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This post, by Bill de hÓra, has reawakened my interest in things self-referential.

Growing up, I was deeply inspired by Gödel Escher Bach (like almost everyone else in comp sci) and always loved René Magritte and Escher (I had a picture of Le Chateau des Pyrenees over my bed as a teenager).

Self reference is a technique used to show paradoxes and prove a lot of interesting stuff, like Gödel's incompleteness theorems. Of course, self-reference by itself is not always bad - e.g. it's the basis of recursion, which is pretty useful. Paradoxes have two more components: a variant of the Liar Paradox and an evaluation system. Consider the classic example:

This statement is false.

There are three components here:

1. The self reference. Here the sentence refers to itself, but any system that can do so will work.
2. The liar paradox is needed to create the dissonance: The content are contrasted with their meaning.
3. But more importantly, the evaluation system is needed to give this statement context and meaning. Without evaluating the statement (in our heads), it is just that - a statement.

Only by combining all three elements will we create paradoxes. Deliciously tagging your delicious tags probably won't create a system panic and bring it down: (a) How will we create a dissonance, and (b) How will we evaluate the this? What can these self referential links give us? The following are a few rambling thoughts.

* The "tag" tag lives in the same spaces as the other tags. By this, the system includes its own meta-information.

* The purpose of tagging tags is to add some meta information on the tags themselves. If I wanted the content of the tag I'd just look at the list of tagged items (the items - don't forget the items), matching this tag. Thus we get a recursive reference to the self - tags (meta-data) whose content (data) is other tags (meta-data).

** We could build a hierarchy this way: here's my programming tag, containing the ruby tag, containing Ruby relevant items (the items - don't forget the items). In fact, this is why I use del.icio.us direc.tor - it imposes an on-the-fly contextual tree on my bookmarks.

** But hierarchies can also obscure information. This may be good if its too much to view at once, or may be bad if it's obscuring what I'm looking for and how to get at it. At uni, I worked for IBM Research on a sharable bookmarks project (all the rage then. How much has changed ;). Items were tagged and stored discreetly, but presented hierarchically per user: Tags were not inherently related; Each user saw all the tags but constructed their own (display) hierarchy for the tags (and the items - don't forget the items). In that system, tags were not part of the item space, kinda like a file-system with folders are distinct from files. (Items could appear multiple times, under different tags in the tree). When I opened my Comics folder under my Humor folder, I also saw everyone else's webcomic links, regardless of whether they also tagged it as humorous or not.

* So if I tagged all my programming-related tags (say ruby, dynamic and language) as you did the same (with say perl, python and proglang), when we looked at sharing information about items we could also share our taxonomies when categorising these items. Of course, who guarantees that our taxonomy-taxonomy is the same? Enter recursive self-references :-)

* Would these taxonomies ever converge? What is the practical recursion level where the simple process of reviewing and retagging (gardening your links) is sufficiently stable to expose to you the information you need?

* Will there be an rss feeds for the contents (actual items) of my tags tag? Will I be able to see, under my ruby tag things people have filed under the rails tag? They thought it was obvious, by I want a simple connection.

If you've read so far, I must applaud you for sheer tenacity in the face of my obvious insanity. I'll reward you with an interesting thought experiment - try to experiment in thinking about your thinking. Try and get an echo in your head. It's a lovely experience, experiencing your thoughts before and after you think them, almost atemporally.