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12/19/2006: "On the Border of the Metaphysic"

To Infinity and Beyond

This morning I was attacked by infinity. Normally, the view from my bed is comforting because there are four walls, one ceiling and a limited number of books, drawers, and precious knick-knacks.

Suddenly it struck me that as I took one step away from my bed toward the bathroom, the earth was rotating me at 1000 miles per hour, the sun was flying away from its beginning, and our galaxy was heading off to the never-ending oblivion of infinity. Aaaagh!

And then I realized that if I looked at all the numbers from one going up, I would never stop. Even worse, I realized that if I removed all the odd numbers, I would still have an infinite number of numbers. Did that mean that the odd infinity was only half as many as the total infinity? Attacked by infinity, I felt tiny and weak and vulnerable and wanted to hide under the bed.

I was so troubled that I asked a mathematician. “Is two times infinity twice as many?”

He replied, “No, you can’t multiply infinity because infinity is not a number. If you could multiply or add infinities, then you could prove zero equals one, and if you could do that, you could prove anything, which would mean you would have nothing.”

Oh. Hmmm. Okay.

Well, I got the mathematical part of infinity out of the way. I realized that infinity in mathematics was just a construct, just something we could imagine. But what about the infinity out there, outside my bedroom door, outside my planet—in the stars and the UNIVERSE?

Are there an infinite number of stars? Can we always find one more, just like we find one more number after the last number? An interesting observation is that if there were an infinite number of stars, wherever we looked we would see one, and the sky would be lit at every point in every direction. But it isn’t, so there are not an infinite number of stars.

And what about time? Could the universe have always been here and always be here from now until–keep counting–infinite and forever?

I looked into Stephen Hawking’s book, “A Brief History of Time.” He says that before the universe began with the big explosion out of nothing, there was no time. So there was no "before." Actually, I like that, for even the scientists studying the facts of stars millions of light years away confirm that the universe appears to have a beginning–just like it says in the Bible. Those who take the Bible literally think the earth was created a few thousand years ago while the astronomers and cosmogonists believe it was a few billion. If this universe had a beginning, the astrophysicists and creationists disagree only on the element of scale.

By all evidence this universe had a finite, limited start date. How about the ending? Cosmologists formulate this question like this: Will the universe continue to expand forever or will it one day begin to shrink and then collapse on itself? Right now, all the facts say that it’s expanding and in fact expanding faster all the time.

However, it turns out that even an ever-expanding universe isn’t necessarily an infinite one, for even as it’s moving out, it’s moving in. That’s a hard one to get our thoughts around. But it’s true that astronomers say that the universe is curved, coming back around like a circle on the equator. Perhaps the very essence of space is being limited.

I spent the day wrestling with infinity, and I think I’ve got it in a full nelson, subdued, under control. Even all the grains of sand on the earth (though many) are finite. They are just as described by some number (though only God knows it) like 37 or 53–just a lot bigger. One estimate I found for all the grains of sand on earth is 6.63 × 10 to the 22nd. And the number of stars, though as Carl Sagan told us, included billions and billions, is another straight up number–somewhere between 10 to the 22nd and 10 to the 24th or so. Realize that the high end numbers (ten followed by 24 zeroes) is just fifteen times the number of grains of sand. The lower estimate is fewer than the number of atoms or molecules to make a mole. You remember what a mole is from high school chemistry, I trust. That would be Avogadro’s number. That’s 6.02214199 × 10 to the 23rd. It’s an awful lot of atoms, but it doesn’t scare chemists, who use this number like you and I make change for a dollar.

With the entire universe tidily finite, I felt snug and potent inside a firmament that goes on and on but still has a limit. This universe is certainly bigger than a breadbox, but a whole lot smaller than infinity. Kind of like from my bed to the bathroom. I find that rather comforting.