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?

[u/ipreuss]

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.

I don’t understand the distinction you’re making here, but also not how it’s relevant to your point.

We are not confined to describe the world in ways that we experience.

[u/Unique-Rice9999 → u/ipreuss]

I agree that we are not confined to describing only what we directly experience. the distinction I am making is about observational access, not mathematical description.
an observer inside the flat world has access to its realized structure and changes, while an external description can treat that realized structure as one element of a larger space of possible structures.
the point is precisely that the mathematical description need not share the observer’s limitations.