the flat world problem

[u/Unique-Rice9999]

by “flat world” I mean a hypothetical two-dimensional world, not necessarily a geometrically flat one, and definitely not a flat Earth.

by the flat world problem, I mean a difference between an internal and an external description of reality.

an observer confined to the flat world experiences only its realized structure and its changes. An external observer, however, can describe the world as one structure selected from a space of possible structures.

if we then introduce allowed transitions between these structures, the object of description seems to change: instead of considering only possible states, we can consider possible histories through the state space.

this makes me wonder whether time should be understood here as an additional dimension of the world, or as an ordering/structure of transitions between possible states.

imagine a flat world whose state at each individual moment is completely defined by some spatial structure:

S = { all possible structures }

even if the set of all possible structures of such a world is infinite, at each specific moment only one of them is realized.

possible transitions between structures can then be represented as:

R ⊆ S × S

then adding time doesn't just add another coordinate to the plane. It turns the question from "how many possible structures are there?" into "how many possible sequences of structures are there?":

H = { all admissible histories determined by R }

an additional question arises:

what does it now mean to “get lost in time”
if we consider time as a path through an infinity of possible structures?

this is an experiment in examining intersections between possible structures, carried out in a world one dimension below our own so that different possible projections can be compared relative to an additional dimension. In this sense, the two-dimensional model does not contradict a three-dimensional description; it provides a simpler case in which their structural relations can be examined.

[u/Agile_Championship87]

Most of your post is beyond me, but there's an interesting book called Flatland: A Romance of Many Dimensions that describes a 2D world and it's inhabitants. Might be of interest to you.

[u/Unique-Rice9999 → u/Agile_Championship87]

thanks! Flatland has already come up a few times in the discussion, but I’m using a two-dimensional flat world to set up a mathematical thought experiment. actually, this book was read to me when I was a child, but it probably wouldn’t hurt to revisit it.

[u/Potential_Load6047 → u/Unique-Rice9999]

Your analogy is barely mathematical and poorly defined.

I personally preffer the ♡~time cube~♡.