Scale in Geogr~_hy

aggregate saving data. (See Deaton and Paxson (1997)for an example.) Until these approaches are recon-ciled, a firm consensus about the magnitude ofdemographic effects is unlikely to emerge.

Kotlikoff L J 1988 Intergenerational transfers and savings.Journal of Economic Perspeftives 2(2): 41-58

Lee R D 2000 Intergenerational transfers and the econ-omic life cycle: A cross-cultural perspective. In: Mason A,Tapinos G (eds.) Sharing the Wealth: Demographic Changeand Economic Transfers Between Generations. Oxford Uni-versity Press, Oxford, UK

Lee R D, Mason A, Miller T 2000 Life cycle saving and thedemographic transition: The case of Taiwan. In: Chu C Y, LeeR D (eds.) Population and Economic Change in East Asia,Population and Development Review. 26: 194-219

Mason A 1987 National saving rates and population growth: Anew model and new evidence. In: Johnson D G, Lee R D(eds.) Population Growth an~ Economic Development: Issuesand Evidence. University of Wisconsin Press, Madison, WI,pp. 5230-60

Modigiiani F 1988 The role of intergenerational transfers andlife cycle saving in the accumulation of wealth. Journal ofEconomic Perspective.v 2(2): 15-40

Modigliani F, Brumberg R 1954 Utility analysis and theconsumption function: An interpretation of cross-section data.In: Kurihara K (ed.) Post-Keynesian Economics. RutgersUniversity Press, New Brunswick, NJ

A. Mason

Scale in Geography

4. Unresolved IssuesThere are a number of important issues that have notbeen resolved and require additional work. First, thesaving literature does not yet adequately incorporatethe impact of changing institutional arrangements.Studies of saving in the industrialized countries andrecent work on developing countries considers theimpact of state-sponsored pension programs onsaving, but the impact of family support systems hasreceived far too little emphasis. The erosion of theextended family in developing countries is surely oneof the factors that has contributed to the rise of savingrates observed in many developing countries.

Second, the role of mortality has received inad-equate attention. The importance of lifecycle savingdepends on the expected duration of retirement. Inhigh mortality societies, few reach old age and manywho do continue to work. Only late in the mortalitytransition, when there are substantial gains in theyears lived late in life, does an important pensionmotive emerge.

Third, the saving models currently in use are staticmodels and do not capture important dynamics.Recent simulation work that combines realisticdemographics with lifecycle saving behavior showsthat during the demographic transition countries mayexperience saving rates that substantially exceed equi-librium values for sustained periods of time (Lee2000).

Scale is about size, eithe~ relative or absolute, andinvolves a fundamental set of issues in geography.Scale primarily concerns space in geography, and thisarticle will focus on spatial scale. However, thedomains of temporal and thematic scale are alsoimportant to geographers. Temporal scale deals withthe size of time units, thematic scale with the groupingof entities or attributes such as people or weathervariables. Whether spatial, temporal, or thematic,scale in fact has several meanings in geography.

1. Three Meanings of Stale

The concept of scale can be confusing, insofar as it hasmultiple referents. Cartographic scale refers to thedepicted size of a feature on a map relative to its actualsize in the world. Analysis ~cale refers to the size of theunit at which some problem is analyzed, such as at thecounty or state level. Phenomenon scale refers to thesize at which human or physical earth structures orprocesses exist, regardless of how they are studied orrepresented. Although the three referents of scalefrequently are treated independently, they are in factinterrelated in important ways that are relevant to allgeographers, and the focu$ of research for some. Forexample, choices concernirtg the scale at which a map

BibliographyBarro R J 1974 Are government bonds net wealth? Journal of

Political Economy 6 (December): 1095-117Coale C A, Hoover E M 1958 Population Growth and Economic

Development in Low-income Countries: A Care Study of India'sProspects. Princeton University Press, Princeton, NJ

Deaton AI989 Saving in developing countries: Theory andreview. Proceedings of the World Bank Annual Conference onDevelopment Economics, Supplement to the World BankEconomic Review and the World Bank Research Observer,pp. 61-96

Deaton A, Paxson C 1997 The effects of economic andpopulation growth on national saving and inequality. Demo-graphy 34(1): 97-114

Higgins M, Williamson J G 1997 Age structure dynamics in Asiaand dependence on foreign capital. Population and Devel-opment Review 23(2): 261-94

Kelley A C, Schmidt R M 1996 Saving, dependency anddevelopment. Journal of Population Economics 9(4): 365-86

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Scale in Geography

should be made depend in part on the scale at whichmeasurements of earth features are made and the scaleat which a phenomenon of interest actually exists.

1.1 Cartographic Scale

Maps are smaller than the part of the earth's surfacethey depict. Cartographic scale expresses this relation-ship, traditionally in one of three ways. A verbal scalestatement expresses the amount of distance on themap that represents a particular distance on the earth'ssurface in words, e.g., 'one inch equals a mile.' Therepresentative fraction (RF) expresses scale as anumerical ratio of map distance to earth distance, e.g.,'1:63,360.' The RF has the advantage of being aunitless measure. Finally, a graphic scale bar uses aline of particular length drawn on the map andannotated to show how much earth distance itrepresents. A graphic scale bar has the advantage thatit changes size appropriately when the map is enlargedor reduced. Alternatively, all three expressions of scalemay refer to areal measurements rather than linearmeasurements, e.g., a I-inch square may represent1 square mile on the earth.

Given a map of fixed size, as the size of therepresented earth surface gets larger, the RF getssmaller (i.e., the denominator of the RF becomes alarger number). Hence, a 'large-scale map' shows arelatively small area of the earth, such as a county orcity, and a 'small-scale map' shows a relatively largearea, such as a continent or a hemisphere of the earth.This cartographic scale terminology is frequently feltto be counterintuitive when applied to analysis orphenomenon scale, where small-scale and large-scaleusually refer to small and large entities, respectively.

An important complexity about cartographic scaleis that flat maps invariably distort spatial relations onthe earth's surface: distance, direction, shape, and/orarea. How they distort these relations is part of thetopic of map projections. In many projections, es-pecially small-scale maps that show large parts of theearth, this distortion is extreme so that linear or arealscale on one part of the map is very different than onother parts. Even so-called equal area projectionsmaintain equivalent areal scale only for particularglobal features, and not for all features at all places onthe map. Variable scale is sometimes shown on a mapby the use of a special symbol or multiple symbols atdifferent locations.

'resolution' or 'granulJrity' are often used as

synonyms for the scale of analysis, particularly when

geographers work with dIgital representations of the

earth's surface in a computer by means of a regular

grid of small cells in a sat~llite image (rasters) or on a

computer screen (pixels). Analysis scale here refers to

the area of earth surface~ presented by a single cell. It has long been recogn ed that in order to observe

and study a phenomenon ost accurately, the scale of

analysis must match the ctual scale of the phenom-

enon. This is true for al three domains of scale--

spatial, temporal, and the atic. Identifying the correct

scale of phenomena is, t us, a central problem for

geographers. Particularly ""hen talking about thematic

scale, using data at one sc~le to make inferences about

phenomena at other scale$ is known as the cross-level

fallacy (the narrower case of using aggregated data to

make inferences about ~saggregated data is well-

known as the ecological f~llacy).

Geographers often an~lyze phenomena at what

might be called 'availabltl scale,' the units that are

present in available data. Many problems of analysis

scale arise from this pra~tice, but it is unavoidable

given the difficulty and ex~ense involved in collecting

many types of data over large parts of the earth's

surface. Geographers havtllittle choice in some cases

but to analyze phenomen~ with secondary data, data

collected by others not spe!;ifically for the purposes of

a particular analysis. For ~xample, census bureaus in

many countries provide a wealth of data on many

social, demographic, and ~conomic characteristics of

their populace. Frequently, the phenomenon of

interest does not operate aPcording to the boundaries

of existing administrative dr political units in the data,

which after all were not c*ated to serve the needs of

geographic analysis. The resolution of image scan-

ners on remote-sensing ~atellites provides another

important example. Lands~t imagery is derived from

thematic mapper sensors, producing earth measure-

ments at a resolution O ~fl about 30 by 30 meters.

However, many phenome a occur at finer resolutions

than these data can provi .

Most useful is theor)[ about the scale of a

phenomenon's existence. I1requently lacking this, but

realizing that the available! scale may not be suitable,

geographers use empirical 'trial-and-error' approaches

to try to identify the ap ~ roPriate scale at which a

phenomenon should be an lyzed. Given spatial units

of a particular size, one can readily aggregate or

combine them into largeli units; it is not possible

without additional info~ ation or theory to dis-

aggregate them into small r units. Even given obser-

vations measured at very s all units, however, there is

still the problem of decid ng in what way the units

should be aggregated. Thi ~ iS known as the modifiable

areal unit problem (MA P, or MTUP in the case

of temporal scale). Vari us techniques have been

developed to study the implications of MAUP

(Openshaw 1983).

1.2 Analysis Scale

Analysis scale includes the size of the units in whichphenomena are measured and the size of the units intowhich measurements are aggregated for data analysisand mapping. It is essentially the scale of under-standing of geographic phenomena. Terms such as

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_Scale

in Geo~raphy.

cation, but also includes aspects of selection andenhancement of features of particular interest. As onestudies or represents smaller pieces of the earth, onetends strongly to deal witb more detailed or more fine-grained aspects of geographic features. For example,large-scale maps almost always show features on theearth's surface in greater detail than do small-scalemaps; rivers appear to meander more when they areshown on large-scale maps, for instance. Studied mostextensively by cartograph~rs, generalization is in factrelevant to all three meanings of scale, and to all threedomains of spatial, tempdral, and thematic scale.

3. Conclusion

Issues of scale have always been central to geographictheory and research. Advances in the understanding ofscale and the ability to investigate scale-relatedproblems will continue, particularly with theincreasingly common representation of geographicphenomena through the medium of digital geographicinformation (Goodchild and Proctor 1997). Carto-graphic scale is becoming 'visualization' scale. Howis scale, spatial and temporal, communicated indynamic, multidimensional, and multimodal repre-sentations, including visul\lization in virtual environ-ments? Progress continues on the problem ofautomated generalization, programming intelligentmachines to make generlllization changes in geo-graphic data as scale changes. The ability to performmultiscale and hierarchical analysis will be developedfurther. M ore profound th,n these advances, however,the widespread emergence of the 'digital world' willfoster new conceptions of scale in geography.

1.3 Phenomenon Scale

Phenomenon scale refers to the size at which geo-graphic structures exist and over which geographicprocesses operate in the world. It is the 'true' scale ofgeographic phenomena. Determining the scale ofphenomena is clearly a major research goal in geo-graphy. It is a common geographic dictum that scalematters. Numerous concepts in geography reflect theidea that phenomena are scale-dependent or aredefined in part by their scale. Vegetation stands aresmaller than vegetation regions, and linguistic dialectsare distributed over smaller areas than languages. Thepossibility that some geographic phenomena are scaleindependent is important, however. Patterns seen atone scale may often be observed at other scales;whether this is a matter of analogy or of the sameprocesses operating at multiple scales is theoreticallyimportant. The mathematics of fractals has beenapplied in geography as a way of understanding andformalizing phenomena such as coastlines that areself-similar at different scales (Lam and Quattrochi1992).

The belief has often been expressed that the disci-pline of geography, as the study of the earth as thehome of humanity, can be defined partially by its focuson phenomena at certain scales, such as cities orcontinents, and not other scales. The range of scales ofinterest to geographers are often summarized by theuse of terminological continua such as 'local-global' or'micro-, meso-, macroscale.' The view that geo-graphers must restrict their focus to particular rangesof scales is not shared universally, however, andadvances have and will continue to occur whengeographers stretch the boundaries of their subjectmatter. Nonetheless, few would argue that subatomicor interplanetary scales are properly of concern for

geography.It is widely recognized that various scales of geo-

graphic phenomena interact, or that phenomena atone scale emerge from smaller or larger scale phenom-ena. This is captured by the notion of a 'hierarchy ofscales,' in which smaller phenomena are nested withinlarger phenomena. Local economies are nested withinregional economies, rivers are nested within largerhydrologic systems. Conceptualizing and modelingsuch scale hierarchies can be quite difficult, and thetraditional practice within geography of focusing on asingle scale largely continues.

BibliographyButtenfield B P, McMaster R B,(eds.) 1991 Map Generalization:

Making Rules for Knowledge Representation. Wiley, NewYork

Goodchild M F, Proctor J 1997 Scale in a digital geographicworld. Geographical and Environmental Modeling 1: 5-23

Hudson J C 1992 Scale in space and time. In: Abler R F, MarcusM G, Olson J M (eds.) Geography's Inner Worlds: PervasiveThemes in Contemporary American Geography. Rutgers Uni-versity Press, New Brunswick, NJ

Lam N S-N, Quattrochi D A 1992 On the issues of scale,resolution, and fractal analysis in the mapping sciences. TheProfessional Geographer 44: ~8-98

MacEachren AM 1995 How Maps Work: Representation,Visualization, and Design. Guilford Press, New York

Meyer W B, Gregory D, Turner B L, McDowell P F 1992 Thelocal-global continuum. In: Abler R F, Marcus M G, OlsonJ M (cds.) Geography's Inner Worlds: Pervasive Themes inContemporary American Geography. Rutgers University Press,New Brunswick, NJ

2. GeneralizationThe world can never be studied, modeled, or repre-sented in all of its full detail and complexity. Scale isimportant in part because of its consequences for thedegree to which geographic information is generalized.Generalization refers to the amount of detail includedin information; it is essentially an issue of simplifi-

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Scale in Geography

MuehrckeP C, MuehrckeJ 0 1992 Map Use: Reading,Analysis,Interpretation, 3rd edn. JP Publications, Madison, WI

Openshaw S 1983 The Modifiable Areal Unit Problem. GeoBooks, Norfolk, UK

and practical consequences. For example, if onlyviolent crimes are subject to classification as homi-cides, then 'homicide' is a kind of 'violent crime,' anddeaths caused by executive directives to release deadlypollution could not be homicides.D. R. Montello

Scaling and Classification in SocialMeasurement

Social measurements translate observed characteris-tics of individuals, events, relationships, organi-zations, societies, etc. into symbolic classifications thatenable reasoning of a verbal, logical, or mathematicalnature. Qualitative research and censuses togetherdefine one realm of measurement, concerned withassignment of entities to classification categoriesembedded within taxonomies and typologies. Anothertopic in measurement involves scaling discrete items ofinformation such as answers to questions so as toproduce quantitative measurements for mathematicalanalyses. A third issue is the linkage between socialmeasurements and social theories.

1. Classifications

Classification assimilates perceived phenomena intosymbolically labeled categories. Anthropological stud-ies of folk classification systems (D' Andrade 1995)have advanced understanding of scientific classifica-tion systems, though scientific usages involve criteriathat folk systems may not meet entirely.

Two areas of social science employ classificationsystems centrally. Qualitative analyses such as ethno-graphies, histories, case studies, etc. offer classifica-tions-sometimes newly invented-for translatingexperiences in unfamiliar cultures or minds intofamiliar terms. Censuses of individuals, of occur-rences, or of aggregate social units apply classifica-tions-usually traditional-in order to count entitiesand their variations. Both types of work depend ontheoretical constructions that link classification cat-egories.

1.2 Typologies

A typology differentiates entities at a particular levelof a taxonomy in terms of one or more of theirproperties. The differenti!lting property (sometimescalled a feature or attribute) essentially acts as amodifier of entities at tbat taxonomic level. Forexample, in the USA kinship system siblings aredistinguished in terms of whether they are male orfemale; in Japan by comparison, siblings are schem-atized in terms of whether they are older as well aswhether they are male or female.

A scientific typology differentiates entities into typesthat are exclusive and ex¥ustive: every entity at therelevant taxonomic level is of one defined type only,and every entity is of some defined type. A divisioninto two types is a dichotomy, into three types atrichotomy, and into more than three types a poly-tomy.

Polytomous typologies are often constructed bycrossing multiple properties, forming a table in whicheach cell is a theoretical type. (The crossed propertiesmight be referred to as variables, dimensions, orfactors in the typology.) For example, members of amultiplex society have been characterized according towhether they do or do not accept the society's goals onthe one hand, and whether they do or do not accept thesociety's means of achieving goals on the other hand;then crossing acceptance of goals and means producesa fourfold table defining conformists and three typesof deviants.

Etic-emic analysis involves defining a typology withproperties of scientific interest (the etic system) andthen discovering ethnographically which types andcombinations of types are rccognized in folk meanings(the emic system). Latent structure analysis statisti-cally processes observed properties of a sample ofentities in order to confirm the existence of hypothe-sized types and to define the types operationally.

1.3 Aggregate Entities

Aggregate social entities s\Jch as organizations, com-munities, and cultures may be studied as unique cases,where measurements identify and order internalcharacteristics of the entity rather than relate oneaggregate entity to another.

A seeming enigma in s<?cial measurement is howaggregate social entities can be described satisfactorilyon the basis of the reports of relatively few informants,even though statistical theory calls for substantialsamples of respondents td survey populations. The

1.1 TaxonomiesEvery classification category is located within a tax-onomy. Some more general categorization, Y, deter-mines which entities are in the domain for the focalcategorization, X; so an X always must be a kind of Y.'X is a kind of Y' is the linguistic frame for specifyingtaxonomies. Concepts constituting a taxonomy form alogic tree, with subordinate elements implying super-ordinate items.

Taxonomic enclosure of a classification category isa social construction that may have both theoretical

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Copyright @ 2001 Elsevier Science Ltd. All rights reserved.International Encyclopedia of the Social & Behavioral Sciences ISBN: 0-08-043076-7