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Quantitative Geography III

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Quantitative Geography III Quantitative Geography III: Future Challenges & Challenging Futures Levi John Wolf1, Sean Fox, Rich Harris, Ron Johnston, Kelvyn Jones, David Manley, Emmano il !ranos, Wenfei Winnie Wan" Abstract #n the $revio s t%o $arts of this series, %e discussed the history and current stat s of & antitative "eo"ra$hy. #n this final $art, %e focus on the f t re' We ar" e that & antitative "eo"ra$hers are most hel$f l %hen %e can sim$lify di)c lt $ro*lems sin" o r distinct domain expertise' !o do this, %e m st clarify the theory nder$innin" core conce$t al $ro*lems in & antitative "eo"ra$hy. !hen, %e examine the social forces that are sha$in" the f t re of & antitative "eo"ra$hy. We concl de %ith criteria for ho% & antitative "eo"ra$hy mi"ht succeed in addressin" these challen"es. Keywords+ & antitative "eo"ra$hy, data science, spatial de$endence, modifia*le areal nit $ro*lem, ca sality, incl siveness, re$lication, o$en science Introduction !he f t re of & antitative "eo"ra$hy lies in the comparative advanta"e of its theory. While it may *e that ,*y o r theories yo shall -no% s.” /Harvey 1010, 231), ,%hat ni& e o t$ t or conse& ences occur d e to spatial and "eo"ra$hic thinkin"5” /6olled"e 7887, 11) Searchin" & estions li-e this %ere common in the early 7888s as & antitative "eo"ra$hers so "ht to mo*ilize the field for a ne% millenni m. Yet, they remain difficult to answer a*o t the $ast t%enty years of & antitative "eo"ra$hy, let alone the next' ;nfort nately, $redictions a*o t the $ast are less sef l than $redictions a*o t the f t re' !o clarify the f t re of & antitative "eo"ra$hy, it %ill hel$ to first discuss the core theory of & antitative "eo"ra$hy. !hen, %e discuss current forces that act $on this core' We %ill concl de %ith a sketch of %hat success mi"ht look like' 1 School of 6eo"ra$hical Sciences, ;niversity of <ristol' = thors listed al$ha*etically after lead' Theoretical forces driving uantitative geography It is true, as in the case of other ossifications, that attacking this ossification is almost sure to reduce the apparent neatness of our subject. But neatness does not accompany rapid growth. (Tukey 1 !", #$ !o nderstand %hat & antitative "eo"ra$hy may o>er in the f t re, %e need to take stock. Accumulation of kno%led"e in & antitative "eo"ra$hy is a cyclical $rocess: %aves of scholars conver"e on similar empirical & comp tational challen"es, then follo% their o%n rivulets *ack to common conce$t al nderstandin"' Historical shifts in $erspective are tidal@ "eo"ra$hy is transformed *oth *y individ al "eo"ra$hers’ mercurial interests as %ell as shifts in socially or scientifically-relevant & estions (Johnston and Sida%ay 781C4' Beyond contin al chan"e, it is erosion of complexity— slo%ly & $ro"ressively *y accum lated kno%led"e—that is the $oint' !h s, %e $resent "eo"ra$hical theories as heuristics & antitative "eo"ra$hers se to simplify reality. Fort nately, ,accumulated” kno%led"e in & antitative "eo"ra$hy involves only a fe% he ristics /6oodchild 78824' Previo s re$orts in this series have traced them thro "h time' Here, %e define their main $oints. !beying the law is not the point of the law Spatial de$endence is often ex$lained in terms of !o*ler’s La%+ everything is related to everything else, but near things are more related than distant things (Tobler 1 &', "(!$. Flaims a*o t the “death of distance” and the di"ital economy /Fairncross 7881) raised more critical attention to the definition of “near” (Miller 7882), * t !o*lerAs La% is flexi*le eno "h to still *e meanin"f l after this redefinition /e'"' Hecht and Moxley 7880@ !ranos and HiIkam$ 781J4' When Miller /7882) *olsters !o*ler’s La% %ith ,near is a more flexi*le and $o%erf l conce$t than commonly a$$reciated” /$' 73C), he is ri"ht' < t, he also *ends the meanin" of “la%” (Smith 78824' #n this definition, !o*ler’s La% is too va" e for most of social science (Merton 10204' F rther, as 6i**ons and Kverman /7817) arg e, o r kno%led"e a*o t "eo"ra$hical $rocesses $ro*a*ly %ill not *enefit from explorin" the many notions of “near” that may su$$ort !o*ler’s La%' !he im$act of de$endence implied *y !o*ler’s La% often stays the same (LeSa"e & Pace, 7812), and is rarely the $oint of the model' #nstead, !o*ler’s La% sho ld *e sed as !o*ler (10L8) intended+ to simplify $ro*lems. #n this spirit, Fh rch /7813) ses !o*lerAs la% to simplify %areho se location $ro*lems. Flassical methods consider all %areho ses %hen su$$lyin" each demand site, so odd decisions are considered * t never made, like Detroit, MI su$$lyin" <akersfield, F=' Fh rch /7813) only explicitly models “near” facilities, and finds o$timal sol tions *y "rad ally increasin" %hat is “near” each facility. !his is !o*lerAs La% enforced, not o*eyed' F t re %ork sho ld $ rsue sim$lification in this manner, too' "A#$ & the challenge of uncertainty laws !he Modifyable Areal +nit Problem /K$ensha% 1032) and its recent relatives (Kwan, 7813), reflect another -ernel of "eo"ra$hical kno%led"e' !he MA;P implies se$arate “scale” and “zonin"” $ro*lems (Fotherin"ham et al' 78884' Heither hel$s s sim$lify analyses, * t each clarifies assumptions %e must ma-e' !he “zonin"” $ro*lem implies: Place characteristics are contingent on where place boundaries are drawn. Alternatively the “scale” $ro*lem echos Broido and Fla setAs /7810) result a*o t the rarity of “scale-free” net%orks: -haracteristics of a geographical process are contingent on the scale at which the process is measured. #nteractions *et%een *o ndaries, scale, $lace, and $rocess are complex, so assumptions are re& ired to avoid the MA;E' Fort nately, Fotherin"ham and Won"As (1001) three methods to resolve the MAUP o tri"ht remain hel$f l' !he first, “frameB inde$endent” analysis, has vexed "eo"ra$hers (cf' !o*ler 10304' #ndeed, Kin" (1001) arg es scale sensitivity can *e theoretically im$ortant' !h s, %e focus on the remainin" t%o+ dra%in" *etter areas & movin" *eyond the area' %uilding a better MA#$&trap K$timal zonin" methods have lon" sho%n $romise for solvin" the MA;E' K$timal zonin" methods estimate *o ndaries/$laces "iven assumptions a*o t ho% they sho ld loo-' !his sually solves the “zonin"” $ro*lem, and the “scale” component is solved se$arately. Promisin" %ork $rovides mathematical $roof of minimum-error a""re"ations (Bradley et al' 7811), ri"oro sly characterizes the sensitivity of statistics to the MA;P (D & e et al' 7813), * ilds zones %ith less internal ncertainty (Spielman and Folch 781C), or develo$s "eneralB$ r$ose zones from demo"ra$hic data (Johnston et al' 7882@ Sin"leton and Spielman 78124' Nonin" al"orithms have improved remarka*ly /!am Fho 7813), so this remains $romisin"' Beyond an “o$timal” 9onin", %e mi"ht analyze random sam$les from a distri* tion of zonin" systems /!a$$ 78104' !his %o ld li*erate s from any sin"le 9onin" and $rovide tests on ho% n s al o*served zones are' Ho%ever, %e must *e ca tio s: !am Fho and Li /7813) sho% that fail re to sample uniformly from the nfathoma*ly many $ossi*le zonin" systems %ill n$redicta*ly *ias even simple statistics. '(pirical answers to theoretical uestions Kne so rce of o$timal 9onin", #sardAs (10C1) ruminations a*o t “true” re"ions /$' 1L), ill strates a tension from Jones (10034' Kne $erspective on scale and zonin" is that they define an e$istemolo"ical frame—a hierarchy in %hich "eo"ra$hical $rocesses “make sense'. Another is ontolo"ical, %ith scale & zonin" descri*in" a system of relationshi$s from %hich inde$endently meanin"f l contexts emerge' !his ontolo"ical $erspective "ro nds the half-cent ry search for “conchorations” Helson /7878) %here re"ions fo nd in di>erent $rocesses conver"e to common *o ndaries /#sard 10C1, 784' < t, convergence itself does not ma$ sef l theoretical conce$ts like “context” or “expos re” onto empirical zones (Kin" 1001@ K%an 78134' !his means o$timal 9onin" o>ers “empirical answers to theoretical & estions” (Kin" 1001, 1184' K$timal 9ones themselves are atheoretical, %ith no direct link to a specific $rocess or theory a*o t $lace, context, or exposure' As such, they only “fix” o r frame of analysis. !hey cannot tell s if estimates a*o t this frame make sense' !herefore, %e must acce$t that the MAUP “is not an empirical $ro*lem; it is a theoretical $ro*lem” (Kin" 1001, 11J4' Re-a""re"ation is a theoretical act %ith empirical e>ects. A ne% theory a*o t the relevant ,$lace” or “context” is $osited *y each ne% a""re"ationMscale@ %e sho ld not *e surprised that estimates chan"e, too (Petrović et al', 78134' !h s, %e cannot esca$e the MA;P *y dra%in" more or *etter areal nits: %e must make stron"er theories a*o t %hat context, exposure, or $lace does' The future of areal data Finally, Fotherin"ham and Won" (1001) su""est %e leave the areal nit alto"ether.
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