Many systems are organized hierarchically. The CERNDOC documentation system is an example, as is the Unix file system, and the VMS/HELP system. A tree has the practical advantage of giving every node a unique name. However, it does not allow the system to model the real world. For example, in a hierarchical HELP system such as VMS/HELP, one often gets to a lead on a tree such as:
HELP COMPILER SOURCE_FORMAT PRAGMAS DEFAULTS
only to find a reference to another leaf: Please see
HELP COMPILER COMMAND OPTIONS DEFAULTS PRAGMAS
and it is necessary to leave the system and re-enter it. What was needed was a link from one node to another, because in this case the information was not naturally organized into a tree.
This, I think, is the brilliance of Notion, and what makes it one of the best examples of “fidelity to digital information” that I’ve come across. The structure of the app reflects the structure of the web itself: digital content is purposefully formatted, like semantic HTML elements, and exists in a hierarchical structure (directories on the web, nested pages in Notion), yet can be linked and referenced to create a complex network of information. And pages in Notion reveal the structure of the information: when nesting a page within a page, the child page always displays on the parent page. There’s no way to create a child page that doesn’t display on a parent page, no way to obscure the structure of the information. The semantic structure of Notion reflects the semantic structure of the web itself.
Truchet's approach was more topological than geometric, and the qualitative aspects of pattern take priority over the metric ones. His principles provide a kind of metaphor for the hierarchy of separation and connection in all things.
But the coppersmiths themselves, in their desire to do better or otherwise than their predecessors, soon quit the line of truth and propriety. There comes then a second coppersmith, who proposes to modify the form of the primitive vase in order to seduce the purchaser with the attraction of novelty...and it becomes fashionable, and everybody in town must have one of the vases made by the second coppersmith. A third, seeing the success of this expedient, goes still further, and makes a third vase, with rounder outlines, for anybody who will buy it. Having quite lost sight of the principle, he becomes capricious and fanciful...yet everyone applauds the new vase, and the third coppersmith is regarded as having singularly perfected his art, while in fact he has only robbed the original work of all its style, and produced an object which is really ugly and comparatively inconvenient.