Pictorial representations are characterized by a high potential for abstraction, which is evident in the different scales of building drawings: a wall at a scale like 1:20 is depicted by a large number of lines indicating various layers and materials; at 1:100 the wall may be reduced to just two parallel
lines; at 1:500 it may even become a single, relatively thick line. Similarly, a door in a floor plan at 1:20 is quite detailed (Figure 6), at 1:100 it is abstracted into a depiction that primarily indicates the door type (Figure 7) and at 1:500 it becomes just a hole in a wall (Figure 8). At all three scales both the wall and the door are clearly recognizable, albeit at different scales of specificity and detail.
Such abstraction is largely visual: it mimics the perception of a drawing (or, for that matter, of any object) from various distances. It also corresponds to the design priorities in different stages.
In early, conceptual design, one tends to focus on general issues, zooming out of the drawing to study larger parts, while deferring details to later stages. Therefore, the precise type, function and construction of a door may be relatively insignificant, making abstraction at the scale of 1:500 suitable. However, that abstraction level is inappropriate for the final technical design, when one has to specify not just the function and construction of a door but also its interfacing with the wall.
To do so, one has to zoom in and use a scale like 1:20 to view and settle all details.
Figure 6. Wall and door at 1:20
Figure 7. Wall and door at 1:100
Figure 8. Wall and door at 1:500
In addition to visual abstraction, one may also reduce common or pertinent configurations, however complex, into a single, named entity, e.g. an Ionic or Corinthian column, a colonnade (Figure 2) or “third floor” and “north wing”. Such mnemonic or conceptual abstraction is constrained by visual recognition, as outlined above, but also relies on cultural convention: it is
clearly not insignificant that we have a term for a colonnade. As a result, mnemonic abstraction plays a more important role in symbolic representation than purely visual abstraction.
Pictorial representations are also relatively immune to incompleteness: a hastily drawn line on paper, with bits missing, is still perceived as a line (Figure 9). A house partially occluded by an obstacle is similarly perceived as a single, complete and coherent entity (Figure 10).
Figure 9. An imperfectly drawn line may still be perceived as a line
Figure 10. A house partially occluded by another object is still perceived as a single house
Dealing with incomplete descriptions is generally possible because not all parts are critical for understanding their meaning, even if they are not redundant. In English, for example, keeping only the consonants in a text may suffice for recognizing most words:
TH QCK BRWN FX JMPS VR TH LZY DG
(THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG)
This practice, currently known as disenvoweling, is widely applied in digital short messages. In the past, it was used to similar effect by telegraph operators, note takers and others who wanted to economize on message length and the time and effort required for writing or transmitting a message. Identifying the missing vowels is often a matter of context: ‘DG’ in a farmyard setting probably means ‘DOG’ but in an archaeological one it may stand for ‘DIG’. If a word contains many vowels, it may be hard even then: ‘JMPS’ is highly probably ‘JUMPS’ in most contexts but ‘DT’ as a shorthand of ‘IDIOT’ may be far from effective in any context.
Likewise in images, some parts are more critical than others for recognition. A basic example is dashed lines: even with half of the line missing, the human visual system invariably recognizes the complete lines and the shapes they form (Figure 11).
Figure 11. A square drawn with dashed lines
Interestingly, a shape drawn with dashed lines is more easily recognized if the line junctions are present. This relates to a general tendency of the human visual system to rely on points of maximum curvature in the outline of shapes.2 Corners, in particular, are quite important: the presence of corners often suffices for the perception of illusory figures (Figure 12). The form of a corner gives perceivers quite specific expectations concerning the position and form of other corners connected to it, even if the geometry is curvilinear (Figure 13). The presence of compatible corners in the image leads to perception of an illusory figure occluding other forms. Perception of the illusory figure weakens if occlusion occurs at non-critical parts of the figure, such as the middle of its sides (Figure 14).
Figure 12. An illusory square
Figure 13. A curvilinear illusory figure
Figure 14. Missing corners make perception of illusory figures uncertain or vague; in this case, it is uncertain if the illusory square has rounded-off or bevelled corners
The importance of corners underlay one of the early successes in artificial intelligence. Based on a typology of edge junctions (Figure 15), expectations about the connectivity of these types and the orientation of resulting surfaces, computers were able to recognize the composition of scenes with trihedral geometric forms: faces, volumes and their relative positions (Figure 16).3
Figure 15. The four basic edge junction types in trihedral scenes
Figure 16. Recognition of objects in a trihedral scene can be based on the types of edge junctions in Figure 15 and their connectivity
The above examples illustrate how analogue representations can be parsimonious and simultaneously effective but only if complemented with quite advanced and expensive recognition capacities. Empowering computers with such capacities is an emerging future but for the moment at least symbolic representations that contain explicit information are clearly preferable.