regarding the analogy that there is no edge to the U just as there is no edge on E

robertjford80

We are often told that to understand why the universe does not have an edge think of it like the Earth which has no edge. But I think this analogy breaks down because you can escape from the Earth's gravity and enter into outer space, plus you can dig into Earth and theoretically come out the other side. Do we have any good evidence for understand what would happen if we kept traveling in one direction in the universe?

twofish-quant

That's the problem with analogies. They break down. Ultimately you have to recognize that the analogy is merely a way of presenting a mathematical model. It's not the model itself.

We have very good mathematical models for what happens if you go in one direction.

robertjford80

well, could you give me explanation of what they say roughly? Does it have to do with Riemannian Geometry?

oli4

Hi robertfjord80,
You are missusing the analogy, you would have to think of the earth as a 2D surface only, you being a dot on its surface. there is no notion of up or down (otherwise, here is your edge of the earth)
In this setting, the Universe being a standard 2D sphere (but not embedded in a 3D space, you just embed it in a 3D space because it's easier for you to visualize it, but you must know that this 'container' space does not exist for the inhabitants of the sphere)
So try to picture this: you are a dot, you live in (not on) the surface of the sphere with a bunch of friend dots.
Someday you want to explore the whole of your universe so you setup a plan that goes like this:
Guys, we are going to explode in every direction maintaining radio contact as long as possible, and let's see what happens !
So here you go, all the bunch of you initially packed together at some point, let's call it the north pole.
As you all spread away from each other, you draw a circle that gets bigger and bigger, of course, because you are going in spreading directions
But funnily, at some point, you will cross the equator and although noone changed his direction, the circle will start getting smaller and smaller, until you all meet again at the south pole.

Now, you're no long a dot (congratulations for your promotion), you are full blown futuristic human being with many friends and spaceships to try the same experiment in the known universe.
What would happen ? all spaceships 'explode' away from each others, going all in straight lines. looking at them from a distance, they draw a growing sphere, everyone gets farther and farther from everyone else,
until... you pass the universe's equator, and then, although you never changed your direction, you suddenly start getting closer and closer and eventually meet back


Hope this helps,
Cheers...

robertjford80

yea, that really helps, that space is not inside another space, like the earth is inside space, i hadn't thought of that, plus the description of being on a 2D sphere, that was also particularly helpful. thanks.

Chalnoth

Well, you have to understand the analogy within the context it was meant. There is no edge of the surface of the Earth. That is, if you could imagine that you could only move along the Earth's surface (and could move along water as easily as land, and didn't care about mountains/cliffs/etc.), then you would never reach any sort of edge.

DaveC426913

Another type of 2D surface with no boundary is akin to an old video game that has a wrap-around world. You go off the bottom of the screen and reappear on the top.

Like traveling on the surface of the Earth, you can go in any direction you like and never encounter a boundary. Unlike Earth, you cannot climb above it to dig through it. Also unlike Earth, it is not curved.

Chalnoth

Asteroids :)

petm1

What about the edge between yourself, juxtaposition, and the 2d surface you are moving around on?

Chalnoth

Does that boundary stop you from moving around the surface of the Earth?

petm1

No it is the boundary that allows me to move around the surface of the earth as an individual.

The boundary you see as the outline of a ship.

DaveC426913

I don't get it. How is this relevant to the topic?

I assume what you talking about is the boundary between any given thing's insides and its outsides. In the case of a 3D human it is akin to their skin. In the case of a 2D circle it is the circle's perimeter. Is this correct?

What does it have to do with the topic other than adding confusion?