Volume visualization - The Visualization of Spatial Social Structure - page 249

When does a variable become a dimension? That is essentially a question
of the resolution of measurement. If place is just one of the dozen regions and
nations of the British state then it is a variable that should be put in tables, not
mapped. Once a variable has numerous possible values it can be considered a
dimension. Movement and measurement along the variable must be possible, and
the three-dimensional space created should theoretically be continuous. Time in
the study of the ten 1955 - 1987 general elections is too discrete to consider as
being approximately continuous, and interpolation of votes between the elections
would be meaningless.
If we have a third dimension, how can we see it, let alone understand it? 2
This is the problem that is responsible for relegating this chapter to the end of
the topic. Basically, the answer is - not easily. The traditional way to see in
such blocks is to show some two-dimensional slices, as we might cut open a
human brain in a medical scan. It is a small step from there to take many slices,
allowing animation. To create more of an illusion of three dimensions, perspective
and various lighting effects can be employed. These too can be animated. 3
All that we are really showing with traditional three-dimensional graph-
ics is a series of surfaces - two-and-a-bit-dimensional, but a long way from
three - often containing almost one-dimensional information (Figure 9.1). Dur-
ing recent decades many innovations were made in computer visualization that
can create far better illusions of more complex three-dimensional worlds. The
problem is then no longer deceiving the eyes, they are easily deceived, but
teaching the mind. However, in the social sciences it simultaneously became
fashionable to move away from looking at any illustrations based on numbers
just as all these new ways of looking at numbers were being invented.

9.2 Spaces, times and places

It is by positioning our geography between space and time, and by
seeing ourselves as active participants in the historical geography of
space and time, that we can, I believe, recover some clear sense of
purpose for ourselves, define an arena of serious intellectual debate
and inquiry and thereby make major contributions, intellectually and
politically, in a deeply troubled world.

(Harvey, 1990, p. 433)

2 We are well equipped for visualization, but still often find it difficult: 'It is estimated that fifty
percent of the brain's neurons are involved in vision. 3D displays light up more neurons and thus
involve a larger portion of our brains in solving a problem' (van Dreil, 1989, p. 2).
3 Animation is almost always required to gauge depth correctly: 'Although it is not obvious why
it should be, small, rapidly repeated, changes in the viewing transformation are seen as continuous
motion of a rigid object - the point cloud. We automatically see the three-dimensional shape of the
point cloud, using the unconscious human ability to perceive shape from motion' (McDonald, 1988,
p.184, quoting from Marr, 1982).