RuneNet

The initial object of the blog

Simply consider this page as white noise. This dry pastry of a site needed a random filling.

Many useful categories have "initial objects": Objects which have exactly one morphism into every object of a category.

Now lets consider a blog. Each article may have links to other articles. The blog together with its links describe a directed graph. We can extend this graph to a category, by choosing our morphisms to be the "paths" (lists of links, which one can follow link-by-link).

Thus we have a suitable notion of an initial blog article. An article with a single path into every other article under this definition. So for this very article to be initial, then for every article on this site, one of these conditions hold:

  1. The page is this very article, then no links into it are allowed, the only path here is the "empty" path.
  2. The page is directly linked to by this article.
  3. The page is linked to by a page with a unique path from this article. (So a different page matching 2. or 3.)

Afterall, this has to be exclusive, or the uniqueness property is lost. Cycles are right out. In other words: The graph must be a directed tree, with our article as the root.

That seems quite restrictive. But as the case now is, with this being the only article at the time of writing, it satisfies the conditions of being the initial blog article. Trivially, it's also the terminal blog article, which sounds rather pessimistic.