Gamers Rule! Universe Shaped Like a d12

[DMScott]

From the article:

For anyone who is bewildered by the idea of infinite space, the new model could prove slightly comforting.

I guess those of us who are bewildered by the idea of finite space are left to find comfort in ice cream. Somebody pass the neapolitan...

 

[shilsen]

Just out of curiosity, is the theory laid out in that article really so new? I know I've heard this elsewhere, because I've been saying to my gamer-geek buddies for a while now that travelling through the universe was like moving around on the inside of a sphere - eventually you'd return to your point of origin, and never reach a defined "boundary" that marked the limit of the universe.

It's been done - if not precisely the same - before. Even the old Ptolemaic system of the universe being divided into a series of spheres one around the other has a lot of analogues to this one as far as the shape of the universe and the impossibility of travelling to the "edge" or beyond is concerned.

 

[Pbartender]

Could you explain please?

Certainly...

Consider a two-dimensional man. He has only height and depth, no width. He universe is a flat plane, much like a sheet of paper, but with no thickness at all. To us, looking at him from the third dimension, he'd look like an odd cartoon person. We'd be able to see his insides, since only a sinlge loop of line would be necessary to hold them in. He would only need two legs (not three or four) to create a stable base. He would need an arm (and eyes) on each side, since he cannot truly turn around with standing on his head. His mouth would necessarily be on top of head, to be reached by both arms. He would have no *AHEM* anus, since a digestive tract with two exits (or entrances, depending on how you look at it) would split him in two. There's other neat effects to be explained here, but I'll get on to the universe bending stuff...

Now, right now, his universe sits on a table top. It's flat with no curvature. If our alien travels in any direction, he will eventually reach the edge of the 'universe'. This is a "flat" 2-dimensional universe. In terms of the big bang, this is a stable universe, which has a perfect amount of mass and will continue on for all time. After its creation, it expands for a finite peroid of time, before ceasing expansion and maintaining a fixed size. Eventually, all mass and energy will be evenly distributed across the universe, which results in 'heat death'.

Ok. Next, (this is a little tricky) we take the flat universe, bend two opposite corners down, while bending the other two corners up. This should produce an odd shape vaguely reminiscent of a saddle. This universe has a negative curvature. It is the "open" 2-D universe. In terms of the big bang, this is a super-stable universe, which has too little mass to maintain its size. After its creation, it expands, and continues to expand (essentially, all the mass of the universe is moving faster than the escape velocity of the universe). Since our alien will never be able to travel fast enough to catach the edges of the universe, the universe is essentially infinite from his point of view. Much like the "flat" universe, this universe will continue forever, and eventually suffer from heat death.

Finally, we take the flat universe and carefully wrap it around a balloon. The result is a universe shaped like a hollow sphere. This universe has a positive curvature. It is the "closed" 2-D universe. It is an ultimately unstable that has too much mass for its own good. The universe cannot exape its own gravitational pull. After creation, its expansion will eventually slow down and reverse itself, to finally 'crush' the universe in upon itself in a 'Big Crunch'. Our poor doomed alien can travel in any diretion he likes, but because of the curvature of space, he cannot escape as he eventually returns to his starting point. To our alien, the universe looks infinite, but it eternally and regularly repeats itself. Depressing, eh?

You can vary the topologies by creating cylinders, or toroids, or ridges or whatever, but those are the three basic ideas.

The favored theory varies from year to year, and is continually argued over. It appears the latest cosmologists think that our universe is a variation on the last.

Now... You just need to imagine our 3-dimensional universe bending into the 4th dimension.

Good Luck.

 

[der_kluge]

Pbar, that's interesting. Now, maybe you can explain this to me -

If the universe has a shape, doesn't that imply that there is something beyond it? I mean, if I have a soccer ball in my hand, where is the hand?

Can't it be enough to just say that it is infinite in every direction and be done with it? This whole shape business has me confused.

I think whoever came up with the elephants on the back of a giant tortoise idea had it right!

 

[MerakSpielman]

Pbar, that's interesting. Now, maybe you can explain this to me -

If the universe has a shape, doesn't that imply that there is something beyond it? I mean, if I have a soccer ball in my hand, where is the hand?

Your hand in this instance would not exist in any definable sense as far as anything in that universe is concerned.

Let's stick to the sheet of paper 2D universe. The sheet of paper is infinite in all directions. As a 3D person, we see a 2D creature as a flat thing moving on the flat surface of it's universe. The vision of the flatlander )) is limited to his plane - he can't see us. No matter how far he travels in any direction he can never reach us. To him, we exist is a mythical place that can only be theorized and never interacted with. To him, we might as well not exist at all.

We could poke the piece of paper, bending it, folding it, whatever, and the Flatlander wouldn't percieve a thing because his universe is being manipulated in ways that are invisible to him. Maybe we, as mysterious creatures from the Third Dimension could take his universe, and fold it so that one layer was parallel to the other. Then, using Universe Scissors, we cut a strip from one layer and tape it to the end of a strip from the other layer, creating a bridge between two remote locations in Flatland. This would look very odd indeed from the perspective of the Flatlander, who could now magically travel from one place to another instantly (though horrible things would happen should he wander off the edge of the strip while traversing it).

This is essentially what sci-fi writers propose we do for space travel - except we use the fourth dimension (assuming it's a spacial dimension, not "time") and connect two distant points of physical space so that we can travel instantly across far distances without breaking any rules about the speed of light. Nobody has any idea how to go about doing this.

This is also where the term "parallel universes" comes from. If we're a Flatlander, perhaps there are other "sheets of paper" universes, also infinite in all directions, but existing in the mystical 3rd Dimension and parallel to ours, so they never intersect. Perhaps there are infinite numbers of these.

All the Flatlander examples (pretty much stolen from the book Flatlander) are supposed to be analogies to try to try to understand the 4th dimension (if it exists). It's easy to imagine parallel, infinite plane-universes, but hard to imagine parallel, infinite sphere universes.

More fun with dimensions:

If we can see all sides and the inside of a 2D creature, then a 4D creature would be able to see all sides and the inside of us, all at once.

If a sphere were to pass through a 2D universe, the confused flatlander would observe a circle, expanding rapidly from a single point, and then contracting again (more accurately, he would "see" a line, but assuming he has some sort of depth perception, he would realize it was a curved surface and assume a circle). Thus, if a hypersphere (a 4th dimensional sphere) were to pass through our 3D universe, we would see a sphere, expanding rapidly from a single point, and then contracting to a single point again and vanishing. Seeing a 4th dimensional creature would be strange indeed, since we would only be able to see and interact with the portion of it that was currently in our universe, really only a tiny "slice" of the whole creature.

 

[Ashrem Bayle]

Einstein was wrong after all. God does play dice with the universe!

Our universe is His d12. Maybe there are other universes that are his d4, d6, d8, d10 and d20. I always suspected He was the big DM in the sky.

So are you a PC, or an NPC?

 

[Kamard]

I find this highly disturbing. Mostly because the ancient greeks picked the dodecahedron to represent the universe. So, we haven't discovered anything the greeks didn't already know.

spooky.

 

[DanMcS]

Most scientists theorize that the universe is one of three general "shapes"...

Open, flat, and closed refer to the expansion rate of the universe, not its shape. Unless they use it for that too. Now I just blew my mind.

 

[Caliber]

Theres something about the mortality of the Universe that always makes me a little sad.

Poor Universe. What did it ever do you?

 

[MerakSpielman]

Theres something about the mortality of the Universe that always makes me a little sad.

But think of it this way. Most scientists are agreeing (at this moment in time) that the universe is most likely going to keep expanding forever, and eventually suffer heat-death as all the available energy is expended.

Now, if the universe repeats after a certain (huge) distance, eventually all of that matter, while still accelerating away from the central point, and never having changed direction, will suddenly end up there again. Voila! Heat death and Big Crunch.

Another way I like to say this is that after an infinite amount of time, all matter in the universe will be infinitly far away from all other matter in the universe. This seems to me to be in some bizarre way the same as all matter occupying the same infinitely large single point, which is very much like the state of the universe that resulted in the Big Bang in the first place.