Just seven links, in Wikipedia.

John Quiggin, of Crooked Timber, poses the challenge of finding a shorter route. This seems like the sort of game that our readers would be good at.

Just seven links, in Wikipedia.

John Quiggin, of Crooked Timber, poses the challenge of finding a shorter route. This seems like the sort of game that our readers would be good at.

Comments are closed.

%d bloggers like this:

I was so about to write this post myself.

I can get from “The Moster Lie Algebra” to “University” in two links, and from “Political Correctness” to “University” in two links. By symmetry of the metric and the triangle inequality, this ought to imply that the answer is at most 4.

Nick – the wikipedia metric is not symmetric.

in seven clicks:

0. Political correctness

1. Straw man

2. Base rate fallacy

3. Bayesian probability

4. Philosophy of mathematics

5. Mathematical beauty

6. Monster group

7. Monster Lie algebra

(Although one can of course do better; there are known six-link solutions.)

To continue on the theme of the Wikipedia metric not being symmetric, the reverse can be done in 5:

0. Monster Lie algebra

1. Mathematics

2. Social sciences

3. Sociology of gender

4. Sex segregation

5. Political correctness

5 clicks:

0. Political correctness

1. University of Michigan

2. Fields Medal

3. Richard Borcherds

4. Monster group

5. Monster Lie algebra

The answer is obvious: one. I’ll let you figure that one out (or revert it).

One can talk about the Wikipedia function, which is evidently not symmetric, or about the metric induced by the Wikipedia function, which I would like to call the Wikipedia metric. The metric is symmetric (as all metrics are, by definition). It seems to me that the metric is just as interesting as the function, if not more.

This is not quite the best but going via string theory…

0 political correctness

1 religion

2 universe

3 string theory

4 bosonic string

5 no ghost-theorem

6 monster lie algebra

Nick, there’s also a quasimetric space, as a commenter on my weblog tracked down.

It’s true that the usual definition of a metric assumes both the triangle inequality and the symmetry condition d(x,y) = d(y,x). But you can have a perfectly good metric theory using only the triangle inequality. For instance, the set of open balls still forms the basis of a topology. The set of topologies that you can get in this way is more general: for example the lower limit topology is the topology of an asymmetric metric on the reals (exercise). Actually you get two topologies at the same time, because you have both left-balls and right-balls. (Or if you like, distance-to balls and distance-from balls.)

If you ignore the “what links here” button in Wikipedia, the asymmetric metric generated by following forward links is then more germane to the discussion than the symmetric metric generated by backward and forward links.

Re the crossed comment: I didn’t know that it is called a quasimetric. It even has a Wikipedia article — le cri du jour.

If we take the question metric-style, using both backwards and forward links, then the distance is at most 3:

political correctness ← The Adventures of Tintin → mathematics ← Monster Lie algebra

(The arrows look like something from a localized category, don’t they?) I would be a bit surprised if the distance turns out to be 2.

Meanwhile:

Monster Lie algebra → Mathematics → Social sciences → Sociobiology → Political correctness

(I thought of a trick to make it a bit easier to find these.)

Greg: are you thinking categorically? ;)

Aha!

Political correctness → University of Michigan → List of University of Michigan faculty and staff → Monster group → Monster Lie algebra

So I’m a little late to the party, and I didn’t bring a present, but I

couldn’t resist hitting this problem with a big hammer.

The http://dbpedia.org/ project has been doing a wonderful job of

extracting data from wikipedia, and in particular representing it all in

RDF, which is a simple mechanism for describing arbitrary directed graphs, with edges and vertices all labelled by URLs. You can do many wonderful things with RDF — there are query engines which try to solve subgraph isomorphism problems, so you can ask completely ridiculous questions like “Find me all the soccer players with tricot number 11 from clubs with stadiums with >40000 seats born in a country with more than 10M inhabitants”.

Now in particular, the dbpedia project exports RDF data describing all

links between wikipedia articles, so in principle we could use one of

these query engines to just ask for examples of “Political correctness

#wikilink ?A #wikilink ?B #wikilink ?C #wikilink Monster Lie algebra”.

Unfortunately for theory, for some reason they don’t expose the

information about links through their query engine, and you’d also put a pretty heavy load on their server while asking these sorts of questions!

In practice, though, you could download and run my little program for

doing this locally. Assuming you have both Subversion and Maven installed (unlikely, perhaps), just type:

svn checkout http://tqft.net/svn/java/dbpedia/

cd dbpedia

mvn install

# now download a ~400mb file, and decompress it to ~8gb!

./get-dbpedia-triples.sh

# now look for chains of links, of length 4.

./find-chains.sh ./chunks/ Political_correctness Monster_Lie_algebra 4

and you’ll hopefully find 26 chains from ‘Monster Lie algebra’ over to

‘Political correctness’, many that zigzag both ways, but very sadly not

the chain of length 4 that Greg found! Why not? Well, the link from

‘University of Michigan’ to ‘List of University of Michigan faculty and

staff’ isn’t just a plain old wiki link, but part of a “{{seealso|}}”

template, and dbpedia doesn’t catch it. Oh well! :-)

There are various other zigzagging paths of length 3, such as

Monster_Lie_algebra –> Mathematics <– Reasonable_person –>

Political_correctness, but nothing of length 2.