Replication of Results - Spatial Mathematics: Theory and Practice through Mapping - page 98

2, 3, or 5. Anyone downloading the original could not resize it without distor-
tion: Distortion, for once, becomes the mapmaker's friend.
4.9 Theory finale
The abstract lessons learned in modern algebra are as important in the elec-
tronic world as they are elsewhere. Indeed, the current technical realm there-
fore offers a refreshing host of new examples to motivate theory, as suggested in
this simple scaling example that drew on a variety of algebraic concepts includ-
ing: The distributive law, the commutative law of addition, the Fundamental
Theorem of Arithmetic and the needed associated concept of prime number,
facts involving square roots and divisors, the Sieve of Eratosthenes, basic mate-
rial on permutations and combinations together with the convention that 0! = 1,
and the idea of relatively prime numbers. The web is a rich source of example
when one brings a rich source of abstract liberal arts training to it. The prob-
lem of “replication of results” has a long and deep history, extending its roots
into often surprising corners of the world of spatial mathematics.
In the following section, you will have the opportunity to apply the theory and
discussion in this chapter. First, you will use a web-based GIS called ArcGIS
Online to change the color and size of symbols on maps that you create, assess-
ing as you do so how meaning and interpretation are altered in the process.
4.10 Practice using selected concepts from this chapter
4.10.1 Changing symbol color and size to enhance
meaning on maps
Access the web-based GIS known as ArcGIS Online using a web browser:
http://www.arcgis.com/home . In the contents search box, search for a map
using the following phrase: “Extreme temperature same owner:jjkerski.” On
the results screen that appears upon searching for this phrase, click under the
thumbnail to open the map in the ArcGIS.com map viewer. Alternatively, open
a web browser and go directly to the map at the following URL: http://bit.ly/
NPviC0 . Click on the show map legend button and you will see a map similar
to that below ( Figure 4.8 ) .
This map shows the daily high and low temperature for each day of January
and July 2011 in the USA. Toggle off the high and low temperatures for each
of the four map layers. What pattern do you notice for the high and low tem-
peratures, and what is the reason for these patterns? How does altitude, lati-
tude, and proximity to oceans relate to the extreme temperatures, and why?
How does the fact that each extreme temperature is drawn with the same
symbol affect your understanding of the data? You should notice that the high
temperatures migrate from the coastal areas to the interior of the country