Separate, Unequal Infinities

Adam Elenbaas
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German mathematician George Cantor has discovered that within the infinite realm of natural numbers (1,2,3,4, etc), there are realms of infinite real number sets (1.234235, etc) that vary in size - some larger or smaller than others. In other words, there are entrances or gateways to many separate infinities and some really are bigger than others.

If we make the quantum leap between numbers and experiences, figures and questions, sets and seasons, then the implications are vast. It may be important to keep in mind that all of our concepts and experiences of love and judgment, all of our "natural" questions of divinity, and all of our paradoxical dilemmas may in fact have some "real" answers - and though the infinite is infinite, depending on where you're at, things might not all be equal.

Comments

um, could you elaborate on

Submitted by amoneymoore on Wed, 08/22/2007 - 23:45.
um, could you elaborate on this?

The article itsel does a

Submitted by Adam Elenbaas on Thu, 08/23/2007 - 11:20.
The article itsel does a much better job than I can of explaining the mathematics. But, philosophically, I can try to help. We often think of all things as relative. We think that the universe exists without absolutes---but we'd need an absolute statement to suggest that absolutes, absolutely, don't exist. What math like this suggests is that, in an infinite universe, absolutes do in fact exist. They just exist relatively. In other words, lock into an absolute and its real. Disengage from it and it becomes a relative absolute. Some infinities are bigger than others. I think that this is vital. It means that we have to recognize that our absolutist thinking enemies we so often despise are not "wrong." Hierarchy and quantitative or qualitative comparison, perhaps, need not be feared. Adam Elenbaas

I still don't get it

Submitted by bopes on Thu, 08/23/2007 - 16:40.
the fact that, logically, there's not a one-to-one correspondence between two infinite sets of numbers means "absolutes exist"? Are you saying that the number in one set that lacks a correspondent in the other set is an "absolute" number?

numbers and grass

Submitted by Andy Hahn on Thu, 08/23/2007 - 16:29.
I remember learning about these in college and was quite blow away because I always thought of infinity as something just really big. It was a bit a challenge to understand that there are an infinite number of counting numbers (1,2,3,4...) and an infinite number of integers (...-2,-1,0,1,2,...) when it seems there should be twice as many integers as counting numbers. I never thought of it much beyond that because our class didn't go any further than that. But it seems like the different sets take on different characteristics if they are looked at as a whole. In this way they might be comparable to other entities in the natural world which are also in a sense infinite yet discrete. This is what I think Adam was getting at with relativism and absolutes (correct me if I'm wrong). We can look at something like a blade of grass and see it as the manifestations of very real (absolute) laws inherent in the universe and also see it relatively as it individually compares with other entities.

yo

Submitted by Adam Elenbaas on Fri, 08/24/2007 - 09:37.
Andy just did what I apparently wasn't doing a good job of explaining! I'm just teasing out an analogy. If relative degrees of infinity exist (infinity itself being a necessary concept), then we have to come to see the universe as something that contains both the relative AND absolute. It's just that we all love to get-off on relative thinking--my point was that we almost get off on relative thinking absolutely! A strange conundrum that I was happy to find exists similarly in the world of these number sets. Adam Elenbaas

If absolutes are some sort

Submitted by Andy Hahn on Sat, 08/25/2007 - 15:04.
If absolutes are some sort of ideal that overrides more relative judgements, as our friends tend to say they are, then we might have to say, as Adam is suggesting, that each number and each infinite set is in itself an absolute since they each have their own overriding qualities. Very basicly for individual numbers, one shows most clearly unity, two shows duality, etc. These qualities are contained wholly within the ideas of the numbers and it is by a comparison, in seeing how they are relative to each other, that these qualities are more fully flushed out. That there are many infinities breaks apart the idea of infinity, as it is normally imagained, as THE absolute. Instead there are different cases of infinity that have to be taken individually. When they are compared, their qualities come out more. The set of even numbers (2,4,6...) is a sort of progressing, jumping, open-ended expansion of duality in comparison to the set of real numbers between one and zero [1, 0.99_99, 0.99_98,..., 0.00_01, 0] (where _ is an infinite repition of the two surrounding numbers) which is more a central deepening, smooth, closed filling in. These are both expressions of inifinity. This could be applied to morals in recognizing that moral ideals so exist beyond our individual selves yet they are expressed uniquely through each individual human.