Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
Conspansive duality is one of several duality principles in the CTMU.
On the surface, conspansive duality says that there is no difference between the expansion of the universe with respect to its contents, and the contraction of its contents with respect to it. This follows from the self-containment of reality. If there were an external scale by which to measure reality, the external scale would itself be real and therefore internal to reality (a contradiction). Hence the real universe has no external size; it can only be measured internally, by the size ratio of the system to its contents. Since the ratio is all that matters, expansion of the universe is equivalent to a contraction of its contents.
At a deeper level, conspansive duality relates two complementary views of the universe, the conventional geometric model and a dual generative model, by conjoining the "ectomorphism" of the former with the endomorphism of the latter.
Cosmic expansion and ordinary physical motion have something in common: they are both what might be called ectomorphisms. In an ectomorphism, something is mapped to, generated or replicated in something external to it. However, the Reality Principle asserts that the universe is analytically self-contained, and ectomorphism is inconsistent with self-containment. Through the principle of conspansive duality, ectomorphism is conjoined with endomorphism, whereby things are mapped, generated or replicated within themselves.
In the conventional geometric model, known as ERSU (Expanding Rubber Sheet Universe), the universe is a physical dynamical system in which objects move through an expanding space. In the generative model, known as USRE (Universe as a Self-Representational Entity), nothing expands or moves "through" space; rather, objects evolve through a kind of logical substitution, with new states forming "inside" previous states. The CTMU unites these two models and extracts the implications.
Conspansive duality can accordingly be seen as spacetime-object (ST-O) duality, in which objects are dualized to spatiotemporal transducers. In this dualization, the physical universe is internally "simulated" by its material contents, and objects contain space and time in as real a sense as that in which spacetime contains the objects.
The process by which the universe evolves in light of conspansive duality is called conspansion.
"SCSPL relates space, time and object by means of conspansive duality and conspansion, an SCSPL-grammatical process featuring an alternation between dual phases of existence associated with design and actualization and related to the familiar wave-particle duality of quantum mechanics."
- Langan 2002, p. 27.