Engines of Our Ingenuity

No. 1072:
PROBABILITY

by John H. Lienhard

Click here for audio of Episode 1072.

Today, let's try to predict the future. 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.

Well, no one can predict the future. We can only say what's likely to happen. That uncertainty has always left us uneasy. I suspect uneasiness is what kept us from inventing probability theory until the 1600s.

Today, we take it for granted that the world is indeterminate, and we work within its fuzziness. We use laws of probability to write life insurance and to pull signals out of surrounding noise.

But first we had to change the way we looked at things. When an English mathematician, Isaac Todhunter, wrote the history of probability in 1865, he found it'd been created by people wrestling with two great unpredictables of life -- with dice and death!

When you roll dice, there's only one way to roll a two or a twelve, but six ways to roll a seven. The ancients played more complex games -- using three dice, not just two. Yet they wrote little about the likelihood of numbers. Dante touched on the dice question in his Purgatory. But not 'til the 1600s did people begin writing tables of outcomes in dice and other games. Only then did mathematicians start formalizing those ideas.

Two people began converting vague feelings about likelihood into a theory of probability. During the 1650s, Pascal and Fermat wrote to one another. They went back and forth on questions about gaming. Soon they were joined by Huygens, Leibnitz, and the Bernoullis -- then by every great mathematician of the age.

Johannes Kepler had already warned that processes like throwing dice are actually determined by laws of physics. That idea has come back to haunt us in the 20th century, first with quantum indeterminacy -- then with deterministic chaos theory. Today we struggle to understand what's really predictable and what isn't.

In any case, the most important gambling game is our own life and death. "Lord, let me know mine end and the number of my days," said the 17th-century Book of Common Prayer.

By then we had crude records of mortality and were trying to make sense of them. In 1692 a scholar noted that, since one person in 26 died anually, you could take a random group of 13 people and wager even money on one death in a given year. Nice thought!

That was the beginning of a new mathematics, but it's one we accept only when we choose to. You know people who smoke cigarettes yet worry about flying on an airplane. Part of the Texas budget is paid by people chasing the hopeless hope of winning a lottery. In fact, state lotteries make a fine way to tax the vulnerable.

For the last three centuries, dice and death have touched our intellects and forged the new science of probabliity. If we accept that science, it offers some hint of the future -- which otherwise remains shrouded from our view.

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

(Theme music)


Todhunter, I., A History of the Mathematical Theory of Probability. New York: Chelsea Publishing Co., 1949 (Preface dated 1865).

I am grateful to Lionel Issem for drawing my attention to the works of Isaac Todhunder.


The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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