7. Dimensionality: VIhA

The following cmavo are discussed in this section:

     vi'i    VIhA                on a line
     vi'a    VIhA                in an area
     vi'u    VIhA                through a volume
     vi'e    VIhA                throughout a space/time interval

The cmavo of ZEhA are sufficient to express time intervals. One fundamental difference between space and time, however, is that space is multi-dimensional. Sometimes we want to say not only that something moves over a small interval, but also perhaps that it moves in a line. Lojban allows for this. I can specify that a motion “in a small space” is more specifically “in a short line”, “in a small area”, or “through a small volume”.

What about the child walking on the ice in Examples 5.1 through 5.3? Given the nature of ice, probably the area interpretation is most sensible. I can make this assumption explicit with the appropriate member of selma'o VIhA:

7.1)   le verba ve'a vi'a cadzu le bisli
       The child [medium space interval] [2-dimensional] walks-on the ice.
       In a medium-sized area, the child walks on the ice.
Space intervals can contain either VEhA or VIhA or both, but if both, VEhA must come first, as Example 7.1 shows.

The reader may wish to raise a philosophical point here. (Readers who don’t wish to, should skip this paragraph.) The ice may be two-dimensional, or more accurately its surface may be, but since the child is three-dimensional, her walking must also be. The subjective nature of Lojban tense comes to the rescue here: the action is essentially planar, and the third dimension of height is simply irrelevant to walking. Even walking on a mountain could be called “vi'a”, because relatively speaking the mountain is associated with an essentially two-dimensional surface. Motion which is not confined to such a surface (e.g., flying, or walking through a three-dimensional network of tunnels, or climbing among mountains rather than on a single mountain) would be properly described with “vi'u”. So the cognitive, rather than the physical, dimensionality controls the choice of VIhA cmavo.

VIhA has a member “vi'e” which indicates a 4-dimensional interval, one that involves both space and time. This allows the spatial tenses to invade, to some degree, the temporal tenses; it is possible to make statements about space-time considered as an Einsteinian whole. (There are presently no cmavo of FAhA assigned to “pastward” and “futureward” considered as space rather than time directions — they could be added, though, if Lojbanists find space-time expression useful.) If a temporal tense cmavo is used in the same tense construct with a “vi'e” interval, the resulting tense may be self-contradictory.