You can't apply this stuff mindlessly. Consider this suggestion from the article: "Differences between people: (Height, Weight, Age)". If you use the formula, you end up with inch^2 + pound^2 + year^2. Mixing units is bad enough. Now imagine how the results will change if you switch to the metric system.
I think the missing element is this: you need to establish that the domain that you are trying to measure is a metric space before trying to measure distance using this formula.
Exactly! It is a big mistake to assume that you can express relations between the entities you study with a single number. I've never heard however of non-metric topological spaces used in applications.
