The Law of Truly Large Numbers

Laura and I were watching a science show the other night on the latest theories of the universe and its origins. It was probably a NOVA episode, or maybe Nature. Lawrence Krauss was one of the interviewees, along with a few of the other usual suspects in the field of cosmology. This particular episode discussed some recent findings about dark matter, dark energy, black holes, and the like. One segment described, quite effectively, the nature of galaxies, galaxy groups, galaxy clusters, and filaments. Each stage zoomed out, as it were, to illustrate how utterly immense the universe is. The discussion ended with a final representation of the entire cosmos, with its web-like structures of matter strewn about in the totality of the universe. It was pretty cool, and awe-inspiring to say the least. I know of no word in the English language that can adequately describe the unfathomable vastness of the cosmos.

I remember a few years ago, when Laura and I (perhaps with my daughters) visited the science museum in Fort Worth, Texas. There were a lot of interactive displays in the exhibit, and on this day, the place was packed with kids running about flipping switches, turning knobs, working cranks, pushing buttons, etc. One exhibit attempted to illustrate the concept of very large numbers. A transparent plastic cylinder, roughly three feet long and four or five inches in diameter, was filled with exactly one million tiny beads. Each bead was maybe two millimeters in diameter, but perhaps a bit smaller. Next to the tube was a chart showing the distribution of colored beads in the container. I don’t recall the exact distribution, but it was something like this:

  • 938,899 blue beads
  • 50,000 yellow beads
  • 10,000 green beads
  • 1,000 orange beads
  • 100 purple beads
  • 1 red bead

The trick of course was to locate the one red bead by continually turning the cylinder on its axis and letting the beads cascade around inside. It was almost impossible to find the lone red bead unless you were willing to be patient and turn the cylinder slowly and deliberately, carefully scanning the multitude of beads along the length of the tube. Not only was it difficult to find the red bead, it was  unlikely you would even encounter a purple bead. This was the first time I’d seen a million of anything in one place like that. It was staggering to behold. I was not able to find the red bead, and I didn’t feel comfortable continuing the search when other museum-goers wanted to give it a shot. So I moved on to other displays, but I went back to the cylinder a couple more times to try and comprehend the sheer number of beads in that tube.

So as Laura and I were watching this episode of NOVA the other night, the narrator surmised that there were perhaps 400 billion galaxies in the universe, and each galaxy might contain around 100 billion stars. Forget the stars for a minute and just think about the number 400 billion. That cylinder at the museum held one million beads. Multiply that by one thousand. It’s not too difficult to imagine a thousand of these tubes in a large room of a museum, but now multiply that by 400. Okay, most museums would be hard-pressed to house 400,000 of these tubes and still have them accessible to the public. So imagine them instead in a coliseum or football stadium. 400,000 of those tubes, each with a million “galaxies” in them. And that’s not even remotely close to describing the size of the universe, simply because the space that exists between matter is vastly larger than the matter itself. And that’s just the galaxies! Now multiply 400 billion times 100 billion…you’ll have a number that, to paraphrase a line from Team America, nobody even knows. Actually, I think it’s a four with 22 zeroes after it. I don’t know what the name of that number is.

Pardon me, I think I just blew my own mind.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>