From a mathematical perspective, this is actually not that surprising.
Think of the act of clicking the first link in the Wikipedia article as a function that takes in the page you're on and outputs another page.
If you call this function on itself over and over again (ie use the output of one step as in the input of the next step), you will eventually enter a loop. The proof of this is simple: there are only a finite number of Wikipedia articles, therefore you must eventually reach an article you've seen before. (This is the same reason systems with a finite number of states cannot be chaotic.)
Since it's necessarily true that all articles will eventually reach a loop when you iteratively click the first link, we have to ask: how unusual is it that they usually reach the SAME loop?
The fact that many lead to the same loop(1) of Argument <-> Logic in unsurprising, too. Wikipedia articles usually define their subject in in the first sentence. Defining things works by saying what general category they belong to, then by differentiating them within that.
E.g.
A fish is any member of a paraphyletic group of organisms that consist of all gill-bearing aquatic craniate animals that lack limbs with digits.
Google Inc. (NASDAQ: GOOG) is an American _multinational corporation_ which provides Internet-related products and services [...]
A table is a form of _furniture_ with a flat and satisfactory horizontal upper surface [...]
And so on. If you always walk up the abstraction chain because you're picking the first link (the general category), you'll end up at the root of the categorization tree, which is likely something along the lines of Argument, Logic, Fact etc.
Note however that the current state of wikipedia has a different root loop for me, Logic leads to Philosophy.
(1) or one of a very limited number of loops, I also saw Science <-> Knowledge.
Another way of thinking about it: There are N nodes that loop back to themselves. When starting at a given node, what are the odds that you'll never hit one of these N nodes? Additionally, we know that many of the N nodes are very general ones, like "truth", under which many topics roll up.
Agreed. I'd love to know how many different cycles the wikipedia article graph contains. If most articles lead to 1 out of 20 possible cycles, it's much less interesting than if it's 1 out of 5,000,000.
I've been looking to do something like this with the Networkx library in Python, though on an internal company MediaWiki with a much smaller article base. Going to try to visualise much the same thing, the major loops and cliques in the graph.
This is the same reason systems with a finite number of states cannot be chaotic
Without more information, I don't think this is true. It is true if the transition function between states depends on a finite number of previous ones (WLOG if s_n is a function of only s_{n-1}), but I think that it isn't if the transition depends on an infinite number.
(Though, in this case, clearly there is no history, so what you say is true.)
If your model only depends on at most a maximum fixed length of history, you can always model your finite systems to only depend on the most recent state. (Just make a copy of the history part of that state.)
In the case of depending on up to an infinite history, I wouldn't call that system to have a finite number of states any longer.
Think of the act of clicking the first link in the Wikipedia article as a function that takes in the page you're on and outputs another page.
If you call this function on itself over and over again (ie use the output of one step as in the input of the next step), you will eventually enter a loop. The proof of this is simple: there are only a finite number of Wikipedia articles, therefore you must eventually reach an article you've seen before. (This is the same reason systems with a finite number of states cannot be chaotic.)
Since it's necessarily true that all articles will eventually reach a loop when you iteratively click the first link, we have to ask: how unusual is it that they usually reach the SAME loop?