Session 1 June 20, 9a.m. to noon. Identifying Useful Online World Studies Resources and an Introduction to Searching for Maps on the Internet

 STATIC AND DYNAMIC MAPS:  Maps on the computer--an application of mathematics in geography--maps that are static images are available in numerous locations on the internet; dynamic maps are available in limited locations on the internet.  Dynamic maps can be made using GIS software.  It is important to understand the difference between static and dynamic maps. STATIC MAPS:  maps on the World Wide Web and elsewhere.  Click here for sample.  More on this topic will come below. DYNAMIC MAPS (maps that change when there is a change in the underlying database).  Geographical Information Systems (GIS).  Two desktop GISs:  compare and contrast them.  Generally, Atlas is based more on classical cartography than is ArcView; however, ArcView makes much greater use of the capability of the computer than does Atlas. ArcView GIS (Environmental Systems Research Institute, ESRI)--open a map of the world.  Note the latitude and longitude read-out.  Default projection generally just a flat map. Zoom-in tool:  magnifying glass with a plus sign in it. Zoom-out tool, magnifying glass with a minus sign in it, or use a menu. Distance tool:  distance from Chicago to Cape of Good Hope to Sri Lanka; shows individual distance for last leg of trip as well as accumulated distance, after the default flat map is projected to some standard projection--here the Robinson. Atlas GIS (ESRI)--open a map of the world.  Note the latitude and longitude read-out.  Default projection is a Robinson projection. Zoom-in tool:  magnifying glass with a plus sign in it. Zoom-out tool, magnifying glass with a minus sign in it, or use a menu. Distance tool:  distance from Chicago to Cape of Good Hope to Sri Lanka; shows individual distance for last leg of trip as well as accumulated distance.  (Distance used is great circle distance.) Concepts: Map scale Latitude and longitude (related reading:  The Longitude; Mapping). Map projection:  Stereographic projection. The One-point Compactification Theorem (blackboard demonstration):  shows that the skin of a spherical globe cannot be perfectly flattened into the plane; it fails to do so by at least one point. Thus, there can be no perfect map in the plane. Map projection as a transformation:  Thompson's fish Links to various projections.  Geosystems Handouts on Map Projections Classification--move the center of projection; alter the plane of capture (roll it up into a cylinder, torus, Möbius strip, or Klein bottle--developable surface; try a cone).  Cylindrical and conical projections--choose a projection suited to need. Mercator--conformal--well-suited as a navigation chart.  Equal area projection better-suited to showing map of the world.  Making GIS maps using onboard information and base maps--demonstration of thematic mapping.  Different methods of partitioning the data can lead to very different maps.  When considering a thematic map made by someone else, it is therefore important to consider how the underlying database might have been partitioned. Quantiles--there are roughly the same number of observations in each interval but the size of the interval might vary. With a map of the world in view, double click on the "legend" on the left (in ArcView).  A "legend editor" pops up.  Choose "graduated color" from the pull-down menu.  The default value colors each country a unique color (called "unique value").  Choosing "graduated color" will enable you to group countries with similar characteristics as one color.  The map will have a theme, such as the world's lands grouped by area.  Data about area will be grouped into ranges, or categories, by color (e.g. all countries of less that 1.6 million square miles are colored pink). You will need to choose a classification field; that is, you will need to choose some set of data.  For example, choose "sqmi_cntry" or number of square miles in each country shown on the map. Choose the classification method for the data.  That is, how is the information about area to be split into different categories?  One way is to choose by "quantile." Notice now that back in the legend editor you can choose various color schemes; the default scheme is red monochromatic (different shades of red come up for different data ranges--pink for lower values, deep red for higher values). Now, look at the map made using this process.  There are many countries in the deep red category that are visible on the map and none that are easily visible in the pink range.  This observation should not be surprising, but it should be noted. Equal interval--the size of the interval is uniform but the number of observations within each interval might vary. Repeat the steps above, but instead of choosing "quantile" as the method by which to partition data, choose instead "equal interval." Look at the result back in the legend editor; keep the color scheme the same (red monochromatic). Now, look at the map made using this process.  Compare and contrast the result with the map above.  Notice the importance of selecting a method for partitioning of data and its implication for resulting maps.  (Related reference:  Monmonier, How to Lie with Maps.) Other methods of data partitioning and consequences for associated maps are available, as well, in most GIS packages.  Each has its own merits and drawbacks; each produces maps different from other data partitioning methods. Concepts: Partition--choose method according to data arrangement.  Jordan Curve Theorem; implications for mapping.  The Jordan Curve Theorem:  permits correct assignment of addresses on either side of streets  permits visually appropriate coloring of polygons  illustrates the need to split complex curves apart at nodes where the curve crosses itself in order to ensure that the two properties above will hold on maps.  This fact is important in digitizing (and elsewhere).  Coloring--no more than four colors are ever required to color a map in the plane.  The Four Color Theorem:  shows that four colors are enough to color any map in the plane with adjacency of regions defined across an edge only. Defining adjacency in other ways is a topic of current research. suggests that if distinctions need to be made that correspond to gradations in data, that a graded scale of four colors will always be enough to color a map in the plane. More than four colors may be useful in making a graded gray-scale or variations in intensity of color that reflect intensity in data sets. Other surfaces may require different numbers of colors--consider the sphere (use stereographic projection). Planetary Pictures... http://www.jpl.nasa.gov http://mpfwww.jpl.nasa.gov http://mgs-www.jpl.nasa.gov http://www.msss.com/mars/pictures/viking_lander/viking_lander.html http://mars.compuserve.com/default.html http://www-mgcm.arc.nasa.gov/mgcm/research.html

Sandra L. Arlinghaus