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Comment by sytelus | Hacker News Reader

It's a great axiom until it isn't. One thing I still cannot visualize is exapanding universe. If there is an expanstion then there must be a shape and then there must be a center and then must be one direction that is not exactly same as another because expansion rates are different. I read that universe expands same everywhere and there is no "center" which is very hard to visualize but it is a requirement for this axiom to be true. If you think in these terms, this axiom seems very problematic.

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The visualization that works for me is to imagine the surface of a balloon as a 2D universe. As you inflate the balloon it stretches out despite the skin having no “center” to speak of.

Put some ink dots on a balloon and blow it up.

The surface is expanding fairly well uniformly, and the dots are getting further apart. Now if you did the same with a uniform spherical balloon that's inflating somehow, there's no center and no shape to the 2d surface.

Similarly you could be inside a giant cake as it's cooking. Any two raisins will be moving apart and this happens the same way near the middle or halfway to the edge (excluding temperature/pressure unevenness). Now if you make the cake bigger until you can no longer reach the edges it all works the same everyhwere in the cake.

If you take out the non-raisin parts, and the bit where you consider that there might be edges, and that the cake started already big rather than tiny, you get the universe.

> If there is an expanstion then there must be a shape and then there must be a center

However intuitively plausible this seems to you, it's still false. The fact that our intuitive visualization capabilities cannot directly visualize the mathematical entities involved does not change that.

Mathematics is a simplification methodology and doesn't necessarily match what actually exists. So to say that the original comment is "false" means that you have to "prove" that it is false in the sense of the logical and mathematical axioms you use.

If those axioms are changed, you get a different logical and mathematical outcome.

> to say that the original comment is "false" means that you have to "prove" that it is false in the sense of the logical and mathematical axioms you use.

The comment I responded to was making a categorical statement. A single counterexample is sufficient to falsify it. The entire family of FRW models used in cosmology, in all of which the statement I responded to is false, are counterexamples.

What I was commenting on was your categorical claim that the selected portion of the original comment was false and you have not provided that mathematical "proof".

As for a single counter example, you need to demonstrate that the counter example is applicable. I don't think you have. At least not to the degree that would support your categorical claim.

In regards to both of your views, I am making no statement as to validity or otherwise of those statements. This is simply a matter of asking for you and him to provide supporting evidence for your respective positions.

This would then allow further discussion on the views and their evidence.

At same time that a center does not exists it exists. Take a line between the two sides from the theoretical border, divide in the middle and will be a center. But isn't a center.

> Take a line between the two sides from the theoretical border

There is no "border" to our universe. The fact that you have trouble visualizing such models does not mean they don't exist.

There is an "effective" border because of speed of light limits. Technically we are "at the center" of our intractable universe.

> Technically we are "at the center" of our intractable universe.

We are at the center of our observable universe, yes, but that fact does not support any of the claims I have been responding to in this thread.

But if the matter on the big bang was limited wouldn't a limit on the universe size based on how much matter exists?

> if the matter on the big bang was limited

It wasn't, according to our best current model. In that model the universe is spatially infinite and always has been, so it contains an infinite quantity of matter.

> wouldn't a limit on the universe size based on how much matter exists

There are mathematical models in which the universe has a finite size and contains a finite amount of matter. (These models are not completely ruled out by our current data, but they are considered very unlikely as compared to the ones in which the universe is spatially infinite.)

However, even in those models, the universe has no boundary: it is spatially a 3-sphere, which has a finite volume and no boundary similar to the way the surface of the Earth, a 2-sphere (at least approximately) has a finite area and no boundary.

You can have expansion with no center.

For a 2D model, consider only the surface of a balloon. As the balloon expands, each point on the surface increases in distance from every other point, but there is no center of the surface.

Be sure to consider only the surface, not the 3D embedding your (flawed) intuition wants to inject.

You can do the same thing in 1D with a circle.

This works in any dimension, including the 3+1 spacetime manifold.

The classical 'visualisation' of this is 'cake expansion'.

If you think about what's happening inside a cake when you put it in an oven, it expands in all directions, and the center has only a meaning there because the cake is finite.

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