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No. 1215:
The Tyranny of Large Numbers

Today, large numbers do some strange things. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

In the field of statistical physics we talk about the tyranny of large numbers. For example: I flip a coin three times, I wouldn't be surprised to get three heads. In fact I will get three heads one out of eight times I try it. But if I flip a coin a million times, I'm virtually certain to get 50 percent heads and 50 percent tails. The larger the population, the more consistently average is its behavior. Large numbers hold us in an iron hand.

That tyranny of large numbers turns up again in our concept of beauty. Psychologists have shown that the face which at first glance we call beautiful is the most average face. That's the reason we can seldom remember who Miss America was last year.

Here in Texas we have a state lottery. That's a sophisticated means for increasing the tax burden on people who aren't very swift with numbers -- and it's a strong reason for being math literate.

To play, you choose six different numbers between one and 99. If those numbers are drawn, you win several million dollars. But since the Lottery takes in far more money than it gives out -- since the average prize is far less than the cost of playing -- it's a bad bet. If I were going to play the lottery, I'd simply pick the numbers 1, 2, 3, 4, 5, and 6. They're easy to remember and they're just as likely as any other numbers to win.

But it's on the molecular level that large numbers really take hold of us. The number of sodium-chloride molecules in a grain of salt is like a one followed by 19 zeros. If it had a trace element in it -- say one part in a trillion -- that grain of salt would still hold ten million molecules of the trace alone.

Here's a way to think about those numbers: Seven years ago, my body was made up of entirely different molecules. The process of cellular death and regeneration has gradually replaced me. That vast number of old molecules has reacted, turned into water and CO2, been reprocessed by plants, and stirred back into the biosphere. By now I'm all around you. I'm growing in your window planter. I'm in your soup. You breathe me out and I breathe you in.

You and I were made of so many molecules seven years ago that we're everywhere on earth today. We occupy almost every ounce of water, and every puff of air. I can't help but think, when I see people making ceremony of scattering ashes, that the cremated loved one is spreading through the biosphere while those few inorganic fragments represent almost nothing of She-who-was.

The perceived world is statistical tyranny. Solidity is an illusion born of large numbers. So is time. But come back a moment to that matter of beauty being a statistical illusion. Thoreau called beauty a moral test. In that he offers a way out from under tyranny, a ray of hope. He reminds us that we're still responsible for how we perceive reality -- and what we do with it.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

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The statistical arguments may be found in many texts on mathematical statistics and/or statistical thermodynamics. See, e.g., Tien, C. L., and Lienhard, J. H., Statistical Thermodynamics (revised printing). New York: Hemisphere Publishing Corp., 1979. See especially Chapter 3.

N. Shamsundar, UH Mechanical Engineering Department, takes pains to point out to me that the "me" which is spread through the biosphere is not me at all. The true me is my Atman (in Hindu thinking) or soul or breath of God. In more technical terms, it is the "system" which comprises me at any moment and which is never the same collection of either atoms or thoughts at any given time. What is interesting about Shamsundar's observation is that this episode emerged from a conversation with Lutheran Minister Joan Lepley in which she was exploring Christian implications of our material ubiquity.