Saxton's Maps of England and Wales: The Accuracy of Anglia and Britannia and Their Relationship to Each Other and to the County Maps

ABSTRACT

From measurements of the graticules on Saxton's two general maps of England and Wales—the atlas map Anglia and the wall map Britannia—together with other evidence, it is argued that neither map was drawn according to any specific projection, but that both were effectively produced as ‘flat-earth’ maps with the graticules superimposed afterwards. Digital versions of Saxton's maps and of a modern map, the 1:1 million Ordnance Survey transport map, are used in a number of comparisons by means of the computer program MapAnalyst. These comparisons allow the scales of the two Saxton maps to be determined. They also show that the maps are of almost the same accuracy in terms of the positioning of settlements, typically within about 4.6 kilometres, in spite of a difference in scale of a factor of about 3.6. This fact and the direct comparison of the two Saxton maps in MapAnalyst show that they are basically the same map, and it is concluded that a version of the wall map was the first to be drawn and that Anglia is a reduced copy prepared for the atlas. The lengths of Saxton's miles as used on the two maps are calculated and compared with other determinations. The relationship between the two general maps and the county maps is briefly considered, and it is provisionally concluded that the relationship is a close one.     

Spatial autocorrelation tests and the Classic Maya collapse: Methods and inferences

Spatial autocorrelation, resulting in pattern or structure in geographically distributed data, is discussed in theoretical and practical terms. Tests for spatial autocorrelation are presented, along with an explication of the relationship between autocorrelation models, the product-moment correlation coefficient and the spatial autocorrelation test statistic. Two archaeological examples illustrate the application of the auto-correlation test statistic. The first uses a hypothetical data set, which shows the type of map patterns that appear with various levels of spatial autocorrelation, and the second examines the terminal distribution of long-count-dated monuments at lowland Classic Maya sites. The results of the second example fail to support arguments for simple patterning in the cessation of the erection of these monuments and, by inference, in the Maya collapse itself. Finally, it is argued that while the identification of spatial autocorrelation is often the goal of spatial analyses, the presence of autocorrelation violates the assumptions of certain statistics used in such analyses.     

A Topological Representation for Taking Cities as a Coherent Whole

A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life‐giving order or simply a living structure. To characterize the wholeness and in particular to advocate for wholeness as an effective design principle, this article develops a geographic representation that views cities as a whole. This geographic representation is topology‐oriented, so fundamentally differs from existing geometry‐based geographic representations. With the topological representation, all cities are abstracted as individual points and put into different hierarchical levels, according to their sizes and based on head/tail breaks—a classification and visualization tool for data with a heavy tailed distribution. These points of different hierarchical levels are respectively used to create Thiessen polygons. Based on polygon–polygon relationships, we set up a complex network. In this network, small polygons point to adjacent large polygons at the same hierarchical level and contained polygons point to containing polygons across two consecutive hierarchical levels. We computed the degrees of wholeness for individual cities, and subsequently found that the degrees of wholeness possess both properties of differentiation and adaptation. To demonstrate, we developed four case studies of all China and U.K. natural cities, as well as Beijing and London natural cities, using massive amounts of street nodes and Tweet locations. The topological representation and the kind of topological analysis in general can be applied to any design or pattern, such as carpets, Baroque architecture and artifacts, and fractals in order to assess their beauty, echoing the introductory quote from Christopher Alexander.     

Information Entropy of Non‐Probabilistic Processes

We derive an expression for the entropy of non‐probabilistic distributions encountered in spatial and mathematical mappings. The entropy of non‐probabilistic distributions can be formulated using probabilistic notions of the hypothetical random redistribution of finite information. We show that the discrete approximation to the information content of spatial maps can be based on the discrete hypergeometric distribution. The resultant “associative” entropy is distinct from the Shannon entropy for probability distributions and addresses several shortcomings of the current entropy paradigm as applied to spatial analysis. The associative entropy statistic is distributed approximately as a chi‐squared random variable under limitations of variation. We formulate a univariate logical equivalent of the associative entropy statistic, freeing the paradigm from the degrees of freedom constraint to which it has been traditionally shackled. This entropy has application in spatial analysis and fuzzy set theory. The associative entropy is based on the concept of proportional information and is related to the Getis G‐statistics of spatial association and the Chi‐squared statistics of sample means. We explore the utility of the theory when applied to spatial distribution of vegetation in New Brunswick, Canada. The limitations and implications of the entropy expression are discussed and suggestions are made for future applications of the theory. This work is part of the development of an information theory framework for the analysis of landscape patterns of animal habitat.     

Feminist cartography and the United Nations Sustainable Development Goal on gender equality: Emotional responses to three thematic maps

Thematic maps facilitate spatial understanding of patterns and exceptions. Cognitive ability, spatial cognition, and emotional state are related, yet there is little research about map readers’ emotions. Feminist critiques of cartography recognize emotion and affect as legitimate experiences on par with quantitative ways of knowing. We conducted an online survey to measure users’ affective states before and after engaging with three thematic map types. The maps showed data from the United Nations Sustainable Development Goal to achieve gender equality, on the proportion of girls and women aged 15 to 49 who have undergone female genital mutilation/cutting. Participants viewed a choropleth, a cartogram, and a repeating icon tile map; completed map-related tasks; rated certain map qualities; rated their affective states before and after engaging with the maps; and answered open-ended questions. The maps piqued curiosity and evoked emotions for most users, while some users perceived the thematic maps as clinical or neutral despite the sensitive topic. After viewing the maps, female participants who were affected expressed deeper engagement in their open-ended comments than males. Traditionally, cartography construes the human experience as male experience and denies or trivializes women's experiences. Our findings corroborate feminist critiques of this disembodiment and entrenched rational rhetoric of maps.     

美国国会图书馆藏《松江府海塘图》的年代判定及其价值

在前辈学人研究的基础上,根据美国国会图书馆所藏《松江府海塘图》和乾隆《太镇海塘纪略》中所附地图的比对,可知两图所载各县海塘长度的差异主要是由各自丈量尺度的不同造成。加之镇洋北岸海塘长度以及两图所示地域范围的差别,可以判定美国国会图书馆所藏的《松江府海塘图》绘制于乾隆十七年,该图更名为《乾隆松太海塘图》较为合适。《乾隆松太海塘图》是清代江南海塘的通塘体系形成之前最完整的一幅海塘图,图中所画内容反映了官方绘制江南海塘图"兵农并重"的特殊要求,是同类海塘图中的珍品。     

Investigating Global and Local Categorical Map Configuration Comparisons Based on Coincidence Matrices

The simple and intuitive nature of the coincidence matrix has not only made it the current "gold standard" for accuracy assessment (based on a sample of map pixels), but also a common tool for describing difference between two categorical maps (when all pixels are enumerated). It is this latter case of map comparison that this article explores. Coincidence matrices, although providing significant information regarding thematic agreement between two categorical maps (composition), can lack significantly in terms of conveying information about differences or similarities in the spatial arrangement (configuration) of those map categories in geographic space. This article introduces means for distilling the available configuration information from a coincidence matrix while demonstrating some simple categorical map comparisons. Specifically, while the coincidence matrix summarizes per-pixel compositional persistence or change, the introduced technique further quantifies the global and local configurational uncertainty between compared maps. I demonstrate how this quantification of configurational uncertainty can be used to gauge which thematic mismatch types are most significant and how to measure/present local configurational uncertainty in a spatial context. Implementation is through a straightforward mathematical algorithm in R that is illustrated by several examples.     

Accuracy of Count Data Estimated by the Point‐in‐Polygon Method

This paper analyzes the accuracy of count data estimated by the point‐in‐polygon method. A point‐in‐polygon interpolation model is proposed, based on a stochastic distribution of points and the target zone, in order to represent a variety of situations. The accuracy of estimates is numerically investigated in relation to the size of the target zone and the distribution of points, and the optimal location of representative points is discussed. The major findings of this paper are as follows: (1) though the relative accuracy of estimates generally increases monotonously with the size of the target zone, the monotoneity is often disturbed by the periodicity in the spatial configuration of source zones and the point distribution; (2) the point‐in‐polygon and the areal weighting interpolation methods have the same accuracy of estimates when points are concentrated in less than 12–15 percent area around the representative point in source zones; (3) the point‐in‐polygon method is not so robust against the locational gap between points and the representative point; (4) the optimal location of representative points is given by the spatial median of points.     

陕西窑洞传统乡村聚落景观基因组图谱构建及特征分析

窑洞聚落是黄土高原最典型的聚落形态，它具有悠久的历史、深厚的精神文化内涵以及独特的文化景观特征，在陕西渭北地区和陕北黄土高原丘陵沟壑区分布广泛。本研究基于传统聚落景观基因组图谱的相关研究，以陕西31个窑洞传统乡村聚落为研究对象，按照“单个窑洞聚落、多个窑洞聚落、特定研究区”三个层次，构建了窑洞聚落的典型院落图谱、空间序列图谱、院落模式图谱、排列模式图谱和空间格局图谱五大类型图谱体系。通过分析窑洞聚落景观基因组图谱的基本特征，进一步验证了构建窑洞聚落景观基因组图谱的必要性和迫切性。本研究旨在丰富景观基因组图谱层次，推动景观基因研究向区域层面发展，并为窑洞聚落景观基因信息链修复及景观基因区域识别系统构建等相关研究奠定基础，为保护与发展窑洞聚落提供科学依据。     

Enhancing spatial learning and mobility training of visually impaired people—a technical paper on the Internet-based tactile and audio-tactile mapping

Thanks to advances in technology such as Internet-based mapping and the development of special inks, papers and global positioning systems, map making for vision impaired people can provide a range of products (e.g., tactile, haptic and audio-tactile maps) that can improve their independence, self-confidence and everyday life. The applications of tactile maps include learning spatial concepts and geography; audio-tactile maps combined with access to geospatial information can enhance mobility and independence. In 1998, the Mapping Services Branch (MSB) of the Earth Sciences Sector of Natural Resources Canada initiated a tactile mapping program. Now referred to as the Government on Line—Mapping for the Visually Impaired Project (Natural Resources Canada 2003a), it aims to serve the community with special needs, with emphasis on those who are blind or visually impaired, their teachers and mobility instructors. This technical paper discusses the various types of tactile and audio-tactile maps of Canada developed by the MSB in cooperation with its partners and describe the current research and development activities carried out within the project. It also leads the reader to further information on audio-tactile maps and touch- and sound-based computer interfaces.     

A Map Overlay Error Model Based on Boundary Geometry

An error model for quantifying the magnitudes and variability of errors generated in the areas of polygons during spatial overlay of vector geographic information system layers is presented. Numerical simulation of polygon boundary displacements was used to propagate coordinate errors to spatial overlays. The model departs from most previous error models in that it incorporates spatial dependence of coordinate errors at the scale of the boundary segment. It can be readily adapted to match the scale of error–boundary interactions responsible for error generation on a given overlay. The area of error generated by overlay depends on the sinuosity of polygon boundaries, as well as the magnitude of the coordinate errors on the input layers. Asymmetry in boundary shape has relatively little effect on error generation. Overlay errors are affected by real differences in boundary positions on the input layers, as well as errors in the boundary positions. Real differences between input layers tend to compensate for much of the error generated by coordinate errors. Thus, the area of change measured on an overlay layer produced by the XOR overlay operation will be more accurate if the area of real change depicted on the overlay is large. The model presented here considers these interactions, making it especially useful for estimating errors studies of landscape change over time.     

“Follow the Tree Flowers”: Fugitive Mapping in Beloved

This article attempts to analyse mapping practices at the intersection of geography, black studies and literary studies, in order to reassess the political and pedagogical possibilities of mapping under late capitalism. I turn to Toni Morrison’s novel Beloved to track black cartographic practices otherwise obscured or, as Katherine McKittrick writes, “rendered ungeographic”. The novel offers a hidden and unauthorised archive for the often clandestine geographic practices that make possible fugitivity from the mechanics of “slaveholding agro‐capitalism” and its ongoing legacy. As an unofficial archive of black geographic practice, Morrison’s novel might itself be thought of as a map: a contemporary mode of memorialising the depth of place, relation, and navigation—a depth no two‐dimensional map can accommodate. Finally, this article demonstrates the valuable interventions that black studies and black creative production can make within the subfields of critical cartography and critical geography.     

Mapping reflexive communities: visualizing the geographies of emotion

Whereas ‘simple modernity’ was characterized by objective space, the grid of the map, and a removal of all subjective symbols or signs, ‘reflexive modernity’ is characterized by a re‐subjectivization of space. Within this space ‘reflexive communities’ emerge to make sense of emotions and experiences, reflecting particular ways of behaving, thinking and being. As geographers one task facing us now is to visualize and map the spaces of reflexive modernization. This paper presents a means of visualizing the text of emotions uncovered in the research encounter—a way of ‘mapping’ reflexive communities—and shows how we can articulate, negotiate and represent, complex emotional landscapes. The ‘maps’—which draw on spatial metaphors that permeate everyday emotions—such as ‘distancing’ ourselves, ‘engaging’, ‘joining’, ‘feeling detached’, ‘embracing’—were developed initially through analysis of in‐depth interviews with long‐term sufferers of myalgic encephalomyelitis (ME). Although the key focus of the paper is the experience of long‐term illness, the method of visualizing emotional geographies of everyday life could be applied in any number of fields. As such, it adds to the search across the social sciences for understanding the reflexive nature of contemporary space.     

5. PAST AND “PRESENCE”: REVISITING HISTORICAL ONTOLOGY

The last thirty years have brought about a fundamental revision of historical epistemology. So intense a concentration on the nature of history as a form of inquiry has diminished attention given to the thing that history inquires into: the nature of the past itself. Too readily, that entire domain has turned into a place for dreams, as Hayden White put it: a lost world only available now through the imagination of the author and subject to aesthetic whim. The next thirty years will, I propose, be the period in which ontology returns to the center of historical theory. And nothing short of the reconceptualization of the past—indeed of time itself—must be its objective. It must achieve that objective, moreover, in establishing arguments that are congruent with what revisions of epistemology have taught us about the limits of historical knowledge and the inevitability of textual representation. This paper enters this field by discussing some of the issues involved in rethinking the place of time in historical constructions since Bergson. It demonstrates the confusions inherent in spatial reductions of temporality, which historians have done so much to entrench rather than eradicate, and argues that historians have yet to accommodate the fundamental conceptual shifts inaugurated by heidegger. It then moves to propose a methodological doctrine to which I have given the name “chronism” and seeks to sketch the utility of such a doctrine for bringing one form of presence—that of authenticity—back into the domain of historical study. Doing so invites a number of conceptual and practical difficulties that the paper will address in its conclusions; these may disturb those who have closed their minds to anything beyond the present. Taking ontology seriously interferes both with structuralist assumptions about the nothingness of time and with some of the styles of historical representation that have become fashionable in the postmodern climate. There may be painful lessons to be learned if we are to rescue the past from its current status as a nonentity.     

HOW THE VISUAL IS SPATIAL: CONTEMPORARY SPATIAL HISTORY,NEO-MARXISM,AND THE GHOST OF BRAUDEL

Contemporary spatial history is founded on the potential for maps and other visualizations to show the historical constructedness of space, usually in broadly neo-Marxist terms, yet neo-Marxist geographical theory is famously critical of visual representation, especially mapping. At stake in this contradiction isn't just the relationship between digital enthusiasm and spatial theory (or the wider spatial turn), but the theoretical status of the visual itself in spatial scholarship. It raises a crucial question: how does visual material—everything from today's statistical maps and cutting-edge data graphics to the broader use of primary-source photographs or drawings—in fact shape our understanding of space, and what theoretical work does it do? By extension, how can humanists make critical theoretical interventions through their own visual production? This article proposes an analytic vocabulary of “visual argument” grounded in an image-focused rereading of two canonical bodies of work: the neo-Marxist theory most cited by spatial history (Henri Lefebvre, David Harvey, Doreen Massey, and Edward Soja) and the conspicuously uncited work of Fernand Braudel. By focusing on how these authors’ illustrations make claims about spatial subjectivity and the historicity of space—especially through visual relationships of background and foreground—I argue for a new way of understanding and responding to this work and to the visual project of spatial history today. A visual analysis highlights not only the limitations of neo-Marxism but also the pervasiveness of certain assumptions—shared across the neo-Marxists, Braudel, and digital visualization—about temporality, the natural/human dichotomy, and the methodological tensions between argument and visualization. I present my own mapping of Phoenix as one possibility for an argument-driven rethinking of familiar visual commitments, which also suggests a broader meditation on the relationship between visual and textual scholarship.     

A Classification of Spatial Distributions Based upon Several Cell Sizes

Several procedures, based upon cell count analysis, have been proposed for classifying spatial distributions, or maps, associated with some region R. Such procedures are rather imprecise and are known to depend upon the sixes and shapes of the cells in the particular partition of R under consideration. In this paper, the problem is considered from the point of view of hypothesis testing. A test of randomness based upon an arbitrary number of partitions of R is giuen. If the hypothesis of randomness is rejected, additional tests may be performed to classify the map into one of two categories, clustered or regular. These tests provide a number of advantages over existing procedures. Based upon multiple partitions of R, they decrease the dependence upon any particular partition, and the colresponding classification is precise since the null hypothesis distribution of the test statistic is (asymptotically) known. Finally, they allow a great deal of flexibility in testing for certain alternatives to randomness, and are applicable to one-, two-, and three- dimensional maps.     

Multi‐Type,Multi‐Zone Facility Location

The placement of facilities according to spatial and/or geographic requirements is a popular problem within the domain of location science. Objectives that are typically considered in this class of problems include dispersion, median, center, and covering objectives—and are generally defined in terms of distance or service‐related criteria. With few exceptions, the existing models in the literature for these problems only accommodate one type of facility. Furthermore, the literature on these problems does not allow for the possibility of multiple placement zones within which facilities may be placed. Due to the unique placement requirements of different facility types—such as suitable terrain that may be considered for placement and specific placement objectives for each facility type—it is expected that different suitable placement zones for each facility type, or groups of facility types, may differ. In this article, we introduce a novel mathematical treatment for multi‐type, multi‐zone facility location problems. We derive multi‐type, multi‐zone extensions to the classical integer‐linear programming formulations involving dispersion, centering and maximal covering. The complexity of these formulations leads us to follow a heuristic solution approach, for which a novel multi‐type, multi‐zone variation of the non‐dominated sorting genetic algorithm‐II algorithm is proposed and employed to solve practical examples of multi‐type, multi‐zone facility location problems.     

Academic Cartography,Internal Map History,and the Critical Study of Mapping Processes

ABSTRACT

Academic cartographers consistently expressed an interest in the history of map form (design and practice), at least until the 1980s. This essay reviews the formation of academic cartography, primarily in central Europe and the United States, and the scholarly work on the internal history of cartography that was clearly manifested in Imago Mundi. Internal map history catalysed the development of socio-cultural map histories after 1980 but did not itself change along those new lines. This was unfortunate because it is by paying attention to internal questions of the physical and graphic form of maps and the practices of mapping—albeit critically reconfigured as the processes of producing, circulating and consuming maps—that map historians will discover new and fertile intellectual ground.     

Crime Risk Maps: A Multivariate Spatial Analysis of Crime Data

In crime analyses, maps showing the degree of risk help police departments to make decisions on operational matters, such as where to patrol or how to deploy police officers. This study statistically models spatial crime data for multiple crime types in order to produce joint crime risk maps. To effectively model and map the spatial crime data, we consider two important characteristics of crime occurrences: the spatial dependence between sites, and the dependence between multiple crime types. We reflect both characteristics in the model simultaneously using a generalized multivariate conditional autoregressive model. As a real‐data application, we examine the number of incidents of vehicle theft, larceny, and burglary in 83 census tracts of San Francisco in 2010. Then, we employ a Bayesian approach using a Markov chain Monte Carlo method to estimate the model parameters. Based on the results, we detect the crime hotspots, thus demonstrating the advantage of using a multivariate spatial analysis for crime data.     

晚清民国乌鲁木齐地区村落类型与社会治理——以个案分析为中心

晚清民国乌鲁木齐地区的村落,根据人口结构不同,可以分为宗族、地理相近与地理相错三种类型。由于三种类型村落的自治程度不同,造成了政府对其治理方式上存在区别,也突出了国家对其控制力上存在差别。文章主要以村落个案分析为中心,针对每种类型的村落,以个案的形式说明村落类型与治理之间的关系及反映出的乡村社会治理的空间差异性。