the universe is a soccer ball? (1 Viewer)

[RobertR]

The universe is finite," he said, "but there's no boundary to it," implying that there is no beyond, or that if there is, then its nature is left to your imagination and is outside the closed system that astronomers can ever hope to see.

This is exactly why I have so much trouble with the "finite, unbounded" 3D speherical (or multihedron) analogy. Every time we picture it, it's from the viewpoint of an observer who is external to it. It's a given that there is existence external to the object. So when we apply the analogy to the Universe, it seems to me that it's clearly implied that the Universe is contained within still HIGHER, external dimensions.

And that tells me that, therefore, we aren't really talking about the Universe, as in "the sum total of everything that exists".

We're only talking about an infinitely small part of it that our minds can cope with having knowledge of.

 

[Andrew Testa]

Every time we picture it, it's from the viewpoint of an observer who is external to it.

That's a problem of having to drop it to lower dimensions to describe it. It's kinda hard to draw a geometric representation from the inside and make any sense of it. We understand the difference between circles and squares because we can see the 2D shapes from a 3D perspective. If we only had a 2D perspective they would both look like lines. We couldn't distinguish between them. As was stated in the article, the dodecahedron doesn't really exist somewhere where you can see it from he outside. You could see it if you could cut sections out of the universe. It's really more a map that describes how the sides connect together than a representation of the actual shape.

The unbounded part means that there is no outside to observe from. No "edge" or "wall" exists to delineate inside from outside. Everything is inside. There is no outside. So we are talking about the sum total of all that exists, since "existance" can only be defined in terms of the physics internal to the universe.

Andy

 

[BrianW]

Exactly. The lower-dimension models are simply visualization tools, and not intended to suggest that some pan-dimensional being may be observing this thread from outside the Universe and commenting to his pan-dimensional friend, "Uh oh, Frank, they're on to us."

But these visualization tools don't exactly rule that possibility out, either. So if you find it interesting or entertaining to think about higher-dimensional possibilities, like our 3-D Universe (not counting time) being the product of the the intersection of two 4-D universes within a 5-D space (just as two planes intersect to form a line withinin a 3-D space), and that every particle in our Universe is produced by an intersection of two filaments within the intersecting 4-D universes, and that the two 4-D universes moving relative to one another within the 5-D space produces what we perceive as time, then I say ponder away!

...not that I would ever be caught doing such a thing, mind you.

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Someone brought up the old Atari Asteroids video game. Just for fun, and to see how well we can visualize these lower-dimensional manifolds in 3-D space, can someone name the three-dimensional object whose surface is described by the Atari Asteroids universe?

Hint: It's not a sphere. (Or a dodecahedron, for that matter. )

 

[Andrew Testa]

can someone name the three-dimensional object whose surface is described by the Atari Asteroids universe?

(hand waves wildly) OOH! OOH! Mr. Kotter! Mr. Kotter! I know! OOH!

yeah, I don't count, I know.

But, can someone also tell what topological feature distinguishes this manifold from a sphere?

Andy

 

[Mike Wladyka]

But, can someone also tell what topological feature distinguishes this manifold from a sphere?

well, it still kinda has corners, and also null space

am i close?

also, on the topic of more dimensions i remember something that stephen hawking said in which he stated that there was 11 dimensions...does anyone know what they are?

 

[BrianW]

am i close?

Forget the corners for now, and just work with the edges. All the corners do meet (so you're close), but you've also got to stitch up the edges (which is actually easier to do than the corners).

The 11 dimensions that Hawking was refering to was probably in reference to Superstring Theory, which is a mathematical model that employs 11 dimensions to explain, not just our Universe, but just about any universe you could possibly imagine. (Indeed, that's the biggest problem. It has an infinite number of solutions, but only one of them is "ours.") Though theoretical physicists adore this theory and often speak as if its 11 required dimensions actually exist, it is just a mathematical model and has yet to undergo even a single test to prove (or disprove) its underlying assumptions. As such, I think it's premature to state as fact that there are 11 dimensions to our Universe (though I've been guilty of doing just that in the past).