The Rudin-Keisler ordering of ultrafilters is extended to complete Boolean algebras and characterised in terms of elementary embeddings of Boolean ultrapowers. The result is applied to show that the Rudin-Keisler poset of some atomless complete Boolean algebras is nontrivial.

Open peer commentary on the article “Modeling Subjects’ Experience While Modeling the Experimental Design: A Mild-Neurophenomenology-Inspired Approach in the Piloting Phase” by Constanza Baquedano & Catalina Fabar. Upshot: Baquedano and Fabar’s provoking article highlights several difficulties of neurophenomenology, and brings into light the necessity of further clarification of its basic concepts such as human experience, first-person perspective, phenomenological validation, explanation, adequate measurement and so on. Particularly, it becomes more and more clear that the “explanatory gap” cannot be liquidated by means (...) of explanation procedures alone, for the unavoidable variety of modes and forms of human understanding cannot be exhaustively reduced to just any one of these modes. (shrink)

A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...) of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography. (shrink)

Open peer commentary on the article “Consciousness as Self-Description in Differences” by Diana Gasparyan. Upshot: The aim of my commentary is to support some of Gasparyan’s ideas and to reformulate them in a more constructive way in terms of both formalized hermeneutical procedures and networks and in the light of game-theory approaches.

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation process should be statistically similar, i.e. their fractal dimensions and their form factors should be equal. In this paper, we analyze 49 woodlot fragments (Pinus sylvestris (...) L.) in the Belgian Kempen region to study the direct relationship between a transformation process and the concomitant patch geometry. Although the fractal dimension of the woodlots is scattered (i.e. they are not statistically similar), the perimeter-area relation of the fragments is characterized by a single, ‘dimension-like’ exponent. This exponent suggests a certain shape homogeneity among the patches, which is confirmed by the absence of hierarchical levels associated with sharp increases of the fractal dimension at scale transitions. The interaction of different natural (soil factor, vegetation type) and anthropogenic (afforestation, urbanization) processes during patch development is assumed to have generated this feature. Comparison of the area and perimeter fractal dimension with an ecological index for habitat quality, the interior-to-edge ratio, shows that the fractal dimension is suitable for predicting interior habitat presence, which is more likely for patches with smooth perimeters and compact areas. The ratio of the area to the perimeter fractal dimension confirms this observation, with high values for high interior-to-edge ratios, characteristic for regularly shaped patches. (shrink)

We attempt to defend the species-as-individuals hypothesis by examining the logical role played by the binomials (e.g., "Homo sapiens," "Pinus ponderosa") in biological discourse about species. Those who contend that the binomials can be properly understood as functioning in biological theory as singular terms opt for an objectual account of species and view species as individuals. Those who contend that the binomials can in principle be eliminated from biological theory in favor of predicate expressions opt for a predicative account (...) of species and view species as kinds. We contend that biologists' talk about species is talk about species as individuals, and we conclude that the most plausible account of species is an objectual account. (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)

Excerpt from An Estimate of the Manners and Principles of the Times Quamvis Pontica Pinus, Silqilia nobilis, Jae'tcs 8c Genus 8: Nomcn inutile. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the (...) original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Both the physiological and the pathological morphogenetic processes that we can meet in embryogenesis, neogenesis and degenerative dysgenesis present common features: they are ruled by three different kinds of mechanisms, one related to cell migration, the second to cell differentiation and the third to cell proliferation. We deal here with an application to the cambial growth which essentially involves the third type of mechanism.Woody plants produce secondary tissue (secondary xylem and phloem) from a meristematic tissue called vascular cambium, responsible for (...) the radial growth of a tree. This paper focuses on the formation of secondary xylem, considered in two dimensions in a cross-section framework. A new discrete modelling approach is used, based on the cellular scale, in order to attain a more accurate understanding of how the elementary microscopic behaviour of each cell takes part in the macroscopic morphogenesis. The mathematical model essentially uses an occurrence method simulating the main features of radial growth with simple geometric rules, such as Thom's division rule (Thom,1972)to account for the cell proliferation. The study applies to concrete instances in which the changes made in the geometrical cellular patterns of the vascular cambium clearly affect the shape of the tree, as in Pinus radiata (D. Don.). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:News and ViewsMark Gonnerman Click for larger view View full resolutionWhen I think of Roger Corless, I think of the bristlecone pine trees in the White Mountains of east-central California, about an hour's drive from Bishop up White Mountain Road. These trees (Pinus longaeva) are the world's oldest living beings. The senior member of the stand in Patriarch Grove, named Methuselah, is more than 4,700 years old.It is (...) not because Roger lived an especially long life—he was granted only sixty-nine-and-a-half years of calendar time—that he and these trees fuse in my mind. While Roger was an old soul from an older world, this association arises from Roger's adherence to the kind of "become who you are" eccentricity celebrated by Henry David Thoreau and other sages who remind each of us to "step to the music" of "a different drummer."When visiting the bristlecones, one is impressed by the various odd poses struck by each tree. Of course no two are alike; each holds a unique gnarly stance that says, "You are among a community of nonconformists." These trees remind us that each being is a unique expression of Nature and ought to be honored as such.Thoreau does not use the word "eccentric" in Walden, but writes of extravagance instead:I fear chiefly lest my expression not be extra- vagant enough, may not wander far enough beyond the narrow limits of my daily experience, so as to be adequate to the truth of which I have been convinced. Extra vagance! [End Page 155] it depends on how you are yarded.... I desire to speak somewhat without bounds; like a man in a waking moment, to men in their waking moments.A lover of words, as was Roger, Thoreau splits extravagance in two to highlight its root meaning: "to wander" (vagari) "outside" (extra). To learn the truth of matters requires the courage to follow one's own path, even when—especially when—it takes one beyond the pale. Only then might wanderers become convinced of those truths they know, for they have been encountered firsthand and tested, experimentally, in the realm of personal experience.When one sets about the challenging work of claiming a natural right to eccentricity, one discovers self-authenticating feedback loops that encourage further steps along an always unfolding, yet untrammeled path. It takes courage to stay in motion, for the way is often rough. People get lost—and found. One's own authentic way leads to wakefulness. This in turn enables recognition and enjoyment of other liberated beings and compassion for those who have yet to hear chanticleer crow (to stay with Thoreau) or the lion's roar (as Buddhists might say).As Mas Kodani, a Jodoshinshu minister in South-Central Los Angeles has observed, "One does not stand still looking for a path. One walks; and as one walks a path comes into being." This walk requires a balance of both confident perseverance and an ability to respond to ever-changing conditions. Lives of both the bristlecones and Roger demonstrate perseverance in spite of hostile habitats: the pines, rooted in sandstone and dolomite, hang on in a cold and dry climate at 11,200 feet; Roger made his way with difficulty in spite of challenges he faced as a gay, Buddhist-and-Christian intellectual in Durham County, North Carolina. When, after thirty years, Roger became an emeritus professor at Duke and relocated to the San Francisco Bay Area, he found himself in a much more hospitable setting.It may seem strange to draw out this comparison of Roger and those ancient White Mountain pines, but when I first met those trees in the summer of 1998, they set a standard for authenticity that came to mind whenever Roger and I interacted. His extravagant accomplishments as a teacher, scholar, and person who lived a life of genuine service to others were attained through the real work of daily spiritual practice, critical reflection, and adherence to the truths—always plural for Roger—of which he had been convinced. I'll always be grateful for his inspiring example of a human life well lived. It... (shrink)

I have conducted a similar investigation on a text by a different author. The results of this investigation, which was performed on a text passage of 100,000 letters, are presented in the following tables from which one can see how and to what extent the limit theorems of the calculus of probability actually become evident.

We investigate to what extent theorems about quantum mechanical or classical entropy can be generalized to functionals of the type ρ→Tr f(ρ), or ψ→∫f(ψ)dμ, respectively, wheref is an arbitrary concave function.

Presentation of the thesis that Kumāril Bhaṭṭa and Dharmakīrti, 7th cent., Sanskrit philosophers, were Assamese by birth, contrary to the traditional belief that they are from South India.

Buddhist connections in Friedrich Nietzsche's philosophy; a study.

Upshot: Since all my commentators express some reservation about the distinction between the cognitive and non-cognitive aspects of knowledge in general, and its applicability and relevance in the domain of religious belief in particular, I will address the question of why this distinction is important and whether these two modes of knowledge can be communicated. Further questions I try to address include: Can a radical constructivist be an atheist, or alternatively a religious believer? What exactly would these designations mean? Is (...) it at all possible to discuss meaningfully the question of whether God exists? Can two or more people ascertain whether they in fact share their concept of a God? (shrink)