North, east, south, and west are the four cardinal directions. The term derives from the Latin cardo, which can mean “hinge” or “pivot,” and thus figuratively a turning point or pole. It also had a derived meaning of “something on which something else depends”—because a door de-pends (i.e. hangs) on its hinges and turns about them—and thus also could mean “principal thing.” Many modern word senses of “cardinal” derive from this idea. For example, a high Catholic official was an episcopus cardinalis (i.e. “principal bishop”), and thus ultimately just a “cardinal.” The red bird was named after the red robes worn by cardinals, and the baseball and football teams are named after the bird. (Of course, they have red uniforms and logos.) The association with the compass points, however, is an ancient one that has endured. A north-south street was a cardo, and the four principal directions were quattuor cardines orbis terrarum (“the four pivots of the world”).
What should we call the four intermediate directions: northeast, southeast, southwest, and northwest? Two names with perfectly respectable Latinate justifications would be semi-cardinal (cf. “semi-annual” or “semicircle”) or intercardinal (cf. “interpolation” or “interregnum”) directions. But some sources, including Wikipedia, refer to them as the ordinal directions, a usage that is close enough to right to sound plausible if you don’t think too closely about it.
The English “ordinal” comes from the Latin ordo, which means “order,” “line,” or “regular arrangement.” Thus, a ordo could be a course of stones in a wall, a line of soldiers, a class of citizens, or anything else arranged correctly in its place. One sense that has endured in several meanings of “order” is that of a linear series, so that the adjective ordinalis described things arranged by order of succession: first in line, second in line, third in line, and so on.
And this, it appears, is how “cardinal” and “ordinal” collided. A cardinal number is a counting number: 1, 2, 3, and so on. They are so-called because they are the principal numbers; other senses in which numbers are used depend on this one. An ordinal number describes something’s place in an order: first, second, third, and so on. They are so called because they describe the order in which things are arranged. For finite numbers, cardinals and ordinals correspond exactly. You use a cardinal number to describe how many things there are in a group, but use an ordinal number if you want to pick out where one of those things falls within the group. (Mathematicians would say that the two senses diverge for infinite numbers; infinite cardinals have very different properties than infinite ordinals.) And thus, generations of students have been taught to think of “cardinal” and “ordinal” as closely related, with “cardinal” being the
At this point, you can probably guess what happened. One finds occasional pre-1970 references to “ordinal directions” in a Google Books search, but most of them appear to be by people who have mistaken “ordinal” for “cardinal” when they meant to refer to the principal directions. It’s in 1972, as noted by Redditor phalp, that we find an attested use of “ordinal” in this sense:
… classics, though as intervening routes were made the cardinal and ordinal directions were gradually used up and so arrived at South-West by West.
I think this is simply wrong, but as with all matters of language use, it will become right if enough people use it that way over time. And if Wikipedia is any guide, we are well along that road already.
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