Four-dimensional Space - Orthogonality and Vocabulary

Orthogonality and Vocabulary

In the familiar 3-dimensional space that we live in there are three coordinate axes — usually labeled x, y, and z — with each axis orthogonal (i.e. perpendicular) to the other two. The six cardinal directions in this space can be called up, down, east, west, north, and south. Positions along these axes can be called altitude, longitude, and latitude. Lengths measured along these axes can be called height, width, and depth.

Comparatively, 4-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w. To describe the two additional cardinal directions, Charles Howard Hinton coined the terms ana and kata, from the Greek words meaning "up toward" and "down from", respectively. A length measured along the w axis can be called spissitude, as coined by Henry More.