h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Apology excepted! Just be careful in future.

Tango

The consequences of an infinite universe have been bugging me for a while now. I'm excited to find someone who thinks along the same lines! I think you put across the argument well, although perhaps it may be an idea to include the consequences of a finite universe too.

The main problem I find with the finite universe arguments is that, if the universe is finite, what is outside it? Maybe it might be infinite empty space. OK, that's fine, but it's still an infinite universe, effectively. And in an infinite universe, you can have a finite universe with infinite empty space outside it, *and* anything and everything else as well. This may not make logical sense, but we're dealing with infinity here, and infinity + infinity = infinity.

The main problem I find with the arguments for the consequences of the infinite universe is that with infinities, you can argue almost anything, because mathematical calculations involving infinity are often undefined.

The world as a whole needn't work like things of everyday life. So I can well imagine a finite universe with really *nothing* outside it. It hurts even less than imagining an infinite universe.

Hmm. A finite universe with nothing outside it...

...is a universe with no detectable boundary, because if there was a boundary, there would be an outside. There is no outside. The universe is all there is. The space within the universe is all the space there is. There is no boundary to that space. Space continues indefinitely. You might arrive where you started after a while. But after how long? If you can say how long, or how far you must travel to arrive where you started, you have found a universal boundary, like the circumference of the earth. A boundary suggests an outside. There is no outside. Therefore space must be infinite for there to be no boundary. The universe is still infinite.

Take the old example of the flat people. They live on the surface of a sphere. The shpere is their universe. It is finite but boundaryless. There is no way for the flat people to feel/see/detect a boundary. They can measure the space bending and draw conclusions, that's all.

The space inside and outside the surface is not part of the universe, since no interaction is possible.

Think about the surface of the earth. A few centuries ago, many people allegedly thought that the Earth was flat, and so a similar question could be asked, i.e.: does the earth go on forever in all directions, or is there a boundary?

The answer is neither, if you walk in a straight line as far as you can go, you neither carry on forever seeing new stuff, nor do you hit a boundary. Instead something surprising happens - you end up back where you started (and the surface of the earth is finite area without a boundary).

The same is possible in 3 dimensions. The universe could link up with itself in such a way that you travel far enough in one direction and come back to where you started.

That doesn't imply a boundary beyond which there is something else. In the case of the surface of the earth we know that the earth 'curves around on itself' because we can look at it in 3d. However, it isn't necessary that the surface be sitting inside some higher dimensional space in order to be 'curved' on itself. The 3d universe doesn't necessarily sit inside a 4d space in which you could see the curving, it might just be curved on itself and there really isn't anything else bigger.

>There is no way for the flat people to feel/see/detect a boundary.

How about walking around it until they get back to where they started and measuring the distance? Thus they get the circumference of the Sphere. They then realise they are in a closed universe, and that it must have a boundary.

>The space inside and outside the surface is not part of the universe,
>since no interaction is possible.

Maybe no interaction is possible - but isn't that space still there?

>That doesn't imply a boundary beyond which there is something else.

Why not?

>However, it isn't necessary that the surface be sitting inside some
>higher dimensional space in order to be 'curved' on itself.

So in what space does it curve?

Isn't a finite object, by definition, something that has a boundary?

"So in what space does it curve?"

No space.

What we're really talking about here is something called a 'manifold'.
I'll describe a 2d manifold:

You have a collection of 'blobs' of space, for example 2 blobs. Each blob looks like a chunk of normal, flat 2 dimensional plane. You also know how the blobs connect together, so you know for example that the boundary of the first blob is joined onto the boundary of the second.

Now what you end up with when you imagine joining the blobs in this way is something that doesn't have a boundary (we joined the whole boundary of the first blob to the whole boundary of the second, so we got rid of all the boundary then), and if you think of the first blob as the northern hemisphere, and the second as the southern, then you end up with the joined blobs being a sphere.

*But* we didn't ever need to mention any curving in 3 dimensions or anything like that to define this thing. It is defined purely in terms of chunks of 2d stuff. Its still finite area and has no boundary.

First, something that our universe can't interact with doesn't exist.

Secondly, just because you walk straight away and get to your starting point doesn't mean that you have experienced a boundary. A boundary is something that prevents you from getting somewhere. But there is no 'somewhere' outside the sphere since it's not part of the world.

Our discussion is actually a discussion about different ways to define the concepts. But I don't see any point in defining the things like you do.

I try to get this across with a similar thing that I always use in such discussions: the poeps. The poeps is an elementary particle without mass and charge. It cannot interact with any other particle at all. I could create a totally valid theory with the peops. But if I drop the poeps, it's still valid. Therefore scientists do that and declare that such a particle doesn't exist.

This 'space' outside and inside the sphere is something I don't think about because it doesn't exist in my image of the world. In yours it does, but it means nothing. It is a merely artificial extension to the necessary set of laws that you use in order to describe our universe.

Another example occured to me: When a train runs along a wall, is the wall a boundary for the train? Note that it can't leave the track!

No wait, I'm confused, HenryS. You end up with a sphere, and yet that isn't using 3D space? Eh? Do ya mean two 2D blobs wherein if you go to the edge of one, you are instantaneously on the edge of the other one? That would be cool, you'd go round and round and never get to an edge and eventually get back to where you started. Finite space, with no boundary. Cool. Me likey the concept. This is effectively a constrained path in 2D space, bit like the train track Cefpret mentioned. The train can never leave the track, a 2D being can never leave the 2D finite unbounded blob-space.

The train cannot interact with the untracked terrain, the 2D being cannot interact with anything outside the 2D finite unbounded blob-space. OK. But is it really justified to state, that, without a doubt, there is nothing beyond the track, that there is nothing beyond the 2D blob-space, just because neither train nor 2D being has found a way to interact with it?

On that note, I leave you with this weblink: http://oneartrow.com/Images/Photography/Paris/GareMontpar.jpg

Yes, you get a 2d sphere without using 3d space. Well, its a 2d sphere as far as a 2 dimensional creature walking around in it can tell, which is all that matters.

Yes, 2d blobs and when you get to the edge of one you are suddenly on the edge of the other.

Is it justified to say there is nothing beyond the 2D blob space? This is Occam's razor I guess - If you are a 2D being studying your world, which is a 2D sphere, and none of your experiments can detect anything but that 2D sphere, you would be justified in saying that there isn't anything else, or at least if there is, it cannot be detected, so might as well not exist.