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Dorling, D. (1991) The Visualization of Spatial Structure, PhD Thesis, Department of Geography, University of Newcastle upon Tyne

Chapter 8: The Wood and the Trees

The world is complex, dynamic, multidimensional; the paper is static, flat. How are we to represent the rich visual world of experience and measurement on mere flatland?
[Tufte E.R. 1990 p.9]

8.1 Sculptured Characters

So far in this dissertation we have only considered the simultaneous visual representations of a handful of variables — three or four at once, at most. We are often presented with situations in which far more aspects are available, from the census for instance. What is more, we know that there are strong but subtle relationships lying among all these numbers. One aim of visualization is to take understanding beyond simple numerical relationships — the idea that when one variable goes up another always goes down. The ideal situation in which to do this is multivariate analysis, where the connections are known to be complex and are usually hardly understood. How can visualization illuminate the situation?

The position of an object in the visual plane exhausts our first and most valuable two dimensions. The colour of an object can capture three variables. After employing position and colour we are left with control over the size, shape and orientation of the objects which represent our cases or places107. An almost infinite number of subtle alterations could be made to these aspects of the visual representation. It is not the number of variables which can be crammed into its features, but the number of variables which can be visually appreciated and interpreted in its context (Figure 23), that limits and forms our multivariate visualization methods (Evans I.S. 1983b, La Breque M. 1989).

These visual objects are often referred to as glyphs, meaning sculptured characters or symbols. In this chapter I begin with the simplest and move through to some of the more complex, though not less successful, representations. We learn what it is that makes glyphs work as visual representations, and how, when and why they fail108.

8.2 Circles, Pies and Rings

The basic shape I have used up to now for spatial objects, when they were large enough to have shape, has been the simplest — the circle (or hexagon). This has been because I did not want the shape to distract attention from the overall impression of the image. Rotation has no effect on the circle, but it can reflect one variable through its size. This has been used most effectively in this work to represent the total population of a place. Circles have also been used here to show the discrete states at two points in time across many places (Prints CXXXVIII & CXXXIX). Could the circle be subdivided to show the relative sizes of different sections of that population?

Pie charts may well be the first possibility to spring to mind. These appear ideal; a dozen sub-groups could be shown simultaneously. The circle could be cut into male and female slices, these then each divided into the proportions working and not working, further subdivided into full-time and part-time workers and so on. There are, however, many problems associated with this. We are not particularly good at comparing angles, especially when they are presented to us at differing orientations, or at gauging the slight differences in the area of the slices. Worse still, when we are presented with more than a couple of these symbols, we quickly become visually perplexed. We see a multitude of individually complicated parts, which we cannot comprehend as a whole.

The basic requirements of glyphs is that not only should they each form an acceptable single entity individually, but that when viewed together, they should melt into a gestalt collection so that overall patterns in the multivariate information can be discerned109. A group of leaves can combine into differently shaped trees, and groups of trees create different looking woods. We must be able to see the woods, not just the trees, from the pictures of the leaves.

This explains why many initially promising ideas often fail in practice. One method envisaged for depicting the changing spatial distribution of unemployment was to draw a series of rings inside the circle representing each place110. There would be one ring for each of twelve years, like the old bark of a tree trunk, and the rings would be coloured increasingly darker, the more people there were out of work. It did not work (Print CXL). The image that appeared held little meaning, even when only a few dozen circles were employed. This was because it was not possible to compare across space any more, as it had been cut up by circles of time. Each circle was an accurate individual record of unemployment in that place, but the places could not be seen as a group.

One of the most popular forms of glyph in the current use is the polygon, or its inverse structure, the weather vane. This is formed by representing each case as a point and projecting spokes from it at regular intervals, their lengths in proportion to the value of each variable being shown. If the tops of the spokes are connected an irregular polygon is drawn, containing aspects of size, shape and orientation.

This symbol works well when the direction in which the spokes point has some meaning, for instance when showing wind speed in certain directions, or the numbers going that way to work. The polygon can produce ambiguous images, however, as two different sets of numbers create the same object. As the number of variables increases, the glyph quickly becomes a formless blob. Perhaps the basic problem with all of these methods is that they are not producing naturally comprehensible images. What is needed are collections of objects we are used to seeing as a group, and already have the skill of assessing as a group.

8.3 Bars and Pyramids

If we were trying to show the multivariate information about a single place in isolation, we would probably not draw circles, we would use charts (Prints CXLI & CXLII).

The simplest chart is made up of bars, one bar for each variable, its height in proportion to the value of that variable. Thus we could show, for instance, the numbers of people employed in eight types of industry simultaneously. If we divided the bars we could also try to show the proportions of male and female, full and part time111. We would obviously be limited in the number of places that could be compared, as the number of aspects we chose to include increased. One basic problem with glyphs is that to have shape requires size. There may well even be a predictable maximum amount of information than can fit on a piece of paper. Thus the number of places shown declines in line with the number of variables added.

The problem with the bar chart is that the order in which variables are placed along the bar greatly influences the visual impression given, and the order is arbitrary. If the order of the industries, say, were made the same as their national ranking, then charts where a gradual rise was broken would show areas where the industrial mix was at odds with what would be naively expected (Frost M.E. & Spence N.A. 1981, Begg I. & Moore B. 1987).

The bar chart is taken to one more level of detail when population pyramids are constructed. These are simply two charts placed back to back and standing vertically, usually used to depict the detailed age/sex structure of an area. What is most important about these symbols (as with glyphs) is that they create a recognisable shape. It is the outline of the pyramid that is important, and this is often simple enough to compare places across space, particularly if differences are exaggerated. Finally the pyramid can be reflected again, horizontally, to show four related distributions as a cross (Figure 24), which has been done for some of the illustrations shown here (Prints CXLIII & CXLIV).

However, the fundamental difficulty remains. Bar charts, graphs and pyramids were originally designed to stand alone, and thus contain enough complexity and detail as single entities. Glyphs, to be used in a spatial context, must generalize and simplify the information if the overall patterns are to be understood, particularly if more than a few dozen areas are to be compared112. As the number of areas grows bigger so to do the differences. The industrial structure becomes less predictable and the population structure more varied. Unfortunately our symbols get smaller and comparison becomes more difficult. We must design simple glyphs which do not require a lot of space, and which the eye can quickly comprehend, without excessive examination.

8.4 Flocks of Arrows

A glyph which can satisfy the above criteria is the arrow. This is the simplest sign expressing mainly orientation, although size and shape can also be incorporated. Its simplicity allows trajectories at many hundreds of places to be shown. Most importantly at this level, the aggregate begins to express a form of its own — the sum of its parts, and what imagination and intuition adds to that. Like a flock of birds in flight, a group of arrows pointing in a similar direction appears to be going that way; they become a visual group. This is exactly the impression I am trying to create, and it is through an analogy with a natural image that I am able to do this.

Arrows have been used in many ways in this dissertation. The direction of the arrow can represent the levels of two variables as a vector. Here they have been used to show the three-party swing in constituencies between general elections113. The arrow can point in the direction that a dot representing the constituency would move on the electoral triangle. The length of the arrow can be used to show another variable — the size of the swing. The size of the arrow is in proportion to the electorate, and its colour shows the proportions of the vote going to the three major parties (Print CXLV). The position of the arrow is dictated by the constituency cartogram, which could be animated to show changes over time (Prescott J.R.V. 1959, Miller W.L. 1977, 1990, Johnston R.J. 1981, Crewe I. 1988, Johnston R.J. & Pattie C.J. 1988b, Cochrane A. & Anderson J. (eds) 1989, Galbraith J.W. & Rae N.C. 1989).

In one sense, nine dimensions were being seen in this relatively simple picture — two for position, two for direction, three for colour and one for each of length and size; but that would be a gross exaggeration. The position of the constituency is shown by two dimensions, while the image is representing seven very closely knit variables. It is the strength of the relationships between the variables that allows so much to be depicted. Ten elections worth of results are shown on an A4 page containing over six thousand visible arrows (Print CXLVI).

The arrows worked well in this example because direction was meaningful, and the two variables which made up direction were really one, just as the latitude of a place means little without knowing its longitude. They also worked well because the spatial relationships in voting were strong enough for discernible patterns to exist. If I had wished to look at the effect of changing employment, migration, housing and industrial influences upon the elections visually, these simple arrows would not have been so useful.

8.5 Trees and Castles

More complex glyphs than arrows have been specifically designed to allow quick comparison of the overall pattern of multivariate information. The most accepted of these usually take the form of trees or castles, where various aspects of a basic shape are altered to produce many variations of an underlying structure which aids their comparison. It is the maintenance of this basic structure which easily assimilates into a picture, that distinguishes these glyphs from the polygons, bars and pyramids described earlier. They have specifically been designed as glyphs.

Castles have various parapets, which alter in height and aspect as the values of the variables change. In many ways they are simply an embellishment of the bar chart, altered so as to allow the mind to form an impression of the general shape of the place more easily, using a more familiar symbol. Bar charts can only go up, or down, have a peak here or there, but they are still charts. Castles appear more as single objects, and so it is hoped that an overall image can be obtained. A more familiar alternative of houses could be employed, where the shape of the roof, size of the windows and so on would be altered to show information. So a town of houses would be created, allowing particular suburbs, estates, and streets to be identified. This method might be especially appropriate if it were aspects of housing amenity at different places in which we were interested. House prices for broad categories of housing have been shown in this work using the branches of trees to show the shape as well as local buoyancy of the owner occupied market114 (see Appendix D).

Just as castles grew out of bar charts, trees have grown out of weather vanes. Rather than order the spokes as a wheel, they become the branches of a tree. This works because we are used to seeing trees which vary in their shape but have a rough symmetry about them, whereas all wheels are round. The order in which the variables are assigned to the trunk, branches and twigs is crucial for the impression gained. What is usually done is to place the most important variable at the base, and so on. Whether this works or not depends on the information being depicted. A relatively convincing wood can be created. Again, thickets, copses and spinneys of different species can be identified. Overall tendencies for trees to have a certain combinations of features in certain parts of the picture, and for other combinations never to occur can also be noticed (Print CXLVII).

The idea of using the two-dimensional position of the glyphs to show information has often been mentioned, but, because of technical problems, in particular inability to create cartograms, is rarely used. Glyphs really come into use when the order in which they are drawn on the page has meaning, as well as the order of variables within their own structure115. At this point it really becomes possible to see the wood through the trees through the leaves. Here I show the housing situation in Britain (Prints CXLVIII & CXLIX), through individual areas’ markets and the changing prices of different types of houses therein (Storrie M.C. 1968, Kleiner B. & Hartigan J.A. 1981, Hamnett C. & Randolph B. 1983, Champion A.G. & Brunsdon C. 1988, Brunsdon C., Coombes M., Munro M. & Symon P. 1991).

8.6 Crowds of Faces

The most contentious glyphs created to date are based on human faces, drawn by Herman Chernoff. Faces, it is argued, are the visual image we are best equipped and experienced to decipher. We naturally combine their features to interpret moods — such as happy or sad, sly or stupid. What is more, we can easily compare faces to look for family resemblances or the mood of the crowd116. Faces maintain a basic structure in which even slight variation often holds meaning.

The original Chernoff faces aimed to show the values of as many as eighteen variables simultaneously (Jacob R.J.K., Egeth H.E. & Bevin W. 1976, Chernoff H. 1973, 1978, Chernoff H. & Rizvi M.H. 1975, Wang P.C.C. (ed.) 1978, Webber R. & Craig J. 1978, Flury B. & Riedwyl H. 1981, Rahu M. 1989). Here I am being somewhat less ambitious (Figure 25, Print CL). Chernoff faces have been used to study general election voting patterns in Britain in relation to just five variables — the electorate (head size), house price (thin face for low, fat for high), employment (smile), election turnout (nose size) and industrial structure (large low eyes for younger industries). The colour of the face can then represent the actual voting patterns, when the faces are arranged as a group on the constituency cartogram (Print CLI).

This is intended to be a tongue-in-cheek extension of Chernoff faces to the level of crowds. Nevertheless the inner-city/outer-city and north/south divides in many aspects, as well as voting, can clearly be seen (Print CLII). The difficulty of drawing precise lines between the regions and around cities is clear. What is more, specific outliers can be identified, which do not fit in (just as before with arrows that did not go with the flow). Variables which appear to be unrelated to the rest of the picture can be identified. Complex three or four way interactions, where certain levels of some variables apparently combine to produce a particular effect, can also be identified.

The use of the population cartogram developed here, as the spatial base for these faces, has particular advantages. None of the faces overlap to obscure each other, and they are all, by their size, in proportion to their importance based on the numbers of people they represent. It may well be that glyphs have not been used in spatial images before, because of the very problems of spatial congestion, which the creation of cartograms overcomes. It would be difficult, for instance, to use them in place of the circles which overlap and cluster on the electoral triangle, although that may produce an interesting picture to compare with the crowd on the cartogram.

Strong local relations in space are perhaps the clearest message formed by the images. Sharp divisions are also immediately apparent, as are more gradual changes. The faces can also be used to show that the changes over time in the variables might be contributory to the changes over time in voting117. Thus the expressions become places’ reactions to a changing situation, their colours perhaps indicating some of the electoral results of those changes (Print CLIII).

Chernoff faces are contentious for the very reasons they are seen as so useful. People’s reactions to faces are much stronger than to more neutral objects, which are claimed to depict the information more objectively. We have moved along a continuum, from personal likes and dislikes of certain colours in maps, to individuals’ reactions to cartoon faces. Visualization, at a higher level, is all about engaging our imaginations and emotions.

8.7 Information Overload

A serious criticism of the use of glyphs is that they can overload the viewer with information. Too much is being asked of the eyes and the mind118. In this chapter I have shown that badly designed symbols are impossible to decipher spatially. I have also shown that well thought out images can help the viewer form higher level structures out of the simple pictures of collections of places. A most efficient way to achieve this is to use arrows, but these require direction to have some meaning, and can show only a few other related features.

The creation of crowds of faces is certainly the most ambitious use of symbols. This may well be the first time they have been used in this way — pictures of people’s faces on paper, to show information about people in places. Whether these glyphs work spectacularly or not at all, one thing is for certain: they get people’s attention and make them think. The use of symbols which bear some relation to the subject being studied is an asset. How better to show differences in the sizes and quality of houses than by a collage of images of those houses? How better to show factory closure and growth than with pictures of industries being born and dying?

It is a mistake to think that these symbols can add another dimension to the two we have on paper. Glyphs show multivariate structure, not multi-dimensional form. We can look at a lot of categorical aspects of many places in space simultaneously. We cannot see how some feature varies with, say, place and varying wealth, multi-party voting, or disease in spacetime. Varying the features of an object is not a good substitute for varying its position. Features of an object have no geometry and thus a limited ability to take only a few values. To get a real extra dimension, beyond the first two, we must begin to think in terms of volume, and the final chapter of this dissertation.


CXXXVIII The changing distribution of first place party in Britain, 1983-1987 (Colour).
CXXXIX The changing distribution of first place party in Britain, 1955-1987 (Colour).
CXL The space/time trend of unemployment in Britain, 1978-1990.
CXLI The detailed national composition of industry in Britain, 1981
CXLII The changing national composition of industry in Britain, 1984-1987.
CXLIII The distribution of employment by industry, status and gender, 1987.
CXLIV The change in employment by industry, status and gender, 1984-1987.
CXLV The changing distribution of voting composition in Britain, 1983-87 (Colour).
CXLVI The changing distribution of voting composition in Britain, 1955-87 (Colour).
CXLVII The distribution of housing by price, attributes and sales, 1987.
CXLVIII The distribution of housing by price, attributes and sales, 1987 (Colour).
CXLIX The changing distribution of housing by price, attributes and sales, 1983/1987 (Colour).
CL Chemoff faces showing all permutations of five levels of four features.
CLI The distribution of voting, housing, employment and industry in 1983 (Colour).
CLII The distribution of voting, housing, employment and industry in 1987 (Colour).
CLIII The change in voting, housing, employment & industry, 1983-1987 (Colour).


Statistics have often had to be reallocated among areal units in this dissertation. Where the destination level was a super-set of the source level this was a simple amalgamation, but where the boundaries of the two did not coincide the problem was somewhat more difficult:

The formulae used to estimate the value of a statistic (v) from one set of units (i) to another (j) relies upon there being available a second variable (p) known to be related to the prevalence of the first variable. The value of the second variable must be known for every areal unit created from the intersection of the two sets of boundaries (pij). The formulae is then, put simply:

Figure 23: Areal Interpolation

Two unusual glyphs were designed specifically for this dissertation. While appearing very different they share a number of common traits.

The reflected pyramid is a collection of bar charts showing four closely related distributions. Here, they are of eight industries sub-divided by the proportions of male and female, full-time and part-time workers in each place. The area of the symbol is proportional to the number of employees. The height of the bars gives the share of workers in each industry, the width shows how they are spread among the different categories of employment.

A similar use of height and width is used with the trees showing house price structure. Here lengths are average price and width is number of sales in each sector, giving total revenue as area. Now, however, the combined statistics of sub-markets are shown in branches lower down the tree, the trunk giving the total sales, average price and revenue for the whole market. The angle at which the branches divide has not been used here, but could be employed to present yet more information.

Figure 24: Trees and Pyramids

The face glyphs used in this dissertation are a modern, and somewhat less ambitious development of those originally created by Chernoff (1973). Here, only five variables are shown, and the faces are made to look somewhat more life-like through the use of curves, rather than lines, to describe them. The faces are each described by a single path made up of eleven Bezier curves, each consisting of two control points and an absolute point (which the curve must lie on). Three curves are used to describe the shape of the face, and two each for the eyes, nose and mouth. Their positions are shown, shaded in grey, behind the faces opposite.
The minimum, maximum and average extent of each curve is shown. The absolute points remain fixed, ensuring the general character of the shape does not alter too much, and that features will not overlap. The faces used here are symmetrical, as that produced the most pleasing results. After shape, eye size, nose size and smile, the overall size of the face allows up to five variables to be presented at once, in a novel manner.

Figure 25: Constructing Face Glyphs


107 [a] Position and colour are the most effective visual tools:
One way to see high dimensional structures is to try to invent pictures that show as many dimensions at a time as possible.
One of the simplest ways to add dimensions to a picture is through color. We start with a three-dimensional scatter plot. We can add a fourth variable to the picture by giving each point in the scatter plot a color that depends on the value of a fourth variable. With an appropriately chosen color spectrum, we can easily see simple or gross dependence of the fourth variable on position in the three-dimensional space. Our ability to perceive distinctions in color does not compare to our ability to perceive position in space; we should expect to miss subtle or complicated relationships between a color variable and three position variables. Color works best for a variable that takes on only a small number of discrete values. [Friedman J.H., McDonald J.A. & Stuetzle W. 1988 p.126]

[b] Researchers have often found great difficulty in trying to visualize beyond two dimensions:

Eventually EXPLOR4 will be pushed into representing five interval or ratio variables. Ray length is suitable for showing one more dimension so a viable 5-D symbol is available. We have little hope of finding a viable symbol for 6-D data. We have looked at 6-D plots of PDE solution set velocity vectors. The base of each vector was located in 3-D space. The relative coordinates of the tip of each 3-D vector represented three additional variables. This stereo ray did not work well because the depth angle is poorly represented by small stereo separation differences and the angle complicates interpretation of ray length. For the near term the task of interpreting 4-D graphics provides sufficient challenge. [Carr D.B. & Nicholson W.L. 1988 p.328]

[c] Some say we can only comprehend four variables simultaneously, some say five:
At best we may be able to achieve perhaps five dimensions of display using a two-dimensional display plus color. Perhaps stereo displays might achieve six dimensions and animation (time) could in some applications present a seventh dimension. How can we display data values representing points in a ten-dimensional data space? What kinds of display techniques demonstrate patterns in such a way that a scientist can perceive those patterns? [Bergeron R.D. and Grinstein G.G. 1989 p.393]

[d] Others claim as many as nine or more variables can be understood:
Ellison’s solution: an artist’s “sleight of hand”. Donna Cox created an innovative technique that clearly displayed a record nine distinct variables simultaneously changing in an animated videotape. To pack variables to such a density, Cox invented a unique 3-D wedge shape, the glyph (from hieroglyphics, the Egyptian pictographs), to represent each computed portion of the flowing plastic. The shape, color (the blue side of the spectrum for pressure and the red for temperature), and orientation of the wedge indicate the state of the flowing material at particular points. The finished videotape shows the plastic (in the form of an army of small wedges) marching into the mould, swivelling, changing direction and color, and eventually settling and hardening in a series of complex steps. [Anderson G.C. 1989 p.17]
108 [a] Conventional glyphs may not be enough:

Often it is desirable to utilize maps showing age-sex characteristics of tracts, either as a tool to help the planner visualize possibilities or to communicate alternatives to interested groups. Two types of maps are typically utilized to display such information: (1) choropleth maps for individual age-sex groups (eg: males 65 years or older) or (2) multiple population pyramids superimposed upon a base map. The choropleth map suffers by requiring as many maps as age-sex groups, making intergroup comparisons difficult. The use of pyramids permits a single map, but is visually so complex that comprehension of spatial patterns is difficult. [Lycan R. 1980 p.172]

[b] Complex relationships need to be shown through such symbols:
This type of presentation makes it easy to grasp the interacting relationships between age and race. For example, there are tracts in which most of the children are nonwhite but a majority of the elderly are white. [Applied Urbanetics INC 1971 p.4]

[c] Various possibilities were experimented with in early grid square mapping:
Other experiments include shading the centre of a square to indicate the denominator where the size of the square indicates the ratio. [Rhind D. 1975 p.12]

109 [a] Individually well designed glyphs may fail to combine into a single overall image:

The dimensions of the trees and castles also lack perceptual integrality (Garner 1974). They do not provide their observer a single image or concept or gestalt that he or she can process and remember, binding together the values of all the coordinates of the point. For example, polygons and faces tend to provide observers with such a concept, while glyphs and bar charts tend to look simply like the accretion of their several elements. Trees and castles appear to fall in the latter category. [R.J.K. Jacob, in Kleiner B. & Hartigan J.A. 1981 p.271]

[b] Glyphs must be simple to produce a gestalt impression:

Except for extremely simple forms (3), the superimpostion of several images destroys each of them. We must use a more elementary level of reading, which excludes perception of the overall form of each characteristic and activates the memory. [Bertin J. 1981 p.182]

110 [a] The distribution of employment is renowned for its spacetime complexity:

Apart from the difficulties of reconciling information for different areal frameworks, one of the inevitable consequences of adopting a nation-wide perspective is the need to rely on statistically aggregated information. Nowhere is the limitation of this approach clearer than in the study of employment change, where net changes need to be decomposed into their various components — the birth, death, migration, expansion or contraction of manufacturing or service establishments. [Goddard J.B. & Champion A.G. 1983 p.xvii]

[b] There are many well researched interconnected relationships operating through the employment characteristics of an area:

In this broad context, some of the stability of unemployment characteristics becomes more easy to understand. The dominant trend of increasing female participation in the labour force is one that is likely to find only a weak reflection in unemployment statistics as a result of the generally low level of female registration for benefit. [Frost M. & Spence N. 1981 p.70]
111 [a] Subdivision by industry, gender and status is essential to understanding employment geography:

A more detailed appreciation of sub-regional employment trends requires a disaggregation into primary, manufacturing and service sectors in order to establish in general terms the industrial nature of the total relative employment changes which have already been discussed. From this analysis two dominant and more or less ubiquitous effects on employment structure can be identified. A consistent relative decline of male employment in primary activities is matched against an equally consistent relative increase in female service employment. Between these two extremes are found the more varied performances of male and female manufacturing together with male service employment. Female primary employment is generally too small to be of much interest. [Spence N.A. & Frost M.E. 1983 p.90]
[b] Migration patterns also strongly influence the relationships:
In the London boroughs the dominance of net out-migration tends to produce different relationships between the components of labour-force change. In boroughs with increasing or stable economically active populations (which are all suburban boroughs), the pattern is generally that net out-migration offsets large increases in female economic activity. [Congdon P. & Champion A. 1989 p.188]
[c] Different places can exhibit very different employment statistics:
Job losses in London over the period since 1966 have been shared more or less proportionately by men and women. This is in sharp contrast to the national trend, which showed an increase in women’s employment (at least until 1979) as against a substantial decline in jobs for men. [Buck N., Gordon I., Young K., Ermish J. & Mills L. 1986 p.73]
112 [a] The supply of information on employment has been particularly poor recently:

Between 1971 and 1978 the Census of Employment was held annually and thus became known as the Annual Census of Employment (ACE). In the early 1970s, processing of the data was carried out clerically (which proved costly) but, by the 1977 and 1978 Censuses, computerised processing was underway. However, this was insufficiently planned and led to the delay of the 1977 and 1978 Census results. As a result of these delays and in an attempt to find economies following the Rayner Report, the 1979 and 1980 Employment Censuses were cancelled (England, 1985). Since 1978, the Census of Employment has been carried out only once every three years, in 1981, 1984 and 1987. [McKee C. 1989 p.9]

[b] Unemployment is indelibly linked to industrial structure:
Thus, the sub-regional results have raised a number of interesting questions. These centre upon the role of industrial structure in determining sensitivity levels, the apparent lack of change in regional sensitivities and the apparent stability of the ‘system of unemployment’ with few overall shifts in relative rates of unemployment between areas. To this list may be added the differences that exist between male and female patterns and, in particular, the poor female performance of the West Midlands. [Frost M.E. & Spence N.A. 1983 p.257]

[c] The role of London is of crucial importance to the developing geography of industrial structure:

For what we must remember above all about service activities are that they are growing; that although they are increasingly dispersed within regions, their growth is increasingly concentrated in areas within about 100 miles of London but excluding London itself; and that in this respect especially, and in the close relationship of their distribution to functional areas, their behaviour is unlike that of manufacturing. [Marquand J. 1983 p.134]

[d] An apparently favourable industrial structure will not necessarily improve levels of unemployment:

The persistent decline in London’s employment over the past twenty-five years or so has occurred despite an industrial structure which has been consistently biased towards activities in which there has been expanding employment nationally. [Buck N., Gordon I., Young K., Ermish J. & Mills L. 1986 p.66]

113 [a] The same electoral swing does not necessarily imply the same political behaviour in different constituencies:

In fact a uniform swing could only come about if a party’s voters behaved differently, not the same, according to the constituency in which they lived: a uniform 5% swing from Labour to Conservative logically requires Labour voters to defect at higher rates in hopeless seats than safe seats.That this tended to happen reflected the ‘partisan neighbourhood’ effect: [Crewe I. 1988 p.5]

[b] The geographical pattern to political swings is not simple:
Using entropy-maximising estimates of the flow-of-the-vote matrix for each constituency in the 1979-83 and 1983-7 inter-electoral periods, this paper explores the extent of that polarization. It indicates clear geographical variations that are more complex than the simple north-south and urban-rural dichotomies often applied. [Johnston R.J. & Pattie C.J. 1988 abstract, p.179]

[c] Localities have become more politically polarized in recent years:

Overall, despite the decline in the class alignment among individuals, social groups within the British electorate have not become more politically homogeneous. Parliamentary constituencies have never been more politically polarized and, in consequence, the number of marginal constituencies held by small majorities has halved since the 1960s (Curtice and Steed, 1988, p.354). [Miller W.L. 1990 p.49]

114 [a] House price differentials show clear regional patterns:

At the end of the 1980s, such a claim would be almost unbelievable. Instead, numerous newspapers and television programmes, politicians and market researchers announce that the country is divided between a poor north and a rich south. The evidence to support — or, more rarely, contest — this finding is provided by government statistics on employment and income, building society figures on house-price trends, investigative reports comparing living conditions in different towns and increasing polarization in the electoral support of the main political parties. A north-south divide is now presented as one of the distinctive characteristics of Britain in the 1980s. It is thought to be a feature that affects the lives of ordinary people, as well as the fortunes of politicians. It raises vital questions about efficiency and equity in the country today. [Lewis J. & Townsend A. 1989 p.xi]

[b] It is interesting that places with extreme (high and low) house prices (Appendix D), also shair the extreme positions in analysing their census data:
There were six clusters with fewer than five districts including two in which single districts are so distinctive that they each form a cluster on their own. These are the City of Glasgow and the London borough of Kensington and Chelsea. [Webber R. & Craig J. 1978 p.13]

115 [a] Early on in the development of glyphs it was realised that position could be used to advantage:

Both the glyphs and the triangles can raise the dimensionality by two by locating the center on a point in two-dimensional space. [Chernoff H. 1973 p.365]

[b] Later, others independently made the same suggestion:
Nevertheless, because we can now plot high-dimensional data on a two-dimensional surface we should not squander the two dimensions of the page. As earlier displays have shown, their use can provide a very evocative image. Thus planting the trees into a Cartesian forest with specified axes may be a useful notion. [H. Wainer in Kleiner B. & Hartigan J.A. 1981 p.275]

[c] The use of faces on a cartogram has been proposed before:

As noted by Johnston engineers prefer line graphs, sales people bar charts, demographers pie charts and medical personnel lists of numbers. Epidemiologists, at least those dealing with cancers seem to appreciate horizontal bars. In cancer statistics and epidemiology the discrepancy between sophisticated statistical methodology and elementary graphical techniques is large. Certainly, elegant technical refinements can be found in cancer mapping, but even here there is exciting potential for maximizing the information content of maps by combining cancer frequency levels with, eg indices of data quality. Moreover, no objections exist to combining cartograms and faces. [Rahu M. 1989 p.765]

116 [a] Research has found that even slight changes in expression are perceived:

This latter finding suggests that extreme caricature like faces are not crucial in obtaining good performance [Jacob R.J.K., Egeth H.E. & Bevin W. 1976 pp.193-193]

[b] Aesthetics are, as always, important:
Undoubtedly, the faces give a more attractive gestalt impression than the other symbols; people like to look at them. [Kleiner B. & Hartigan J.A. 1981 p.261]
117 [a] The dependancy of voting on other measures of change is a widely held, but infrequently substantiated, hypothesis:
As yet, this remains a hypothesis. What it suggests is that the changing electoral geography of Great Britain is linked to the changing economic and social geography because people in the relatively prosperous areas are more likely to vote for the incumbent government than those who live in areas where revival has yet to come (if it ever does). Thus although the 1983 and 1987 campaigns were largely waged at the national scale, via the mass media, substantial proportions of the electorate apparently interpreted the messages not in the national context but in the context of circumstances in their constituency and geographical region. The Conservative party argued that it was producing a new, prosperous, disciplined country, where enterprise flourished. For those whose local circumstances confirmed that message, there was a greater propensity to vote for that party than was the case for those whose local circumstances indicated that if the government was restoring prosperity, it was doing it elsewhere. [Johnston R. & Pattie C.J. 1989 p.104]
[b] Faces can provide an alternative to the use of aggregate indices in studying multivariate spatial change:

The over-riding impression of the changes taking place in local economies since 1981 is clearly of the division between north and south. The map evidence (Figure 3.4) shows how few are the places south of the Severn-Lincolnshire line with a Change Index score below the median, though it also reveals that more buoyant local labour-market conditions extend across this boundary in the English Midlands and into parts of central and north Wales. [Champion T. & Green A. 1989 p.84]

[c] The north/south divide in attitudes and variables such as housing price is clear at certain scales:
However, until Britain moves decisively towards a more-equal society again, its inequalities will continue to express themselves as a north-south divide. [Lewis J. & Townsend A. 1989 p.19]

118 [a] More and more information is being loaded into spatial displays:

The observation was made that maps portraying more than one aspect (variable) of a phenomenon are being published in increasing numbers and that the comprehension and understanding of these maps is likely related to some basic structural characteristics of the maps. [White R.D. 1984 p.45]

[b] Research has produced some rough rules to deal with the problem:

Furthermore, every test has shown that visual reading leads to a heavy loss of information. In order to limit this and obtain maps with efficient messages, the following rules must be acknowledged:
- the first glance of a reader takes in the map as a whole and records the shapes and the figures (Rimbert, 1968);
- groups are unconsciously set up in a hierarchy around which a fuller reading is organized (Salichtchev, 1983);
- as attention span is limited, the reader’s mental efforts should be spared (Rimbert, 1968, Zipf, 1949);
- the perception of separate elements is done mainly through the surface differences: size variations in point symbols are feebly perceived when those variations are small, as was widely demonstrated by Dobson (1983);
- past a certain level, too complex a picture leads to diminution of received information. [Cauvin C., Schneider C. & Cherrier G. 1989 p.97]
[c] We are, however, used to seeing and understanding complex situations:
Under natural conditions, vision has to cope with more than one or two objects at a time. More often than not, the visual field is overcrowded and does not submit to an integrated organization of the whole. In a typical life situation, a person concentrates on some selected areas and items or on some overall features while the structure of the remainder is sketchy and loose. Under such circumstances, shape perception operates partially. [Arnheim R. 1970 p.35]

[d] The more effective the technique — the more information can be shown:

Secondly, the ability of humans to analyze effectively spatial distributions is alleged to deteriorate progressively as the number of variables increases, inter-relationships among variables becomes subtle, and the magnitude of variations decreases. This suggests that cartographic presentation must demand as little mental computation and conceptualization as possible if the full potential of creative intuition and decision making is to be realized. If the cartographer can develop more effective data reduction techniques, and the map reader can be taught to understand their underlying concept (i.e., readily decode them), then the amount of information communicated by a single map might be greatly increased. [Muehrcke P. 1972 pp.19-25]