Understanding infinity and the infinity of understanding

Scientists and mathematicians are like the rest of the world in that we all accept things that have a concise value given to them far more readily than something that cannot be given one.  In the various sciences, some have accepted the fact that we might simply be fixated on completely understanding something that cannot be fully understood.  As a society, our progress might as well be representing an approach to an infinity: simply, we are striving for reaching a point of understanding that cannot be reached.  Sounds a bit too depressing and damning, right?  It's actually the opposite.  There is the possibility that our ability to understand might accelerate to an infinity that is greater than the infinity of an understanding.  The easiest way to break this possibility down is to dumb down infinity and infinities.

Some infinities are bigger than others.  How can that be?  A simply demonstration of this is:  there are an infinite number of numbers that can exist.  That being said, there are also an infinite number of numbers between numbers (ie. 1-->2; in that, 1.1,1.01,1.001,1.0001,...-->2).  Which means, there are twice as many numbers that can exist in 1-->3 than 1-->2.  So, all the numbers that can possibly exist could be represented by a mathematical equation (Cantor's Theorem is a nice place to start if you're good at math and/or have years to kill).

Some infinities are bigger than others, so what?  Understanding the universe might hinge upon understanding infinities.  The expansion of the universe is widely accepted to be accelerating.  But to what end?  Some suggest we are heading towards a "big rip"- a cosmic limit and tipping point.  Some suggest that it can just as easily be representing an infinity that could be better understood if we had something to compare it to.  I like to compare it to the evolution of chemistry, physics, and beyond.  What people called magic 2000 years ago is called science and technology today.  Eternity hasn't changed much.  Eternity is, in fact, a little different, but it based on the same principle of something not having a limit, an infinity.  What does this have to do with understanding it instead of just accepting it?  If we can gain an understanding of how infinities behave and what laws might govern infinities, we might solve mysteries that have plagued man since...

Possible infinities:
-Size of the universe (current accepted age based on what we can extrapolate from what we can see)
-Number of dimensions (3 dimensions satisfies most, but a fourth, time, resolved problems in physics.  Now, we think there might be as many as 11, but who can prove that there has to be a limit of dimensions?)
-Smallest pieces (energy seems to be that limit, but what if energy could be broken down further?)
-Consciousness (there might be an infinite number of variables involved)
-God
-Age of the universe (if the universe cycles, that implies that it could have existed before the big bang and we'll keep bangin' forever: thus, the possibility of an infinite measure of time)
-Understanding (it might simply be impossible to figure it all out: that's what God is for)
...