by Andy Boyd

Click here for audio of Episode 2986

Today, we get the point. The University of Houstonís College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

Itís so common it seems utterly natural. We purchase a can of soup for $1.59. We write a check for $87.43. Our currency expresses fractions of a dollar using a decimal point. And it does so in large part due to the simple yet inspired efforts of Flemish scholar Simon Stevin.

Flemish scholar Simon Stevin Photo Credit: Wikimedia Commons

The idea of using decimal numbers at all was late in coming to Western Civilization. The West struggled with Roman numerals throughout the Middle Ages, and the vastly superior decimal system from the Arab world didnít firmly establish itself in the West until around 1600.

But even as the decimal system was embraced for whole numbers, fractions remained on the sidelines. For one reason, we tend to think in fractions. Take a pie and cut it into four equal pieces. Each piece represents one-fourth of the pie, which we can easily represent as the number 1 over the number 4. When we learn fractions in school, this is exactly where we begin. Itís only later that we learn how to represent the fraction one-fourth as the decimal ex-pression point-two-five (.25), or two-tenths plus five-hundredths.

Pie chart in quarters. Photo Credit: Wikimedia Commons

So far so good. But suppose we cut our pie into thirds. If youíve ever typed ď1 divided by 3Ē into your calculator, you know what pops out: a decimal point followed by a long string of threes. Mathematically, the string goes on forever. And that didnít sit well with scholars of the Late Middle Ages. Fractions, they quite reasonably surmised at the time, were superior.

one third
One divided by three. Photo Credit: Andy Boyd

Simon Stevin began his career as a bookkeeper in Antwerp, but his interests and capabilities were broad. He wrote eleven books, covering many disciplines. But his most influential work was a twenty-nine page booklet entitled La Theinde Ė The Tenth. It was a thorough, practical treatment of decimal fractions. And within the book he predicts that decimal fractions are so easy to work with, it would only be a matter of time until the entire world adopted currencies and measures commensurate with decimal notation.

In 1608 Stevinís work was translated into English under a title that borrowed from the Old French word for tenth — Disme; and itís reasonably conjectured this translation influenced our nationís founders. Ten cents to the dime. Ten dimes to the dollar. They fit together so nicely.

A US dime. Photo Credit: Wikimedia Commons

Stevin proved clairvoyant. Non-decimal currencies were wide-spread throughout history, but today theyíve all but disappeared. The same is true of weights and measures, where the metric system is used by all but a handful of countries. The one big exception, of course, is the U.S. Three feet to the yard. Seventeen-hundred-sixty yards to the mile. Ah, sigh U.S. engineers, as they dream decimal dreams…

Iím Andy Boyd, at the University of Houston, where weíre interested in the way inventive minds work.

(Theme music)

For a related episode see In Which Europe Quantifies.

The complete title of the English translation of Stevinís booklet was Disme, The Arts of Tenths or Decimal Arithmetike.

Formally, the metric system has been replaced by the International System of Units, also known as the SI System. Reference to the metric system is made for the benefit of listeners unfamiliar with the SI System.

Hindu-Arabic Numeral System. From the Wikipedia website: Accessed January 8, 2015.

Non-Decimal Currency. From the Wikipedia website: Accessed January 8, 2015.

J. O'Connor and E. Robertson. Simon Stevin. From the University of Saint Andrews MacTutor History of Mathematics Archive: Accessed January 8, 2015.

This episode first aired on January 22 , 2015.