The Fractal Theory of Central Place Geometry: A Diophantine Analysis of Fractal Generators for Arbitrary Löschian Numbers

We develop material to determine whether or not an arbitrary number is Löschian; the procedure embodied in the theorems achieves the desired result more swiftly than do previous solutions to this problem. The correspondence between a partition of the central place lattice and a quadratic form permits the rapid determination of the lattice coordinates of an arbitrary Löschian number and of the exact shape of a single fractal generator used to form an entire central place hierarchy associated with an arbitrary Löschian number. Central place hierarchies may be generated geometrically using a single shape applied initially to a hexagon and subsequently, scaled appropriately, to resultant polygons. Fractional dimensions of arbitrary central place hierarchies, measuring their “space-filling” characteristics, follow naturally from this general procedure.     

LÖSCHIAN COMPETITION VERSUS SPATIAL COLLUSION: PRICE AND WELFARE COMPARISONS*

ABSTRACT. Löschian duopoly under heterogeneous cost conditions is examined to show that it is not equivalent, contra past findings, to spatial collusion. Moreover, within the confines of the assumed demand and cost conditions spatial collusion is shown to be superior to Loschian competition in terms of both (aggregate) consumer surplus and producer surplus, which implies a possible welfare gain from collusion. A general, if not the general, prices-and-welfare comparison of alternative pricing schema including collusive, Löschian, and optimal pricing is summarily presented in a table.     

A NOTE ON THE STABILITY PROPERTY OF SPATIAL COMPETITION*

ABSTRACT. Our study extends the standard comparative static analysis to allow for dynamic aspects of equilibrium in spatial competiton. We investigate dynamic stability properties via the Routh-Hurwitz criterion. Nontrivial equilibria in the so-called Löschian, Hotelling-Smithies, and Greenhut-Ohta models are shown to be stable even under heterogeneous cost conditions among competing firms, conditions not considered hitherto. We can thus provide powerful support to the comparative static analyses which can only be developed via equilibrium concepts with stability properties.     

GENERAL EQUILIBRIUM OF SPATIAL PRODUCT AND LABOR MARKETS*

ABSTRACT A simple general equilibrium model relates spatial product markets and spatial labor markets. The firm is treated as being a spatial monopolist or as a Löschian competitor in the output market and as a spatial monopsonist in the labor market. Derived free spatial demand and free regional labor supply are defined, and their properties examined. The model provides the framework for analyzing the impact of a technological improvement in labor productivity on the structure of the spatial markets. The impact of entry on spatial labor supply is an important determinant of whether or not entry lowers wages and raises output prices. Unlike the spaceless competitive paradigm, zero-profit long-run equilibrium can occur in a space economy under conditions of increasing returns to scale.     

Cournot Retail Chains

In this paper a model of spatial Cournot competition among retail firms is devised and used to assess the effect of a variety of structural factors on retail prices and profits. The model illustrates the spatial chain of interaction that firms must anticipate to reach equilibrium when organized in chains or as independents. It shows the sensitivity of price to the location of stores, the number of stores per location, and transportation cost.     

互联网信息对健身俱乐部连锁店空间竞争的指示研究

以北京浩沙健身连锁俱乐部为例,尝试利用公众在大众点评网、新浪微博等网络社区中发布的关注度、评价等作为加权因子,分析连锁网点之间的竞争状态,建立了一个基于互联网信息的加权因子计算模型,计算各连锁店的市场竞争域,结果显示互联网空间信息能够对连锁店之间的空间竞争产生指示作用,各分店表现出明显的竞争力差异;提出对加权Voronoi图区位意义上的地理学新解释:它不仅反映连锁店基本市场域,而且其边线弯曲度和单元面积的变化还可折射各连锁店在互联网空间中的吸引力差异。     

LÖWITH,LÖWITH'S HEIDEGGER,AND THE UNITY OF HISTORY

This article is about the problem of the unity of history as seen through the writings of Karl Löwith. By “unity of history” I understand the notion that all history constitutes one and only one range of kinds of objects and/or one field of knowledge. The article argues that the problem of the unity of history—though often neglected as a matter of mere argumentative infrastructure—is central to a number of wider problems, most prominently the possibility of a plural understanding of historicity and the possibility of ultimately avoiding a unified historical teleology. The article revisits Löwith's writings and proposes a variety of novel interpretations with the aim of evincing the centrality, and of exploring diverse aspects, of the problematic of the unity of history. This problematic is shown to have informed Löwith's work on the secularization thesis as well as his debate with Hans Blumenberg. The foundations of Löwith's discussion of the problem are pursued across his ambivalent critique and appropriation of Heidegger's model of an ontology of historicity as marked by inevitable internal conflict and thus disunity. The paper reconstructs the manner in which, after the Second World War, Löwith's philosophy of history sought to salvage basic traits of the Heideggerian model when it tried to establish the possibility of plural historicity from a notion of the natural cosmos. It is demonstrated that the motives for this salvage operation ultimately extended beyond the problem of Löwith's reception of Heidegger and concerned the possibility of continuing any debate on the philosophy of history.     

A WOMAN'S PLACE: SPACE,MEETING PLACES AND GENDER IN 16TH‐CENTURY NYA LÖDÖSE,SWEDEN

In this article, archaeological and archival data are used to discuss gender in 16^th‐century Nya Lödöse in western Sweeden with a focus on women. Four areas for social space are identified and analysed. The result shows that women seem to have had a somewhat higher degree of agency in Nya Lödöse compared with the surrounding countryside and smaller towns.     

Existentialism as a Political Problem in Karl Löwith's Thought

The aim of this paper is to make a case for the claim that Karl Löwith's thought is predominately preoccupied with one major philosophic–historical problem that may be broadly labelled existentialism. This notion is usually employed by Löwith in order to grasp the various phenomena and developments within the European (or Western) history in the modern age. I claim that the meaning assigned by Löwith to the notion of existentialism is inseparable from its political consequences. In other words, I attempt to reconstruct the notion of existentialism in Löwith's thought primarily as a political problem. By advancing this argument, I am inclined towards the view that Löwith’s ?uvre deserves more careful reception from political theorists than it has yet received.     

Jüdischer alltag in Deutschland, 1933–1945

While discussions of the debate between Karl Löwith and Hans Blumenberg over ‘secularisation’ focus primarily on the methodological utility of the concept, the difference between them was also one of the philosophical commitments and substantive claims about modernity. This difference is not always obvious. One way of bringing it out is to address the different contexts in which they produced their most famous statements about secularisation. But another, and one that will be pursued here, is to consider the critical dialogue that both thinkers engaged in with Nietzsche. Put briefly, while Löwith thought that Nietzsche misunderstood the ancients, Blumenberg thought that he misunderstood the moderns. For Löwith, Nietzsche's doctrine of the eternal return is not Greek, but an aggressive countergospel that owes much to the Christian culture it seeks to oppose; for Blumenberg, Nietzsche assumes, wrongly, that the self-belittlement of man by theology has been succeeded by the self-belittlement of man by science. In addition, Blumenberg – unlike both Nietzsche and Löwith – thinks that he can mount a robust defence of both modern science and progress.     

SOURCING OBSIDIAN FROM NEOLITHIC ÇATALHÖYÜK (TURKEY) USING ENERGY DISPERSIVE X‐RAY FLUORESCENCE*

This paper details the chemical sourcing of 42 obsidian artefacts from a single Neolithic structure at Çatalhöyük (central Anatolia), using Energy Dispersive X‐Ray Fluorescence (EDXRF). The chemical signatures of the samples match those of two geological sources in southern Cappadocia: East Göllü Da? and Nenezi Da?. The data provide a counterpoint for previous analyses at the site, and suggest possible intra‐community distinctions with regard to shifts in raw material procurement and technical change.     

Spinners and weavers of auffay. Rural industry and the sexual division of labour in a French village, 1750–1850

German scholars of Jewish origin who were students of Martin Heidegger in the 1920s and 1930s are frequently criticized for their supposed postwar refusal to ‘disavow earlier liaisons with Heidegger.’ These scholars are thus indicted for being fundamentally anti-liberal or apolitical, and for those reasons dangerous disciples of Heidegger. By examining the works of Karl Löwith and Hans Jonas, two of Heidegger's influential former students, the following paper presents a more nuanced reading of the relationship between master and disciples, namely that Jonas and Löwith operate with Heidegger's philosophical grammar in order to turn against Heidegger, philosophically and politically. Within this framework, the article fleshes out the crucial importance of theology to the understanding of Jonas’ and Löwith's philosophical critique of Heidegger's thought. Following this theological turn, the paper demonstrates the complexity of Jonas’ and Löwith's postwar approach, that is an anti-Heideggerian ethical and political quest which is anchored nonetheless in Heidegger's philosophy. As such, Jonas’ and Löwith's political projects demonstrate the manner in which Heideggerian categories are not exhausted by Heidegger's own political interpretation; they grippingly denotes the aptitude to steer Heideggerian philosophy towards new ethical and political shores.     

Aires de marché et choix des destinations de consommation pour les achats réalisés au cours de la semaine – Le cas de la région de Québec

Since the early 1990s, big box stores have profoundly modified the retail structure of Canadian cities. This entails multiple consequences, beyond the mere competition between establishments, for the evolving relationships between diversity of retail forms, consumer behaviour and urban planning. These relationships are explored in the Québec Metropolitan Community, using detailed databases, including establishment directories, mobility surveys and a virtual road network, integrated into a regional GIS. Trade areas of commercial streets, shopping centers and big box stores are delineated and analyzed. Consumers' attributes, such as age, gender, type of household, mode of transport, which putatively influence the probability of patronizing one type of retail cluster compared to another type, are modelled using logistic regression. The influence of the relative location of cluster types on their capacity to attract consumers is also modelled in order to gain some understanding of the competition among and between types. The analysis suggests that, by and large, the growing number of big box stores has more negative consequences for shopping centres than they have for commercial streets. The study also clearly reveals the growing importance of shopping trips in the mobility profile of households and provides a knowledge base useful for urban planning.     

The Lösch System of Market Areas: Derivation and Extension

Certain aspects of Lösch's classic work on the network of markets and the system of networks have not yet been clearly explained in the literature. Lösch did not describe his derivation procedures in full, and apparent printing errors in certain förmulae confuse the issue further, with the result that several recent texts reproduce Lösch's diagrams but offer no explanation of how they are constructed. Accepting the network of hexagonal market areas for a continuous system of markets, given an even but discrete distribution of population, the derivation from first principles of the complete system of different market areas is presented. Apparent errors in the translated text of Lösch's work are corrected. Limitations in some other authors' work and accordance with earlier empirically derived formulae are mentioned. The production of “city-rich” and “city-poor” sectors is shown to be a constraint on, rather than a result of, the system, and Lösch's statement that the coincidence of centers is maximized is clarified. The extension of the Lösch system to the internal tertiary structure of the city is presented and attention drawn to the empirical attractiveness of this approach.     

New Evidence for Neolithic Habitation in the Hinterland of the Troad

This essay introduces two newly discovered Neolithic sites identified through the archaeological surveys conducted in the hinterland of the Troad in north‐western Turkey. Most of our knowledge about the Neolithic period of the region comes from the coastal site of Co?kuntepe, as well as U?urlu on the island of Gökçeada (Imbros) and Kara?açtepe (Protesilas) on the Gallipoli Peninsula. The lack of evidence for Neolithic habitation in the hinterland of the region was apparently due to the state of research. The recently discovered rock shelter‐type site of Evkayas? and the mound of Taraçc? imply that the hinterland of the Troad also bears traces of Neolithic habitation. Each of these sites yielded a single obsidian artefact of Melian origin, suggesting that these two settlements were on a land‐based route that connected the Gulf of Edremit with the southern coast of the Sea of Marmara.     

ON THE SHAPE OF MARKET AREAS IN LÖSCHIAN SPATIAL MODELS*

ABSTRACT. The paper analyzes the lattice shape of equilibrium configurations of firms in spatial models. Lösch's assertion that free entry will result in hexagonal market areas is proved for a variety of assumptions about the nature of the market equilibrium, and about the preferences of customers. All the models considered, however, incorporate rational entry behavior and identify the stable lattice as an entry deterring equilibrium. A simple proof is presented of the optimality of hexagonal market areas, at least among regular space-filling configurations.     

TRAUMA DELEGITIMIZED: KARL LÖWITH AND THE COSMIC VIEW OF HISTORY

This article uncovers the work of trauma in Karl Löwith's historical thought. Although best known for his critique of the philosophy of history and for the conception of secularization in his 1949 book, Meaning in History, Löwith deepened his positive historical vision in several essays that he wrote in the 1950s and 1960s. From these texts emerges a unique historical orientation, which I call the “cosmic view of history.” This perspective was at once a critique of modern historical consciousness and an embodied corrective to that consciousness, one in which the catastrophes of the twentieth century were relativized and made endurable. In both the origin and structure of this historical orientation and in its textual expression in Löwith's work, trauma is a residual force that links Löwith's language, his experiences, and the postwar context. The role of trauma in Löwith's thought further reveals a process of delegitimization in which historical consciousness and historical events lose their power to determine historical meaning, thus enabling a response to and an escape from catastrophe. This article also explores the significance of this cosmic view of history for contemporary theoretical concerns related to the Anthropocene and its consequences for historical theory.     

THE STREETS AS A MEETING PLACE FOR DIFFERENT ACTORS AND AGENDAS: BUILDING AND USE OF OPEN SPACE IN 16TH‐CENTURY NYA LÖDÖSE,SWEDEN

The town of Nya Lödöse, close to present‐day Gothenburg, Sweden, existed from in 1473‐1624. The material from the extensive archaeological excavations 2013–2017 presents the opportunity to study construction, use, and change of the streets. There seems to have been a clear hierarchy of streets, ranging from main streets to local streets and private alleys. This variety of streets covered different needs in the town's infrastructure. They were also the meeting point for different public and private actors with shifting objectives. Over time the authorities gained increased control over the streets, apparent in the material from the 1580s and onwards. This can be seen as a part of a Scandinavian trend linked to the emergence of the early modern state.