Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
Universe as a Self-Representational Entity
According to Langan, conventional physics and cosmology uses the "ERSU" model of the universe (i.e. Expanding Rubber Sheet Universe). Presumably, Langan is referring to the four-dimensional curved spacetime of general relativity. In this picture of the universe, gravitational masses curve spacetime, much like placing bowling balls on a rubber sheet.
However, Langan seems to take issue with this representation of the universe, because, according to him, it is not sufficiently "self-contained". According to the CTMU, it requires a kind of external "background" space in which objects change their state of motion. In ERSU, the expansion of the universe is represented by an expanding balloon with dots drawn on it. Space expands "intrinsically". However, Langan takes issue with the notion of "intrinsic expansion", claiming that it is self-contradictory on its face, and that if the universe is expanding, it must be expanding into something. This is central to thesis of conspansion, which claims that the universe is not actually expanding, but only appears to be from our local viewpoint.
Motion based on "ERSU", as Langan calls it, is based on something called "ectomorphism". Ectomorphism is the view that objects change their state of motion relative to some fixed background space. However, because the universe is self-contained, Langan claims that motion is actually represented by "endomorphism", a kind of motion that Langan purports does not contradict the Self-Containment criterion of reality.
In a radio interview, when Langan asked "what travels fastest in the universe?", Langan responds that from an ectormophic viewpoint it would be light, but that you have to "formulate motion so that it's mathematically correct." Clearly, by "ectomorphism", Langan is referring to the four-dimensional curved spacetime model of the General Theory of Relativity, which he calls the "Expanding Rubber Sheet Universe." Prima facie, he believes that on some level it must be paradoxical, violating the Self-Containment Principle of Reality.