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Richard Heimann © 2011
Human Terrain Analysis
GIS270
George Mason University
!
Richard Heimann
Richard Heimann © 2011
What will we discuss…?
Laws of Spatial Science - the primitives of spatial
analysis!!

!
…what are they and why are they important? 

!
…how do we begin to measure and quantify the
existence of such laws?

!
Richard Heimann © 2011
GIS270: Purpose of this lecture
Richard Heimann © 2011
Teaching

!
Laws allow courses to be structured from first
principles

!
Laws provide the basis for predicting performance,
making design choices

!
An asset of a strong, robust discipline
GIS 270: LAWS
Richard Heimann © 2011
GIS
StatisticsStatistical Packages
X
GIS270: LAWS/Statistics
Richard Heimann © 2011
Are Laws of Social Science…
!
Deterministic?

!
Does a counterexample defeat a law?

!
Empirical statements?

!
Verifiable with respect to the real world?

!
Do the Social Sciences have Physics Envy?
Richard Heimann © 2011
ALL will know what is meant by an idiographic
and nomothetic approach

!
MOST will be able to say which approaches are
idiographic and which are nomothetic

!
SOME will consider the implications of a
nomothetic and idiographic approach for
geography as a science
GIS 270: LAWS
Richard Heimann © 2011
GIS 270: LAWS
idios = private or personal

!
Idiographic: personal, few observations, exhaustive,
“humanistic”

!
Idiographic Theories: Based on the assumption we are all
unique and can only be understood by contemplating our
uniqueness. 

!
Idiographic Methodologies: Difficult to teach, tenuous to
claim and lack all classical definitions of science.
Richard Heimann © 2011
GIS 270: LAWS
nomos = law

!
Nomothetic: positivist, many observations, comprehensive,
“dehumanistic”

!
Nomothetic Theories: Investigating the group (large scale) to
find behavior shared by /everyone/ that apply everywhere
over time and space. Goal to classify and develop theories
principles and laws where. 

!
Nomothetic Methodologies: Difficult to accomplish, tenuous
to claim but conforms to classical definitions of science.
Richard Heimann © 2011
GIS 270: LAWS
Can there be laws in the social
sciences? 

!
Ernest Rutherford: “The only result that
can possibly be obtained in the social
sciences is: some do, and some don’t”
Richard Heimann © 2011
Can there be laws in the social sciences? 

!
Anyon (1982): social science should be
empirically grounded, theoretically
explanatory and socially critical.
GIS 270: LAWS
Richard Heimann © 2011
Based on empirical observation

!
Observed to be generally true

!
Sufficient generality to be useful as a norm

!
Deviations from the law should be interesting

!
Dealing with geographic process rather than form

!
Understanding of social process in context

!
…the Nomothetic & Idiographic debate in geography is /solved/!!
GIS 270: LAWS can be…
Richard Heimann © 2011
TFLG: “All things are related, but
nearby things are more /related/ than
distant things”

!
!
W.R.Tobler, 1970. A computer movie simulating urban
growth in the Detroit region. Economic Geography 46:
234-240
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
Teenage Birth Rates – US.
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
GIS would be impossible
!
!
!
!
!
Life would be impossible
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
S-ZAR RAN-VAR
GIS 270: The First Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The /Second/ Law of Geography (TFLG)
!
TFLG describes a second-order effect
(Properties of places taken two at a time)

!
!
…is there a law of places taken one at a
time?

!
Richard Heimann © 2011
Total Fertility Rate – US.
GIS 270: The /Second/ Law of Geography (TFLG)
Richard Heimann © 2011
The geography of the 2004 US presidential election results (48 contiguous states)
Spatial heterogeneity

Non-stationarity / Regional Variation 

Uncontrolled variance / Equilibrium
GIS 270: The /Second/ Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The /Second/ Law of Geography (TFLG)
Globalization is thought of a
homogenizing the world, but it
cannot and will not happen. The
underlying processes that drive
these systems both look for
unevenness and produce
unevenness. Homogeneous
processes cannot happen, which
necessitate the development of
methods to describe the
unevenness and account for it when
describing process.
Richard Heimann © 2011
With the global
population distribution
being ~50% male and
~50% female would the
average be a person
with one uterus and
one testis?
GIS 270: The /Second/ Law of Geography (TFLG)
Richard Heimann © 2011
GIS 270: The Blended Approach
Small (Local) Theory: Nomothetic laws are tenuous, nomothetic
methodologies are difficult in geographic process but the goal is
a good one.

!
Spatially Explicit Stylized Facts: is a simplified presentation of an
empirical finding observed to be generally true. A stylized fact is
often a broad generalization that summarizes some complicated
statistical calculations, which although essentially true may have
inaccuracies in the detail.

!
From the TFLG -> TSLG:

General truths, sufficient generality to be useful norms
and deviations from these norms should be interesting.
Richard Heimann © 2011
Extreme Heterogeneity
Multiple Equilibrium:
One process for every
observation over
space.

!
Harvey’s view

!
Idiographic Laws
Single Equilibria: A
singular process
over space and
across study area.

!
Smith’s view

!
Nomothetic Laws
Stationarity
Equilibrium < n: The
number of processes
under investigation are
less than the number of
observations.

!
/Sweet Spot/
!
Blended Approach 

!
Small Theory 

!
Spatially Explicit Stylized
Facts
GIS 270: The Blended Approach
Richard Heimann © 2011
“I can’t believe Nixon
won. I don’t know
anybody who voted for
him.” attributed to Pauline
Kael, movie critic for the
New Yorker

!
Availability bias: the
tendency to generalize
based on nearby
information
GIS 270: Candidate Laws
Richard Heimann © 2011
GIS 270: Candidate Laws
Richard Heimann © 2011
Fractal principle: that geographic phenomena reveal more
detail the more closely one looks; and that this process
reveals additional detail at an orderly and predictable rate
(Goodchild and Mark, 1987; Mandelbrot, 1982).
GIS 270: Candidate Laws
Richard Heimann © 2011
!
…describes discontinuity. Mandelbrot
found that when something changes, it can
change abruptly. For example, a stock
priced at $40 a share can quickly fall to $5
without ever being priced at $30 or $20, if
something significant triggers its collapse.
GIS 270: Candidate Laws
Richard Heimann © 2011
!
…describes persistence: i.e. trends tend to persist;
that is, if a place has been suffering drought, it's
likely it will suffer more of the same. In other words,
things tend to stay the way they've been recently. 

!
Healthy people tend to stay healthy;

Winning teams tend to keep on winning; and,

Products that have been successful for the past five
years will probably be successful next month.
GIS 270: Candidate Laws
Richard Heimann © 2011
Richard Heimann © 2011
Laws do exist in Geography …but need to be stated.

!
Generalizations about the geographic world can be
blindingly obvious …but stating them is important.

!
Laws have practical value in GIS and Social Science.

!
Laws have more than just pedagogic value.
GIS 270: Conclusions
Richard Heimann © 2011
…HTA help(s) to resolve the timeless dilemma in
geography about whether to focus on the local (L) or the
global (G) – whether spatial science should be
idiographic or nomothetic. As [Phillips] suggests in his
discussion of L and G, there is increasing sympathy in
many disciplines, including geography, for a middle
position in which the specific details of law-like
statements are allowed to vary geographically. Recent
contributions to the tools of such as Geographically
Weighted Regression now provide the techniques to
implement this interesting methodological position.
GIS 270: Conclusions
Richard Heimann © 2011
GIS 270: QUESTIONS?!
Richard Heimann © 2011
Spatial Thinking in Social Science (Lab
1: Spatial Thinking in the Social
Sciences)

!
60 minutes…
GIS 270: LAB

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Human Terrain Analysis at George Mason University (DAY 1)

  • 1. Richard Heimann © 2011 Human Terrain Analysis GIS270 George Mason University ! Richard Heimann
  • 2. Richard Heimann © 2011 What will we discuss…? Laws of Spatial Science - the primitives of spatial analysis!! ! …what are they and why are they important? ! …how do we begin to measure and quantify the existence of such laws? !
  • 3. Richard Heimann © 2011 GIS270: Purpose of this lecture
  • 4. Richard Heimann © 2011 Teaching ! Laws allow courses to be structured from first principles ! Laws provide the basis for predicting performance, making design choices ! An asset of a strong, robust discipline GIS 270: LAWS
  • 5. Richard Heimann © 2011 GIS StatisticsStatistical Packages X GIS270: LAWS/Statistics
  • 6. Richard Heimann © 2011 Are Laws of Social Science… ! Deterministic? ! Does a counterexample defeat a law? ! Empirical statements? ! Verifiable with respect to the real world? ! Do the Social Sciences have Physics Envy?
  • 7. Richard Heimann © 2011 ALL will know what is meant by an idiographic and nomothetic approach ! MOST will be able to say which approaches are idiographic and which are nomothetic ! SOME will consider the implications of a nomothetic and idiographic approach for geography as a science GIS 270: LAWS
  • 8. Richard Heimann © 2011 GIS 270: LAWS idios = private or personal ! Idiographic: personal, few observations, exhaustive, “humanistic” ! Idiographic Theories: Based on the assumption we are all unique and can only be understood by contemplating our uniqueness. ! Idiographic Methodologies: Difficult to teach, tenuous to claim and lack all classical definitions of science.
  • 9. Richard Heimann © 2011 GIS 270: LAWS nomos = law ! Nomothetic: positivist, many observations, comprehensive, “dehumanistic” ! Nomothetic Theories: Investigating the group (large scale) to find behavior shared by /everyone/ that apply everywhere over time and space. Goal to classify and develop theories principles and laws where. ! Nomothetic Methodologies: Difficult to accomplish, tenuous to claim but conforms to classical definitions of science.
  • 10. Richard Heimann © 2011 GIS 270: LAWS Can there be laws in the social sciences? ! Ernest Rutherford: “The only result that can possibly be obtained in the social sciences is: some do, and some don’t”
  • 11. Richard Heimann © 2011 Can there be laws in the social sciences? ! Anyon (1982): social science should be empirically grounded, theoretically explanatory and socially critical. GIS 270: LAWS
  • 12. Richard Heimann © 2011 Based on empirical observation ! Observed to be generally true ! Sufficient generality to be useful as a norm ! Deviations from the law should be interesting ! Dealing with geographic process rather than form ! Understanding of social process in context ! …the Nomothetic & Idiographic debate in geography is /solved/!! GIS 270: LAWS can be…
  • 13. Richard Heimann © 2011 TFLG: “All things are related, but nearby things are more /related/ than distant things” ! ! W.R.Tobler, 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography 46: 234-240 GIS 270: The First Law of Geography (TFLG)
  • 14. Richard Heimann © 2011 Teenage Birth Rates – US. GIS 270: The First Law of Geography (TFLG)
  • 15. Richard Heimann © 2011 GIS 270: The First Law of Geography (TFLG)
  • 16. Richard Heimann © 2011 GIS 270: The First Law of Geography (TFLG)
  • 17. Richard Heimann © 2011 GIS 270: The First Law of Geography (TFLG)
  • 18. Richard Heimann © 2011 GIS 270: The First Law of Geography (TFLG)
  • 19. Richard Heimann © 2011 GIS would be impossible ! ! ! ! ! Life would be impossible GIS 270: The First Law of Geography (TFLG)
  • 20. Richard Heimann © 2011 GIS 270: The First Law of Geography (TFLG)
  • 21. Richard Heimann © 2011 S-ZAR RAN-VAR GIS 270: The First Law of Geography (TFLG)
  • 22. Richard Heimann © 2011 GIS 270: The /Second/ Law of Geography (TFLG) ! TFLG describes a second-order effect (Properties of places taken two at a time) ! ! …is there a law of places taken one at a time? !
  • 23. Richard Heimann © 2011 Total Fertility Rate – US. GIS 270: The /Second/ Law of Geography (TFLG)
  • 24. Richard Heimann © 2011 The geography of the 2004 US presidential election results (48 contiguous states) Spatial heterogeneity Non-stationarity / Regional Variation Uncontrolled variance / Equilibrium GIS 270: The /Second/ Law of Geography (TFLG)
  • 25. Richard Heimann © 2011 GIS 270: The /Second/ Law of Geography (TFLG) Globalization is thought of a homogenizing the world, but it cannot and will not happen. The underlying processes that drive these systems both look for unevenness and produce unevenness. Homogeneous processes cannot happen, which necessitate the development of methods to describe the unevenness and account for it when describing process.
  • 26. Richard Heimann © 2011 With the global population distribution being ~50% male and ~50% female would the average be a person with one uterus and one testis? GIS 270: The /Second/ Law of Geography (TFLG)
  • 27. Richard Heimann © 2011 GIS 270: The Blended Approach Small (Local) Theory: Nomothetic laws are tenuous, nomothetic methodologies are difficult in geographic process but the goal is a good one. ! Spatially Explicit Stylized Facts: is a simplified presentation of an empirical finding observed to be generally true. A stylized fact is often a broad generalization that summarizes some complicated statistical calculations, which although essentially true may have inaccuracies in the detail. ! From the TFLG -> TSLG: General truths, sufficient generality to be useful norms and deviations from these norms should be interesting.
  • 28. Richard Heimann © 2011 Extreme Heterogeneity Multiple Equilibrium: One process for every observation over space. ! Harvey’s view ! Idiographic Laws Single Equilibria: A singular process over space and across study area. ! Smith’s view ! Nomothetic Laws Stationarity Equilibrium < n: The number of processes under investigation are less than the number of observations. ! /Sweet Spot/ ! Blended Approach ! Small Theory ! Spatially Explicit Stylized Facts GIS 270: The Blended Approach
  • 29. Richard Heimann © 2011 “I can’t believe Nixon won. I don’t know anybody who voted for him.” attributed to Pauline Kael, movie critic for the New Yorker ! Availability bias: the tendency to generalize based on nearby information GIS 270: Candidate Laws
  • 30. Richard Heimann © 2011 GIS 270: Candidate Laws
  • 31. Richard Heimann © 2011 Fractal principle: that geographic phenomena reveal more detail the more closely one looks; and that this process reveals additional detail at an orderly and predictable rate (Goodchild and Mark, 1987; Mandelbrot, 1982). GIS 270: Candidate Laws
  • 32. Richard Heimann © 2011 ! …describes discontinuity. Mandelbrot found that when something changes, it can change abruptly. For example, a stock priced at $40 a share can quickly fall to $5 without ever being priced at $30 or $20, if something significant triggers its collapse. GIS 270: Candidate Laws
  • 33. Richard Heimann © 2011 ! …describes persistence: i.e. trends tend to persist; that is, if a place has been suffering drought, it's likely it will suffer more of the same. In other words, things tend to stay the way they've been recently. ! Healthy people tend to stay healthy; Winning teams tend to keep on winning; and, Products that have been successful for the past five years will probably be successful next month. GIS 270: Candidate Laws
  • 35. Richard Heimann © 2011 Laws do exist in Geography …but need to be stated. ! Generalizations about the geographic world can be blindingly obvious …but stating them is important. ! Laws have practical value in GIS and Social Science. ! Laws have more than just pedagogic value. GIS 270: Conclusions
  • 36. Richard Heimann © 2011 …HTA help(s) to resolve the timeless dilemma in geography about whether to focus on the local (L) or the global (G) – whether spatial science should be idiographic or nomothetic. As [Phillips] suggests in his discussion of L and G, there is increasing sympathy in many disciplines, including geography, for a middle position in which the specific details of law-like statements are allowed to vary geographically. Recent contributions to the tools of such as Geographically Weighted Regression now provide the techniques to implement this interesting methodological position. GIS 270: Conclusions
  • 37. Richard Heimann © 2011 GIS 270: QUESTIONS?!
  • 38. Richard Heimann © 2011 Spatial Thinking in Social Science (Lab 1: Spatial Thinking in the Social Sciences) ! 60 minutes… GIS 270: LAB