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Thought for the Day: The Problem with Infinity, Perfection, and Appearance

I have an interesting demonstration of our inability to fully grasp infinity. Start with the set of all counting numbers, we'll call that A. So set A contains 1,2,3,4,.... Now we are going to make two new sets using A as a start and applying a rule.

For the first new set, the rule is to take each element from A and square it; we'll call this set B. So B contains 1^2, 2^2, 3^2, 4^2 --> 1, 4, 9, 16, ... 
Note well: for every number in A there is a corresponding number in B.

For the other new set, we are going to filter elements from A. That is, we won't copy all the elements of A, we'll only copy the perfect squares. So:
1 from A gets copied to C
2 from A does *not* get copied to C
3 from A does *not* get copied to C
4 from A gets copied to C
etc

So C contains: 1, 4, 9, 16, ...
Note well: Not every element in A has a corresponding element in C; we only copied some of them. A quite small fraction, actually, when you consider how perfect squares get more and more spread out.

Here's the magic part, though: B and C both contain exactly the same numbers! Every number in B is also in C; every number in C is also in B. Yet, B took everything from A, but C only took some elements from A -- there are plenty of elements in A that have no corresponding element in C. We can see logically that they are the same, but our experience (with the finite) tells us that B should be somehow bigger than C. It takes work to reconcile our knowledge (B and C are the same) with our experience (B is surely bigger than C, isn't it?!). We can never completely reconcile them, but we can at get a feel that our finite nature prevents us from completely understanding the infinite.

That helps to clarify an absolutely fundamental issue or our existence. Namely, we know with absolute clarity that the Creator is completely perfect and all good -- the Creator, after all, is the very definition of infinite and also good. Our experience, however, tells us otherwise. In the words of the Ramchal in his classic work דעת תבונות, the soul presents her quest for understanding this way:
The existence of the Creator, His oneness, the eternity of His existence, His incorporeality, His absolute freedom of will, ... all clear. But divine providence, reward and punishment, the coming of the messiah, and ultimately the resurrection of the dead -- I believe, because those are fundamental beliefs of our religion, but I am seeking at least a way to understand the idea of them.

From my little math example above, we see that HaShem is not hiding anything from us. Rather it is our result of our bounded and finite nature. There are things in creation that are just beyond us -- and even contradict our experience and intuition.

It takes work to reconcile our knowledge with our experience. It it will never be -- well, perfect, since we ourselves are limited/bounded. Using our G-d Given minds -- and use them me must, since He built us with them -- to reconcile our knowledge/reason with our experience and intuition is a lifetime of work. 

It is, in fact, the reason that we have a life in this world at al.

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