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.
There is a story of Rikyu which well illustrates the ideas of cleanliness entertained by the tea masters. Rikyu was watching his son Shoan as he swept and watered the garden path. "Not clean enough," said Rikyu, when Shoan had finished his task, and bade him try again. After a weary hour the son turned to Rikyu: "Father, there is nothing more to be done. The steps have been washed for the third time, the stone lanterns and the trees are well sprinkled with water, moss and lichens are shining with a fresh verdure; not a twig, not a leaf have I left on the ground"
"Young fool," chided the tea master, "that is not the way a garden path should be swept. "Saying this, Rikyu stepped into the garden, shook a tree and scattered over the garden gold and crimson leaves, scraps of the brocade of autumn! What Rikvu demanded was not cleanliness alone, but the beautiful and the natural also.