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Previous Challenge Entry (Level 3 – Advanced)
Topic: Space (01/23/06)

TITLE: So Much Space
By Joe Pagano


We always hear the knee-jerk comment about space being infinite. Outer space, that is. This brings up a very interesting point: that of infinity and how this connects with the notion of God. When I was in my senior year in college back in the early eighties, my last two courses of study to complete my undergraduate degree in mathematics were Statistics and Set Theory. Although the former was quite interesting in and of itself, it was the latter course that had earth-shattering implications for me.

The day is easy to recall when I first learned the momentous fact: there is no such thing as one kind of infinity! What? I remember the day well. Spring was here and the flowers were blooming all around college: some persistent daisies were dotting the lawn which covered the campus quadrangle, the oaks were budding their new verdant leaves, and the perennials were struggling to make their case known after the long cold winter. It was on a spring day such as this when I was sitting through a class of Set Theory and was shown a proof which demonstrated how the counting numbers, that is the set of numbers {1, 2, 3...} were not as numerous as another set of numbers called the reals, which include all the numbers in the first set as well as others like the fractions and irrationals. “But wait, I cried out to myself. Both sets are infinite. There is no limit to the number of elements in each, so how can one set have more than the other?” As the proof was carefully laid out, the truth hit me like a thunderbolt. I was awestruck, yet the best was to come. For as we continued prodding our way into the higher echelons of the theory, via some extensions and corollaries, the momentous conclusion was brought forth: Not only are there different types of infinities, but there are actually an infinite number of distinct ones!

After digesting the implications and truth of all this, I recall gingerly rising from my seat after class and slowly and methodically strolling down the hall corridor, pondering the import of what had just happened. To say I was dumbstruck would be understatement. And though during this time of life, I was a self-proclaimed agnostic, there was something curiously tantalizing about this whole thing vis-a-vis the existence of God and things of this nature. As much as I wanted to hang on to my agnosticism, I knew that if there could be whole hiearchies of infinities—each distinct and of its own flavor—then the concept of so much space—infinite space, that is—or more importantly, the existence of a Higher Authority, the Almighty God, that is—was no harder to fathom then the recent discovery that had just impinged on my senses.

For this reason I always approach the subject of mathematics with both reverence and humility, knowing full well that I can be both exalted and abased by its magnificence. Through this incredible language of mathematics, which explains the world around us—indeed the universe of space—we learn that infinite space and infinite infinities are no harder to comprehend that an infinite God.

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Member Comments
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Phyllis Inniss01/31/06
What an interesting article. How you remembered the day of your new discovery - a spring day with the flowers coming into bloom - something that would seem opposed to each other - and yet it impinged on your mind. Isn't God wonderful? in His infinite way.