Is and why is information two-dimensional?

The first ideas about the physical nature of information and its two-dimensionality came from Hawking's famous paradox of Black Holes. Externally, looking at a body that is collapsing into that strong gravitational field, it flattens and shrinks like a layer of the sphere of its event horizon, while time flows more slowly and its radial lengths become shorter.

I also explained the information surface on the example of concentric water waves moving away from the place where the pebble fell into the water. Wave energy and physical action are diluted as a circular ring of constant wavelength expands and it ironed its irregularities out. This increasingly flat surface, with decreasing wave amplitudes, and its leveling represent information that is consumed in interactions (friction) with the rest of the water mass.

A slightly more abstract example of two-dimensional information is given by the similarity of triangles, applied to an object that we observe at an ever-increasing distance, treating it as a triangle with ever-smaller bases and ever-increasing heights but constant surfaces. This is followed by much more convincing, but more formally mathematical, examples of the mutually unambiguous association (bijection) of the action of central constant forces and surfaces (read information), such as Kepler's second law.

Finally, the "information of perception" itself is such, which we can understand as a scalar (dot) product of two vectors, the ability of the subject and objective obstacles, which, no matter how many components they have, always span one two-dimensional vector space.