Wednesday, 25 May 2011

Philiosophising Wikipedia

Today's xkcd cartoon has an interesting alt-text.  It claims that:
Wikipedia trivia: if you take any article, click on the first link in the article text not in parentheses or italics, and then repeat, you will eventually end up at "Philosophy".
In discussion, it seems that this is mainly true, although there are isolated examples of start pages that lead to an infinite loop.

What surprises me is that people find this surprising.  Thinking about it, if you have a finite set of pages (such as Wikipedia: it is not yet infinite, it just feels that way) which include links to each other, then logically speaking if you keep clicking according to a particular rule then you must eventually start to loop.  OK, it may take a long time - at the time of writing this, Wikipedia has 3,643,714 pages so at 1 click per second that is slightly over 42 days (assuming neither your mouse nor your index finger break during this time) but the claim has no limit of time or clicks.

By then, you will have been to every page, so you must start looping*.  Therefore, every start point must lead to a loop.  So the real question is, which loop will you reach first?  Or, given that the "Philosophy" page is itself in a short loop (Philosophy, Reason, Rationality, Philosophy), why that loop?

The answer to that is quite simple, I think.  Human nature, and the style of Wikipedia articles, is to start an article along the lines of "[Subject] is a type of [genus] in which....".  So the first link will usually be to a more general, less specific subject.  And what could be more general or less specific than philosophy?

(Of course, my example might fail if people are creating new pages at more than 1 per second - in that case a human clicking away might theoretically never reach a loop.  But the rule is absolute, and allows for a period when Wikipedia is static, or for some kind of automated searcher that could click away at a near-infinite speed, so I have discounted this slight problem.  POSTCRIPT: As of 14:49 on 27 May, Wikipedia had added 1,437 pages after 191,880 seconds, i.e. about 133 seconds per new page...)

(*this assumes every page has a link.  In Wikipedia, I think this is a reasonable assumption, at least of the pages that another page links to.  It is also an assumption made by the claim that we are considering)


  1. A variant on the Poincare recurrence theorem, I see.

  2. "42 days"

    Coincidence, or an underlying meaning to the universe? Was Douglas Adams right?

  3. Carl - Hmm, yes. Neat. That would suggests that every subject starts with philosophy, as well as leading to philosophy....

    Blue - yes, that struck me too! Mind you, Adams was right about everything - how dare you suggest there is some doubt?