In mathematics, the idea of infinity takes on some very complex, powerful, and sometimes paradoxical properties. There is, for instance, Cantor's Paradox. The paradox can be described using the set of whole (or "counting") numbers and the set of decimal (or "real") numbers.
First, realize that there are an infinite number of whole numbers. However high you can count, you can always count one more. So, there are an infinite number of whole numbers.
The look at any two consecutive whole numbers. How many real (fractional or decimal) numbers can you come up with between those two whole numbers? An infinite number of real numbers could appear between any two whole numbers.
Intuitively, then, there have to be more real numbers than there are whole numbers, right? But there are an infinite number of whole numbers, already. So what does that say about how many more real numbers there are?
Remember when you were a kid an you told your friend that you "infinity dog-dared" him to do something and he "double infinity dog-dared" you back? Well, there's something to that idea. The paradox suggests that the concept of something being infinite has many dimensions to it that can qualify the relative "infiniteness" of something.
I think this mathematical paradox shows us just how hard it is to fully comprehend the idea of God's infinite love. No matter how we rationalize and justify and prove, there comes a point in the discussion where faith graciously takes over, creates a paradox for us, and grants us the freedom to believe rather than prove. As an engineer, I struggle with those places where I feel free to believe, but I also find them gloriously spacious.
Thank you God, for paradoxes.
2 comments:
Are we talking a warm fuzzy intimate love here, Paul, or real love that is sometimes tough?
If God's love is infinitely warm & fuzzy, then there's no need for the Cross, for His infinite fuzziness would excuse our sins repeatedly.
However, if this is tough love then as CS Lewis points out in his book "The Great Divorce," God loves us so deeply that when we choose to reject Him, He lovingly allows us to live eternally without Him. He loves us enough to let us go our own way and be forever without Him.
Thanks Stushie. I think that's a really good way to draw the challenging and fulfilling mathematical paradox into a challenging and fulfilling perspective on faith, too.
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