What is infinity?

[Cliffy]

It is everything ... and it is nothing.

Or... it's neither here nor there. To me it is like the idea of god. It is too vast for our finite minds to comprehend. We might be able to imagine the concept but never the reality of it.

 

[hermanntrude]

the same is true of 4-dimensional shapes. No-one can imagine a hypersphere... but nevertheless they're a conrete concept... we know how many faces it has, how many edges, vertices, we know what a plan of it looks like, we know what the shadow looks like... but we can't possibly imagine the actual shape.

 

[SirJosephPorter]

I think infinity is a concept, a mathematical tool to tide scientists over awkward spots in mathematics, nothing more.

In simplest terms, imagine the largest number you can, the largest number possible. Infinity is bigger than that.

Without the concept of infinity, many expressions in mathematics would become meaningless. 1 divided by zero, tan (π/2) etc. Infinity lets us conveniently express these quantities. I wouldn’t put much more significance than that, infinity doesn’t really have any physical meaning.

Can somebody give me an infinite number of dollars? I sure could use them.

Then of course, there are orders of infinity, aleph null (set of integers), aleph one (set of real numbers), aleph two (set of complex numbers) etc. Alephs themselves can go to infinity.

These are all wonderful, fascinating mathematic concepts, but don’t really have any physical interpretation.

 

[SirJosephPorter]

the same is true of 4-dimensional shapes. No-one can imagine a hypersphere... but nevertheless they're a conrete concept... we know how many faces it has, how many edges, vertices, we know what a plan of it looks like, we know what the shadow looks like... but we can't possibly imagine the actual shape.

I think hyper sphere or hyper cube is different from infinity. While infinity is strictly an imaginary concept, a convenient tool, the String Theory of Cosmology tells us that hyper cubes and hyperspheres may actually exist.

String theory postulates the presence of ten dimensions, and eleventh of time. So there is nothing imaginary about four dimensional objects, they may really exist. Infinity however, remains a concept, with no representation in reality.

 

[darkbeaver]

Infinity and the big bang. Are they both true in the same way or is only one true or are both wrong? I know it's a clumsey question, but to bad, there it is.
If we accept the big bang then we accept the finite limits of the universe don't we? How do we stuff the infinite into the finite, even in a theroretical way? Psycologically why do some of us require fixed limits and some of us cannot envision them comfortably?

 

[Cliffy]

I think that since we are born, those around us have been very diligent in imposing limits on everything we think and do, establishing our boundaries. We become uncomfortable without boundaries. We may rebel against them but in short order we seek them and then continue the practice when parenthood comes along. This is social conditioning and it imposes limits on what we can conceive and perceive. It keeps us stuck in 3rd dimensional reality.

But if we could raise a child without limits, it would in all probability break free of our limitations and be able to not only conceive of infinity but perceive it as well.

 

[hermanntrude]

I think hyper sphere or hyper cube is different from infinity. While infinity is strictly an imaginary concept, a convenient tool, the String Theory of Cosmology tells us that hyper cubes and hyperspheres may actually exist.

String theory postulates the presence of ten dimensions, and eleventh of time. So there is nothing imaginary about four dimensional objects, they may really exist. Infinity however, remains a concept, with no representation in reality.

My point is that we can't imagine either of them. But you are correct in your distinction between the two... assuming, of course, that string theory is correct, which is a long way from true.

 

[darkbeaver]

The circle was invented to address infinity. The tail eating the head. The torus.