Transductive algebra

The following is an excerpt from page 42 of "The Cognitive Theoretic Model of the Universe: A New Kind Of Reality Theory":

The laws that govern a system may be reposed in the space that contains its objects, or in the objects themselves. Classical physics reposes everything in space, applying spatial concepts like vectors and tensors to fields outside the objects. However, it is possible to apply a logical transformation which inverts this picture, turning it “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.

This view, which is complementary to the conventional geometric one, is called transductive algebra. The “dual” relationship between geometry and transductive algebra is called conspansive duality.