Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
Hology is a logical analogue of holography characterizing the most general relationship between reality and its contents. It is a form of self-similarity whereby the overall structure of the universe is everywhere distributed within it as accepting and transductive syntax, resulting in a homogeneous syntactic medium. This means that analysing any one object, the most general features of reality as a whole must be present in it. Hology is justified by the fact that the universe has nothing other than its own syntactic "coding" to double up as its own "state"/objects.
For example, suppose you hit a tennis ball with a racket. In the conventional picture, its fate—whether it will hit the net, or bounce into a wall, or fly out of the court—depends on the state of reality outside of you: the positions of surrounding objects, the wind speed, etc. But according to hology, all of this information is already present in your "syntax", or set of laws that governs you. In this new picture, what you see happen to the tennis ball is determined by your own internal processing, and all of the objects which you see as "outside" of you are actually being simulated by your syntax. Hology says that every part of reality has the structure needed to internally simulate its external environment in this way, turning the conventional picture "outside-in":
This results in a “distributed subjectivization” in which everything occurs inside the objects; the objects are simply defined to consistently internalize their interactions, effectively putting every object “inside” every other one in a generalized way and thereby placing the contents of space on the same footing as that formerly occupied by the containing space itself. Vectors and tensors then become descriptors of the internal syntactic properties and states of objects. In effect, the universe becomes a “self-simulation” running inside its own contents.
For more on the "dual" relationship between this picture and the conventional one, see conspansive duality.
- Langan 2002, p. 42.