[bza]

It's not physics woo; the way the OP's using "duality" is common among mathematicians and physicists. The different types of duality listed in the physics and math sections of the Wikipedia article you linked to are thought of, by typical practitioners in these areas, as all being instances of a more general phenomenon. That's why these various things end up being called dualities.

That generic kind of duality is well described in the first sentence of [1], and the OP's explanation of a duality as "a connection between two things where the properties of one defines the properties of the other" is pretty obviously an attempt to convey, to a lay audience, that sense of duality.

[1] http://en.wikipedia.org/wiki/Duality_(mathematics)

[stcredzero]

It's not physics woo; the way the OP's using "duality" is common among mathematicians and physicists.

You seem to be right. I must backtrack and say, "One learns something new everyday!"