Fundamental Spatial Concepts
Michael F. Goodchild
University of California
Santa Barbara
A spatial turn in science
• Adding space to theory
– the New Economic Geography
• space impeding flows of information, operation of markets
• transport costs
– Spatial Ecology
• a heterogeneous resource base
• space impeding interactions, breeding
• metapopulations
• Reasoning from spatial data
– cross-sectional
– new tools to overcome methodological problems
– impacts in all social, environmental disciplines
A growing literature
Spatially Integrated Social Science (Goodchild and
Janelle, OUP, 2004)
The drivers
• New technologies, new data
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geographic information systems (GIS)
remote sensing
positioning (GPS)
using location to integrate
providing spatial context
delivery mechanisms
• Applications of science in policy, decision
making, design
What fundamental concepts?
• How do people organize knowledge about
space?
• How should we organize the tools?
• What does it mean to think spatially?
– are people who do fundamentally different?
– can one train to be a spatial thinker?
– would you know one if you met one?
Spatial thinking
• Larger than GIS
– compare GIScience
• What every Google Earth user needs to
know
• One of Gardner’s seven types of intelligence
“1. Linguistic
Children with this kind of intelligence enjoy writing, reading, telling stories or doing
crossword puzzles.
2. Logical-Mathematical
Children with lots of logical intelligence are interested in patterns, categories and
relationships. They are drawn to arithmetic problems, strategy games and experiments.
3. Bodily-Kinesthetic
These kids process knowledge through bodily sensations. They are often athletic,
dancers or good at crafts such as sewing or woodworking.
4. Spatial
These children think in images and pictures. They may be fascinated with mazes or
jigsaw puzzles, or spend free time drawing, building with Lego or daydreaming.
5. Musical
Musical children are always singing or drumming to themselves. They are usually quite
aware of sounds others may miss. These kids are often discriminating listeners.
6. Interpersonal
Children who are leaders among their peers, who are good at communicating and who
seem to understand others' feelings and motives possess interpersonal intelligence.
7. Intrapersonal
These children may be shy. They are very aware of their own feelings and are selfmotivated.”
Howard Gardner
http://www.professorlamp.com/ed/TAG/7_Intelligences.html
What is spatial thinking?
“Three aspects of spatial ability:
• Spatial knowledge
– symmetry, orientation, scale, distance decay,
etc.
• Spatial ways of thinking and acting
– using diagramming or graphing, recognizing
patterns in data, change over space from
change over time, etc.
• Spatial capabilities
– ability to use tools and technologies such as
spreadsheet, graphical, statistical, and GIS
software to analyze spatial data”
http://www.nap.edu/catalog/11019.html
“Spatial thinking tasks
• Extracting spatial structures (encoding)
– perception and creation of representation
– show the spatial or conceptual relationships between
elements with respect to reference frame
• Performing spatial transformations
• Drawing functional inferences
– complex spatial reasoning
– combining representations and transformations to evaluate
or predict situations or events”
“The spatially literate student
• Knows where, when, how, and why to think
spatially
• Practices spatial thinking with
– broad and deep knowledge of spatial concepts and
representations
– well-developed spatial capabilities for using supporting
tools and technologies
• Adopts a critical stance to spatial thinking
– can evaluate the quality of spatial data based on source,
likely accuracy, reliability
– can use spatial data to construct, articulate, and defend
a line of reasoning in solving problems and answering
questions”
Thinking about space
• Wayfinding skills
– mental maps
• Three levels of knowledge
– landmark
– route
– survey
Landmark knowledge
• Geography as a list of places
– no spatial relationships
• no adjacency
• "if this is Tuesday it must be Belgium“
• which two pairs of US states are adjacent both in space
and in alphabetical order?
– no spatial context
• "how long is this flight?"
– no knowledge of intervening places
Tract
1
2
3
4
5
6
7
8
Pop
3786
2966
5001
4983
4130
3229
4086
3979
Location Shape
x,y
x,y
x,y
x,y
x,y
x,y
x,y
x,y
What value is location as an explanatory variable?
Route knowledge
• Sequences of intervening places
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–
–
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no ability to short-cut
no directions, distances
context along the route
distorted context off the route
Michael Gastner, Cosma
Shalizi, and Mark Newman
University of Michigan
http://wwwpersonal.umich.edu/~mejn/election/
Survey knowledge
• Full two-dimensional representation
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distances
orientations
shortcuts
context
• vertical and horizontal
Metric space
List of places
Adjacency matrix
Attribute table
W matrix of proximities
Linear network
Non-metric spaces
Point, extended
features and
attributes
Cartograms
Developing intelligences
• Mathematical, verbal, musical
– attention throughout K-16
• Spatial
– IQ tests
– trivia questions
Which is further west, San Diego or Reno?
Naïve geography
• Popular misconceptions
• Can a GIS be built to honor popular
misconceptions?
– direct people to drive north from LA to Santa
Barbara
– no, because such a GIS would violate the basic
principles of geometry
What fundamental concepts exist in
spatial intelligence?
• Are they sophisticated and abstract enough
to warrant a place in the curriculum?
– like mathematics, statistics, language, music
– can spatial intelligence gain more respect?
• Are they an appropriate basis for improved
GIS user interface design?
– does the interface need improvement?
A complex set of tools
• A GIS is capable of virtually any conceivable
operation on spatial data
– how many conceivable operations are there?
• ArcGIS 9.2 toolkit
– 510 operations
– 10 headings, up to 4 levels of hierarchical organization
– headings include:
• Analysis, Spatial Analyst, 3D Analyst, Geostatistical Analyst,
Spatial Statistics
• Data Management, Conversion
• Under which heading would you find the routine to
convert a shapefile to KML?
Map algebra
• Local, focal, zonal, global
– raster only
– is there something equivalent for vector?
• van Duersen’s scripting language
– c=a+b
• Andy Mitchell’s books
– ESRI Press
Volume 1:
Mapping where things are
Mapping the most and
least
Volume 2:
Calculating the center,
dispersion, and trend
Identifying patterns
Mapping density
Identifying clusters
Finding what’s inside
Analyzing geographic
relationships
Finding what’s nearby
Mapping what’s changed
Redundancy in operations
• SELECT FROM soilmap WHERE
soiltype=“A” AND county=“Santa Barbara”
– if county is not an attribute in the soilmap
shapefile
– invoke an identity operation
• Extend van Duersen’s language to allow
references to fields irrespective of their
representation
– rasters with different pixel size
– area shapefiles with non-congruent areas
– a TIN and a collection of sample points
1. Location
• Defining and measuring location
– the impossibility of exact measurement
• From infinitesimal point to extended area
• Place
– how many places are there in the U.S.?
– what is the most populous city in the world?
• Location as context
• Location as common key
• It is important to know where events occur
2. Distance, direction
• Measurement
– plane, globe
– buffers
• Distance decay
– decline of interaction with distance
– cost, time impediments
– footprints of human behavior
from Lance Waller, Emory University
Snow, J. (1949) Snow on Cholera.
Oxford University Press.
Johnson, S. (2006) The Ghost Map.
Riverhead
!
3. Neighborhood/region/territory
• The context of individuals
– action space
• Homogeneous areas
• The reporting zone containing the individual
– arbitrarily imposed on a continuous Earth
• The ecological fallacy
– the modifiable areal unit problem
• Competition for space
– trade areas, bird territories
– functional regions
4. Scale
• Level of detail
– the inevitability of generalization
• Extent
– generalizability of results
• Methods of upscaling, downscaling
• Fractal concepts
• Scale is always important
– many properties cannot be defined independently of scale
• length of a coastline
• slope of a topographic surface
• land use class
Unique to spatial thinking?
• Analogs of spatial scale in other domains
• Observed properties of spatial data
– what makes spatial special?
5. Spatial dependence
• “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: 234240
– “nearby things are more similar than distant things”
– geostatistics, Moran statistic
– the most important property of any spatially distributed
phenomenon
• Challenges the normal assumptions of statistical
tests
– independent, randomly chosen samples
6. Spatial heterogeneity
• TFL describes a second-order effect
– properties of places taken two at a time
– a law of spatial dependence
– is there a law of places taken one at a time?
• Spatial heterogeneity
– non-stationarity
– uncontrolled variance
Practical implications
• A state is not a sample of the nation
– a country is not a sample of the world
• Results of any analysis will depend explicitly on
spatial bounds
• Classification schemes will differ when devised by
local jurisdictions
• Figures of the Earth will differ when devised by local
surveying agencies
• Global standards will always compete with local
standards
• Strong argument for place-based analysis, local
statistics, geographically weighted regression
Summary
• Working with spatial data is not always
simple and intuitive
– but it can yield great insights if handled
appropriately
• There is a substantial body of knowledge that
needs to be acquired by anyone working with
spatial data
– you would never think of doing a t test without
taking a course in statistics
– why would you consider using a GIS without
taking a course in spatial thinking?
Other spaces
the human brain
molecular chemistry
the cosmos
nanoscience
UCSB is spatial
Social Sciences
Physical & Bio
Sciences
Cognition
Humanities
Fine Arts
Perception
Representation
Visualization
Engineering
Space-time
Computation
Simulation
Patterns &
Modeling
Processes
Education
Analysis
Application
Management
Planning
& Policy
Information-technology
Integration
• Exchange ideas and resources
• Promote new tools, research, and
applications
• Enhance spatial literacy
• Community of spatial thinkers
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Web portal on spatial UCSB
Seminars and workshops
Spatial help desk
General course(s) on spatial
thinking
Conclusions
• It is possible to enumerate the fundamental
concepts of a spatial approach
– six broadly defined concepts
– 27 in recent publication
– De Smith, Goodchild, and Longley (2006)
Geospatial Analysis
– www.spatialanalysisonline.com
Conclusions (2)
• This is more than GIS
– an enveloping conceptual framework for many
new technologies
– many drivers
• One of a minimal set of intelligences
– part of everyone’s education