Finite but unbounded, what does this mean?

I'm confused by this terminology, when someone tells me the universe might not be infinite, but rather, "finite but unbounded."

What in the world are they talking about?

Relevance

Finite means that it can be measured using a real number.

Unbounded means that it has no "end".

Normally these two words are contradictory.

However, in geometry, they can be used separately.

Take Earth's surface: it can be measured with a real number.

Knowing Earth's radius (a finite number), we can measure Earth's surface area. It is finite.

However, if you start off in a given direction, you will never reach the end. In the 2 dimensions of the surface, you can travel in one direction and never reach the end. It is unbounded. There is no real number that can represent the maximum number of kilometres (or miles) that you can travel in one direction.

Mind you, you will pass over your starting point over and over again, but that is because the surface is finite.

Some people think that space is a similar arrangement, except that it is a 3-dimension volume, "wrapped" around a finite radius in a 4th dimension. You start off in any direction, you will never find an end. However, if you could travel long enough in that direction (without turning around) and if it were not for expansion, you would eventually pass your starting point.

Others believe that the universe is really infinite in spatial extent (it extents forever in any given direction. Of course, if it is truly infinite, then it is also unbounded (there is no end).

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The word "unbounded" also has other applications which are similar -- but not quite the same.

Two objects are "bound" if they are held together by gravity. Earth is in a "bound" orbit around the Sun. The Voyager probes are on "unbounded" orbits and will (eventually) leave the solar system, never to come back.

The term can also be used to describe the density of the universe: is there enough matter in the universe, so that gravity will eventually win and cause expansion to stop? If yes, then the universe would be "bounded" by gravity. However, for now, it appears "unbounded": expansion would continue forever.

• Anonymous

The surface of a sphere is a finite but unbounded two dimensional surface. It is 2D because any point on it can be referenced by latitude and longitude (just like on earth). It is finite because it has a fixed size. It is unbounded because it does not have an 'edge'. Traveling along the surface you don't come to an 'end of the sphere'.

One of the models of the shape of the universe is a 'finite but unbounded' 4-dimensional space-time. I can't visualize it either.

• 4 years ago

What Does Unbounded Mean

• Anonymous

"Finite but unbounded" refers to a concept that involves multi-dimensionality.

We are three-dimensional beings in four dimensional universe. We live on the surface of a four-dimensional hypershere. There is no "end" to that surface, but if we were able to perceive the universe from the perspective of the higher dimensionality, we would see that it is in fact finite. However, as long as we are bound to the surface, we are unable to perceive this directly and must infer the true nature of the universe without direct observation.

Here's a video from the late great Carl Sagan explain it a little better.

• Anonymous

It means the universe is only so big, but you can roam around as much in it as you want to and you'll never find any walls blocking your way. It's a little like an ant crawling around on a basketball. He can go around and around and around. But that doesn't mean that the basketball is infinitely big, does it? No. The basketball is finite in size, but its surface is unbounded. See the ant go around and around. Never does it meet any walls to stop him.

The surface of the Earth is finite -but unbounded...

• ?
Lv 5

The answer to this and many other questions may be found on a web site called

The Universe Explained. A Yahoo search finds it near the top of the page and it is

the .org.uk one. Use the feedback to have your say on the content. It is written in plain

everyday English so is easy to understand even for novices on the subject.

• Irv S
Lv 7

The simplest way to imagine it is that there may be a

limited amount of 'curved space/time'.

Think of the surface of a ball.

There are no edges. - A line will continue indefinitely,

meeting no obstacle.

But there IS a limited amount of area.

That's the easy part.

The hard part is imagining such a two dimensional surface expanded to

three dimensions.

• 6 years ago

Just maybe the universe is in a sphere and the end is the beginning it's in closed and it has always been in existence ,