Tobler’s-First-Law-and-Spatial-Analysis.doc

Tobler’s First Law and Spatial Analysis

Harvey J. Miller
Department of Geography
University of Utah
260 S. Central Campus Dr. Room 270

Salt Lake City, UT 84108-9155 USA

[e-mail]
I never thought that others would take them so much more seriously then I did. Albert Einstein on his theories (www.famous-)
Introduction
“I invokeinvoke v.调用 the first law of geography: everything is related to everything else, but near things are more related than distant things” (Tobler 1970). How could a sentence justifying heuristicadj.启发式的 calculations in a crude urban growth simulation generate an iconn.图标, 肖像, 偶像 now known as Tobler’s First Law (TFL)? Why has this “law” resonated (使)共鸣, (使)共振 so strongly in geography? geography n.地理学, 地理

Waldo Tobler could invoke v.调用 a “first law of geography” since the propositionn.主张, 建议, 陈述, 命题 that near things are more related seemed reasonable in 1970. It is enduring adj.持久的, 不朽的 since near and related are useful concepts at the core of spatial analysis and modeling. And in 2003 and beyond, TFL is still useful since the rise of geographic information science and technologies allow greater sophisticated when measuring and analyzing these concepts. This is ironicadj.说反话的, 讽刺的 considering that Tobler apparently invoked the law in part to apologize for the slow computers at that time.
I am going to sidestep sidestep [简明英汉词典]
[5saidstep]
n.横跨的一步, (侧面的)台阶
vt.横跨一步躲闪, 回避(困难)
vi.回避问题, 躲避打击 the issue of whether TFL is in fact a “law” by noting that science accepts the concept of empirical laws or compact compact [简明英汉词典]
[5kRmpAkt]
adj.紧凑的, 紧密的, 简洁的
n.契约, 合同, 小粉盒descriptions of patterns and regularities. These are not required to be immutableadj.不可变的, 不变的, 不能变的, 永恒的 truths (Casti 1990; Swartz 2001). We certainly have ample evidence to support TFL: you may have noticed on the way to work this morning that the world is orderly with respect to space. Scientific laws are also not required to be causal, e.g., Newton’s Law of Gravity is not an explanation. Although not causal, TFL is consistent adj.一致的, 调和的, 坚固的, [数、统]相容的 with an elegant process argument: overcoming space requires expenditure of energy and resources, something that nature and humans try to minimize (although not exclusively, of course). I accept TFL as reasonable regularity that generally holds true.

The issues I am going to examine are the central roles of “near” and “related” to spatial analysis and the increasing levels of sophisticationn.强词夺理, 诡辩, 混合 that we can achieve when measuring and analyzing these concepts. I also suggest that relations among near entities do not imply a simple, sterile adj.贫脊的, 不育的, 不结果的, 消过毒的, 毫无结果的 geography: complex geographic processes and structures can emerge from local interactions. Indeed, the sensitivity of geographic and other phenomena to local interactions implies that we should carefully measure and analyze relations among near things.
What is related?
What do we mean when we say that two geographic entities are related? At the very least, we are claiming that there is a positive or negative correlation between these entities. Spatial association does not necessarily imply causality. Two things that are associated may be involved in a causal relationship, or there may be other hidden variables that cause the association. Although correlation is not causality, it provides evidence of causality that can (and should) be assessedvt.估定, 评定 in light of theory and/or other evidence.

TFL is at the core of spatial autocorrelation n.[统]自相关 statistics, that is, quantitative adj.数量的, 定量的 techniques for analyzing correlation relative to distance or connectivity n.连通性relationships. Although spatial autocorrelation is often treated as confounding vt.使混淆, 把...搞混, 挫败, 讨厌(e.g., something to be corrected in regression n.衰退 modeling), it is information-bearing since it reveals the spatial associations among geographic entities. In 1970, techniques for measuring and analyzing spatial autocorrelation were crude, providing only a single, summary number for an entire spatial dataset indicating the overall intensity of the spatial association. Spatial analysts now recognize every location has an intrinsic degree of uniqueness due to its situation relative to the rest of the spatial system. Similar to spatial autocorrelation, spatial heterogeneity n.异种, 异质, 不同成分 is not just “parameter drift” to be corrected: it is information-bearing n.轴承, 关系, 方面, 意义, 方向, 方位 since it reveals both the intensity and pattern of spatial associations. Disaggregate v.使崩溃,分解,聚集 spatial statistics such as local indicators of spatial association (LISA) statistics (Anselin 1995), the G statistics (Getis and Ord 1992) and geographically weighted regression(反距离权重)n.衰退 (Brunsdon, Fotheringham and Charlton 1996) capture spatial association and heterogeneityn.异种, 异质, 不同成分 simultaneouslyadv.同时地. These techniques generate abundant information that can be used in both exploratory and confirmatory adj.确定的, 证实的 analysis to generate and test hypotheses 臆测, 假定 about spatial relations. Their data requirements and demands on geovisualization techniques make them unimaginable adj.,想不到的, 不可思议的 prior to the rise of widely available digital geo-data and GIS.

Another core spatial analytic technique that exploits vt.开拓, 开发, 开采, 剥削, 用以自肥v.使用 TFL is spatial interpolation or techniques for generating missingadj.不见的, 缺少的 or hidden variables in geographic space. Some of these techniques are very sophisticated in their implementation n.执行 of TFL. For example, kriging（克里金） treats the spatial variable being interpolatedadj.以内插值替换的 as regionalized v.分成地区, 按地区安排, meaning that it varies continuously across space according to some spatial lag n.落后, 囚犯, 迟延, 桶板, 防护套
adj.最后的
vi.缓缓而行, 滞后
vt.落后于, 押往监狱, 加上外套 or distance in a partly random and partly deterministic manner. This admits a wide range of distance functions and clustering聚类 patterns. It also allows ad-hoc adjustments based on qualitative information. Despite this flexibility, kriging is also powerful in the sense that there are well-established techniques for estimating parameters that minimize interpolation error given sample data and a hypothesized spatial lag model. These error measures are spatially disaggregate and can be mapped and visualized, providing a detailed record of interpolation n.篡改, 添写, 插补 accuracy across space (see Isaaks and Srivastava 1989; Lam 1983; Oliver and Webster 1990).

A stricter type of spatial association is spatial interaction or the movement of individuals, material, or information between two geographic locations. Spatial interaction is closely related to spatial autocorrelation: spatial interaction models are special cases of a general model of spatial autocorrelation (Getis 1991). Similar to spatial autocorrelation, advanced techniques for spatial interaction and spatial choice modeling recognize spatial heterogeneity n.异种, 异质, 不同成分 or “map pattern” effects. These effects result from individuals simplifying spatial choice problems by clustering 聚类 or lumpingadj.很多的, 重大的 choices together, often based on proximity (Bhat, Govindarajan and Pulugurta 1998; Fotheringham 1983; Kanaroglou and Ferguson 1996). Computational adj.计算的techniques such as genetic algorithm-based parameter estimation and artificial neural networks are improving the robustnessadj.精力充沛的 of spatial interaction modeling for noisy and non-quantitative data (Diplock and Openshaw 1996; Dougherty 1995).
What is near?

The discussion in the previous section leaves the concepts of “near” and “distant” as vague and undefined, as Waldo Tobler did when invoking TFL. This section, based on Miller and Wentz (2003), suggests that near is central to measurements and analysis of geo-space in spatial analysis. It also suggests that near is a more flexible and powerful concept than commonly appreciated.

As Gatrell (1983) points out in his excellent book Distance and Space, geographers do not have a solitary adj.孤独的 claim on the concept of “space”: we can form a mathematical space by defining a set of objects and relations between all pairings 配对[偶] (核子等)成对 of these objects. These relations can be quantitative adj.数量的, 定量的 or qualitative adj.性质上的, 定性的. However, as geographers we are really only interested in a subset n.[数]子集 of all possible spaces, namely adv.即, 也就是, geo-spaces or those that can be meaningfully represent phenomena on or near the surface of the Earth

What distinguishes geospaces from other spaces? In geospaces, the objects correspond to locations on the surface of the Earth (at least conceptually adv.概念地) with defined shortest path relations between all pairings. These are the minimum cost routes for physical movement or virtual interaction between objects, where “cost” is interpreted generally. The shortest path relations determine the measurement and analysis of geographic attributes (Beguin and Thisee 1979).

In most of the geographic and related literature n.文学(作品), 文艺, 著作, 文献, “nearness” is typically defined based on the straight-line segment connecting two locations, i.e., the Euclidean a(古希腊数学家).欧几里得的, 欧几里得几何学的 distance for the location pair. This is only one possibility. There are an infinite number of shortest-path relations that also obey the metric adj.米制的, 公制的 space conditions of symmetry, non-negativity and triangular inequality (Love, Morris and Wesolowsky 1988; Puu and Beckmann 1999). If we are willing to relax these metric requirements so that only the triangular inequality condition holds, the resulting space is a quasi adj.类似的, 准的-metric. This can still support measurement and spatial analysis (Huriot , Smith and Thisse 1989; Smith 1989).

Geographic phenomena that do not appear to be consistent with TFL may in fact be following non-Euclidean nearness relations. This can include geographic diffusion n.扩散, 传播, 漫射 processes such as disease propagationn.动植物, 繁殖, (声波, 电磁辐射等)传播 (Cliff and Haggett 1989), movement and interaction at the urban, regional and national scales (Puu and Beckmann 1999; Worboys, Mason and Lingham 1998) and human perception n.理解感知,感觉 of geographic space (Montello 1992). Waldo Tobler has spent much of his career trying to convince us using cartographic transformations and other clever analytical and visualization techniques (e.g., Tobler 1976a, 1976b, 1978, 1987, 1994).

Nearness relations need not be restricted to empty space. Some geographic phenomena are conditioned by geographic attributes such as terrain, land cover and traffic congestion n.拥塞, 充血. To capture these effects, we can generalize the concept of distance to least cost paths through geographic space (Angel and Hyman 1976). This requires treating a spatially continuous attribute or attributes as a cost field that affects movement or interaction. This is a well-studied problem in spatial analysis and geographic information science; several tractable adj.易驾驭的, 驯良的, 易管教的, 易处理的 computational algorithms n.[数]运算法则 are available for special cases of this general problem. (e.g., Smith, Peng and Gahinet 1989; de Berg and van Kreveld 1997).

Nearness is a central organizing principle of geo-space, but it is not required to be a function of Euclidean, metric or even an empty space. There are a wide range of analytical and computational techniques for representing and analyzing these spaces and no reason in principle why they should not be part of a standard GIS toolkitn.[计] 工具包, 工具箱.

But isn’t the world shrinking?

Distance was meaningful when von- Thünen contemplated 预期的 the ponderousadj.沉重的, 笨重的, 冗长的, 沉闷的, (指问题等)呆板的 movements of oxcarts n.牛车 between his farm and a central market. The past two centuries has witnessed space-time convergence n.集中, 收敛: transportation and communication technologies have shrunk the world to an incredible degree. Locations on the Earth’s surface are much closer to each other with respect to the time required for movement and interaction (Janelle 1969). Does this make TFL trivial adj.琐细的, 价值不高的, 微不足道的, since many things are now “near”?

Waldo Tobler addressed this issue in a 1999 address to the ESRI User

Conference. Tobler noted that while the world is shrinking it is also shriveling: v.(使)起皱纹, (使)枯萎, (使)束手无策 relative differences in transportation and communication costs are increasing at most geographic scales. When transportation technology was limited to biological or wind power, all persons whether noble or peasant could move only at the same slow speed, albeit conj.虽然 with different levels of comfort. The automobile and airplane make the world much smaller, but only if these technologies are accessible and affordable for you. As population growth and urbanization n.都市化, 文雅化 continue, some transportation networks are becoming saturated and congested, creating a complex geography of accessibility associated with differing abilities to pay the high rents or housing payments to avoid long commute times Transportation cost differentials across space increase when networks (such as airlines and railroads) are pruned v.剪除 and concentrated for economic efficiency or when cities or regions experience collapse of their transportation infrastructure (examples include sub-Sahara Africa and Afghanistan).

Couclelis and Getis (2000) note that the world is also fragmenting [自](文件)分段: many activities are becoming more loosely connected to geographic space. With portable adj.轻便的, 手提(式)的, 便携式的 computing and communications technologies such as laptops 膝上型电脑 and cell phones, a person can work at the office, at home, at a coffee shop or in a park. Thus, there is no longer a single unequivocal adj.不含糊的 location that can be associated with the activity “work.” However, this is predicated on the availability and affordability of telecommunications technologies: these are still out-of-reach of many individuals and families in the United States and especially elsewhere in the world.
Is TFL still valid in a shrinking and fragmenting world? The question is whether near and distant are still valid concepts in this world. The “Death of Distance” argument that dominated much of the early literature on the Internet and cyberspace n.电脑空间 (e.g., Caincross 1997) is simplistic adj.过分单纯化的: this assumes that communication has only a substitution relationship with transportation (i.e., more virtual interaction implies less physical movement). In fact, empirical evidence suggests that the opposite is the case: the rise of telecommunication demand has been paralleled by a corresponding increase in travel demand at all geographic scales (Couclelis 2000). Many of the central places at the end of the Industrial Age are still central in the Information Age: locations such as Midtown adj.市中心区的, 位于市中心区的
n.市中心区(商业区和住宅区的中间地) Manhattan and Soho-London are still highly desirable for corporate adj.社团的, 法人的, 共同的, 全体的 headquarters, particularly in supposedly “footloose adj.自由自在的, 到处走动的” activities such as decision making and creat