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its-octopeople t1_iyczn2m wrote

Flat doesn't mean 2-dimensional. Things can be 2-dimensional and not flat (the surface of a sphere, for example), or 3-dimensional and flat (like the space we live in appears to be). In a flat space, parallel lines stay parallel. In a non-flat space, they don't

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nhabz OP t1_iyczvps wrote

Thank you. The 2D non-flat/3D flat were good examples.

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LOSTandCONFUSEDinMAY t1_iyd6qt5 wrote

We use the word flat because we haven't got a specific word for 3D nor a general word to use so we use the closet one available which is 'flat' a word traditionally for 2D. Not curved/a curvature of 0, might be a less confusing way to describe the universe.

A similar issue arises when talking about 'size' in higher dimensions. An object in 1D is a line and its size is called length, in 2D you have a surface with an area, in 3D your object has a volume.

But in 4D we haven't got a unique name for its size and call it volume again. and it doesn't help that like every 3D object has a 2D surface area, a 4D object has a 3D volume. Therefore every 4D object has two measurements called volume (though its specified surface or interior volume).

And get gets worse as you go up in dimensions because every dimension you go up you get an additional type of volume to consider but the highest dimension measurement is usually considered its size.

TLDR: dimensions are confusing and we haven't got enough words in english to properly or easily talk about it.

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avdolian t1_iyd11w7 wrote

>In a non-flat space, they don't

You can draw parallel lines on a sphere and they stay parallel

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SoulWager t1_iyd1nvi wrote

>You can draw parallel lines on a sphere and they stay parallel.

From the perspective of two people walking on those lines, at least one of them will need to constantly be turning left or right. If you're both walking parallel and straight, your paths will intersect 1/4 the way around the sphere.

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avdolian t1_iyd26av wrote

If my friend stays one metre to my north and we both walk around the globe one of us will have walked further but they wouldn't have to constantly turn and we would never cross.

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stools_in_your_blood t1_iyd2ye5 wrote

The one who isn't walking on a great circle (i.e. an "equator" of the sphere) is constantly turning away from you, in the sense that if they imagine their path laid out in front of them, it appears to curve to one side.

Put another way, imagine doing this not with walking but with cars with the steering fixed dead ahead. Try it with toy cars and a basketball if you have those objects handy.

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SoulWager t1_iyd370q wrote

The only line of latitude that's not bending left or right is the equator. For an extreme example, imagine walking the line of latitude one meter from one of the poles.

A line of latitude one meter from the equator is still bending, just not as much.

Lines of longitude do not bend left or right, and they all intersect at the poles, even though they're all parallel at the equator.

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its-octopeople t1_iyd7xq4 wrote

Okay, not parallel lines but parallel geodesic curves. I don't know if I can ELI5 geodesics, but I'll have a go

Okay, you can't take a straight line on a sphere, obviously. But if you walked around the equator, most people would a agree you'd walked pretty much a straight path. However, if you walked a 1 meter circle around the North pole, no-one would recognise that as a straight path, even though they're both lines of latitude and they're both parallel

What's the difference? Pick any two points on the equator. The shortest path between them (staying on the sphere), also follows the equator. For the small circle you don't have that property - you can find a shorter curve that cuts through the interior of the circle. Curves that have this shortest distance property are called geodesics

So the statement about flatness should be; two geodesics - that is, two shortest distance curves - that are parallel at some point, stay parallel their whole lengths

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Waterknight94 t1_iyczc42 wrote

I'm pretty sure flat in this case means it has no curves or corners. A straight line will remain straight.

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WinBarr86 t1_iycyqim wrote

Perspective.

Take a sheet of paper for example, we call it 2d, but it is infact a 3d object. It has 3 dimensions. It's just the thickness is so small in relation to the other dimensions we kinda pretend it isn't there.

We call it flat for lamens purposes. It makes a few things easier to understand on a basic level.

Edit.

Flat doesn't always mean 2d. You can have a flat 3d object. Like paper.

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nhabz OP t1_iycyvc7 wrote

So the universe is actually 3D but we call it 2D to make certain concepts easier to understand?

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ialsoagree t1_iyd0byk wrote

No no, we call it flat - but flat doesn't mean 2D.

We call paper flat, but paper isn't 2D, it's 3D.

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WinBarr86 t1_iyd0ohk wrote

We don't call it 2d we call it flat.

Flat is a concept. That concept is easier to explain using a 2d method.

Flat does not mean 2d. Flat means, in this case, the "thickness" of the universe is so small in relation to the width and length. Like a piece of paper. Paper has a "thickness" like 2mil or .07mil. Some paper is super thin, like tracing paper, and some a bit thicker, like construction paper but its all flat and 3d.

Edits for clarity.

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urzu_seven t1_iyd39se wrote

That is not at all why the geometry of the universe is described as flat. It has nothing to do with “thickness”

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WinBarr86 t1_iyd5s0i wrote

I'm trying to keep it simple. But plz do explain. Without explaining like your talking to a scientist who knows alot of the concepts of space/time.

Edit.

But we both know space isn't flat.

Spacetime is not flat. It can't be: Einstein's general theory of relativity says that matter and energy curve spacetime, and there are enough matter and energy lying around to provide for curvature.

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WinBarr86 t1_iydcvxm wrote

Trying to explain the concept of flat as to curved without using mathematical terms is hard. Flat is a concept, just means non curved. To explain in detail requires a fair bit of knowledge of things like diffent types of geometry and understanding fundamentals of curvatures and Euclidean geometry. Best way to explain flat is paper.

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drafterman t1_iyczyfw wrote

"Flat" in this context means in terms of curvature. Using 2D as an example you can have a piece of paper which is 2D and flat or something like the surface of a balloon which is 2D and curved.

The problem is that, from the perspective of any beings that live on and are constrained by those 2D surfaces, the world just looks "flat" to them in both cases because any 2D beams of light are also constrained to the surface. The balloon case is curved, but it is curved through a third dimension which 2D beings cannot perceive.

Stepping back up into our 3D work, there is an open question as to whether our 3D space is "flat" or "curved" in the 3D sense. If it was curved, it would be curved through a fourth dimension which we cannot directly perceive, so how could we tell?

Stepping back down into 2D, our 2D beings could indirectly determine the curvature of their world through triangles. In the flat 2D world, any triangles they made would have angles whose sum always equals 180 degrees. But in the curved 2D world, you would be able to make triangles whose angles sum to greater than 180 degrees.

This property also works in 3D. If our universe is flat, then triangles all have angles that sum up to 180 degrees and if it is curved then they could sum up to greater than 180 degrees. By picking distant objects (such as far away stars and galaxies) and measuring the relative distances between those objects, we can calculate their angles. Within a certain margin of error, we've calculate that our universe is either flat or has a very very very very small amount of curvature.

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Verence17 t1_iyd0df5 wrote

This gets asked every week. Flat doesn't mean 2D in that context. Flat means "normal space" where parallel lines stay parallel, sum of angles in a triangle is 180 degrees and so on. For example, surface of a sphere is not flat: straight lines that are parallel in one place (for example, meridians at the equator) will converge in the other. This can be generalized to 3D space.

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MercurianAspirations t1_iyd0gq4 wrote

Space isn't flat in the sense that it is flat like a piece of paper (i.e., it only has two dimensions), space is flat (maybe? we're not %100 sure) in the sense that it isn't a closed curve.

Think about it this way. On a curved object, like the surface of the earth, you can walk along the equator, turn 90 degrees, walk to the north pole, turn 90 degrees again, walk down to the equator, and turn 90 degrees again - tracing out a triangle with 90 degree corners. But that's not standard "flat" geometry, because triangles in that system can't have all 90 degree corners - it only works in a curved, closed system like a globe. On a curved coordinate system, parallel lines - like lines of longitude - eventually meet. (They all converge at the north and south poles.)

The universe could be like this. It could be a closed system that curves in one direction or another. But some data suggests that this isn't the case and parallel lines in space will never meet, just like they don't in two dimensional "flat" geometry.

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fudgyvmp t1_iyd0y57 wrote

General Relativity says that mass bends space. It provides a parameter called the density parameter to determine how space is bent.

If the density parameter is measured to be greater than 1, then there is enough mass that space curves positively and forms into a closed sphere.

If the density is less than 1 then space is curving negatively and the universe is shaped like a saddle.

If the density is 1 then the universe is flat.

In a spherical universe straight lines are always going to curve along the sphere and you will end up back where you start. If we could look up at the sky we could potentially see the same galaxies from two different sections of the sky because we would be looking at them from the front and back (if the radius of the universe was small enough).

Current measurements to my knowledge suggest the density parameter is 1 and the universe is flat.

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internetboyfriend666 t1_iyd6o6t wrote

Flat in this context doesn't mean 2 dimensional, flat means the universe is not curved, or in other words, it obeys Euclidean geometry. Euclidean geometry is the geometry that everyone is most familiar with and is most applicable in our daily lives. It's where parallel lines never meet and the sum of the angles in a triangle is always 180 degrees. There are other types of geometry where these things are not true. For example, the surface of a sphere is not Euclidean - parallel lines will always meet and the sum of angles in a triangle can be more that 180 degrees.

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