if the universe is infinite and we are a part of it, are we (humans) infinite as well. Can you ever carve out a piece that isn't infinite?

This is another question I have pondered.  If the universe is indeed infinite, then it's infinite in every direction.  Wouldn't there be as much infinite space within my body as the rest of the universe?  

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Agree.

Human beings are so many feet tall, most having two arms, two legs and so on and so forth, and in that regard, we are quite finite.  The one thing we have which I'm fairly certain sets us apart from all the other denizens of this planet is Imagination.  That quantity can't be contained in some cases to the interior of an atom or the spaces between galaxies.  Imagination of what might be, when disciplined by what we know already of what IS, may take us anywhere in this universe and possibly beyond it.

If there is an infinite element to this reality at all, I think it may be found in imagination.

Oh! I like this!

Is the universe infinite yes, this means that you could travel for an infinite distance in any direction and not find an end though you may reach an area of space devoid of matter.

However your body is finite it has dimensions and those dimension are relatively fixed so anything travelling through your body will either come out one end or the other.

Some people have difficulty handling finite and infinite together they do seem at times to be concepts that shouldn't exist together. For a look at infinity in the universe - http://youtu.be/t80qywmnADM

Why is it so much easier to imagine infinite as being out there somewhere instead of right here.

Obviously at our scale infinitely small would be the order of the day and that really wouldn't impact our seemingly finite bodies.  If you hold your hands out and extend your index fingers and hold them a couple of inches apart and you say it is infinite in either direction away from each finger, then why wouldn't it be the same in between them.  

It comes down to the definition of infinite. Infinite is completely and absolutely without end or limits The distance between your fingers or even between two stars even if you measure them in diameters of an atom it will still be a finite number even if an incredibly large one. Even if you then multiplied the two numbers together you still have a finite number.

I'm not sure math works here.  Math doesn't like infinite because it really isn't a number.  Although math  can describe much of our physical world and helps to provide the empirical evidence for hypotheses and theories, I just don't think it helps here.  When you start thinking about 11 different dimensions (string/brane theory), black holes, white holes, multiverses, etc., it's not hard to imagine the space between my fingers could be infinite (or close to it) as well.  I'm sure ultimate reality is stranger than that!

I can't get my brain around infinity! What is it? How do I experience it? It is like a million or billion, or trillion of stars. As I look into the night sky on a clear night in the forest of NE Washington state I can't see all of the Pleiades because of my dimming vision, but if I look though binoculars or a telescope I can see many more. Show a picture taken by the Hubble telescope or by the Cassini mission, I am in such awe and full of wonder, that space and time that is present in the moment of viewing is all I can take in. The concept of infinity escapes me, even as the beauty inspires me ... I am part of this universe and all that is, and so are you. We exist for such a very short period of time. By golly, I am conscious of all I can see!

My concept of life, any life form, flora or fauna, made up of atoms, die as part of the scheme of things. I return to atoms from which I came; I dance as an atom through the stars just as I did before my conception.  

The Earth, as a planet, is not permanent either. It will change over time and when our sun explodes into whatever a sun explodes into, it will become the dust that supplies the raw material for new planets.

Well, reality just hit, the dogs and cats are up for the morning and I have at least an hour of rubbing ears and giving tummy rubs. That is my actuality that I comprehend. 

It isn't known whether or not the universe is infinite. 

Whether the universe is infinite or not depends on its shape.  If it curves around like the surface of the earth, it's finite.

If it's flat, it could either be infinite like a flat sheet, or wrap around, which would make it finite.

If it's saddle-shaped, it's infinite.

The universe is now known to be within about 0.4% of being flat

So we still don't know if it's finite or infinite. 

We can only see out to a finite distance, though.  That's because the universe is expanding, and space that is farther away than a certain distance, is expanding away from us faster than the speed of light.  So the light from stars farther away, will never reach us. 

Wouldn't there be as much infinite space within my body as the rest of the universe?

Your body has a certain volume, so there's that volume of space in it.  Other than volume, what could an "amount" of space mean? 

That is a tricky one for me to try and visualize.  How is the universe flat when we live in three dimensions (4 with time).  Unless it's like a when you see a piece of paper is looks flat, but if you magnify the surface, there are actually mountains and valleys.  

As far as volume and what is inside my body (and I used my body because you can say this about anything physical including a single subatomic particle.  If space is truly infinite isn't it infinite in every direction.  Where would you ever find a stopping point.  If I took a cube of space and kept looking deeper into with some kind of device (imaginary of course) what would the stopping point look like.  You have looked as deep as you can and this is the stopping point.  What does that look like or imagine it to look like (represented in some visualized model that is).  Much easier to contemplate is looking out.  It's seems much more plausible you would either come back to where   you started looking or bump into some type of brane (another brane).

If the universe is finite that doesn't mean it has a stopping point.  It could wrap around like a video game screen or like the surface of the earth.  You would never come to an edge where the surface of the earth ends, no matter how far you travel.  But the earth is still finite in size. 

Whether a 4D spacetime is flat, positively curved or negatively curved is described by the scalar curvature.  

In a flat space, the surface area of a sphere of a given volume is the same as it would be in a space with no curvature.  In a positively curved space, the surface area of the sphere is less than it would be in a flat space.  In a negatively curved space, the surface area of the sphere is more than it would be in a flat space. 

Here's an example in 2 dimensions:

If you drew a circle on a sheet of paper, the length of the edge is 2 π r, where r is the radius of the circle.  The area of the circle is π r squared, so the ratio is 2/r.

But suppose you drew a circle on the earth, around the equator.  The length of the edge of the circle is 2 π r, where r is the radius of the earth.  The area of the circle is 2 π r squared, since the surface area of the whole earth is 4 π r squared.

So the ratio of the edge to the area of this circle is 1/r - half of what it was for a flat surface.  So the surface of the earth is positively curved. 

Never thought of it that deeply. I am impressed.

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