Inter Twingled

"Intertwingularity is not generally acknowledged, people keep pretending they can make things deeply hierarchical, categorizable and sequential when they can't. Everything is deeply intertwingled." -- TedNelson

For many (most?), hierarchy is convenient device for finding Internet/ information resources of interest. The information deluge of the modern age is overwhelming. Note the emphasis on rank in search results. Note the economic and cultural success of corporations and capitalism. Conceded that intertwingularity is a property of the universe. But humans can't enjoy drinking from a fire hose. Hierarchy helps us cope. (Not that I'm singing the virtues of capitalism or corporations). -- DaveChristenson
GoogleSearch PageRank does not stem from hierarchy. Page rank is based on the links pointing to each page. Thus it's an epiphenomenon of intertwingularity, not a refutation of it. Hierarchical directories have not proven nearly as useful as page rank.
You may find it illuminating to consider the relationship between graphs and spanning trees.

And unrooted forests.
The phrase "InterTwingled" has never really caught on except with fans of TedNelson, but the general concept has been noted before, for instance, sometimes that's what people mean when they refer to an "organic" design. It's also related to AllModelsAreWrongSomeModelsAreUseful.

Knowledge taxonomies (usually mistermed "ontologies" these days) have become very popular recently, so there are lots of enthusiasts who don't seem to realize that the subject has a very long and deep history. The original Roget's thesaurus, the Dewey Decimal system, etc. As is by now extremely well known in Library Science, no single hierarchical organization can be ideal, although they can be workable -- as is the modern version of Dewey and of the Library of Congress classification system. But to make them work requires a rather high degree of training and experience, more than can really be appreciated without studying those systems in some detail (i.e. I have and was amazed).

On the other hand, having many many trees, each rooted differently (not single rooted) and with difference branching rules, and with massive cross-referencing and indexing -- that works out much more nicely with much less effort and need for specialized training.

Note the non-coincidental resemblence between "cross-reference" and hyperlinks; as coiner of the term "hyperlink", TedNelson really gets into the "InterTwingled" nature of things.
See also CategorizationModels, LimitsOfHierarchies, GraphTheory

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