Tobler's second law of geography

In spatial analysis, it is often (usually) necessary to subset a study area from the globe. Tobler's first law of geography states that "everything is related to everything else, but near things are more related than distant."Tobler W., (1970) [https://web.archive.org/web/20190308014451/http://pdfs.semanticscholar.org/eaa5/eefedd4fa34b7de7448c0c8e0822e9fdf956.pdf "A computer movie simulating urban growth in the Detroit region"]. Economic Geography, 46(Supplement): 234–240. Thus, the geographic area relevant to a phenomenon being studied extends far outside this study area, and this relevant geographic location is not necessarily consistent over time. Due to distance decay, the effect of distant things falls as distance increases but never goes to zero. This has implications in both the modifiable areal unit problem (MAUP), the boundary problem, and the Uncertain geographic context problem (UGCoP).{{cite journal |last1=Kwan |first1=Mei-Po |title=The Uncertain Geographic Context Problem |journal=Annals of the Association of American Geographers |date=2012 |volume=102 |issue=5 |pages=958–968 |doi=10.1080/00045608.2012.687349|s2cid=52024592 }}{{cite book |last1=Openshaw |first1=Stan |title=The Modifiable Aerial Unit Problem |date=1983 |publisher=GeoBooks |isbn=0-86094-134-5 |url=https://www.uio.no/studier/emner/sv/iss/SGO9010/openshaw1983.pdf}}{{cite journal |last1=Chen |first1=Xiang |last2=Ye |first2=Xinyue |last3=Widener |first3=Michael J. |last4=Delmelle |first4=Eric |last5=Kwan |first5=Mei-Po |last6=Shannon |first6=Jerry |last7=Racine |first7=Racine F. |last8=Adams |first8=Aaron |last9=Liang |first9=Lu |last10=Peng |first10=Jia |title=A systematic review of the modifiable areal unit problem (MAUP) in community food environmental research |journal=Urban Informatics |date=27 December 2022 |volume=1 |issue=1 |page=22 |doi=10.1007/s44212-022-00021-1 |s2cid=255206315 |doi-access=free |bibcode=2022UrbIn...1...22C }} In the boundary problem in particular, when geographic boundaries are arbitrary and not based on natural features, the phenomena under evaluation is likely to continue and be influenced by space beyond the study area.{{cite book |last1=Henley |first1=S. |title=Nonparametric Geostatistics |date=1981 |publisher=Springer Netherlands |isbn=978-94-009-8117-1}}{{cite book |last1=Haining |first1=Robert |title=Spatial Data Analysis in the Social and Environmental Sciences by Robert Haining |date=1990 |publisher=Cambridge University Press |language=en|doi=10.1017/CBO9780511623356 |isbn=9780511623356 }}

In general, some dispute the entire concept of laws in geography and the social sciences. These criticisms have been addressed by Tobler and others. However, this is an ongoing source of debate in geography and unlikely to be resolved anytime soon.

{{main|Laws of geography}}

Some have argued that geographic laws do not need to be numbered. However, the existence of a first invites the creation of a second. In addition to Tobler's second law, several scholars have proposed candidates for a second.

• Arbia's law of geography: "Everything is related to everything else, but things observed at a coarse spatial resolution are more related than things observed at a finer resolution."{{cite journal |last1=Arbia |first1=Giuseppe |last2=Benedetti |first2=R. |last3=Espa |first3=G. |title="Effects of MAUP on image classification" |journal=Journal of Geographical Systems |date=1996 |volume=3 |pages=123–141}}{{cite journal |last1=Smith |first1=Peter |title=The laws of geography |journal=Teaching Geography |date=2005 |volume=30 |issue=3 |page=150}}
• Spatial heterogeneity: This concept has a longer history than the first law of geography and dates back to regional geography that emphasizes heterogeneity as "an inescapable characteristic of geography".{{Cite journal |last=Hartshorne |first=R. |year=1939 |title=The nature of geography: A critical survey of current thought in the light of the past |journal=Annals of the Association of American Geographers |volume=29 |issue=3 |pages=173–412|doi=10.2307/2561063 |jstor=2561063 |hdl=2027/coo.31924014016905 |hdl-access=free }} Spatial heterogeneity was first proposed as "a possible candidate" of the second law of geography by Michael F. Goodchild, who attributes this law to David Harvey. Chinese geographers often cite it simply as the "second law of geography".{{Cite journal |last1=Zhu |first1=A. X. |last2=Lu |first2=G. |last3=Liu |first3=J. |last4=Qin |first4=C. Z. |last5=Zhou |first5=C |year=2018 |title=Spatial prediction based on Third Law of Geography |journal=Annals of GIS |volume=24 |issue=4 |pages=225–240 |doi=10.1080/19475683.2018.1534890|s2cid=61153749 |doi-access=free |bibcode=2018AnGIS..24..225Z }}
• Tim Foresman and Ruth Luscombe's Second law of geography: "Things that know where they are can act on their locational knowledge. Spatially enabled things have increased financial and functional utility."{{cite journal |last1=Foresman |first1=T. |last2=Luscombe |first2=R. |year=2017 |title=The second law of geography for a spatially enabled economy |journal=International Journal of Digital Earth |volume=10 |issue=10 |pages=979–995|doi=10.1080/17538947.2016.1275830 |bibcode=2017IJDE...10..979F |s2cid=8531285 }}
• the uncertainty principle: "that the geographic world is infinitely complex and that any representation must therefore contain elements of uncertainty, that many definitions used in acquiring geographic data contain elements of vagueness, and that it is impossible to measure location on the Earth's surface exactly."
• It has been proposed that Tobler's first law of geography should be moved to the second and replaced with another.

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• Ecological fallacy
• Indicators of spatial association
• Level of analysis
• Modifiable temporal unit problem
• Moran's I
• Neighborhood effect averaging problem
• Scientific law
• Spatial autocorrelation
• Spatial heterogeneity
• Uncertain geographic context problem
• Quantitative geography
• Waldo Tobler bibliography

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{{Geography topics}}

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