hierarchy
Excursus: Homage to the Square^3
The problem with trees
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.
The brilliance of notion
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.
Separation and connection in all things
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.
Structure, Substructure, and Superstructure
The monotonous perfection
The mathematical physicist must simplify in order to get a manageable model, and although his concepts are of great beauty, they are austere in the extreme, and the more complicated crystal patterns observed by the metallurgist or geologist, being based on partly imperfect reality, often have a richer aesthetic content. Those who are concerned with structure on a super atomic scale find that there is more significance and interest in the imperfections in crystals than in the monotonous perfection of the crystal lattice itself.
On beauty bare
Even more than Euclid, hath Euler gazed on beauty bare.
In a mass of large bubbles
The froth, therefore, though lacking long-range symmetry, nevertheless has very definite rules as to its composition. It is pleasing in appearance because the eye senses this interplay between regularity and irregularity.
The role of history in structures
Although the ideal crystal lattice of a substance at equilibrium depends only on its composition and temperature, all other aspects of the structure of a given bit of polycrystalline matter depends upon history…the manner in which the crystals impinge to produce the grain boundary as a new element of structure which itself changes shape in accordance with its properties and the particular local geometry resulting from historical accidents. Far more complex, but in principle similar, things occur in biological and social organizations.
A kind of moiré pattern
Everything that we can see, everything that we can understand, is related to structure, and, as the gestalt psychologists have so beautifully shown, perception itself is in patterns, not fragments. All awareness or mental activity seems to involve the comparison of a sense or thought pattern with a preexisting one, a pattern formed in the brain’s physical structure by biological inheritance and the imprint of experience. Could it be that aesthetic enjoyment is the formation of a kind of moiré pattern between a newly sensed experience and the old; between the different parts of a sensed pattern transposed in space and in orientation and with variations in scale and time by the marvelous properties of the brain?
It is what is left over when what is expected has been canceled out.
From a roving viewpoint
There is a kind of indeterminacy, quite different in essence from the famous principle of Heisenberg but just as effective in limiting our knowledge of nature, which lies in the fact that we can neither consciously sense nor think of much at any one moment. Understanding can only come from a roving viewpoint and sequential changes of scale of attention.