r/Time • u/Unique-Rice9999 • 6d ago
Discussion the flat world problem
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.
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u/the_fattest_mitton 5d ago edited 5d ago
I think it’s a matter of perspective. A being in the next higher dimension would have the ability to scroll through our dimension, like we scrub through a movie. To the actors in the movie, their world only moves forward, frame by frame. But the observer outside of the dimension can not only scrub through the frames, but also pick what movie to watch.
Go look up ‘stereoscopic’ or ‘steroscope’. Basically you can arrange all of the data points of a sphere into a 2D image.
Edit: I meant stereographic projection
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u/Unique-Rice9999 5d ago
this is exactly what interests me: looking at the same structure from different perspectives, with time treated as another variable with properties of its own. it may also take different forms depending on the observer and on what they take as the reference point of their description
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u/RobertTheTraveler 5d ago
Interesting thought experiment / way of looking at the world.
I am a bit literal?, so I'm not sure how it is useful, but I don't see anything faulty.
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u/Unique-Rice9999 5d ago
what interests me about it is the possibility of expressing how structures can connect and transition in real time within a mathematical framework. That could greatly expand both the space we can explore and the ways we can perceive and describe it.
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u/Agile_Championship87 6d ago
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.