**Announcement:** Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal *Cosmos and History*.

# Triality

In the CTMU, **triality** refers to the universal possibility of consistently permuting (per- ‘through, completely’ + mutare ‘to change’) the attributes *space*, *time*, and *object* with respect to various structures.

Space can be defined in terms of objects e.g. the relation between the objects. Similarly objects can be defined in terms of space. This is space - object or S-O duality. Time can be defined in terms of objects and spaces e.g. objects moving with a space. Space and objects can be defined in terms of time. This is time - space/object or T-S/O duality. These concepts when added together form the concept of a triality whereby space, time and object are inextricably linked and can be described of 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 leads to another duality: spacetime-object or ST-O. This takes the form of objects moving around in a 4 dimensional space time manifold 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.

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