernity is spawned by the technique of mathematical construction deployed and interpreted by the major early-modern thinkers and their legatees. ;Chapter I is a survey of this legacy as it appears in Vico, Kant, Fichte, Marx and Nietzsche and in the post-Nietzschean inheritance of contemporary philosophy, hyperbolic in the case of Derrida et al., elliptical, in the case of Carnap and Goodman. ;In Chapter II I try to show how the pre-modern mathematical tradition, (...) represented by Euclid, aimed at keeping the enticements of technical facility in check by means of didactic phronesis and how the post-Kantian interpretation of "existence" in Euclid as constructibility betrays his usage and self-understanding. I suggest that his focus in the postulates and elsewhere is on the undistorted iterability of graphic evocations of the items already intelligible thanks to the definitions or to the pre-understanding shared by the teacher and student. ;In Chapter III, devoted to Descartes the principal claims of modern constructivism are brought to sight. After examining Descartes' fabulous autobiography and its emphasis on self-origination, I turn to the style, contents and under-pinnings of the Geometry in an effort to extract from that text what he once referred to as "the metaphysics of geometry." The latter yields the conditions of successful problem-solving, i.e., dimensional homogeneity and kinematic continuity. These conditions, in turn, find their justification in Descartes' theses in the Rules concerning order, measure and the uniformity of "mental" activity. In the final section I apply the lessons learned from the Geometry and the Rules to one critical issue in the later Meditations, the transition from essence to existence. Descartes' "solution" generates a sequence of perplexities with Hobbes, Leibniz, Kant and other radical moderns continue to wrestle. (shrink)

Measures of student ethical sensitivity and their increases help to answer questions such as whether accounting ethics should be taught at all. We investigate different sensitivity measures and alternatives to the well-established Defining Issues Test (DIT-2, Rest, J. R. et al. [1999, Postconventional Moral Thinking: A Neo-Kohlbergian Approach (Lawrence Erlbaum Associates, Mahwah, NJ]), frequently used to measure the effects of undergraduate accounting ethics education. Because the DIT measures cognitive development, which increases with age, the DIT scores for younger accounting students (...) are typically lower, have limited range, and are not likely to vary sufficiently with corresponding choices in ethical dilemmas. Since the DIT measures only the moral judgment component of ethical decision-making, we consider the multidimensional ethical scale (MES) to allow respondents to provide explanations for their moral and other judgments. The MES has been used to measure attitudes related to justice, utility, contractualism, egoism, and relativism. Unfortunately, the MES is not comparable in one-dimension to the DIT, and unlike the DIT, the MES has no theoretical or objective base. Therefore, we construct a comparable one-dimensional relative measure, a Composite MES Score, obtained from previous research on practicing accountants. We compare the reliability of this measure to the DIT in explaining the ethical choices of 54 specially chosen, somewhat homogeneous students, whose ages range from 18 to 19, and who are taking a second semester freshman accounting course at a private, religion-affiliated university. These particular students are relatively untrained in the formal use of questionable accounting choices. These students are less likely to recognize the dilemmas of the MES and are also less likely to demonstrate sufficient variation in their DIT scores, traditionally low for freshmen students. As freshmen, they are recent graduates of high school and more likely guided by other ethical influences including friends, family, or contractual obligations (some of the MES constructs) rather than higher cognitive development. This study confirms suspicions. We find the DIT scores do not vary sufficiently to explain the moral reasoning of freshmen. For eight dilemmas and 24 choices we find the DIT score correlates with only three choices, whereas the MES regression models have at least one significant construct for 23 out of 24 ethical choices. The Composite MES Score (a relative measure) also explains 23 out of 24 choices and is statistically related to the DIT in only one of the choices. Unlike the DIT, the Composite MES permits pretest and retesting with different dilemmas to evaluate changes in ethical sensitivity. These results argue for relative rather than absolute measures of sensitivity and guides beyond cognitive development (the DIT-score) to explain undergraduate student sensitivity. (shrink)

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (...) (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)

Background: The three-dimensional model of nurses’ moral sensitivity has typically been studied using a variable-centered rather than a person-centered approach, preventing a more complete understanding of how these forms of moral sensitivity are expressed as a whole. Latent profile analysis is a person-centered approach that classifies individuals from a heterogeneous population into homogeneous subgroups, helping identify how different subpopulations of nurses use distinct combinations of different moral sensitivities to affect their service behaviors. Objective: Latent profile analysis was used to (...) identify three distinct profiles of nurses’ moral sensitivity. Associations of the profiles with service behaviors were then examined. Methods: Five hundred twenty-five nurses from three tertiary hospitals in China were investigated with Moral Sensitivity Questionnaire and Nurses’ Service Behavior Scale. Latent profile analysis was used to analyze the data. Ethical considerations: Approval was obtained from the Ethics committee for biomedical research of Medical College, the Hebei University of Engineering. Results: A three-profile moral sensitivity model provided the best fit to the data. The resulting profiles were low moral sensitivity, moderate moral sensitivity, and high moral sensitivity. There were significant differences in service behaviors among different profiles of moral sensitivity. Conclusion: The results provide a new and expanded view of nurses’ moral sensitivity, which may be used to monitor nurses’ service behaviors comprehensively and to evaluate nursing ethics management strategies. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Subjective Experiences of Tourette SyndromeBeyond the Premonitory UrgeThe authors report no conflicts of interest.There is an evolving recognition in healthcare that the patient's subjective experience needs to be privileged both in understanding clinical phenomena and also ensuring the salience of outcomes used to evaluate the impact of treatment interventions. This is reflected in the expansion of patient-reported outcome measures to capture a person's perception of their own health, and (...) the increasing requirement of involving people with lived experience in the co-design of research studies (National Health and Medical Research Council, 2016) and care improvement initiatives. In mental health it has been long understood that observable behavioral phenomena can only partially inform clinical understanding of the experience of the patient living with the condition. However, capturing the patient's subjective experience faithfully remains a challenge.Tourette syndrome (TS) is a complex condition in which there are clearly observable behavioral phenomena (vocal and motor tics, compulsive and socially inappropriate behaviors), but also a broad and varied range of subjective phenomena reported by different individuals. These may include sensory phenomena such as the premonitory sensory urge preceding a tic, compulsions to touch things a certain number of times or do something repeatedly until it feels "just right," or bothersome intrusive thoughts or images. To further complicate the picture most patients with TS have one or more co-occurring conditions such as attention deficit hyperactivity disorder, obsessive-compulsive disorder, and anxiety, which may actually cause a greater burden of dysfunction and distress than the Tourette symptoms.In their paper, Curtis-Wendlandt et al. (2024) challenge the dependence of current psychiatric diagnostic criteria (e.g., the Diagnostic and Statistical Manual of Mental Disorders, 5th edition) on observable tics, and propose a broader and more dimensional approach to nosology which incorporates sensory, cognitive and affective phenomena. [End Page 47] Data from interviews they conducted identified that premonitory phenomena and urge experiences in tic disorders are more complex and diverse than what is currently reflected in the literature and clinical scales. They also interviewed participants who reported "no urges" or "no premonitory sensations." They commented that the literature generally treats reports of urge absences at face value, and does not address the likelihood that such reports may be ambiguous or problematic. Overall, they concluded that their research suggests that premonitory urges in TS are a complex and diverse phenomenon that requires further study. This reflects with our clinical experience in working with TS patients. Although a large proportion of older patients describe sensory-based premonitory urges, descriptions are not homogenous, with many describing other experiences preceding their tics.When evaluating a patient's response to an intervention (either behavioral or pharmacological) clinicians incorporate a range of information. This includes the severity of their tics (number, type, frequency, intensity, and associated impairment), as well as their mood, participation and performance in study, work, and social activities, and overall quality of life. Standard clinical practice would not typically include assessment of some of the subjective experiences which precede tics. If it was accepted that these subjective phenomena are indeed salient to the patient's well-being, then a challenge would be how to consistently and reliably capture these feelings to operationalize a comprehensive patient-centered assessment.The primary evidence-based treatment for tic disorders, comprehensive behavioral intervention for tics (CBIT), involves training to increase the awareness of premonitory urges (Woods et al., 2008). Furthermore, successful 'blocking' of tics during the course of CBIT requires the patient to be aware of premonitory urges. Clinicians having a better understanding of the complexity and diversity of experiences which precede tics, as well as using open-ended questioning styles, may assist with improving CBIT outcomes. [End Page 48]Related ArticlesFeature Article: Dimensions, Not Types: On the Phenomenology of Premonitory Urges in Tourette SyndromeCommentary: Priming and Narrative Habits in the Phenomenological Interview: Reflections on a Study of Tourette SyndromeCommentary: Subjective Experiences of Tourette Syndrome: Beyond the Premonitory UrgeResponse: Phenomenological Interviews and Tourette’sDaryl EfronThe Royal Children's Hospital MelbourneIvan MathiesonThe Laneway ClinicDaryl Efron Daryl Efron is a Consultant Pediatrician, Royal Children's Hospital Senior Research Fellow, Murdoch... (shrink)

Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments (...) based on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

Everything is Something is a book about Stoic metaphysics. It argues that the Stoics are best understood as forging a bold new path between materialism and idealism, a path best characterized as non-reductive physicalism. To be sure, only individual bodies exist for the Stoics, but not everything there is exists — some things are said to subsist. However, this is no Meinongian move beyond existence, to the philosophy of intentionality (as the language of subsistence might suggest), but a one-world metaphysics (...) that both counts its entities by logical criteria, and grounds them in body by physical principles, yielding a tightly ordered ontology in which everything is Something and nothing is not. -/- This last phrase is not innocent. It invokes the Stoic innovation of Something (ti) as the highest genus of reality, and takes the stand that it is not only principled and coherent, but comprehensive — anything that is not Something is nothing at all (for the initiated: there is no class of Not-Somethings between Something and nothing). Further, everything that is Something is either itself a body, or ontologically dependent on body. Herein lies the Stoics’ non-reductive physicalism, and the beating heart of their response to the Battle of Gods and Giants in Plato’s Sophist: a one-world metaphysics. -/- The foundation of Stoic metaphysics is their ground-breaking corporealism, which introduces an alternative to both atomism and hylomorphism. The Stoics are continuum physicists for whom body as such, i.e. solid, three-dimensional extension, is homogeneous, partless, uniform, and infinitely divisible without reaching minima (atoms). And because body is not conceived along hylomorphic lines, i.e. as a composite of matter and form, the Stoics are free to make body fundamental. Out of two basic bodies, then (the archai), and by the tantalizing mechanism of through and through blending (krasis di’ holou), Stoic physics constructs the cosmos (and every body it contains) in completely corporealist terms, composing one thing out of many. And once those bodies are built, Stoic logic gives an account of their identity conditions, kinds, and qualities according to the vexed schema of the Categories, making now many out of one by the constitution relation, as a statue is constituted by its clay. With these distinct mereological relations of composition and constitution, Stoic corporealism artfully divides the labor of Plato’s Forms between physics and logic. -/- Next in the ontological order, with bodies as their foundation, are the incorporeals (asōmata): space (place, room, and surface), time, void, and the (awkwardly named) sayables, or lekta (roughly, though controversially, the meanings of our words). These entities do not exist; they do, however, subsist, inheriting their physical properties and, hence, their subsistence, from the bodies on which they depend. For example, place depends for its three-dimensional (non-solid) extension on the bodies that occupy or delimit it. The ontological dependence of space, time, and their novel semantic entities (the lekta) on body, is what takes Stoic metaphysics beyond corporealism to non-reductive physicalism, beyond a merely sorted ontology to an ordered, one-world metaphysics. Each incorporeal counts as Something according to the Stoic criterion for subsistence (hence, the theory is non-reductive), and what they have in common as incorporeals (and what makes the account physicalist), is their dependence on underlying body. -/- In addition to the incorporeals, the Stoics also recognize the subsistence of things like creatures of fiction and geometrical limits, which they classify as neither corporeal nor incorporeal. What these entities have in common is that they are products of thought; and since thoughts are themselves bodies according to Stoic corporealism, this remains a physicalist account. As before, the account is not Meinongian; neither all objects of thought, nor all products of thought count as Something. Indeed, the Stoics’ eliminative treatment of universals (and Forms) turns on their denying concepts (ennoēmata) a place on the ontological map altogether — concepts are simply not Somethings (and, again, not some further category of Not-Somethings, intermediate between Something and nothing at all). If all this is right, then the Stoics are not flat-footed materialists or ersatz Platonists, as so often assumed, but our first non-reductive physicalists. (shrink)

We show that a first category homogeneous zero-dimensional Borel set X can be embedded in as an ideal on ω if and only if X is homeomorphic to X × X if and only if X is Wadge-equivalent to X × X. Furthermore, we determine the Wadge classes of such X, thus giving a complete picture of the possible descriptive complexity of Borel ideals on ω. We also discuss the connection with ideals of compact sets.

Narratives of seed ‘loss’ and ‘persistence’ remain at loggerheads. Crop genetic diversity is rapidly eroding worldwide, we are told, and numerous studies support this claim. Other data, however, suggests an alternative storyline: far from disappearing, seed diversity persists around the world, resisting the homogenizing forces of modern capitalism. Which of these accounts is closer to the truth? As it turns out, crop biodiversity is more easily invoked than measured, more easily wielded than understood. In this essay, I contend that the (...) impasse reveals an error in the asking. We must, instead, look to the ontological, epistemic, and narrative dimensions of agrobiodiversity—and to the science, politics, and cultures of each. How is diversity empirically defined and measured? Who creates and categorizes diversity? Who does not? How is such knowledge mobilized in the accounts and narratives of different interest groups? Where, when, and why does a narrative hold true? This multi-dimensional view of agrobiodiversity makes space for a greater understanding of how diversity is created, maintained, and renewed. It suggests policy and institutional support for systems that engender such renewal of diversity, both in and ex situ. (shrink)

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and “proper time” τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic (...) field equations for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for “massive” fields, for which the “mass” squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the “mass” parameter. We derive the Green's functions corresponding to the principal part ΔP and the homogeneous function Δ 1 ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x2⩾τ2, corresponding to spacelike propagation, as well as along the light cone x2=0 (for τ=0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over τ, does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations. (shrink)

Methods of machine learning (ML) are gradually complementing and sometimes even replacing methods of classical statistics in science. This raises the question whether ML faces the same methodological problems as classical statistics. This paper sheds light on this question by investigating a long-standing challenge to classical statistics: the reference class problem (RCP). It arises whenever statistical evidence is applied to an individual object, since the individual belongs to several reference classes and evidence might vary across them. Thus, the problem consists (...) in choosing a suitable reference class for the individual. I argue that deep neural networks (DNNs) are able to overcome specific instantiations of the RCP. Whereas the criteria of narrowness, reliability, and homogeneity, that have been proposed to determine a suitable reference class, pose an inextricable tradeoff to classical statistics, DNNs are able to satisfy them in some situations. On the one hand, they can exploit the high dimensionality in big-data settings. I argue that this corresponds to the criteria of narrowness and reliability. On the other hand, ML research indicates that DNNs are generally not susceptible to overfitting. I argue that this property is related to a particular form of homogeneity. Taking both aspects together reveals that there are specific settings in which DNNs can overcome the RCP. (shrink)

If institutional heterogeneity tends overall to reduce survival chances, it may also persist and be harnessed to good use. This article investigates this ambivalence by looking at how institutional heterogeneity emerges, develops, and survives. An inductive study of the “Metropolitan Opera” archives suggests that what enables heterogeneity to survive and to withstand the pressure for homogenization is its inherent potential for “multivocality.” The analysis shows how institutional discrepancies were bridged over through an opportunistic, “multivocal” action pattern, whereby the organization maneuvered (...) between conflicting institutional demands, seeking to minimize dependence on any single constituency or evaluation principle. Maintaining discretionary options is essential in multi-dimensional space, where ambiguity makes optimization impractical. The trade-off in this action pattern includes remarkable adaptability and operational inefficiencies. (shrink)

Mechanical reductionism, which deals entirely with homogeneous variables, will constrain and enable the activities of richly heterogeneous living systems, but it cannot determine their outcomes. Such indeterminism owes to problems with dimensionality, dynamical logic, intractability, and insufficiency. The order in any living structure arises via an historical series of contingencies that were selected endogenously by stable autocatalytic processes in tandem with, and usually in opposition to, conventional external influences (natural selection). The development of living communities thereby resembles a Heraclitean dialectic (...) between processes that build up and those that tear down. Investigating this unconventional dynamic requires metaphysical assumptions that are complementary to those that have guided science over the past three centuries. The new dynamics can be represented in terms of weighted networks of interacting processes, which facilitate the statement of testable hypotheses. Network analysis thereby implements and tests ideas that heretofore could only be addressed as verbal propositions. (shrink)

The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity (...) conditions required by the modern version of the theory of proportions. Secondly, Grassmann’s conception of mathematical knowledge will be investigated. Parting from the traditional definition of mathematics as a science of magnitudes, Grassmann considered mathematical forms as particulars rather than universals: the classification of the branches of mathematics was thus based on different operational rules, rather than on empirical criteria of abstraction or on the distinction of different species belonging to a common genus. It will be argued that a different notion of generalization is thus involved, and that the knowledge of mathematical forms relies on the understanding of the rules of generation of the forms themselves. Finally, the paper will analyse if Grassmann’s approach in the first edition of the Ausdehnungslehre should be explained in terms of the notion of purity of method, and if it clashes with Grassmann’s later conventionalism. Although in the second edition the features of the operations are chosen by convention, as it is the case for the anti-commutative property of the multiplication, the choice is oriented by our understanding of the resulting forms: a simplification in the algebraic calculus need not correspond to a simplification in the ‘dimensional’ interpretation of the result of the multiplicative operation. (shrink)

For a, b > 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = (-b, a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X(t) reaches the position 0, it is reflected rightward to δ with probability p > 0 and leftward to -δ with probability 1 - p, where δ > 0. Closed analytical expressions are found for the mean exit time from the interval (-b, a), and for the (...) probability of exit through the right end a, in the limit δ → 0+, generalizing the results of Lefebvre, holding for asymmetric Wiener process. Moreover, in alternative to the heavy analytical calculations, a numerical method is presented to estimate approximately the quantities above. Furthermore, on the analogy of skew Brownian motion, the notion of skew diffusion process is introduced. Some examples and numerical results are also reported. (shrink)

The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C 0,2 . This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, $\mathbb{F}^{a}$ of the Euclidean three-space. This (...) enables us to construct a Poisson Clifford algebra, ℍ F , of a finite dimensional phase space which will carry the dynamics. The quantum dynamics appears as a realisation of ℍ F in terms of a Clifford algebra consisting of Hermitian operators. (shrink)

Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component (...) systems) and (iii) at least one system has the structure of a qubit. Using this result, we also characterize finite dimensional quantum theory among probabilistic theories having the structure of a dagger-monoidal category. (shrink)

Traditionally the the problem of time considered the contrast between time (associated with succession) and eternity (associated with simultaneity) (from Parmenides, and via Plato, Aristotle, Plotinus, and Kierkegaard up to Wittgenstein and what theologians presuppose without being aware of it). It may appear as if time measurement can help us to understand what time is. However, the historical development of time measurement alternatively explored different routes – such as counting the days, weeks, months and years, establishing relative positions (the sundial), (...) employing the constant movement of a pendulum (mechanical clock work), and using the irreversibility of radio-active decay (atomic clocks). However, our awareness of time exceeds the confines of physical time. Just think of the heterogenous life cycle of living entities (coming into being, growing, maturing, ageing and dying) that differs from (homogenous) physical time. Likewise emotional time is different from physical time, for an hour can feel like five minutes and vice versa. Since Hegel introduced the concept of “geschichtliche Zeit” (historical time) thinkers like Kierkegaard, Jaspers, Heidegger, and many others followed this characterization. It will be argued that physical time cannot be elevated to true or the only genuine time. In order to substantiate this perspective other modes of time will be discussed – such as jural time. Since it appears that all definitions of “time” are simply definitions of diverse facets or modes of time, the Augustinian question still remains to be answered: what is time really? A possible answer to this question finally explores the multi-dimensional nature of time – acknowledging that there are idneed multiple modes of time and concludes by highlighting the difference between the diverse concepts of time we may have and the concept-transcending nature of the underlying dimensions of cosmic time, that is, the fact that ultimately we can approximate time solely in a concept-transcending idea. (shrink)

This article examines the Kantian thesis of the a priori nature of our knowledge of space. Because it makes the representation of objects possible as external to us and all others, and consequently, as distinct and individualized, space (whatever its structure may be) claims the status as necessary condition and as apriori possibility of all knowledge. However, in the light of various physical, psychological and philosophical considerations, it seems that the particular structure allocated by Kant to space (i.e. uniqueness, infinity, (...) continuity, homogeneity, isotropy, Euclidean character and three-dimensional character) is neither necessary nor a priori but is rather contingent and dependent on experience. For this reason a pragmatist relativization of the transcendental approach appears to be necessary: the structure of space which makes knowledge possible is not apriori in an absolute sense, but rather, it is determined within the context of a certain practice, which is characterized by a certain mode of interaction with the environment and reveals particular empirical constraints to which this spatial structure must fit. (shrink)

This article examines the Kantian thesis of the a priori nature of our knowledge of space. Because it makes the representation of objects possible as external to us and all others, and consequently, as distinct and individualized, space (whatever its structure may be) claims the status as necessary condition and as apriori possibility of all knowledge. However, in the light of various physical, psychological and philosophical considerations, it seems that the particular structure allocated by Kant to space (i.e. uniqueness, infinity, (...) continuity, homogeneity, isotropy, Euclidean character and three-dimensional character) is neither necessary nor a priori but is rather contingent and dependent on experience. For this reason a pragmatist relativization of the transcendental approach appears to be necessary: the structure of space which makes knowledge possible is not apriori in an absolute sense, but rather, it is determined within the context of a certain practice, which is characterized by a certain mode of interaction with the environment and reveals particular empirical constraints to which this spatial structure must fit. (shrink)

The brain, rather than being homogeneous, displays an almost infinite topological genus, since it is punctured with a high number of “cavities”. We might think to the brain as a sponge equipped with countless, uniformly placed, holes. Here we show how these holes, termed topological vortexes, stand for nesting, non-concentric brain signal cycles resulting from the activity of inhibitory neurons. Such inhibitory spike activity is inversely correlated with its counterpart, i.e., the excitatory spike activity propagating throughout the whole brain tissue. (...) We illustrate how Pascal’s triangles and linear and nonlinear arithmetic octahedrons are capable of describing the three-dimensional random walks generated by the inhbitory/excitatory activity of the nervous tissue. In case of nonlinear 3D paths, the trajectories of excitatory spiking oscillations can be depicted as the operation of filling the numbers of octahedrons in the form of “islands of numbers”: this leads to excitatory neuronal assemblies, spaced out by empty areas of inhibitory neuronal assemblies. These mathematical procedures allow us to describe the topology of a brain of infinite genus, to represent inhibitory neurons in terms of Betti numbers and to highlight how spike diffusion in neural tissues is generated by the random activation of tiny groups of excitatory neurons. Our approach suggests the existence of a strong mathematical background subtending the intricate oscillatory activity of the central nervous system. (shrink)

The fact that the mystical experience is a repetitive phenomenon in different social, cultural and religious structures in different periods and has a mysterious element in it has caused that mysticism has taken its place among the basic subjects of the field since the first periods of psychology of religion. One of the sections of The Varieties of Religious Experience, which is regarded as the main source of the area, is mysticism. In general, "mystical experience" is considered as a subcategory (...) of "religious experience", which is a wider area. For this reason, it also carries the characteristics of religious experience. Due to these common features, it can be seen that they are used in place of each other in the literature. If the religious experience is defined as the experience of the individual at the time of encounter with the sacred, such experience can be obtained in two ways. In the “religion-based mystical experience”, which is the first way, institutional or established religious thoughts and understandings and holly writings are influential. The second way, “non-religious or natural mystical experience”, can be said to be spiritual quests that individual needs play an important role in them are effective. Personality is used as one of the basic variables in social and health sciences in general, and in psychology because it is among the main subjects in particular. The common emphasis of research on personality is that the phenomenon is extremely complicated. Despite its widespread use, the abstraction of the concept has been influenced by the diversity of the researchers' perspectives and this has led to a lack of clear consensus on the definition. However, in order to investigate the phenomenon in recent periods, dimensional approaches that their basic assumption is personality can be categorized under certain factors have begun to be preferred. In this study, HEXACO was used, because it was thought that it could make a more detailed measurement of personality. The sample of this study is composed of 345 students studying at Erciyes University Theology Faculty in 2017-2018 academic year. When looked at the gender distribution of the sample, the rate of male students was 21.2% (n=73); and the rate of female students was 78.8% (n=272). This reflects the current situation in the faculty. The average age was 21,13 (sd=1,761). The age range is 18-26. Class distribution was 23,5% (n = 81) in Preparatory class; 15.4% (n = 53) in first-grade; 19.4% (n = 67) in second-grade; 18.3% (n=63) in third grade (n = 63); and 23.5% (n = 81) in the fourth grade. It has been noted that distributions are homogeneous in terms of class variables. The "Mystical Experience Scale" which is developed by Ralph W. Hood to measure the criteria which are offered by Walter T. Stace and which must be in the mystical experience has been used in determining the tendency of mystical experience. Hood et al. have reported reasonable reliabilities for subscales based on 3-factor solution. Alpha coefficients of the original scale were ,76, ,69, and ,76 for the extrovertive mysticism, introvertive mysticism and religious interpretation respectively. The adaptation of the scale to Turkish culture and the validity and reliability study were carried out by Mehmet Süheyl Unal as a graduate thesis and it was stated that the Alpha coefficient was ,89. In this study, the Cronbach Alpha reliability coefficient of scale is ,91. HEXACO, developed by Lee and Ashton, was used to determine personality traits. The scale was adapted to Turkish by Wasti, Lee, Ashton and Somer. The scale consists of Honesty-humility (H), Emotionality (E), eXtraversion (X), Agreeableness (A), Conscientiousness (C), and Openness to experience (O) factors. Pearson Moments Multiplication Correlation Analysis was performed to determine if there is a relationship between mystical experience tendencies and personality traits when the data were analyzed in accordance with the aim of the study. Later, it was tried to determine the power of explaining the variables with Multiple Linear Regression Analysis. In addition, One-way ANOVA was used to determine whether there was any relationship between significance levels. Moreover, descriptive statistics of relevant variables are included in the study. Findings show that participants have the highest average to Positive Affect (m=3,69; sd.=,77) and the lowest average to Temporal/Spatial Quality (m=2,94; sd.=,89) factor in terms of mystical experience. Additively, they obtained close values in Ego Quality, Noetic Quality and Ineffability factors. When the students were evaluated in terms of gender, it was seen that there was a difference in level of significance only in terms of Unifying Quality (t=1,770; p=,028). ANOVA analysis was carried out to determine whether there was any variation in class variable. As a result of this analysis, it is seen that all of the factors are significantly differentiated in terms of class variable. From the standing point of class variable, it is seen that the first grades differed negatively compared to the other classes. According to the data, the scores on the mystical experience scale for preparation and first grade are high while the averages for the next grade are falling. There is no difference on level of significance between age and mystical experience factors, the last independent variable. When looked at the correlations among mystical experience factors, it is understood that all of the factors are in a meaningful relationship with each other. The highest correlation is between Religious Quality and Ineffability (r=,661); the lowest correlation is between the Unifying Quality and the Temporal/Spatial Quality (r=,346). Among the six factors of HEXACO that have been developed to determine the personality traits, the students have the highest average on Humility-Honesty (m=3,76; sd.=,55); the lowest average on eXtraversion (m=3,04; sd.=0,65). In terms of gender, there is a statistically significant difference in factors of Humility-Honesty (t=,606; p=,004), Emotionality (t=,334; p=,000), and Constientiousness (t=,022; p=,033). There is no significant difference between class and age variables and personality traits. According to Linear Regression analysis, Agreeableness, Constientiousness and Openness to Experience factors of personality traits are predictive of mystical experience in a significant level statistically. Personality dimensions that are most related to mystical experience as a result of analysis are Conscientiousness and Openness to Experience. When the mystical experience is compared with the personality traits, it is concluded that Openness to Experience factor is related to all the factors of the mystical experience except for the Ineffability. Although the relationship is regarded as weak in terms of correlation, it is an important finding that there are positive relations in between. In other words, as personality traits evolve, the mystical experience level also increases. The lack of a similar work in the literature in this respect removes the possibility of making comparisons. (shrink)

This study has focused on the mystical experience which is one of the most important topics of psychology of religion, but it is a subject not examined enough in Turkey and also tried to determine the relationship between personality traits and personality. Data were collected from 345 students who were studying at Erciyes University Faculty of Theology by questionnaire method. “The Mysticism Scale”which is developed by Ralph Hood and widely used in international literature to measure the mystical experience and “HEXACO (...) Personality Inventory”were used to measure the personality traits of students. In addition to descriptive statistics of demographic characteristics of the sample, The Pearson Moments Multiplication Correlation Analysis, Independent Sample t-Test and One-Way ANOVA techniques were used in the analysis. Findings show that participants have the highest average to Positive Affect and the lowest average to Temporal/Spatial Quality factor. In addition, they obtained close values in Ego Quality, Noetic Quality and Ineffability factors. When the students were evaluated in terms of gender, it was seen that there was a difference in level of significance only in terms of Unifying Quality. ANOVA analysis was carried out to determine whether there was any variation in class variable. As a result of this analysis, it is seen that all of the factors are significantly differentiated in terms of class variable. There is no difference in level of significance between age and mystical experience factors, the last independent variable. When looked at the correlations among mystical experience factors, it is understood that all of the factors are in a meaningful relationship with each other. Among the six factors of HEXACO, the students have the highest average on Humility-Honesty; the lowest average on eXtraversion. In terms of gender, there is a statistically significant difference in the level of Humility-Honesty, Emotionality, and Conscientiousness. There is no significant difference between class and age variables and personality traits. According to Linear Regression analysis, Agreeableness, Conscientiousness and Openness to Experience factors of personality traits are predictive of mystical experience in a statistically significant level. Summary: The fact that the mystical experience is a repetitive phenomenon in different social, cultural and religious structures in different periods and has a mysterious element in it has caused that mysticism has taken its place among the basic subjects of the field since the first periods of psychology of religion. One of the sections of The Varieties of Religious Experience, which is regarded as the main source of the area, is mysticism. In general, "mystical experience" is considered as a subcategory of "religious experience", which is a wider area. For this reason, it also carries the characteristics of religious experience. Due to these common features, it can be seen that they are used in place of each other in the literature.If the religious experience is defined as the experience of the individual at the time of encounter with the sacred, such experience can be obtained in two ways. In the “religion-based mystical experience”, which is the first way, institutional or established religious thoughts and understandings and holly writings are influential. The second way, “non-religious or natural mystical experience”, can be said to be spiritual quests that individual needs play an important role in them are effective.Personality is used as one of the basic variables in social and health sciences in general, and in psychology because it is among the main subjects in particular. The common emphasis of research on personality is that the phenomenon is extremely complicated. Despite its widespread use, the abstraction of the concept has been influenced by the diversity of the researchers' perspectives and this has led to a lack of clear consensus on the definition. However, in order to investigate the phenomenon in recent periods, dimensional approaches that their basic assumption is personality can be categorized under certain factors have begun to be preferred. In this study, HEXACO was used, because it was thought that it could make a more detailed measurement of personality.The sample of this study is composed of 345 students studying at Erciyes University Theology Faculty in 2017-2018 academic year. When looked at the gender distribution of the sample, the rate of male students was 21.2% (n=73); and the rate of female students was 78.8% (n=272). This reflects the current situation in the faculty. The average age was 21,13 (sd=1,761). The age range is 18-26. Class distribution was 23,5% (n = 81) in Preparatory class; 15.4% (n = 53) in first-grade; 19.4% (n = 67) in second-grade; 18.3% (n=63) in third grade (n = 63); and 23.5% (n = 81) in the fourth grade. It has been noted that distributions are homogeneous in terms of class variables.The "Mystical Experience Scale" which is developed by Ralph W. Hood to measure the criteria which are offered by Walter T. Stace and which must be in the mystical experience has been used in determining the tendency of mystical experience. Hood et al. have reported reasonable reliabilities for subscales based on 3-factor solution. Alpha coefficients of the original scale were,76,,69, and,76 for the extrovertive mysticism, introvertive mysticism and religious interpretation respectively. The adaptation of the scale to Turkish culture and the validity and reliability study were carried out by Mehmet Süheyl Unal as a graduate thesis and it was stated that the Alpha coefficient was,89. In this study, the Cronbach Alpha reliability coefficient of scale is,91. HEXACO, developed by Lee and Ashton, was used to determine personality traits. The scale was adapted to Turkish by Wasti, Lee, Ashton and Somer. The scale consists of Honesty-humility (H), Emotionality (E), eXtraversion (X), Agreeableness (A), Conscientiousness (C), and Openness to experience (O) factors.Pearson Moments Multiplication Correlation Analysis was performed to determine if there is a relationship between mystical experience tendencies and personality traits when the data were analyzed in accordance with the aim of the study. Later, it was tried to determine the power of explaining the variables with Multiple Linear Regression Analysis. In addition, One-way ANOVA was used to determine whether there was any relationship between significance levels. Moreover, descriptive statistics of relevant variables are included in the study.Findings show that participants have the highest average to Positive Affect (m=3,69; sd.=,77) and the lowest average to Temporal/Spatial Quality (m=2,94; sd.=,89) factor in terms of mystical experience. Additively, they obtained close values in Ego Quality, Noetic Quality and Ineffability factors. When the students were evaluated in terms of gender, it was seen that there was a difference in level of significance only in terms of Unifying Quality (t=1,770; p=,028). ANOVA analysis was carried out to determine whether there was any variation in class variable. As a result of this analysis, it is seen that all of the factors are significantly differentiated in terms of class variable. From the standing point of class variable, it is seen that the first grades differed negatively compared to the other classes. According to the data, the scores on the mystical experience scale for preparation and first grade are high while the averages for the next grade are falling. There is no difference on level of significance between age and mystical experience factors, the last independent variable. When looked at the correlations among mystical experience factors, it is understood that all of the factors are in a meaningful relationship with each other. The highest correlation is between Religious Quality and Ineffability (r=,661); the lowest correlation is between the Unifying Quality and the Temporal/Spatial Quality (r=,346).Among the six factors of HEXACO that have been developed to determine the personality traits, the students have the highest average on Humility-Honesty (m=3,76; sd.=,55); the lowest average on eXtraversion (m=3,04; sd.=0,65). In terms of gender, there is a statistically significant difference in factors of Humility-Honesty (t=,606; p=,004), Emotionality (t=,334; p=,000), and Constientiousness (t=,022; p=,033). There is no significant difference between class and age variables and personality traits. According to Linear Regression analysis, Agreeableness, Constientiousness and Openness to Experience factors of personality traits are predictive of mystical experience in a significant level statistically.Personality dimensions that are most related to mystical experience as a result of analysis are Conscientiousness and Openness to Experience. When the mystical experience is compared with the personality traits, it is concluded that Openness to Experience factor is related to all the factors of the mystical experience except for the Ineffability. Although the relationship is regarded as weak in terms of correlation, it is an important finding that there are positive relations in between. In other words, as personality traits evolve, the mystical experience level also increases. The lack of a similar work in the literature in this respect removes the possibility of making comparisons. (shrink)

This article explores how cross-cultural research on sexual and reproductive rights can be vulnerable to ethnocentrism, and in what way ethnocentrism can be reduced in such research. Against the background of feminist debate on equality and difference, it discusses how the concepts of sexual and reproductive rights, within the parameters of development discourse, can reinforce hierarchical dichotomies of North–South, modern–traditional and actor–structure, and undervalue southern women's agency. An analytical framework that combines the entitlement approach and the three-dimensional model of (...) gender is proposed to diminish ethnocentrism and counter homogenization and generalization. This framework aims at balancing agency, actor and structure, and allowing for differences, heterogeneity and contradictions. (shrink)

Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, (...) such that the parts are real and the whole is an ens rationis, while a continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for Peirce’s topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility. (shrink)

We point out that the acceptance of the relativity principle together with the homogeneity and isotropy of space and the homogeneity of time inevitably leads to the Lorentz spacetime transformation with a universal limiting speed σ. Speculations on possible new four-dimensional symmetries involving a variable “speed of light” such as that proposed by Hsu must therefore be dismissed on such a basis alone. In this paper we draw attention to some logical inconsistencies in Hsu's attempt at establishing (...) a new space-light transformation law, and follow with a discussion on why such an attempt must necessarily fail. (shrink)

PurposeTrust is a social factor at the foundations of human action. The pervasiveness of trust explains why it has been studied by a large variety of disciplines, and its complexity justifies the difficulties in reaching a shared understanding and definition. As for all the social factors, trust is continuously evolving as a result of the changes in social, economic and technological conditions. The internet and many other Information and Communication Technologies (ICT) solutions have changed organizational and social life. Such mutated (...) scenarios challenged what researchers know about trust, thus several studies tried to investigate the difference between online and traditional (physical) environments. The purpose of this paper is to solve this multi‐dimensional puzzle by presenting a conceptual framework that will take into consideration the complexity of ICT mediated‐trust.Design/methodology/approachThe extant literature still lacks a homogeneous framework and presents a large amount of different perspectives, each one addressing a very specific issue. By using the methodology suggested by Short and Cropanzano the paper proposes a conceptual model for understanding the dynamics of trust in online settings. In doing so the authors' adopted the Actor Network Theory conceptual frame for disentangling the ambiguous role of technology in its relation with trust.FindingsThis paper provides an ultimate conceptual model on trust in virtual settings.Research limitations/implicationsThe proposed model will help systematize the extant contributions and also identify the gaps that can be addressed by future researches.Originality/valueThe model permits the understanding of the dynamics of trust in online settings. (shrink)

The paper addresses the capabilities and limitations of extrafoveal processing during a categorical visual search. Previous research has established that a target could be identified from the very first or without any saccade, suggesting that extrafoveal perception is necessarily involved. However, the limits in complexity defining the processed information are still not clear. We performed four experiments with a gradual increase of stimuli complexity to determine the role of extrafoveal processing in searching for the categorically defined geometric shape. The series (...) of experiments demonstrated a significant role of extrafoveal processing while searching for simple two‐dimensional shapes and its gradual decrease in a condition with more complicated three‐dimensional shapes. The factors of objects’ spatial orientation and distractor homogeneity significantly influenced both reaction time and the number of saccades required to identify a categorically defined target. An analysis of the individual p‐value distributions revealed pronounced individual differences in using extrafoveal analysis and allowed examination of the performance of each particular participant. The condition with the forced prohibition of eye movements enabled us to investigate the efficacy of covert attention in the condition with complicated shapes. Our results indicate that both foveal and extrafoveal processing are simultaneously involved during a categorical search, and the specificity of their interaction is determined by the spatial orientation of objects, type of distractors, the prohibition to use overt attention, and individual characteristics of the participants. (shrink)

To understand how the photoreceptor protein rhodopsin performs in its role as a receptor, its structure needs to be determined at the atomic level. Upon receiving a photon of light, rhodopsin undergoes a change in conformation that allows it to bind and activate the C-protein, transducin. An important future goal should be to determine the structure of both the inactive and the photoactivated state of rhodopsin, R*. This should provide the groundwork necessary for experiments on how rhodopsin achieves its signaling (...) state R*, and how R* functions to activate transducin. To do this, the crystal structure of both rhodopsin and R* must be determined. Few membrane proteins have been successfully crystallized, so this is not a trivial undertaking. Two- or three dimensional crystals of rhodopsin must be prepared that are well ordered, to produce a high-resolution structure. Rhodopsin must be purified to homogeneity and the appropriate detergent(s) selected for crystallization experiments. Long-term thermal stability of the rhodopsin-detergent complex must be achieved in the presence of a precipitant. Two-dimensional crystals may offer advantages in investigating the structure of R*, but the structure obtained may be limited in resolution. It is necessary to work with rhodopsin in the dark, unless suitable light-stable retinal derivatives are developed. Protein engineering of rhodopsin offers attractive opportunities to improve its ability to crystallize, but is presently hindered by the absence of a high-yielding expression system. Knowledge of the structure of rhodopsin will have general importance. Because rhodopsin is a member of the family of C-protein-coupled receptors, knowledge of the structure and the mechanism of action of rhodopsin suggests by analogy how other members of the receptor family may function. (shrink)

A nonlinear two-variable reaction-diffusion model of bone mineral metabolism, built from an overall self-oscillatory compartmental model of calcium metabolism in vivo, has been studied for its ability to generate spatial and spatio-temporal self-organizations in a two-dimensional space. Analytical and numerical results confirm the theoretical properties previously described for this kind of model. In particular, it is shown that, for a given set of reactional parameter values and certain values of the ratio of the two diffusion coefficients, there exists a (...) set of unstable wavenumbers leading spontaneously to the development, from the homogeneous steady state, of either different types of stationary spatial patterns (hexagonal, striped and re-entrant hexagonal patterns) or more or less complex spatio-temporal expressions. We discuss the relevance of analogies established between some spatial or spatio-temporal structures predicted by the model and some peculiar features of the primary bone trabecular architecture which appear during embryonic ossification. (shrink)

We review the relativistic classical and quantum mechanics of Stueckelberg, and introduce the compensation fields necessary for the gauge covariance of the Stueckelbert–Schrödinger equation. To achieve this, one must introduce a fifth, Lorentz scalar, compensation field, in addition to the four vector fields with compensate the action of the space-time derivatives. A generalized Lorentz force can be derived from the classical Hamilton equations associated with this evolution function. We show that the fifth (scalar) field can be eliminated through the introduction (...) of a conformal metric on the spacetime manifold. The geodesic equation associated with this metric coincides with the Lorentz force, and is therefore dynamically equivalent. Since the generalized Maxwell equations for the five dimensional fields provide an equation relating the fifth field with the spacetime density of events, one can derive the spacetime event density associated with the Friedmann–Robertson–Walker solution of the Einstein equations. The resulting density, in the conformal coordinate space, is isotropic and homogeneous, decreasing as the square of the Robertson–Walker scale factor. Using the Einstein equations, one see that both for the static and matter dominated models, the conformal time slice in which the events which generate the world lines are contained becomes progressively thinner as the inverse square of the scale factor, establishing a simple correspondence between the configurations predicted by the underlying Friedmann–Robertson–Walker dynamical model and the configurations in the conformal coordinates. (shrink)

Mathematically, the fusion of space and time may be explained as follows. In pre-relativity physics, space was envisaged as a three-dimensional Euclidean continuum. Such a continuum is homogeneous and isotropic, and its metrical character can be specified by the definition of the distance between any two points in the continuum: s2 = 2 + 2 + 2. Now, while it is possible to speak of a four-dimensional continuum in pre-relativity physics by adding the time-coordinate to the three space-coordinates, (...) there is no way, corresponding to the definition of s, to define the spatio-temporal "separation" or "interval" between any two points in this new four-dimensional continuum. Thus, while it makes sense from the classical point of view to ask for the distance between two points in space, it does not make sense to ask for the spatio-temporal interval between two events occurring in different places at different times. The spatio-temporal interval between non-simultaneous, spatially separated events is simply not defined in pre-relativity physics. Another way of putting it is that in classical physics space and time are measured in entirely disparate units and no method is provided for making these units comparable with one another. In relativity physics, on the other hand, light--or rather the velocity of light--provides the means for making the results of spatial and temporal measurement comparable quantities: one simply multiplies the time-like intervals by c, the fixed velocity of light, in order to obtain space-like intervals. The interval between any two events is defined as: s2 = 2 + 2 + 2 - c22. Interval, so defined, is an invariant, whereas spatial and temporal "separation" are now relative to the state of motion of the observer. The geometry of the four-dimensional continuum characterized by this formula is called "semi-Euclidean". (shrink)

In this dissertation we explore projective Fraïssé theory and its applications, as well as limitations, to the study of compact metrizable spaces. The goal of projective Fraïssé theory is to approximate spaces via classes of finite structures and glean topological or dynamical properties of a space by relating them to combinatorial features of the associated class of structures. Using the framework of compact metrixable structures, we establish general results which expand and help contextualize previous works in the field. Many proofs (...) in the domain of projective Fraïssé theory are carried out in a context dependent fashion and have thus far eluded clean generalizations. A reason is to be found in the lack of a clear understanding of which spaces are amenable to be studied via projective Fraïssé limits. We give both positive and negative results in this direction. We isolate a combinatorial condition which entails a correspondence between finite structures and regular quasi-partitions of compact metrizable spaces. This correspondence greatly aids the combinatorial-toplogical translation. We apply this machinery to study a class of one-dimensional compact metrizable spaces, which we call smooth fences. To this end, we isolate a class of finite structures—finite partial orders whose Hasse diagram is a forest—whose projective Fraïssé limit approximates a distinctive smooth fence with remarkable properties. We call it the Fraïssé fence and characterize it topologically by carefully exploiting the bridge between the combinatorial and topological worlds. We explore homogeneity and universality features of the Fraïssé fence and the properties of its spaces and endpoints, and provide some results on the dynamics of its group of homeomorphisms. The dissertation is partially based on [1, 2]. (shrink)

Nature and the world can be viewed as complex volumetric computation. Historically, humans have interacted with nature in a reductive and homogeneous manner. However, inexpensive digital computation is now extending our capabilities allowing us to understand the complexity of nature and operate in and modify it as such. It is now possible to use computation to control matter, to design and fabricate natural solutions and objects creating a new class of human-made objects that allow more localized, dynamic, sustainable and natural (...) interactions with the world. Unfortunately, current digital design and fabrication systems have failed to fully capitalize on available computation. These systems are non-exact and fundamentally incapable of accurately representing real objects. Digital materialization proposes an approach, system and symbolic basis for two-way conversion between reality and information, where reality is represented as information in a dimensionally correct and exact manner and is accessible to human understanding, modification and design. (shrink)