In the CTMU, triality refers to the universal possibility of consistently permuting the attributes space, time, and object with respect to various structures.
Space can be defined in terms of the structure of objects e.g. the relation between the objects in space. Similarly objects can be defined in terms of the structure of space e.g. the relation between points in objects. This is space - object or S-O duality.
Time can be defined in terms of the structure of S-O duality e.g. the relation between of S-O duals (aka "instances") or objects moving in space. Space and objects can be defined in terms of the structure of time e.g. the relation between instants (in time). This is time - space/object or T-S/O duality.
Spacetime can be defined in terms of the structure of objects in spacetime or ST-O duality. This takes the form of the relation between objects as 4 dimensional spacetime manifolds in the Theory of General Relativity. However when we look at spacetime-object duality from a Conspansion point of view, objects are actually internally simulating the physical universe including spacetime and actually in a state of perfect stasis. See conspansive duality for more information.
These concepts when added together form the concept of a triality whereby space, time and object are inextricably linked and can be described in terms of each other. Therefore all across the universe various structures can be pointed at and described in terms of space, time and object.
Triality can be seen as expressing the following identities:
- space = object = time
- class = instance = instantiation
- processor = product = process
- input = output = functional syntax
- chooser = chosen = choice
- Langan 2002, p. 25.