system
Given the following post, respond as if you're commenting on Reddit:
human
Theoretically, is it possible for an intelligent being living in the second dimension to 'discover' the third dimension?
gpt
Dimensions aren't places, even though the term is often used that way in science fiction. Rather, dimensions are properties of spaces.

Specifically, when we talk about a space having "n dimensions", what we mean is that it takes n numbers to uniquely specify a point in that space. For example, if you want to specify a point on the surface of the Earth, you need two numbers, latitude and longitude, so the surface of the Earth is 2-dimensional. If you want to specify a point within the Earth, you also need to specift a depth, so the interior of the Earth is 3-dimensional.

Notice in each of these cases, there's not a unique way to specify a given point with numbers. We could, for example, specify a point inside the Earth using a rectangular coordinate system, instead of latitude, longitude, and depth, and it would still take three numbers (x, y, and z) to specify a point. Thus, even though we say a space is three-dimensional, that doesn't mean there are exactly three well-defined values that we could call "dimensions". However, time is a little bit unique in this respect. If we want to specify an event, rather than just a point, we need four values, three to specify a location in space, and one to specify the time at which the event occurred, so "space-time" is four-dimensional. But time is, for various reasons, distinct from space, and so you will sometimes see it referred to as "the fourth dimension". That does not mean, however, that there is a well-defined first, second, or third dimension.

Now, with all of this in mind, we can imagine hypothetical beings in a hypothetical two-dimensional universe (three-dimensional space-time). There are then two ways to interpret the question of whether they can "discover" the third dimension. If we're asking whether they could conceive of a three-dimensional space, there's no reason to think they wouldn't be able to, since we, in three dimensions, can conceive of spaces with arbitrary or even infinite dimension. If we're asking whether they could discover that time is "the third dimension" for them, as it's "the fourth dimension" for us, again there's no reason to think they wouldn't be able to.

On the other hand, if you're asking whether beings living in a hypothetical two-dimensional universe could discover *our* three-dimensional universe, then that question doesn't really make sense.