Containment relations themselves can be expressed not only as configurations of containers, but also as Maps, Networks and symbolic equations.
Most string languages can also be expressed as spatial networks. A difference, though, is that a James icon embodies its operational semantics. In effect there is no distinction between Form and Intent.
The container boundary is the only diagrammatic component we will need. It visually and computationally preserves the dependency of containment, which itself can be interpreted as nesting, sequence, stacking, connectivity and several other types of physical relationship between container and contained, as illustrated in Figures 6-4 and 6-5.
Containers provide a built-in visualization of dependency, appealing for both form and interpretation to our hands and our eyes, rather than to our ears and vocal cords.
Figure 6-4 shows the James form of multiplication expressed as one-, two-, and three-dimensional containers.
The string dialect is digital and encodable. The language consists of delimiters in fractured bracketing relationships with one another.
The bounded dialect shows two-dimensional containment. The language consists of enclosures in nesting relationships with one another.
The block dialect is manipulable. The language consists of physical objects in stacking relationships with one another.
Figure 6-5 shows James multiplication in some other spatial dialects of containment, including two-dimensional maps and paths, three-dimensional physical rooms and dimension-free networks.
The Network Dialect is a traversable acyclic graph. The language consists of nodes and links.
The Map Dialect is a traversable territory. The language consists of areas with shared borders.
The Path Dialect shows border crossings that define the boundary form. The language consists of a single instance of each type of boundary, together with a directed path crossing the boundary archetypes.
The Room Dialect is a three dimensional environment inhabited by a participant. The language consists of rooms and doors.
For examples of James arithmetic in each of these notations, delete the variables A and B in Figure 6-4 and Figure 6-5.
~
Bricken, Iconic Arithmetic Volume I, p. 145–146.
Bricken, Iconic Arithmetic Volume I. Ch. 13, p. 305 ff.