We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ (...) × ℚ with the appropriate topologies. (shrink)

In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B. Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true of a particular system; (...) a criterion for describing counterfactual dependencies in two explanatory modes, i.e. the vertical and the horizontal; and, finally, a third perspectival one that tells us when to use the vertical and when to use the horizontal mode. In the second step, I show how this general theory of topological explanations accounts for explanatory asymmetry in both the vertical and horizontal explanatory modes. Finally, in the third step, I argue that this theory is universally applicable across biological sciences, which helps to unify essential concepts of biological networks. (shrink)

We describe an augmented topological map as an alternative for the proposed bicoded map. Inverting causality, the special nature of the vertical dimension is then no longer fixed a priori and the cause of specific navigation behavior, but a consequence of the combination of the specific geometry of the experimental environment and the motor capabilities of the experimental animals.

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ (...) × ℚ with the appropriate topologies. (shrink)

A chemical compound in the form of graph terminology is known as a chemical graph. Molecules are usually represented as vertices, while their bonding or interaction is shown by edges in a molecular graph. In this paper, we computed various connectivity indices based on degrees of vertices of a chemical graph of indium phosphide. Afterward, we found the physical measures like entropy and heat of formation of InP. Then, we fitted curves between different indices and the thermodynamical properties, namely, heat (...) of formation and entropy. Curve fitting was done in MATLAB through different methods based on linearity and nonlinearity. Furthermore, we depicted our results numerically and graphically. These numerical systems may give an approach to concentrate on the thermodynamical properties of the compound design of InP at an exceptional level that will help understand the connection between framework measurement and these actions. (shrink)

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of (...) rational numbers ${\Bbb Q}\times {\Bbb Q}$ with the appropriate topologies. (shrink)

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ (...) × ℚ with the appropriate topologies. (shrink)

There are many network topology designs that have emerged to fulfill the growing need for networks to provide a robust platform for a wide range of applications like running businesses and managing emergencies. Amongst the most famous network topology designs are star network, mesh network, hexagonal network, honeycomb network, etc. In a star network, a central computer is linked with various terminals and other computers over point-to-point lines. The other computers and terminals are directly connected to the central computer but (...) not to one another. As such, any failure in the central computer will result in a failure of the entire network and computers in star network will not be able to communicate. The star topology design can be represented by a graph where vertices represent the computer nodes and edges represent the links between the computer nodes. In this paper, we study the vertex-edge-based topological descriptor for a newly designed hexagon star network. (shrink)

The primary objective of this study was to propose a functional discrete mathematical model for analyzing folklore fairy tales. Within this model, characters are denoted as vertices, and explicit instances of communication – both verbal and non-verbal – within the text are depicted as edges. Upon examining a corpus of Eastern Slavic fairy tales in comparison to Chukchi fairy tales, unforeseen outcomes emerged. Notably, the constructed models seem to evade establishing certain connections between characters. Consequently, instances where the interactions among (...) fairy tale characters would result in a non-planar graph structure are notably absent. To put it differently, the models refrain from incorporating sub-graphs delineated by the Kuratowski theorem governing planar graphs, specifically the minimal non-planar graphs Κ5 and Κ3,3. Remarkably, even in more extensive texts featuring a larger cast of characters, connections that would yield a non-planar graph pattern are consistently avoided. This leads to the formulation of a hypothesis positing that traditional folk tales adhere to a “planar narrative” design – an identifiable narrative variant characterized by inherent limitations in complexity. This design, in turn, appears deeply entrenched within the societal framework of the cultures that produced these folk narratives. (shrink)

In the poetics of Gaston Bachelard, the natural images, especially the four elements (fire, water, air, earth), occupy the eminent place for literary imagination. Under this main frame, this paper tries to present the relation of ethics and aesthetics in focusing on the ethical image as a synthetic concept. It also argues that the poetic imagination in Bachelard presupposes a metaphysical base managing the being, the force, the will, and the action. There is a dynamic structure in this metaphysics of (...) imagination. Notwithstanding the usual separation of different spheres in philosophy, Bachelard urges a primary fusion in the cosmic scale, i.e.the world and the human are communicative and correspondent. Taking these principles into consideration, this paper explores the topological dimension in those poetic images of elements and space. The ontological sense of being-there is evaluated by the dynamic function of “there” in restoring its ethical meaning. Likewise, the terms “in front of the fire”, “before the water”, “in the water” are given the topological accents. The verticality indicating the dynamic function of the flight, of the falling, and of standing upright is topologically effective. In accordance to the verticality, the concept of survival contains an effect of surpassing the existential conditions, the prefix “sur-“ means that tentative of the higher degree. In sum, the cosmicity as the very place of ethical and ontological unificationreveals Bachelard’s concern on the imaginative transformation of the personality, the appropriation in the cosmos. (shrink)

Topology uses simple geometric and algebraic ideas, but its huge success and vast ramifications make it a tough nut for historians of twentieth‐century mathematics. Two books have addressed it well: Dieudonné chronicles about one thousand key definitions and theorems, and essays in James focus on forty central themes. Both assume considerable mathematics, but neither offers a historical synthesis of the simplest core ideas. Now, Alain Herreman uses semiotics to watch these leading ideas develop through the founding works of Henri Poincaré, (...) Oswald Veblen, James Alexander, and Solomon Lefschetz. Herreman states outright that semiotics will not exhaust these meanings, but he makes it a revealing tool.The method is especially suited to Poincaré, who will define one technical term repeatedly in a single work, each time differently, as if it was the first, and perhaps no definition will match any use of the term in proofs. For Poincaré no term gets meaning from a definition. Each functions in relation to the others—that is, specifically in relation to other terms in Poincaré's work. It is no use invoking standards of rigor current in Poincaré's time and place or then‐current definitions. Poincaré was well known at the time for using neither: Poincaré's meanings must be derived from his writing, as Herreman does.Herreman bases his semiotics on Hjelmslev yet refutes Hjelmslev's concern that mathematics may be “monoplanar,” with no content beyond the signs themselves . The book depicts four levels of content at work in these authors: algebraic, geometric, arithmetic, and set theoretic. Herreman says a sign has algebraic content if its use depends on its written expression, the way polynomials are formal expressions added and multiplied by formal rules. Early topologists—here especially Alexander—sought purely combinatorial methods. Thus a “cube” is a set of six “faces,” twelve “edges,” and eight “vertices,” each taken as primitive and described only by a short table showing which ones meet which. Combinatorics typifies arithmetic content for Herreman. Yet a cube is also an infinite set of points. Herreman speaks of geometric content when a sign indicates both a set of parts and a set of points. Today we might use different notations for the set of points and the set of parts—Poincaré et al. did not. Herreman will not reconstruct their works or restate them in other words; rather, he uses these levels of content to organize extensive quotations and analyze the relations in each text as they move toward deeper union of the algebraic and geometric.The chapter on Lefschetz makes a great finale. Lefschetz is arguably Poincaré's closest and greatest student, though the two never met. Like Poincaré's, his work is at once compelling and baffling, decisive for the future of mathematics yet brutally difficult to absorb. Semiotics serves well in presenting this mathematician who “never stated a false theorem or gave a correct proof,” as his friends joked.The book does not go far into theorems. Yet it requires some background. A beginner might enjoy it with Alexandroff , a gem itself, written with unusually strong historic sense. Specialists will enjoy reading it with the original works for its fresh viewpoints and novel connections. It is a fine way to analyze the works, to see how they create their own meanings. (shrink)

The history of biological systematics documents a continuing tension between classifications in terms of nested hierarchies congruent with branching diagrams (the ‘Tree of Life’) versus reticulated relations. The recognition of conflicting character distribution led to the dissolution of the scala naturae into reticulated systems, which were then transformed into phylogenetic trees by the addition of a vertical axis. The cladistic revolution in systematics resulted in a representation of phylogeny as a strictly bifurcating pattern (cladogram). Due to the ubiquity of (...) character conflict—at the genetic or morphological level, or at any level in between—some characters will necessarily have to be discarded ( qua noise) in favor of others in support of a strictly bifurcating phylogenetic tree. Pattern analysts will seek maximal congruence in the distribution of characters (ultimately of any kind) relative to a branching tree-topology; process explainers will call such tree-topologies into question by reference to incompatible evolutionary processes. Pattern analysts will argue that process explanations must not be brought to bear on pattern reconstruction; process explainers will insist that the reconstructed pattern requires a process explanation to become scientifically relevant, i.e., relevant to evolutionary theory. The core question driving the current debate about the adequacy of the ‘Tree of Life’ metaphor seems to be whether the systematic dichotomization of the living world is an adequate representation of the complex evolutionary history of global biodiversity. In ‘Questioning the Tree of Life’, it seems beneficial to draw at least four conceptual distinctions: pattern reconstruction versus process explanation as different epistemological approaches to the study of phylogeny; open versus closed systems as expressions of different kinds of population (species) structures; phylogenetic trees versus cladograms as representations of evolutionary processes versus patterns of relationships; and genes versus species as expressions of different levels of causal integration and evolutionary transformation. (shrink)

As the accompanying articles in the Special Issue on Semiotic Scaffolding will attest, my colleagues in biosemiotics have done an exemplary job in showing us how to think about the critically generative role that semiotic scaffolding plays “vertically” – i.e., in evolutionary and developmental terms – by “allowing access to the upper floors” of biological complexity, cognition and evolution.In addition to such diachronic considerations of semiotic scaffolding, I wish to offer here a consideration of semiotic scaffolding’s synchronic power, as well (...) – and in particular the ability that it can afford its users to access new and other sign relations “horizontally” as a function of the way that multiple semiotically scaffolded relations intertwine to result in a “definite semantic topology that determines the ways that symbols modify each other’s referential functions in different combinations”.Taking up, in turn, Terrence Deacon’s later challenge that what the sciences of cognition – and biology more generally – needs to “come to grips with [is] the process of semiosis; the dynamic of interpretive activity by which semiotic relationships emerge from other semiotic relationships [as] intrinsically dynamic phases in a generative process”, I attempt here to show how Deacon’s own Peirce-inspired matrix of referential sign relations as presented in The Symbolic Species, when viewed as a semiotic scaffold of interactional constraints and possibility biases, provides the key to understanding the essentially thirdness-manifesting nature of symbol reference, formation and growth. (shrink)

Cultural forms are constrained by cognitive biases, and writing is thought to have evolved to fit basic visual preferences, but little is known about the history and mechanisms of that evolution. Cognitive constraints have been documented for the topology of script features, but not for their orientation. Orientation anisotropy in human vision, as revealed by the oblique effect, suggests that cardinal orientations, being easier to process, should be overrepresented in letters. As this study of 116 scripts shows, the orientation of (...) strokes inside written characters massively favors cardinal directions, and it is organized in such a way as to make letter recognition easier: Cardinal and oblique strokes tend not to mix, and mirror symmetry is anisotropic, favoring vertical over horizontal symmetry. Phylogenetic analyses and recently invented scripts show that cultural evolution over the last three millennia cannot be the sole cause of these effects. (shrink)

Continuous subgraph matching problem on dynamic graph has become a popular research topic in the field of graph analysis, which has a wide range of applications including information retrieval and community detection. Specifically, given a query graph q, an initial graph G 0, and a graph update stream △ G i, the problem of continuous subgraph matching is to sequentially conduct all possible isomorphic subgraphs covering △ G i of q on G i. Since knowledge graph is a directed labeled (...) multigraph having multiple edges between a pair of vertices, it brings new challenges for the problem focusing on dynamic knowledge graph. One challenge is that the multigraph characteristic of knowledge graph intensifies the complexity of candidate calculation, which is the combination of complex topological and attributed structures. Another challenge is that the isomorphic subgraphs covering a given region are conducted on a huge search space of seed candidates, which causes a lot of time consumption for searching the unpromising candidates. To address these challenges, a method of subgraph-indexed sequential subdivision is proposed to accelerating the continuous subgraph matching on dynamic knowledge graph. Firstly, a flow graph index is proposed to arrange the search space of seed candidates in topological knowledge graph and an adjacent index is designed to accelerate the identification of candidate activation states in attributed knowledge graph. Secondly, the sequential subdivision of flow graph index and the transition state model are employed to incrementally conduct subgraph matching and maintain the regional influence of changed candidates, respectively. Finally, extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms. (shrink)

A 4-dimensional periodic table of chemical elements is presented. The 120 elements in the n = 8 system are located on vertices of a 4D-cubic lattice and specified by Cartesian coordinates based on the four quantum numbers. Each quantum number is represented by a vector along a different spatial direction in 4D Euclidean space. The 4D PT has a fixed topology governed by Euler–Poincare-type equation and the chemical elements have a fixed connectivity with neighboring elements within the 4D PT. Various (...) geometric transformations by rotations and elongations of vectors enable morphing of one PT to another in a continuum while preserving the 4D topology. The 4D structure exhibits principles of complementarity and zero-cyclic sum in chemical elements. Complementarity enables the extension to n = 9 elements and beyond. The 4D PT of elements extends to isotopes and also to molecules and compounds with the same underlying principles. (shrink)

This paper explores the meaning of time from three points of view: (1) David Bohm's concepts of "vertical implicate order" and "holomovement"; (2) Alfred North Whitehead's idea of the "actual occasion"; and (3) the author's notion of "nondual duality." The author argues that Bohm and Whitehead alike implicitly divide time into dual and nondual aspects and that, in failing to adequately reconcile these, time, in effect, is denied. The alternative offered seeks to thoroughly integrate dual and nondual (holistic) modalities (...) in the understanding that time as becoming entails a dynamic interpenetration of its opposing aspects. Visual geometry and topology are employed to flesh out the "nondual duality" of temporal structure. (shrink)

Recent research both on the Kyoto School and on the contemporary New Confucians suggests significant similarities between these two modern East Asian philosophies. Still missing is, however, an explanation of the shared philosophical ideas that serve as the foundation for comparative studies. For this reason, I analyze the basic theories of the two distinctly East Asian philosophies of Nishida Kitarō (1870-1945) and Mou Zongsan (1909-95) so as to identify and extract the same type of argument. This is an alternative to (...) the analyses provided by the previous studies of their philosophies, which inevitably regard their theories as an East Asian assimilation of modern European philosophy in the Kantian, Neo-Kantian, or phenomenological tradition, or else as the traditional tenets under the guise of philosophical speculation, without being able to clarify how these theories contribute to philosophy. My analysis shows that both the logic of basho and the theory of perfect teaching formulate the same type of theory, the ontological or topological-onto-topological-turn from the act of consciousness to its basho or its vertical enfolding, which constitutes the bedrock of East Asian philosophy. (shrink)

To avoid exorbitant and extensive laboratory experiments, QSPR analysis, based on topological descriptors, is a very constructive statistical approach for analyzing the numerous physical and chemical properties of compounds. Therefore, we presented some new entropy measures which are based on the sum of the neighborhood degree of the vertices. Firstly, we made the partition of the edges of benzene derivatives which are based on the degree sum of neighboring vertices and then computed the neighborhood version of entropies. Secondly, we made (...) use of the software SPSS for developing a correlation between newly introduced entropies and the physicochemical properties of benzene derivatives. Our obtained results demonstrated that the critical temperature C T, critical pressure C P, and critical volume C V can be predicted through fifth geometric arithmetic entropy, second S K entropy, and fifth N D entropy, respectively. Other remaining physical characteristics include Gibb’s energy qℰ, log P, molar refractivity ℳℛ, and Henry’s law ℋℒ that can be predicted by using sixth N D entropy. (shrink)

A rank function for a directed graph G assigns elements of a well ordering to the vertices of G in a fashion that preserves the order induced by the edges. While topological sortings require a one-to-one matching of vertices and elements of the ordering, rank functions frequently must assign several vertices the same value. Theorems stating basic properties of rank functions vary significantly in logical strength. Using the techniques of reverse mathematics, we present results that require the subsystems ${\ensuremath{\vec{RCA}_0}}$ , (...) ${{\vec{ACA}_0}}$ , ${{\vec{ATR}_0}}$ , and ${{\vec{\Pi^1_1 - CA}_0}}$. (shrink)

Let G = V G, E G be a molecular graph, where V G and E G are the sets of vertices and edges. A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance-based topological indices. In this paper, we described a linear time algorithm that computes the Wiener index for acyclic graphs and extended this algorithm for (...) unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time O n. (shrink)

Being building block of data sciences, link prediction plays a vital role in revealing the hidden mechanisms that lead the networking dynamics. Since many techniques depending in vertex similarity and edge features were put forward to rule out many well-known link prediction challenges, many problems are still there just because of unique formulation characteristics of sparse networks. In this study, we applied some graph transformations and several inequalities to determine the greatest value of first and second Zagreb invariant, S K (...) and S K 1 invariants, for acyclic connected structures of given order, diameter, and pendant vertices. Also, we determined the corresponding extremal acyclic connected structures for these topological indices and provide an ordering giving a sequence of acyclic connected structures having these indices from greatest in decreasing order. (shrink)

What Mamardašvili meant by “process of knowledge” is not an all-embracing vision of reality accomplished “once-and-for-all”; it is not a step by step procedure of deduction; rather it is an anti-dialectical reconstruction of a constellation of signs put together over and over again by the subject by an act of non-premeditated genius. It is a kind of aesthetic act that makes the sense appear, like a vertical cut in the sequential line of space and time.

There are many cases in which the “direction” of architecture seems to be indifferent to the architect who designs it. Among these, the Guggenheim Museum in New York by Frank Lloyd Wright is highly emblematic: through the long and troubled project’s phases it shows a surprising “reversibility”, horizontal and vertical. In most cases, however, the “direction” of architecture is determined by factors which are situated outside of it, as are existing buildings, or the circumstances of the site and the (...) factors of exposure, lighting and ventilation. In this sense, architecture not only reveals the existence of differences but it builds them, becoming itself a system of differences. (shrink)

In “Topology of Balasaguni’s Kutadgu Bilig: Thinking the Between,” Onur Karamercan focuses on the philosophical dimension of Kutadgu Bilig, a poetic work of Yūsuf Balasaguni, an 11th century Central Asian thinker, poet, and statesman. Karamercan pays special attention to the meaning of betweenness and, in the first step of his argument, discusses the hermeneutic and topological implications of the between, distingushing the dynamic sense of betweenness from a static sense of in-betweenness. He then moves on to analyze Balasaguni’s notion of (...) language, which he interprets as an early critique of the instrumental account of language and, by examining several selected fragments from Kutadgu Bilig, illustrates Balasaguni’s designation of language as an inexhaustible phenomenon. In the process, he also points to the possible parallels between Balasaguni’s and Heidegger’s ideas of language. In the final section of the article, building on his argument, Karamercan thematizes the margins of Turkic languages and of Islamic philosophy, suggesting that they need to be reexamined. He problematizes the very meaning of Asia itself by decentering what he calls “its internal East–West antagonism” and puts forth instead a framework based on in-betweenness reinterpreted from a topological perspective, proposing it as an alternative view which might help us make sense of the hermeneutic neighborhoods of Asian philosophies. (shrink)

We consider interpretable topological spaces and topological groups in a p-adically closed field K. We identify a special class of “admissible topologies” with topological tameness properties like generic continuity, similar to the topology on definable subsets of Kn. We show that every interpretable set has at least one admissible topology, and that every interpretable group has a unique admissible group topology. We then consider definable compactness (in the sense of Fornasiero) on interpretable groups. We show that an interpretable group (...) is definably compact if and only if it has finitely satisfiable generics (fsg), generalizing an earlier result on definable groups. As a consequence, we see that fsg is a definable property in definable families of interpretable groups, and that any fsg interpretable group defined over Qp is definably isomorphic to a definable group. (shrink)

갈등은 일차적으로 개인(주관)의 심리문제일 것이지만, 결국은 사회(주체)의 정치적 문제가 된다. 그리고 이 정치적 문제는 갈등의 제거가 아니라 갈등의 승인에서 가능하다. 이는 갈등에 대한 정치적 논의가 사회적 현실에 대한 “탈구와 재구성”의 역학, 즉 ‘해방의 변증법’을 수반하는 ‘갈등의 위상학’을 통해 이루어져야 한다는 것을 의미한다. 주체에 억압된 욕망, 부연하자면 ‘존재론적 욕망’으로 회귀하며 “내재성”의 논리에 입각해 갈등의 ‘위상학’(topology)을 선명히 가리킨 것은 현대의 철학, 특히 후설 이후 메를로퐁티와 하이데거, 그리고 라캉과 들뢰즈의 철학이었다. 이 글은, 이들에 함축된 ‘시(詩)적 인식’의 위상학적 양상을 메를로퐁티의 관점으로 수렴하는 자리에서, 갈등이 (...) 갖는 해방의 변증법적 의의를 짚은 후, 우리사회에서 폭발하는 갈등이 위기가 아니라 사실은 〈외재적 초월의 유토피아적 허구를 넘는 ‘내재적 초월’의 현실에 입각해 정치적 상상력을 재정립할 기회〉의 한 계기임을 제시할 것이다. (shrink)

Hobbes emphasized that the state of nature is a state of war because it is characterized by fundamental and generalized distrust. Exiting the state of nature and the conflicts it inevitably fosters is therefore a matter of establishing trust. Extant discussions of trust in the philosophical literature, however, focus either on isolated dyads of trusting individuals or trust in large, faceless institutions. In this paper, I begin to fill the gap between these extremes by analyzing what I call the topology (...) of communities of trust. Such communities are best understood in terms of interlocking dyadic relationships that approximate the ideal of being symmetric, Euclidean, reflexive, and transitive. Few communities of trust live up to this demanding ideal, and those that do tend to be small (between three and fifteen individuals). Nevertheless, such communities of trust serve as the conditions for the possibility of various important prudential epistemic, cultural, and mental health goods. However, communities of trust also make possible various problematic phenomena. They can become insular and walled-off from the surrounding community, leading to distrust of out-groups. And they can lead their members to abandon public goods for tribal or parochial goods. These drawbacks of communities of trust arise from some of the same mecha-nisms that give them positive prudential, epistemic, cultural, and mental health value – and so can at most be mitigated, not eliminated. (shrink)

The history of climate research in the 20th century has been characterised by a crucial shift from a geography-oriented, two-dimensional approach towards a physics-based, three-dimensional concept of climate. In the 1930s, the introduction of new technology, such as radiosondes, enabled climatologists to investigate the high atmosphere, which had previously been out of reach. This “conquest of the third dimension” challenged the surface-oriented, geographical notion of climate patterns and opened up climatology to a three-dimensional approach, which deeply changed the character of (...) climate research. Two decades later, by drilling deep into polar glaciers and using the downward vertical dimension as an archive of the earth's history, ice core scientists began to reconstruct past climates layer by layer. The data retrieved in deep glacial layers contributed crucially to a temporal expansion of climate history far beyond human timescales. However, the inaccessibility of glaciers and the practical challenges of bringing fragile fragments of ice into transnational networks of scientific exchange meant that this vertical extension of climate knowledge production proceeded through a range of new scientific practices, and was shaped by new forms of international collaboration. Furthermore, this vertical approach to glaciers also asked for a new understanding of glacier volume. Drawing on archival and printed sources, I argue that ice core research represented a second discovery of the third dimension, this time downwards into the depth of the earth's surface, but again with decisive consequences for the research practice, for collaboration politics, and for understandings of climate, spatially as well as temporally. (shrink)

The spatial organization of the genome is intimately linked to its biological function, yet our understanding of higher order genomic structure is coarse, fragmented and incomplete. In the nucleus of eukaryotic cells, interphase chromosomes occupy distinct.

By excavating the ambiguities of the helicopter’s machinic-prosthetic view, a perspective which may be distant and abstract, while also near and viscerally present, this article will explore how megacity security is increasingly waged and consumed. The article argues that megacity security marches to the rotator-beat of the police helicopter, fuelled by military technophilia and in a context of the biopolitical desertion of the megacities’ most vulnerable. The article takes three aspects, visually expressed and constituted through aerial-helicopter security. Drawing from several (...) megacity examples including Mumbai, Lagos, São Paulo and Rio de Janeiro, the first resolves megacity confusion with legibility. In the following section the article examines the mobilization of the security gaze, and the final section explores how helicopter visuality may hold or territorialize megacity space. (shrink)

Drawing from Andean cosmological, mythological and aesthetic lineages, this paper is about the possibility of a phenomenology of things at catastrophic ends. In this regard, I approach things under the sway of a (de)formative emptiness. In the first part, I develop a relational ontology on the basis of the Andean notion of pacha or cosmos, which provides a phenomenological frame for a determination of “place,” “world” and “topology.” I also contrast an elemental topology of the cosmos configured by ouranic sunlight (...) with an elemental catastrophism that overturns it. In the second part, I study a chronological series of artifacts in an Andean aesthetic lineage in order to attempt a phenomenology of “things” (utensils, buildings, mountains) that “spectrally” hover in overturns of the cosmos (pachakuti). (shrink)

This paper argues that besides mechanistic explanations, there is a kind of explanation that relies upon “topological” properties of systems in order to derive the explanandum as a consequence, and which does not consider mechanisms or causal processes. I first investigate topological explanations in the case of ecological research on the stability of ecosystems. Then I contrast them with mechanistic explanations, thereby distinguishing the kind of realization they involve from the realization relations entailed by mechanistic explanations, and explain how both (...) kinds of explanations may be articulated in practice. The second section, expanding on the case of ecological stability, considers the phenomenon of robustness at all levels of the biological hierarchy in order to show that topological explanations are indeed pervasive there. Reasons are suggested for this, in which “neutral network” explanations are singled out as a form of topological explanation that spans across many levels. Finally, I appeal to the distinction of explanatory regimes to cast light on a controversy in philosophy of biology, the issue of contingence in evolution, which is shown to essentially involve issues about realization. (shrink)

We provide three innovations to recent debates about whether topological or “network” explanations are a species of mechanistic explanation. First, we more precisely characterize the requirement that all topological explanations are mechanistic explanations and show scientific practice to belie such a requirement. Second, we provide an account that unifies mechanistic and non-mechanistic topological explanations, thereby enriching both the mechanist and autonomist programs by highlighting when and where topological explanations are mechanistic. Third, we defend this view against some powerful mechanist objections. (...) We conclude from this that topological explanations are autonomous from their mechanistic counterparts. (shrink)

The standard model of precedential constraint holds that a court is equally free to modify a precedent of its own and a precedent of a superior court—overruling aside, it does not differentiate horizontal and vertical precedents. This paper shows that no model can capture the U.S. doctrine of precedent without making that distinction. A precise model is then developed that does just that. This requires situating precedent cases in a formal representation of a hierarchical legal structure, and adjusting the (...) constraint that a precedent imposes based on the relationship of the precedent court and the instant court. The paper closes with suggestions for further improvements of the model. (shrink)

This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent topological reconstruction (...) of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)

This chapter provides a systematic overview of topological explanations in the philosophy of science literature. It does so by presenting an account of topological explanation that I (Kostić and Khalifa 2021; Kostić 2020a; 2020b; 2018) have developed in other publications and then comparing this account to other accounts of topological explanation. Finally, this appraisal is opinionated because it highlights some problems in alternative accounts of topological explanations, and also it outlines responses to some of the main criticisms raised by the (...) so-called new mechanists. (shrink)

Fundamental concrete particulars are needed to explain facts about non-fundamental concrete particulars. However, the former can only play this explanatory role if they are properly discernible from the latter. Extant theories of how to discern fundamental concreta primarily concern mereological structure. Those according to which fundamental concreta can bear, but not be, proper parts are motivated by the possibilities that all concreta bear proper parts and that some properties of wholes are not fixed by the properties of their proper parts. (...) In response, theorists who hold that the fundamental concrete particulars can be proper parts may appeal to the possibility that every concrete particular is a proper part—that there is no mereologically maximal whole world, as well as to the intuition that fundamental concreta are qualitatively homogeneous “blocks” from which non-fundamental concreta are built. After motivating the plausibility of gunk and junk, the present essay proposes a constraint on fundamental concrete particulars based on topology instead of mereology: the fundamental concrete particulars must be appropriately connected. This constraint has the unique advantage of consistency with each of gunk, emergence, junk, and the building block intuition. (shrink)

In this paper, I argue that the newly developed network approach in neuroscience and biology provides a basis for formulating a unique type of realization, which I call topological realization. Some of its features and its relation to one of the dominant paradigms of realization and explanation in sciences, i.e. the mechanistic one, are already being discussed in the literature. But the detailed features of topological realization, its explanatory power and its relation to another prominent view of realization, namely the (...) semantic one, have not yet been discussed. I argue that topological realization is distinct from mechanistic and semantic ones because the realization base in this framework is not based on local realisers, regardless of the scale but on global realizers. In mechanistic approach, the realization base is always at the local level, in both ontic and epistemic accounts. The explanatory power of realization relation in mechanistic approach comes directly from the realization relation-either by showing how a model is mapped onto a mechanism, or by describing some ontic relations that are explanatory in themselves. Similarly, the semantic approach requires that concepts at different scales logically satisfy microphysical descriptions, which are at the local level. In topological framework the realization base can be found at different scales, but whatever the scale the realization base is global, within that scale, and not local. Furthermore, topological realization enables us to answer the “why” questions, which according to Polger 2010 make it explanatory. The explanatoriness of topological realization stems from understanding mathematical consequences of different topologies, not from the mere fact that a system realizes them. (shrink)

The standard mathematical account of the sub-metrical geometry of a space employs topology, whose foundational concept is the open set. This proves to be an unhappy choice for discrete spaces, and offers no insight into the physical origin of geometrical structure. I outline an alternative, the Theory of Linear Structures, whose foundational concept is the line. Application to Relativistic space-time reveals that the whole geometry of space-time derives from temporal structure. In this sense, instead of spatializing time, Relativity temporalizes space.

This paper argues that the direct, vertical toleration of certain types of citizen by the Rawlsian liberal state is appropriate and required in circumstances in which these types of citizen pose a threat to the stability of the state. By countering the claim that vertical toleration is redundant given a commitment to the Rawlsian version of the liberal democratic ideal, and by articulating a version of that ideal that shows this claim to be false, the paper reaffirms the (...) centrality of vertical toleration in the Rawlsian liberal account of state-citizen relations. (shrink)

The basic methodology of rough set theory depends on an equivalence relation induced from the generated partition by the classification of objects. However, the requirements of the equivalence relation restrict the field of applications of this philosophy. To begin, we describe two kinds of closure operators that are based on right and left adhesion neighbourhoods by any binary relation. Furthermore, we illustrate that the suggested techniques are an extension of previous methods that are already available in the literature. As a (...) result of these topological techniques, we propose extended rough sets as an extension of Pawlak’s models. We offer a novel topological strategy for making a topological reduction of an information system for COVID-19 based on these techniques. We provide this medical application to highlight the importance of the offered methodologies in the decision-making process to discover the important component for coronavirus infection. Furthermore, the findings obtained are congruent with those of the World Health Organization. Finally, we create an algorithm to implement the recommended ways in decision-making. (shrink)

We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate (...) early work of McKinsey on topological interpretations of S4 with recent work of Georgatos on topologic. Some of the results of this paper were presented at the 1992 conference on Theoretical Aspects of Reasoning about Knowledge. (shrink)