Tuesday, April 12, 2005
Infinity - Is this a Concept that Fits in Our Minds? Updated April 16
I left this comment at Jack's blog, which I was going to wait to write something here, but since the subject came up there...
What image(s), if any, comes to your mind when you think about infinity?
Update April 13:
Jack replied:
We can certainly imagine things that are infinite (from the Latin: without an end). So I would say that we can "conceive" them. There is certainly an immense amount of mathematics that has been done regarding infinity. In fact, without a good understanding of infinity, one doesn't have Calculus, and Calculus must be valid in some respect, because its applications work so well in the real world!
On the other hand, I would agree that we cannot really "comprehend" the infinite. We are finite, and we can only comprehend finite things, and in fact most mathematics involves reducing questions about infinitely-sized sets (which we can't answer) to questions about finitely-sized sets (which we can).
I replied:
I was thinking along the lines of the problem that infinity is outside the scope of rational thought, or logical thought.
With infinity, everything we know does not make sense anymore.
Like in your math example, I think we always employ this reduction to the finite as if we were still being able to handle the infinite, like fooling ourselves, but the infinite seems outside our capability of precision. I'm not sure your conception/comprehension distinction is what I am trying to posit as the problem. I'm having difficulty wording it.
You said:
'We can certainly imagine things that are infinite (from the Latin: without an end). So I would say that we can "conceive" them.'
For example, what can you conceive as infinite?
Update April 15:
Math is not physical, that's why I think it makes sense to talk about infinite things in math (like numbers and quantities, they are abstract things).
I understand what the definition of infinite material things is (unbounded), but I question that physical things can be infinite. And it all has to do with space. No material thing can be infinite in any aspect if there is no infinite space. And I don't see how space can be infinite going outwardly, unless that "outwardly" turns around back to itself. Even the closed universe model (pictured like a globe) is impossible to make sense visually.
I wish I could take this Cosmology course.
Update April 16:
My problem with the mathematical concept of infinity applied to the physical world (someone wrote it better):
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You know, ever since I stumbled in my philosophy readings and discovered there is such a thing as infinity math (the cardinality thing, right?), I came to wonder if the concept of infinity is really sound. Can we truly conceive of the infinite? I have my doubts at this moment, but it's nothing conclusive, just something I've been wondering now and then. I don't have much time to spend elaborating on why the concept itself may be beyond our minds or our frame of thinking, but it doesn't sit very well with me.
What image(s), if any, comes to your mind when you think about infinity?
Update April 13:
Jack replied:
We can certainly imagine things that are infinite (from the Latin: without an end). So I would say that we can "conceive" them. There is certainly an immense amount of mathematics that has been done regarding infinity. In fact, without a good understanding of infinity, one doesn't have Calculus, and Calculus must be valid in some respect, because its applications work so well in the real world!
On the other hand, I would agree that we cannot really "comprehend" the infinite. We are finite, and we can only comprehend finite things, and in fact most mathematics involves reducing questions about infinitely-sized sets (which we can't answer) to questions about finitely-sized sets (which we can).
I replied:
I was thinking along the lines of the problem that infinity is outside the scope of rational thought, or logical thought.
With infinity, everything we know does not make sense anymore.
Like in your math example, I think we always employ this reduction to the finite as if we were still being able to handle the infinite, like fooling ourselves, but the infinite seems outside our capability of precision. I'm not sure your conception/comprehension distinction is what I am trying to posit as the problem. I'm having difficulty wording it.
You said:
'We can certainly imagine things that are infinite (from the Latin: without an end). So I would say that we can "conceive" them.'
For example, what can you conceive as infinite?
Update April 15:
Math is not physical, that's why I think it makes sense to talk about infinite things in math (like numbers and quantities, they are abstract things).
I understand what the definition of infinite material things is (unbounded), but I question that physical things can be infinite. And it all has to do with space. No material thing can be infinite in any aspect if there is no infinite space. And I don't see how space can be infinite going outwardly, unless that "outwardly" turns around back to itself. Even the closed universe model (pictured like a globe) is impossible to make sense visually.
I wish I could take this Cosmology course.
Update April 16:
My problem with the mathematical concept of infinity applied to the physical world (someone wrote it better):
What I believe to be the basic misconception of modern mathematical physicists - evident, as I say, not only in this problem but conspicuously so throughout the welter of wild speculations concerning cosmology and other departments of physical science - is the idea that everything that is mathematically true must have a physical counterpart; and not only so, but must have the particular physical counterpart that happens to accord with the theory that the mathematician wishes to advocate. [Herbert Dingle, Science at the Cross-Roads, pp. 124-5.]
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