# Finite universe

1. Mar 30, 2006

### wolram

How do you imagine a finite universe ? i find it very difficult.

2. Mar 30, 2006

### marcus

remember we are just talking SPATIAL finite

timewise it can still go on forever

what is the problem imagining a spatially finite universe?

it is the old "surface of a balloon" thing except the surface of a balloon is only 2D and you have to think of what would be the 3D analog of that.

3. Mar 30, 2006

### wolram

Hi Marcus, i do not want to go into the philosophy, it is just that i can not
imagine, (get a picture in my mind) of a finite universe, this is a problem i
encounter, i need a picture to make it real.

4. Mar 30, 2006

### Distant

Indeed it is difficult to imagine a finite Universe. It is much easier to imagine what it must have been like to live in a time before it was known that the Earth was round and that gravity kept us all from falling off the surface. In such a time a similar question to the one of the finite Universe was posed about the surface of the Earth. After all, we can see that the surface extends to the horizon in all directions. If we walk towards the horizon then the limit of the horizon moves with us and we can see how the surface extends further. So surely there can be only two possibilities. Either the surface extends on, forever, and if we carried on walking towards the horizon we would forever encounter new lands, or the surface if somehow ‘bounded’. Maybe we would reach some solid impenetrable wall through which we cannot pass – or maybe we would fall off the edge! (to where exactly wasn’t clear!). Of course, sea voyages set out to investigate the truth of the matter and I am not aware of them encountering either of these problems.

Although we may now view such thoughts in a rather patronising manner, without an understanding of the concepts of gravity and the spherical planet they are natural and logical questions. The spherical shape of the Earth ‘squares the circle’. It does not have a bounded edge to its surface, but it is not infinite – magic! (of a sort).

It required new (rather none intuitive) concepts to understand this problem. We are generally not aware of the curvature of the Earth. The planet is too big and we move too slowly to notice it. It would have been hard to convince to old “flat Earthists” that people living in a far off continent were, in effect, “upside-down” relative us!

Now, back to the Universe. Physicists tell me that the 3 dimensions of space are not the whole story. Time itself can be treated as another dimensions to describe something they call “spacetime”. Just as we once had an inability to notice (or comprehend) the curvature of the earth (nowadays we can view photos from space easily portraying this) we ‘similarly’ have an inability to notice or comprehend the curvature of this spacetime. Trying not be be a modern day equivalent of a “flat Earthist” we may choose to accept the word (and mathematics and experimental evidence!) of the physicists on this point. The point being is that it is postulated that spacetime if also curved, like the Earth is in 3 dimensions in order to produce a 4 dimensional spacetime Universe that is neither bounded nor infinite.

I fear that a more ‘natural’ understanding of such a ‘closed’ Universe, in the same way as we understand and experience a 3 dimensional ‘closed’ sphere, may not be possible. Maybe because our brains are not set up to work in 4 dimensional spacetime.

However unsatisfying this explanation maybe to the none physicist like myself, it surely surpasses the cosmological equivalent of the brick wall at the edge of the Universe, or indeed ‘falling over the edge’!
Ahhhhhhhh!…………

5. Mar 30, 2006

### wolram

A warm welcomb Distant, it all ways gives me a glow inside when people
answer my some times inane questions, your anology with the flat earthers
is good, but when it comes down to all there is, my mind just can not cope,
i try to understand, but some times these theories are just so unintuitive.

6. Mar 30, 2006

### marcus

if you keep telling yourself it is unintuitive you will make it worse.

do a series of "analogy pushups"

start by thinking of yourself as a 1D being living on a straight line
who imagines adding a "point at infinity" to his world, an extra point that fills the gap between + oo and - oo

so that if he goes faster and faster to the east he eventually comes whizzing in from the west

and he doesnt believe this is real, it is just an abstract mathematical idea for him

he has INVENTED THE CIRCLE, never having seen one, as a mathematical idea.

then 1000 years later the 1D astronomers uncover evidence in the CMB that their actually is a circularity of the universe. they discover that what was just a math idea is actually REAL and they are left scratching their onedimensional heads.
====================

push up to the next level analogy, think that you are a 2D being living in a flat plane, or one that looks flat to you. being an abstract thinker you imagine that there is a "point at infinity" so that if you go racing off in a straight line in any direction you will eventually come zooming in from the opposite direction

you have INVENTED THE MATHEMATICAL IDEA OF THE SPHERE as best as you can imagine it with your limited 2D wits.
it is like you are at the south pole and of the earth and it seems like an infinite flat plane, and the point at infinity is the north pole. so any direction you go in, departing from south pole, you eventully return from the opposite direction.

and maybe years later they discover that this idea of a sphere is REAL and actually how nature is.
=====================

push up to the next level analogy, now you are a 3D being living in a regular square-angle normal euclidean 3D space, analogous to the 2D flat plane.........and you imagine a "point at infinity" is added to your 3D space so that if you go off in a straight line in any direction then eventually after a long enough time you come back from the opposite direction.....
you have done something mathematically creative: you have INVENTED THE SOCALLED "THREESPHERE"

and maybe after hundreds of years the astronomers could supply evidence that what you thought was regular 3D space actually was a threesphere all along. All that time you were living in a threesphere, which you thought was a mere abstract concept.
========================

technically the ordinary sphere----the surface of a balloon---can be called a TWOSPHERE because the local neighborhood of a point looks like a normal flat 2D plane

and a circle or a ring could be called a ONESPHERE because the local nbd of a point looks like a bit of an approximately straight line

so all we are doing is imagining this kind of thing with the dimension jacked up, to get a threesphere

and anyway, Wolram, there are SEVERAL kinds of finite 3D spaces possible------the threesphere is not the only one. there are a whole bunch, just like in the 2D situation you can have donut shapes with more than one hole. But this does not matter. It is enough to just imagine one possible spatially finite 3D thing----and the threesphere is good enough.

Before falling asleep every night, try to imagine that you live in a threesphere, and if you shine a light off in one direction then that same beam of light will eventually get back to you from the opposite. (unless the poor lightbeam has been frustrated by having the space go and expand faster than it can cope with but expansion is another business, ignore that for the while)

Last edited: Mar 30, 2006
7. Mar 30, 2006

### wolram

Thankyou very much Marcus, what you say in words makes perfect sense,
but to form an image in ones mind is much harder, maybe i am to stupid, i wish i could understand.

8. Mar 30, 2006

### marcus

it makes it worse to keep supposing that one is stupid---one is a human and that involves certain brain limitations which one tries cheerfully to overcome.

try to imagine what it would be like to BE IN a certain space

don't try to imagine what it would look like to a God who is somehow on the outside of it.

we are not asked to imagine what it would look like to an higherdimensional being outside of space

just get a feel for what to expect if you are a 3D creature, which we all are, living in a threesphere

all it means, really, is that if you send a lite-beam off in some direction out in front eventually it will come back from behind you

as 2D creatures living on a Twosphere (the surface of the earth) we are ALREADY USED TO THAT kind of behavior-----of being able to head off in some direction and eventually get back to the same place having gone around

so the analog (3D "flat" space with a point at infinity added) can't be so hard to imagine what it would be like to live in

(forget about God's point of view, just imagine living in it)

9. Mar 31, 2006

### Chronos

While a spatial finite universe is difficult to imagine, a temporally finite universe is less difficult. It is, for me, easy to picture a universe where you are both at the center and the edge due to the finite speed of light.

10. Mar 31, 2006

### wolram

Thanks Marcus, i do have a picture now, it may be a little fuzzy, almost
abstract, but at least i can think about it now.

11. Apr 1, 2006

### Silverbackman

Hmmm, so I guess it is impossible to imagine looking a threesphere like we look at a balloon or a ball. Damn I hate being human.

Then again I know more than a being from a dot, circle, and twosphere world. Is it possible for a foursphere, fivesphere, ect. ect. till infinite? Of course we can't imagine these other spatial dimensions, similar to how a 2D being wouldn't be able to imagine a 3D world or twospere.

But doesn't the known curvature of the universe suggest that we live in a flat universe and not a saddle or sphere universe? If so then how can we be living in a threespere?

12. Apr 1, 2006

### SpaceTiger

Staff Emeritus
I don't understand the question...

Measurements of flatness are local. If inflation occurred, then the universe will be much, much larger than the region of space we can observe and, regardless of its true large-scale geometry, it will appear flat to our instruments. It's basically the same reason the ancients thought the earth was flat -- they could only see a very small part of it.

If inflation had not occurred, however, this wouldn't be the case and we should, in principle, be able to measure the curvature of the entire universe.

13. Apr 1, 2006

### wolram

I have an idea to call my image the, ( frustrated boomerang), curved space
with expasion.

14. Apr 4, 2006

### VikingF

I think he wondered how many dimensions that can possibly exist. If there may be "infinitely many" dimensions... (1D,2D,3D,4D,....,?D).

15. Apr 5, 2006

### -Job-

One second though. The possibility that we live in continuous unbounded universe, the equivalent of a 4D sphere follows rationally and is more plausible than a finite universe or an infinite universe that does not "wrap-around". But regardless, if we live in a 4D sphere, then this 4D sphere is in 4D space. How is this 4D space then bounded? Is it infinite or finite? Does it wrap around? The alternative is that we live in a 4D sphere which does not reside in space, but then the notion of dimensions should not apply, and it's not a 4D surface at all.

Last edited: Apr 5, 2006
16. May 4, 2006

### Silverbackman

You mean torus?

Yea, I wonder what a eightsphere universe would look like. Or how about a 1,678,489,986sphere?:surprised :surprised :surprised

17. May 4, 2006

### Flatland

I actually have a problem imagining an infinite universe. And a universe with an infinite dimensions? you wouldn't be able to go anywhere.

18. May 4, 2006

### setAI

I conjecture that it is possible for a finite AND flat universe without the topology of a torus or similar form- in fact it can have ANY arbitrary topology as long as it is closed-

how? it is a natural result of computational /category theories and some forms of LQG where the metric of spacetime itself emerges from relationships- for instance the universe can be decribed as a 2-dimensional lattice of 2in/2out quantum logic gates- one could construct such a lattice of quantum logic gates on the surface of a sphere- or any other closed shape- yet the topology of the emergent spacetime metric could compute a FLAT spacetime that wraps around-

consider a classical computational analog: the game Asteroids- where the ship flies straight but wraps around when it hits the edge of the screen- the virtual space of the ship is flat- but the edges are connected in the software- so the virtual space is finite yet unbounded

19. May 4, 2006

### VikingF

Yeah... Me too! :tongue:

According to String theory, there exist 10 dimensions, and M-theory says that there exist 11.

20. May 5, 2006

### Silverbackman

Yea but they say those dimensions may just exist. It doesn't have anything to do with the universe being a tensphere or elevensphere I think. Or does it? Actually it probably does because I assume 10 or 11 dimensions cannot exist unless is within some sort of nsphere (or something like an nsphere).

If we do live in a threesphere only that would mean there are four spatial dimensions and one dimension of time. That sounds pretty aesthetically perfect considering 5 is a "perfect" number. Both 5 and 10 seem like aesthetically perfect because of their place on the number line. Why an omnipotent God or even randomness of Nature would pick 4, 7, or 11 as the "official" number of one of the most important aspects of our universe is beyond me.:uhh: