Chapter 10: Imaginary Journeys: The Lojban Space/Time Tense System
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 ✥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.