Varieties

There are three major classes of structure that distinguish boundary forms.

String varieties enlist encoded characters or sequences of characters, while embedding structure in their ordering.

Geometric varieties enlist different metric structures that share relationships across their measures. Changing a metric is analogous to changing a symbol in a string language.

Relational varieties enlist different spatial structures that embody different tangles of relations. Geometric varieties are topological forms with rubber-sheet geometries, while relational varieties are not limited by the rubber-sheet. The appearance taken by the relational varieties can be generated by extruding and rotating into a higher dimensional space, by converting links to borders, by exchanging objects for processes and by structure sharing. Some varieties of form highlight the neutral background space to delineate structure. For example, the space between typographical words is used to identify grouping but is not taken as a grouping operator.

Figure 13-1: Roadmap for generating spatial dialects pdf

A dominant characteristic of boundary forms is the Point-Of-View [⇒ Viewpoint] of the reader/participant. Forms can be read from the Outside, objectively, or from the inside, subjectively. Subjective reading includes participation within the form itself.

Linear form, in contrast, lacks an inside, forcing the perspective that the reader is outside, in some higher dimension. In its desire to remove human bias, mathematics has embraced the outside, objective Viewpoint, creating a Notation [⇒ Digital Scientific Notations] that lacks both participation and dynamics.

A refinement that appears to have been overlooked is that objectivity, seeing things as objects, viewing reality from the outside, does not achieve neutrality. Objectivity limits our Perspective so severely that we believe we are not only super-human but that we have access to locations outside of our universe!

Objectivity makes us the outermost boundary.

⇒ Block Varieties

⇒ Path Varieties ⇒ Browsing Diagrams ⇒ Diagrams as Base Model ⇒ Room Dialect ⇒ The Passenger

⇒ Map Varieties ⇒ Walls Become Doors

⇒ Centered Map Varieties ⇒ Syntactic Variety in Boundary Logic

⇒ Shared Space Lane