On the surface - The Visualization of Spatial Social Structure - page 201

lines, straight and curved, traversing and enclosing two-dimensional space, more
commonly referred to as graphs.
Graphs show the relationships between two dimensions. Visually, graphs
illustrate the form of the relationship, bring simple equations to life and project
complex dependencies. Several graphs can be drawn on a single plane to com-
pare and contrast them (Figure 7.3). Complex graphs can split and merge into
many lines, but even a single line can contain infinite complexity.
Much work has been done on how best to present graphs in statistical graph-
ics. The problem begins with the axes. If these are not directly related to each
other, the ratio between them is arbitrary and its choice can drastically affect the
visual form. Rules have been developed to aid depiction, but, to date, the most
successful choice has been to put the graph in a window on the computer screen
and allow the viewer to stretch it and view certain parts. This problem reoccurs
when we consider surfaces.
Visual improvement in graphing is achieved by transforming the axes more
generally. Logarithmic scales are most often used, but anything is possible. Here
we have a simple one-dimensional version of the area cartogram problem to solve.
A particularly interesting variant is the triangular graph, 4 where the distance of
any point from the apexes of an equilateral triangle increases as the influence of
what is represented by that apex upon the point declines (Box 7.1). This device
is used here to show the share of the vote among three major political parties for
a number of areas (Figures 7.4, 7.5 and 7.6) and a little later the shares between
four parties. 5 The forms created are extremely interesting given that we now
know it was back in the late 1970s and early 1980s that the polarisation that
would come to define current British society would begin to grow, hollowing out
the middle. Here the beginnings of political separation are made clear, before old
Labour capitulated to the schism and 'New' Labour was born. 6

4 'The method of using the triangle appears to be one of those things which is continually being
rediscovered. The earliest descriptions of the technique that the author has located date from 1964,
but it seems likely that others were using the technique earlier' (Upton, 1976, p. 448). See the next
footnote for an example.
5 Use of the triangle's 'third dimension', the distance above its surface, has a long if largely
forgotten history: 'Before leaving this subject a brief reference must be made to an ingenious form
of solid chart described by Professor Thurston in several of his articles. It is called the tri-axial
model. By its use it is possible to take into account four different variables instead of three as was
previously the case. It is a necessary condition, however that for each set of corresponding variables
three of them should add up to a constant value, generally 100 per cent. The fourth is unrestricted'
(Peddle, 1910, p. 109).
6 The triangular graphs, in hindsight, show key changes in voting patterns marking a new trend
in British politics beginning in the 1970s and only hinted at by work done around then. Between
the February and October 1974 elections: '

...

a majority of those in marginal seats who would
have [previously] either voted Liberal or abstained if the constituency had not been marginal instead
supported the Conservative Party' (Johnston, 1982, p. 51), referring to comments made by Michael
Steed in 1975 (Michael later became President of the Liberal Party from 1978 to 1979).