Richard Rorty's discussions of "romanticism," a term by which he means a set of general philosophical themes, not merely a body of literary and philosophical work of the eighteenth and nineteenth century, are not univocal in their approach. Rorty endorses romanticism within an overall antirealistic view that he interprets as "pragmatism." In some respects, Richard Rorty's view of romanticism is diametrically opposed to Shelley's, for although Rorty invokes Shelley's appeal to poetry as "center and circumference," he has no interest (...) in providing any access to a noumenal world. With logical positivism of the twentieth century, Rorty seems to presuppose that "eliminating metaphysics," where metaphysics would be any appeal to a reality beyond appearances, is not only possible, but highly desirable from an intellectual point of view. Given Rorty's ultimate aim, it is not surprising that Rorty's romantic idol will have his metaphysics up his sleeve. (shrink)

Informed by s socio-historical theory, this paper will report on a study that sought to document the literacy and numeracy outcomes for children living in low socio-economic circumstances in a region south-east of Melbourne, Australia. The research focused on children in preschool and child care centres in the year prior to beginning school, and was designed to map literacy and numeracy experiences of children in the home and in the early childhood centre. In this paper an analysis of the cultural (...) tools that families were intentionally developing in the context of their homes and communities is featured. A socio-historical analysis of the data revealed children’s active engagement in the funds of knowledge (Moll and Greenberg 1990, Moll, 1990, and Moll, 2000) available within the community, the situated nature of learning (Lave and Wenger, 1991) within their communities, and the challenge for families transcending the constraints of ‘everyday learning’ to engage with ‘schooled learning’ (Hedegaard, 1998). The study also revealed the institutional barriers to learning the landscape of schooling (Greeno, 1991) and the deficit positioning evident for children and their families within the official script of middle class early childhood discourse (Fleer, 2003). (shrink)

This study on the cambium of Pinus sylvestris L. examines the intrusive growth of fusiform cambial initials and its possible contribution to the tangential and radial expansions of the cambial cylinder. The location and extent of intrusive growth of the fusiform initials were determined by microscopic observations and by mathematical modeling. In order to meet the required circumferential expansion of the cambial cylinder, the fusiform initials grow in groups by means of a symplastic rather than intrusive growth, leaving no room (...) for the assumption that intrusive growth of the initials takes place between radial walls and has a direct role in the increase of the cambial circumference. Therefore, it is postulated that the fusiform initials grow intrusively between the tangential walls of the neighboring initials and their immediate derivatives and not between the radial walls of the adjacent initials as per common belief. (shrink)

SummaryNormative data are reported for intelligence, height and head circumference for a sample of 1553 6- to 15-year-olds in Saudi Arabia, and for the correlations between these variables. Intelligence was tested with the Standard Progressive Matrices, on which the Saudi sample obtained a British IQ of 76.2. There were no significant differences in means between boys and girls and differences in variability were inconsistent. The heights of the Saudi sample were generally lower than those of the American norms. The (...) differences in head circumferences between the Saudi children and the American norms were inconsistent. Correlations between IQ and height were weaker than those found in other studies but correlations between IQ and head circumference were positive. (shrink)

In this article, David Hansen works with two conceptions of “being with.” The first is Jean-Luc Nancy's ontological version as found in his Being Singular Plural (1999). The second is Hansen's ontic formulation as expressed in his recent book, Reimagining the Call to Teach: A Witness to Teachers and Teaching (2021). Nancy's notion is ethical as well as ontological. It constitutes a vision of human being qua being and is formulated in critical juxtaposition with the viewpoints on ethics and being (...) of Martin Heidegger and other recent thinkers. Hansen's conception is not ontological, as such, but is ethical in the sense of presuming that teaching is a practice with built-in terms of relationship between teachers, students, and the subject matter of education, where “education” differs from socialization and enculturation. “Being with” constitutes a term of art for the priority in teaching of attunement, responsiveness, and receptivity — both to students and to subject matter — over formal processes of teacher reflection. The latter are indispensable, but they take their identity and their warrant from the fundamental ethical terms of the practice that are rooted in being with. Here, Hansen seeks to show how Nancy's conception of being with enriches the pedagogical idea of being with as the center and circumference of teaching. (shrink)

SummaryAnthropometric differences between the two Koreas are of considerable public and scientific interest given the unique socio-political status of North Korea and the fact that the nations share the same genetic ancestry. This study provides new biosocial evidence on these differences by analysing mid-upper arm circumference as a human welfare indicator. This is the first study to compare the nutritional status of adults surveyed inside North Korea with South Koreans. The MUAC measurements of 2793 North Korean women obtained through (...) a household survey conducted in 2002 were compared with those of 1428 South Korean women surveyed around 2003. Comparative analysis was conducted by plotting centiles and calculating mean differences in MUAC by age. This paper finds that the MUAC of the South Koreans was on average 2.8 cm greater than that of their North Korean peers, with MUAC gaps ranging from 1.6 cm to 3.9 cm and becoming more pronounced with age. This research confirms previous studies on height and weight in the two Germanies and in the two Koreas that have shown that biosocial performance is worse in socialist economies as compared with free-market regimes. (shrink)

For each natural number n we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than n and no strictly ascending chains. The case n=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=0$$\end{document} is the Gödel-Löb provability logic. Each logic is axiomatised by adding a single axiom to K4, and is shown to have the finite model property and be decidable. We then consider a number of extensions (...) of these logics, including restricting to reflexive frames to obtain a corresponding sequence of extensions of S4. When n=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1$$\end{document}, this gives the famous logic of Grzegorczyk, known as S4Grz, which is the strongest modal companion to intuitionistic propositional logic. A topological semantic analysis shows that the n-th member of the sequence of extensions of S4 is the logic of hereditarily n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n+1$$\end{document}-irresolvable spaces when the modality ◊\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Diamond $$\end{document} is interpreted as the topological closure operation. We also study the definability of this class of spaces under the interpretation of ◊\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Diamond $$\end{document} as the derived set operation. The variety of modal algebras validating the n-th logic is shown to be generated by the powerset algebras of the finite frames with cycle length bounded by n. Moreover each algebra in the variety is a model of the universal theory of the finite ones, and so is embeddable into an ultraproduct of them. (shrink)

The doxography for Anaximander’s account of the rings of the sky gives proportions for them that are discrepant. So a widely accepted hypothesis proposes that, since the circles of the celestial bodies are compared to wheels, we should add the thickness of their ‘rims’ to the measurements for the celestial rings. This paper proposes an entirely different hypothesis which avoids this awkward expedient by suggesting that there is a ‘geometrical’ reading of the numerical data. The discrepancies can then be explained (...) by there being two different methods for calculating the circumference of the circles. (shrink)

The paper argues that the depiction of the Mediterranean coast of Africa in Ptolemy’s Geography was based on a source similar to the Stadiasmus of the Great Sea. Ptolemy’s and the Stadiasmus’ toponymy and distances between major points are mostly in good agreement. Ptolemy’s place names overlap with those of the Stadiasmus by 80%, and the total length of the coastline from Alexandria to Utica on Ptolemy’s map deviates from the Stadiasmus data by only 1% or 1.5%. A number of (...) serious disagreements between Ptolemy’s map and the Stadiasmus regarding the length of particular coastal stretches can be explained by assuming that Ptolemy had to tailor the distance data derived from periploi to his other sources, especially, to the longitudes of the key reference points, such as Cape Phyces, Cyrena, Berenica, Aesporis, Thena, and Carthage. A notable stretching and the subsequent contraction of the coast between Alexandria and Cyrenaica, as are exhibited by Ptolemy’s map relative to the Stadiasmus’ data, can be explained by assuming that several points on this coast were tied to the position of Crete, which was moved to the west being pushed by the westward shift of Rhodes. A sharp contraction of the two coastal stretches of the Great Sirte, oriented along the north-south direction, can be explained by Ptolemy’s erroneously underestimated value for the circumference of the Earth. The analysis of this contraction, as well as of the east-west stretching of the coast between Alexandria and Cyrene in angular terms relative to the modern map, makes it possible to assess the magnitude of Ptolemy’s error and to determine the length of his stade. This analysis shows that Ptolemy’s value for the circumference of the Earth must have been underestimated by approximately 20–27%, and Ptolemy’s stade must have been approximately 175–185 m length. Comparison of the Stadiasmus distance data with the modern map shows that the average length of the stade was close to 179 m or to the “common” stade of 185 m for the stretch between Alexandria and Berenice. (shrink)

1. Consider a circle. It has both a radius and a circumference. There is obviously a real distinction between the properties having a radius and having a circumference. This is not because, when confining ourselves to circles,1 having a radius can ever exist apart from having a circumference. A real distinction does not depend on that. Descartes thought that a real distinction between x and y meant that x could exist without y or vice versa, if only (...) by the power of God. But Descartes was wrong. Separable existence is a sufficient but not necessary condition of there being a real distinction. The difference between a real and a conceptual distinction derives from medieval philosophy. Aquinas, for one, held that things can be really distinct even though not separable (the form and matter of a material substance or its essence and existence, for example).2 For a merely conceptual distinction between x and y to exist, it is necessary for the distinction to exist in thought only. There is only a conceptual distinction between an upward slope and a downward slope, or between a glass’s being half empty and half full. Not only are the members of such pairs inseparable (whether by God or in any other way), but there is no real distinction between them. There is no numerical distinctness between the entities or qualities between which there is only a conceptual distinction. To this extent alone is Galen Strawson (2008) correct.3 But when it comes to.. (shrink)

ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical (...) property, a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context. (shrink)

In the third century b.c.e., Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. Cleomedes gives a short account of Eratosthenes’ method, his numerical assumptions, and the final result of 250,000 stades. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that Eratosthenes later made (...) better measurements and revised his estimate or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved in the doxographical literature. This essay shows that Eratosthenes’ result of 252,000 stades for the Earth’s circumference follows from a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. The essay discusses the consequences for our understanding of his program. (shrink)

THE CONCEPT of basic action rests upon a not especially controversial observation and a standard sort of philosophical argument. The observation is that there occur a great many actions in which what is said to be done—say a—is not done directly but rather through the agent doing something b, distinct from a, which causes a to happen. Thus I move a stone by pushing against it, and the pushing, itself an action, causes the locomotion of the stone when all relevant (...) conditions are supposed benign. Sometimes an agent m performs an action in which b is done and another occurrence a is caused by b, but as a is only a consequence of b and is not itself said to be done, such cases fall outside the circumference of the observation just described. What falls within that circumference I designate nonbasic actions, leaving it open that there may be species of nonbasic actions other than those specified by this observation. (shrink)

In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, whether (...) a certain outcome is associated with a non-measurable region or a measurable one. (shrink)

First, a brief history is provided of Popper's views on the status of evolutionary biology as a science. The views of some prominent biologists are then canvassed on the matter of falsifiability and its relation to evolutionary biology. Following that, I argue that Popper's programme of falsifiability does indeed exclude evolutionary biology from within the circumference of genuine science, that Popper's programme is fundamentally incoherent, and that the correction of this incoherence results in a greatly expanded and much more (...) realistic concept of what is empirical, resulting in the inclusion of evolutionary biology. Finally, this expanded concept of empirical is applied to two particular problems in evolutionary biology — viz., the species problem and the debate over the theory of punctuated equilibria — and it is argued that both of them are still mainly metaphysical. (shrink)

Fluctuating asymmetry (FA) is small deviations from perfect symmetry in normally bilaterally symmetrical traits. We examined the relationship between FA of five body traits (ear height, length of three digits, and ankle circumference) and self-reported scores of physical and verbal aggression in a sample of 90 boys aged 10 to 15 years. The relationships between FA and scores of aggression (particularly physical aggression) were found to be negative; in other words, the most symmetrical boys showed highest aggression. One trait (...) (ankle circumference) showed the characteristics of “ideal” FA—parametric mean of zero and a normal distribution. Mean asymmetries calculated from six repeated measures of ankle FA in 30 subjects taken over a period of five months showed strong negative associations with scores of physical aggression which were independent of age, height, and weight.It is argued that soft tissue “cyclical” FA (as opposed to “fixed” bony FA) is dependent on the secretion of hormones: for example, cortisol. Causal associations between behavioral traits such as aggresion and hormones will lead to similar correlations between FA and behavior. (shrink)

This article is a spiritual interpretation of Leonhard Euler’s famous equation linking the most important entities in mathematics: e (the base of natural logarithms), π (the ratio of the diameter to the circumference of a circle), i ( d -1),1 , and 0. The equation itself (e π i+1 = 0>) can be understood in terms of a traditional mathematical proof, but that does not give one a sense of what it might mean. While one might intuit, given the (...) significance of the elements of the equation, that there is a deeper meaning, one is not in a position to get at that meaning within the discipline of mathematics itself. It is only by going outside of mathematics and adopting the perspective of theology that any kind of understanding of the equation might be gained, the significant implication here being that the whole mathematical field might be a vast treasure house of insights into the mind of God. In this regard, the article is a response to the monograph by George Lakoff and Rafael Núñez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000), which attempts to approach mathematics in general and the Euler equation in particular in terms of some basic principles of cognitive psychology. It is my position that while there may be an external basis for understanding mathematics, the results are somewhat disappointing and fail to reveal the full measure of meaning buried within that equation. (shrink)

This study analyzes the influence of grandmothers’ household residency on the presence of low height-for-age and excessive fat, waist circumference, and sum of triceps and subscapular skinfolds in a sample of 247 6- to 8-year-old urban Maya children from Yucatan, Mexico. Between September 2011 and January 2014, we obtained anthropometric and body composition data from children and mothers, as well as socioeconomic characteristics of participants and households. Grandmothers’ place of residence was categorized as either in the same household as (...) their grandchildren or in separate households. Multiple logistic regression models were used to analyze the association between grandmothers’ residency and outcome variables. Models were adjusted for maternal anthropometric characteristics and the following socioeconomic variables: family size, location, maternal education, monthly family income, and household crowding. Models showed that the presence of grandmothers in their grandchildren’s households was not associated with any of the outcome variables. In contrast, larger family size, overcrowding in the household, and lower family income predicted low height-for-age in children. Larger family size decreased the risk for being overweight based on the three parameters of body composition. Overcrowding in the household increased the risk for greater skinfolds thickness, while low family income increased the risk for higher fat mass index. The residency of grandmothers in their adult daughters’ households is not significantly associated with the outcome variables in this sample of urban Maya families. Instead, maternal anthropometric characteristics and socioeconomic conditions of the family have a greater influence on the overall growth of children. (shrink)

The holographic principle was proposed by Nobel laureate Gerard ‘t Hooft in the 1990s and it has also been modeled by Leonard Susskind and Stephen Hawking. We’ve heard light mentioned with regard to the fundamental nature of reality for a long time; God said Let there be light, we are the light of the world, etc. But we haven’t investigated a possible role for the speed of light in our illnesses. This paper will do just that. The central premise is (...) that light’s “speed” is a reflection of the degree to which the observer is removed from its source. In its Platonic state, light’s speed is zero. It is light from which time, by degrees, emerges. The Big Bang can be envisioned as a sphere, the center of which is a point, Alpha. Via expansion, Alpha becomes a sphere, Omega, by degrees, where each degree is c. For any given Alpha, the circumference of a circle on the sphere, Omega, is a set of resonant points that represent the speed of light or “end of time.” Every radius—every line drawn from Alpha to Omega—is an arrow of time, a parallel universe. Alpha and Omega increase in tandem, maintaining the degree of separation required by special relativity, E=mc^2. The holographic sphere of points equidistant from the Big Bang on which we find ourselves is not the only sphere of points equidistant from the Big Bang. There are spheres that are smaller and larger than ours. Where an arrow of time intersects a sphere-brane of light’s speed will be treated here as a “2D hologram.” For an observer behind the hologram, reality will appear to be accelerating/expanding. For an observer in front of it, reality will appear to be decelerating/contracting. For an observer at the speed of light, time is no longer a variable. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Transitions to a Modern Cosmology: Meister Eckhart and Nicholas of Cusa on the Intensive InfiniteElizabeth BrientThe Epochal Transition from the late medieval to the early modern world has long been thought in terms of the gradual “infinitization” of the cosmos. Traditionally this process has been studied by focusing on the pre-history and the aftermath of the Copernican revolution, that is, by describing the transition from the finite, hierarchically ordered (...) medieval cosmos to the infinite and homogeneous universe of the new astronomy. I would like to situate this paper within the context of a more general reading of the process of the infinitization of the medieval cosmos. That is, I want to argue that this process of “infinitization” must be understood intensively as well as extensively. Nature, in the modern age, is thought of not only as infinitely extended in space, but also as exhibiting an infinite richness in all of its parts. Each particular, each individual being is grasped as utterly unique, as infinitely rich and consequently as conceptually inexponable. Thus the infinitization of the real leads to an infinitization of the knowable—the radical shift in ontology grounds a corresponding shift in epistemology, so that the progress of human knowledge is understood as an unending project infinitely extended over time. In order to underscore both aspects of the infinitization of the medieval cosmos (intensive as well as extensive) I will focus on the way in which a single metaphor (that of the infinite sphere) is unfolded historically in the thought of Meister Eckhart and Nicholas of Cusa.1 This paper may thus be viewed as a case study of [End Page 575] the way in which the modern notion of “intensive infinity” may be traced back to late medieval speculation on the nature of God’s omnipresence in the world.1. EARLY SOURCES OF THE INFINITE SPHERE METAPHORThe metaphor of the infinite sphere makes its first appearance in the pseudo-Hermetic Liber XXIV philosophorum, a small book in the literary form of an “opus propositionum” which, in twenty-four propositions, describes the ineffable essence of God in the mystical language of Neoplatonic theology. It is in the second proposition of this book that we find for the first time the formulation, “God is an infinite sphere, whose center is everywhere, whose circumference is nowhere.”2 This formulation represents a significant development in the history of the Neoplatonic conception of intensive unity, and in the Christian understanding of divine infinity. The Neoplatonic One is here identified with God as infinite being. As a result the relationship between the One and the many, between God and the world, comes to be viewed in a new light, through the lens of “infinite unity.” The metaphor of the infinite sphere is a paradoxical formulation which pictures the coincidence of divine immanence with divine transcendence. That is, it expresses a double infinity: both intensive and extensive. God’s center is located at every point, as it were, indicating the plenitude and infinite richness of God’s being, while there is no limit, no boundary to the extent of God’s all-encompassing reach. The infinite sphere figures the divine nature as an intensive plenitude without end or bounds. The third and next proposition in this same work goes on to strengthen this sense of divine intensity, by asserting that God in his entirety is present in every part (Deus est totus in quolibet sui). The divine nature is not spread out compositionally, as it were, but is wholly present throughout. Proposition 18 describes God as a sphere which has just as many circumferences as points (Deus est sphaera cuius tot sunt circumferentiae, quot sunt puncta), once again, an exploding image which can only make sense in the case of an infinite sphere. These three propositions taken together provide us with a springboard for considering the nature of infinite unity. The exploding paradox of the infinite sphere [End Page 576] provides a rubric for thinking the coincidence of transcendence and immanence, a way of conceptualizing infinite unity, which cannot be “grasped” with finite concepts or through discursive reasoning. The metaphor of the infinite sphere finds its meaning precisely in the way... (shrink)

This volume opens a set of reviews written by Bueno published by the Institute of Philosophy "Luis Vives" of the CSIC. The first of these reviews also constitute the first texts of Bueno of which we have news and are part of their stage as a CSIC fellow in Madrid, a period in which he develops his doctoral thesis on the philosophy of religion. Formal and material foundation of the modern philosophy of religion, which is dated April 7, 1947. Despite (...) being short texts, small of them small philosophical notes that should not be overlooked: the role of Cartesianism in the History of modern philosophy, the relations between philosophy and literature, the scope of the theory of tomista knowledge, the problem of the logical foundation of mathematics, & c. In any case, the main value of these reviews is to offer a sample of the type of readings that its author made in those years. Therefore it is interesting to verify the use that makes Bueno in his youth works of some of the texts he had previously reviewed. Thus, for example, in the doctoral thesis it is cited, to illustrate some aspects of its "historical" part, Paul Hazard's work on European thought in the 18th century to which a year earlier (1946) dedicated the most extensive review and detailed how many wrote. However, it is in the unpublished book on the picnological processes, dated in 1953 and already written in Salamanca, where we will find the works of logic that Bueno had read and reviewed in the previous years. Here Manuel Granell's logic manual will be quoted, but Hönen's monograph on the Theorie du Jugement d'Arès St. Thomas d'Aquin and Beth's books, Becker and Curry will also be referenced in the numerous examples extracted of the logic that jalonan the work. From the book of Dockx, Vers UNE Synthèse Moderne du Savoir, it extracts good the formulation of one of its favorite examples of the picnological process: that of the polygon inscribed in a circumference with which it ends up identifying, by one step to the limit, after the indefinite multiplication of its sides. This group of writings can also be ascribed in some ways the most extensive work about "a new exhibition of the syllogistic", appeared in the aforementioned Philosophy magazine in 1951. (shrink)

ObjectiveTo confirm the effects of a transtheoretical model based on multidimensional life management on healthy behavior in patients with polycystic ovary syndrome.MethodsIn total, eighty eligible patients were recruited from March 2021 to June 2021 and randomly assigned to either the intervention or control groups. Outcome measures include health-promoting behavior, self-efficacy, anthropometrics, and the number of unplanned outpatient admissions. Data were collected at baseline, 3, and 6 months after the intervention. The chi-square test, rank-sum test, t-test, and repeated measurement analysis of (...) variance were used to analyze the data.ResultsIn total, sixty-six participants completed the study: 35 participants in the intervention group and 31 participants in the control group. After 6 months of intervention, the healthy behavior level of patients with PCOS increased from moderate [health-promoting lifestyle profile -II score of 105.37 ± 12.57] to good in the intervention group; and there was no change observed in the control group. In addition, the total self-efficacy score, PCOS-related unplanned outpatient admissions, waist circumference, and body mass index were found to have a significant difference in the intervention group at 6 months. Meanwhile, repeated measures analysis of variance showed a significantly greater improvement in health-promoting behavior and self-efficacy over time in the intervention group than in the control group.ConclusionThe transtheoretical model based on multidimensional life management positively affected healthy behavior, self-efficacy, the number of unplanned outpatient admissions, and anthropometrics in patients with PCOS.Clinical Trial Registrationwww.chictr.org.cn, ChiCTR2000034572. (shrink)

Radial growth has long been a subject of interest in tree biology research. Recent studies have brought a significant change in the understanding of some basic processes characteristic to the vascular cambium, a meristem that produces secondary vascular tissues (phloem and xylem) in woody plants. A new hypothesis regarding the mechanism of intrusive growth of the cambial initials, which has been ratified by studies of the arrangement of cambial cells, negates the influence of this apical cell growth on the expansion (...) of the cambial circumference. Instead, it suggests that the tip of the elongating cambial initial intrudes between the tangential (periclinal) walls, rather than the radial (anticlinal) walls, of the initial(s) and its(their) derivative(s) lying ahead of the elongating cell tip. The new concept also explains the hitherto obscure mechanism of the cell event called ‘elimination of initials’. This article evaluates these new concepts of the cambial cell dynamics and offers a new interpretation for some curious events occurring in the cambial meristem in relation to the radial growth in woody plants. (shrink)

The article presents an attempt to confirm the circumplex structure of goal contents, identified in 15 cultures around the world, in nine Polish samples. The procedure followed steps from the original study and included testing the assumed 11-factor goal structure and the two-dimensional circular organization of the goal contents. None of the analyses showed outcomes that would explicitly confirm the results attained in the original study. The CFA showed rather poor fits. Results of the MDS generally supported the assumption about (...) the two-dimensional goal contents structure, however ipsative distance analysis reproduced only one of the two assumed dimensions. Finally, although the CIRCUM analysis showed in principle that in the Polish sample the organization of goal contents on the circumference was quite similar to original, the RMSEA indicated poor fit. Methodological and conceptual reasons for the replication failure are analyzed and discussed. (shrink)

Background:Women's health has received renewed attention in the last few years including health rehabilitation options for women affected by breast cancer. Dancing has often been regarded as one attractive option for supporting women's well-being and health, but research with women recovering from breast cancer is still in its infancy. Dancing with Health is multi-site pilot study that aimed to evaluate a dance programme for women in recovery from breast cancer across five European countries.Methods:A standardized 32 h dance protocol introduced a (...) range of Latin American dances presented within a sports and exercise framework with influences from dance movement therapy. Fifty-four women (M age 53.51; SD 7.99) participated in the study who had a breast cancer diagnosis 6 weeks, no indication of metastasis, or scheduled surgery/chemotherapy/radiation treatment for the duration of the intervention. Primary outcome data was collected for anthropometric and fitness measures next to cancer-related quality of life.T-tests and Wilcoxon signed ranked tests were used to establish differences pre and post intervention. Cohen's d was also calculated to determine the effect size of the intervention.Results:Statistically significant changes were found for: (i) weight, right and left forearm circumference and hip; (ii) 6 min walking, right and left handgrip, sit-to-stand and sit-and-reach; (iii) the EORTC-QLQ C30 summary score as well as the subscales of emotional and social functioning and symptoms. In all cases the direction of change was positive, while Cohen's d calculated showed that the effect of the intervention for these parameters ranged from intermediate to large.Conclusion:Changes on the above anthropometric, fitness and quality of life measures suggest that the intervention was of value to the participating women recovering from breast cancer. Results also advocate collaborative efforts across countries to further research. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.2 (2000) 343-346 [Access article in PDF] The Paradox Topos Lisa Gorton As William Egginton points out, 1 when Dante and Beatrice step outside the cosmos, they step into another set of concentric spheres. 2 These surround our (supposedly) geocentric cosmos, and yet they center upon God. The image affronts our logic of space. If these concentric spheres encompass us, how can they (...) center upon something somewhere else? The notion seems to turn space inside-out. But Dante's spatial paradox is not in truth a paradox of space. Instead, it is a spiritual paradox, set in terms of space. When Dante and Beatrice step outside the cosmos, they step outside space into an old philosophical topos, a spatial image of God. For that reason, Dante's image is not really akin to the spatial paradoxes of modern astrophysics, although Egginton's comparison of the two does provoke some fascinating comments upon medieval concepts of space. Egginton assesses Dante's paradox in light of medieval debates about space, place, and God. However, he overlooks the most important source for Dante's paradox--the symbolic geometry of Neoplatonic philosophy. 3Neoplatonic philosophers use spatial forms to imagine spiritual relationships. They develop a symbolic geometry, a spatial language of thought, which borrows nothing from physical space but its shapes: the center, the circle, and concentric spheres. Neoplatonists use this symbolic geometry because it offers a spatial way to imagine the relationship between a cause and its effect, without importing time differences into that relationship. In this way they seek to avoid the problems of time and causality, which the creation-myth in Timaeus introduced into Plato's philosophy: how and when could a timeless being make time? 4 [End Page 343]Plotinus, the first Neoplatonist, uses symbolic geometry to design an "Intellectual Cosmos," which he treats as quite distinct from our physical cosmos. 5 He imagines the source of life as a center: The Highest cannot be divided and allotted... thus a centre is an independent unity; everything within the circle has its own term in the centre, and to the centre the radii each bring their own. (Enneads, V. 1. 11). The "Highest" exists as the center of this "Intellectual Cosmos." Plotinus treats a center's geometric qualities as metaphysical attributes. Like an undimensioned central point, the "Highest" does not exist in space or time, and yet space and time radiate from it as a circumference radiates from its center.The bare symbolic space of Plotinus's "Intellectual Cosmos" has emotional connotations. Plotinus holds that "the center of a circle is distinctively a point of rest" (Enneads II. 2. 1). Lesser beings must turn sequentially through all the angles their center holds altogether at once: There is, we may put it, something that is centre; about it, a circle of light shed from it; round centre and first circle alike, another circle, light from light; outside that again, not another circle of light but one which, lacking light of its own, must borrow. (Enneads, IV. 3. 17) In Plotinus's "Intellectual Cosmos" life emanates from the center in concentric spheres. 6Dante and Beatrice step into such an "Intellectual Cosmos" when they step outside the physical world. They step into a spatial image that stands outside time and space, at the spiritual center of the poem, when they step into spheres that center upon a light too bright to look upon. Dante wonders where that center could be, and Beatrice responds to his silent question: "The nature of the universe, which holds the center still and moves all else around it, begins here as if from its turning point" (XXVII, 106-9). Egginton comments, "Dante's description of this absolute center as the origin of all movement and force in the universe" is "an 'eerie' likeness of what he [the modern astrophysicist, Robert Osserman] terms the retro-verse." More relevantly, it also refers to the "Intellectual Cosmos" of Neoplatonic philosophy, where the "Highest" is a center of rest, the starting point of light, movement, and life. [End Page 344]Plotinus... (shrink)

The paper brings into light and discusses a concentric solar model briefly described in Chapter 5 of Section III of ‘Abd al-Raḥmān al-Khāzinī’s On experimental astronomy, a treatise embedded in the prolegomenon of his comprehensive Mu‘tabar zīj, completed about 1121 c.e. In it, the Sun is assumed to rotate on the circumference of a circle concentric with the Earth and coplanar with the ecliptic, but the motion of the vector joining the Earth and Sun is monitored by a small (...) eccentric hypocycle. The ratio between the distance of the hypocycle’s center from the Earth and the hypocycle’s radius is equal to the solar eccentricity in the eccentric model. The model is to account for the constancy of the apparent diameter of the solar disk as held by Ptolemy. The source of the model is unknown. Since the mechanism employed in it clearly resembles the pin-and-slot device, whose use in mechanical astronomical instruments has a long history from the Antikythera Mechanism to the medieval solar, lunar, and planetary equatoria and dials, we argue that the solar model can be positioned within this long-standing tradition and considered the result of the correct understanding of some Byzantine prototype and thus a typical example of the transmission of astronomical ideas via media of the material culture. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Losing the Self:Detachment in Meister Eckhart and Its Significance for Buddhist-Christian DialogueCharlotte RadlerThe purpose of this article is to probe Meister Eckhart's concepts of self—or, rather, no-self—detachment, and indistinct union, and their positive implications for Buddhist-Christian dialogue. I will examine potential affinities between Eckhart and Buddhist thought with the modest hope of identifying areas in Eckhart's mysticism that may present themselves as particularly ripe for Buddhist-Christian conversations.On April 15, (...) 1329, Pope John XXII issued the bull "In agro dominico" that condemned tenets of Meister Eckhart's teaching. Pope John XXII, who had also dealt harshly with the spiritual Franciscans, was truly concerned about Eckhart's seductive impact on the uneducated in the pews.1 Eckhart's claim that every human's true identity, attainable through detachment, is divine must have created dreams in some of an unmediated experience of and union with the divine, and nightmares in others of the bypassing of the Church's structures, sacraments, and hierarchies.Eckhart, a University of Paris teacher and a preacher, bases his mysticism in part on Proclus and Dionysius the Areopagite. Similarly to Proclus, Eckhart proposes that the soul's circular journey runs from the nothingness of the God beyond God, the God beyond the Trinity, into the somethingness of the world, and back to the nothingness of the God beyond the God. There is a firm ontological link between the One, the Trinity, and creation, which means that creation in its core is Trinitarian and One. In his interpretations of Job 22:14 and Ps. 61:12, Eckhart demonstrates that God is never static as One or Three or creation, but God is at once dialectically One and flowing out into the persons of the Trinity and flowing over into creation.2 This continuity between the Creator and creature, time and eternity, sanctifies creation and transience in all its grittiness and overcomes a duality between Creator and creature similar to the interpretation of samsara and nirvana (conditioned reality is Boundless Openness in Mahayana thought). Furthermore, Eckhart maintains that the One, as transparent and transcendent nothingness, encompasses and penetrates all. The wondrous truth, for Eckhart, is that we are truly all in all, just like the center of the circle is everywhere and its circumference nowhere.3 [End Page 111]To his audience, Eckhart repeatedly underscores that the soul is ontologically rooted in the nothingness of the divine unity and is thus in its deepest essence divine. In fact—and here we find profound resonances with tenets of Buddhist thought such as the concept of no-self (anatta or anatma)—the self's only true existence is the divine nothingness. Contrary to such thinkers as Thomas Aquinas, Eckhart focuses on the principal existence of things in the godhead and maintains that the human being does not possess a true substantial existence or "I" apart from God.4 Hence, the "I" or self can never constitute the foundation of reality. Because of the human being's absolute ontological dependence on God, Eckhart can assert that "where God is, there is the soul, and where the soul is, there is God."5 In his writings, Eckhart therefore differentiates between the true existence that creatures have in their original cause, the esse virtuale, and the particular and ephemeral existence that creatures possess in themselves, the esse formale.6 Thus, instead of autonomy and possessive individualism, "theonomy" implies the realization of the human being's full potential.While the autonomous, individual self is a form of negative nothingness or no-self, it paradoxically constitutes the greatest attachment for the human being. The clinging to the self causes what David Tracy refers to as an individual and cultural terror of transience.7 In the journey toward union, the soul must carefully release itself from all its attachments and detach itself from all its possessiveness. Eckhart's existential letting-go and letting-be imply the profoundest respect for existence itself as well as recognition of the ontological interconnectedness of all life.One of the foremost representatives of the apophatic tradition, Eckhart hooks up the praxis of apophasis to the notion of detachment, the stripping away of... (shrink)

The patterns of physical growth (stature, BMI, subscapular and arm fat-fold thickness, upper and lower extremity length, chest circumference, arm, and hip breadth, and age at menarche) were studied in 857 of Maya and Mestizo girls and 1314 of Creole girls aged 6-18 years. Data were collected between 1998-2001 in primary, secondary, and high schools of Merida, Capital City of the Yucatan State, Mexico. The ethnicity of girls was defined using their two surnames (from the father and mother side). (...) The results show that Creoles are taller, have more abundant fat tissue, and greater BMI, especially at the age of 11 years, which means that they are better prepared to start pubertal spurt. Maya girls have relatively longer upper extremities to lower ones, greater biacromial breadth, and chest circumference to stature than Creoles, which shows their more stocky body build. The adolescent (pubertal) spurt in height starts earlier in Creoles (9-10 years) and its rate is greater (max. = 7.48 cm/ year) than in Maya and Mestizos girls (10-11 years; max. = 6.25 cm/year). In Mayas and Mestizos, there is only a slight difference between the rate of changes before and during the pubertal spurt. There are no significant differences in age at menarche between girls from both ethnic groups (11.96 in Mayas and Mestizos and 12.04 in Creoles), but there are statistically significant differences between age at menarche of studied girls and their mothers (12.4 for both groups) in each ethnic group. There is evidence that the onset of pubertal spurt in height and its rate may depend on ethnicity. Creoles may lead to a more “westernized” style of life than the Maya and Mestizos girls. (shrink)

In 1909, Ehrenfest published a note in the Physikalische Zeitschrift showing that a Born rigid cylinder could not be set into rotation without stresses, as elements of the circumference would be contracted but not the radius. Ignatowski and Varićak challenged Ehrenfest’s result in the same journal, arguing that the stresses would emerge if length contraction were a real dynamical effect, as in Lorentz’s theory. However, no stresses are expected to arise, according to Einstein’s theory, where length contraction is only (...) an apparent effect due to an arbitrary choice of clock synchronization. Ehrenfest and Einstein considered this line of reasoning dangerously misleading and took a public stance in the Physikalische Zeitschrift, countering that relativistic length contraction is both apparent and real. It is apparent since it disappears for the comoving observer, but it is also real since it can be experimentally verified. By drawing on his lesser-known private correspondence with Varićak, this paper shows how Einstein used the Ehrenfest paradox as a tool for an ‘Einsteinian pedagogy’. Einstein’s argumentative stance is contrasted with Bell’s use of the Dewan-Beran thread-between-spaceships paradox to advocate for a ‘Lorentzian pedagogy’. The paper concludes that the disagreement between the two ways of ‘teaching special relativity’ stems from divergent interpretations of philosophical categories such as ‘reality’ and ‘appearance’. (shrink)

IN Physics VIII, 10, Aristotle seems to commit a serious mistake: just before concluding that the first mover required by all motion everywhere remains invariable and without parts or magnitude, Aristotle apparently locates this mover on the circumference of the cosmos.

The western consensus is that obese women are considered attractive by Afro-Americans and by many societies from nonwestern developing countries. This belief rests mainly on results of nonstandardized surveys dealing only with body weight and size, ignoring body fat distribution. The anatomical distribution of female body fat as measured by the ratio of waist to hip circumference (WHR) is related to reproductive age, fertility, and risk for various major diseases and thus might play a role in judgment of attractiveness. (...) Previous research (Singh 1993a, 1993b) has shown that in the United States Caucasian men and women judge female figures with feminine WHRs as attractive and healthy. To investigate whether young Indonesian and Afro-American men and women rate such figures similarly, female figures representing three body sizes (underweight, normal weight, and overweight) and four WHRs (two feminine and two masculine) were used. Results show that neither Indonesian nor Afro-American subjects judge overweight figures as attractive and healthy regardless of the size of WHR. They judged normal weight figures with feminine WHRs as most attractive, healthy, and youthful. The consensus on women’s attractiveness among Indonesian, Afro-American, and U.S. Caucasian male and female subjects suggests that various cultural groups have similar criteria for judging the ideal woman’s shape. (shrink)

The contemporary debate centering round the circumference of feminist discourse has of late been very potent in addressing the issues of certain prejudiced notions in our existing patriarchal structure. This paper is an attempt to show the ongoing paradox existing in the world of feminism which has thoroughly critiqued the patriarchal culture and has naturalized sexual identities, thereby glorifying man’s supremacy and dominion. The patriarchal culture lionized the ideals of brevity, courageousness, and intellect and thought of these as the (...) only special possessions of man in society. The qualities of being submissive, kind and caring in nature is considered to be “ideal” and exclusive qualities of a woman. Even though these qualities are “ideal” to women, they are discarded from being considered as universal in nature and are thought of as insignificant in the mainstream societal structure. These qualities are treated as inferior, and exclusively womanly and hence cannot make their stand in the conventional patriarchal social order. For this reason a dilemmatic situation arises here. My effort is to show that this dilemma cannot be exposed in the sense of gender specific human qualities. (shrink)

The knots of images in Aeschylus’ Septem with their exuberant and powerful vocabulary give the play the aura that prompted Gorgias and Aristophanes to proclaim it “full of Ares”. The ferocity of the ancient siege is brought to life in the destruction of the city the chorus imagines and in the duels at the seven gates that achieve epic proportions through the dueling speeches of Eteocles and his scout. The play’s transparent dependence on language for its emotive effect readily invites (...) close examination. Aeschylus’ Septem abounds with contemporary cosmological and mathematical ideas and images. The poet uses them consistently throughout the play, I suggest, to make of Thebes a seven-sided, shield-shaped cosmos, ruled over by the seven-month lord of sevens (heptamagetes), Apollo, and the completion of whose circumference seals the unified fate of Polynices and Eteocles. (shrink)

The aim of the study was to compare the anthropometrics parameters of young female volleyball players by different court play position. 52 female volleyball players (indoor court) (mean ± SD age: 15.7 ± 1.2 years) participated in the study. Players were divided based on their playing position (middle blocks, setters, liberos, and hitters (outside hitter/left side hitter and opposite hitter/right side hitter). They were examined in the field for anthropometric characteristics such as BM (mean ± SD: 61.4 ± 13.4 kg), (...) height (mean ± SD: 163.6 ± 7.7 cm), Body Mass Index [BMI] (mean ± SD: 22.6 ± 3.1), waist circumference (mean ± SD: 70 ± 8.4 cm).All data are presented as mean ± SD, and the level of significance was set at p ≤0.05. Therefore, a parametric analysis, one-way analysis of variance (ANOVA), was used to determine significant differences among positions in anthropometric parameters.Post hoc comparison indicated that height and body mass differed significantly among most groups; however, no significant differences were found between middle blocker and setters (p = 0.20) for height. In addition, no significant differences (p > 0.05) were detected between the setter and opposite hitters (p = 0.55) and between middle blocker and outside hitter (p = 0.41) for body-height. In conclusion this study indicates that significant differences exist among youth female volleyball players of different playing positions for body-mass, body-height, waist-circumference and BMI. (shrink)

As a result of the development of new technologies such as satellite communication, digitalization, and multimedia computer networks, new media such as blogs, online magazines, and wireless network media have sparked a lot of interest. This study uses 3D clothing display technologies to improve the customer experience of online clothing marketing, aid in the improvement of online clothing marketing efficacy, and extensively discuss the digital clothing anthropometric model. Furthermore, this study employs the convex hull approach and NURBS fitting technology to (...) address concerns with digital clothing anthropometric measurement and provides a practical solution for measuring straight line length, circumference length, and curve length. Furthermore, this research incorporates 3D intelligent technology to develop an online fitting system as well as an intelligent display system for garments. The simulation experiment investigation revealed that the smart clothing 3D display system proposed in this work has a substantial impact on growing online e-commerce clothing marketing as well as improving clothing marketing effectiveness. (shrink)

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.

The correlation between psychopathology and hermeneutics has long been at the forefront of philosophic discussion. In recent years a number of thinkers, particularly in France, have advanced the claim that all hermeneutic acts are themselves part of an intrinsic pathology which makes it impossible to arrive at neutral and binding interpretations. The so-called hermeneutics of suspicion has served to undermine those interpretive norms which guided the depth psychology coming out of Freud and Jung. This hermeneutic and semiotic anarchy derives its (...) impetus from a misreading of the nature and scope of a general psychopathology. Rather than locating psychopathology under the more generic analysis of the self and its relation to the various modes of the encompassing, whether these modes pertain to the self or its world, the hermeneutics of suspicion equates psychopathology with the self in all of its dimensions. Any contrast between the authentic or inauthentic, or the normal and the abnormal, is held to impose a form of privileging on the vast fabric of a self which has no center or circumference. The epoch making work of Freud and Jung is distorted and their basic commitment to hermeneutic norms is undermined. This not only represents a profound misreading of the history of depth psychology but stands as a threat to the drive for transcendence which lives at the heart of the human self. 2012 APA, all rights reserved). (shrink)

Now the visionaries of the high energy physics community are ready to take the next step, the Superconducting Super Collider or SSC. By now you must have heard or read something about this machine. It is being pushed by President Reagan and the Department of Energy. It will have a total cost in 1987 dollars of $4.4 billion and will be built at a location now in the process of selection. It will be a big machine, the largest proton synchrotron (...) ever planned, "the greatest public works project in the history of mankind", as one congressman put it. The tunnel in which it will be constructed does not circle the Earth. It is more modest, with a circumference of "only" 52 miles. Yet the SSC will produce proton-proton collision energies 40 times higher than those of the FermiLab Tevatron or Fermi's dream machine. (shrink)

Explore how mathematics has shaped how we look at and understand the world. From figuring out Earth's circumference using geometry to developing load-bearing arches, young readers will be engaged as they learn about real world math applications.

Macrocephaly is present in about 2–5% of the general population. It can be found as an isolated benign trait or as part of a syndromic condition. Brain overgrowth has been associated with neurodevelopmental disorders such as autism during the first year of life, however, evidence remains inconclusive. Furthermore, most of the studies have involved pathological or high-risk populations, but little is known about the effects of brain overgrowth on neurodevelopment in otherwise neurotypical infants. We investigated the impact of brain overgrowth (...) on basic perceptual learning processes during the first year of life. We recorded high density electroencephalograms in 116 full-term healthy infants aged between 3 and 11 months, 35 macrocephalic and 81 normocephalic classified according to the WHO head circumference norms. We used an adapted oddball paradigm, time-frequency analyses, and auditory event-related brain potentials to investigate differences between groups. We show that brain overgrowth has a significant impact on repetition effects and change detection response in the 10–20 Hz frequency band, and in N450 latency, suggesting that these correlates of sensorial learning processes are sensitive to brain overgrowth during the first year of life. (shrink)

A topological space is hereditarilyk-irresolvable if none of its subspaces can be partitioned into k dense subsets. We use this notion to provide a topological semantics for a sequence of modal logics whose n-th member K4Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}_n$$\end{document} is characterised by validity in transitive Kripke frames of circumference at most n. We show that under the interpretation of the modality ◊\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Diamond $$\end{document} as (...) the derived set operation, K4Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}_n$$\end{document} is characterised by validity in all spaces that are hereditarily n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n+1$$\end{document}-irresolvable and have the TD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_D$$\end{document} separation property. We also identify the extensions of K4Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}_n$$\end{document} that result when the class of spaces involved is restricted to those that are crowded, or densely discrete, or openly irresolvable, the latter meaning that every non-empty open subspace is 2-irresolvable. Finally, we give a topological semantics for K4M, where M is the McKinsey axiom. (shrink)