Editing Four-dimensional space (section)

==Orthogonality and vocabulary==
In the familiar three-dimensional space of daily life, there are three [[coordinate system|coordinate axes]]—usually labeled {{mvar|x}}, {{mvar|y}}, and {{mvar|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, four-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled {{mvar|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.<ref name="Hinton"/>{{rp|160}} 

As mentioned above, Hermann Minkowski exploited the idea of four dimensions to discuss cosmology including the finite [[velocity of light]]. In appending a time dimension to three-dimensional space, he specified an alternative perpendicularity, [[hyperbolic orthogonality]]. This notion provides his four-dimensional space with a modified [[relativity of simultaneity|simultaneity]] appropriate to electromagnetic relations in his cosmos. Minkowski's world overcame problems associated with the traditional [[absolute space and time]] cosmology previously used in a universe of three space dimensions and one time dimension.