Wiki is definitely not a tree.
It is helpful to organize wiki, but it should not be categorized simply or hastily.

* ''Course it's a tree. It's a 2-deep tree whose root node has 30,000 children, all of them leaves. (Of course, other wikis like TheReformSociety did try to be deeper trees, and look what happened.) (''Yes, this is exactly why Pete halted TheReformSociety; he realized his PatternForm made a lattice but then couldn't find and didn't have time to make a good LatticeWiki.'')''

* If it's a tree, explain categories. The moment we add backlinks and cross-linkage wiki becomes, at least in terms of navigability, a graph. What's interesting about Alexander's suggestion is his idea that real human interaction is not a generalized graph, but a lattice, or at least a semi-lattice. Anyone know why he picked the more specialized form?

Instead of insisting on a single ultimate, definitive way to categorize wiki, it is better to allow multiple overlapping categorizations. People can use whatever categorization scheme they find convenient at the moment. (Some of the most popular are StartingPoints, CategoryCategory, RoadMaps, WikiSpringCleaning)
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The Addition of a Category Tag does not a method make. It is simply a notation which takes advantage of an existing artifact which allows the lookup of BackLinks. This does not make a tree, it makes a list. If you want a tree, you will have to use external artifacts. The simple addition of a Category to a page is to provide a N''''''avigationalConvenience. 

You do not automatically take advantage of this convenience by viewing a page, you do so by first clicking the Category Tag, and secondly clicking on the title of the Category page. If you do not want to take advantage of Categories, simply ignore them. There are some who do like the convenience and find it to be a useful way to navigate the wiki.  -- DonaldNoyes 20080107
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PleasePleaseDoCategorizeEveryPageOnWiki and PleasePleaseDontCategorizeEveryPageOnWiki are opposing arguments that can both draw strength from WikiIsNotaTree.

See also: SystemsThinking

Inspired by: "A city is not a tree" www.rudi.net/bookshelf/classics/city/alexander/alexander1.shtml ( BrokenLink EditHint fix if possible, or else delete if impossible - is there a WikiPage discussing this article ?)

Note: The term tree is referring to the mathematical tree, which contains no cycles.

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It maybe would not hurt to attempt a tree-based reference. It may be a UsefulLie for some people.

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See
WikiCategories
LimitsOfHierarchies
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CategoryWiki CategoryWikiIsNot