Letter from Germany: There’s billions and Billions

Last week we wrote about an amazing kinetic sculpture in Phæno, the terrific new German science museum. The sculpture takes an inconceivably long time to cycle through its movements, which is indicated by the accompanying text, in both German and English:

Das ist so langsam, dass es ungefähr 594,000,000,000,000 (594 Billionen) Jahre dauert …

This is so slow that a period of approximately 594,000,000,000,000 (594 billion) years must elapse …

Clearly, something has gone awry: in English we refer to the indicated number as 594 trillion, not 594 billion. But in fact, the German is correct: “Billion” in German translates as “trillion” in English. Just as astronomer Carl Sagan used to (almost) say, there’s billions and Billions! 

It’s definitely not helpful to have the same word refer to different numbers in different languages, but there you have it. And, the confusion is not confined to the billions: except for “million”, all “illion” words have differing meanings in English and German. (Well, presumably “zillion” has the same meaning in the two languages).  Below is a chart comparing the English and German customs of referring to large numbers.

How did this happen? The word “billion” was introduced in France at the end of the 15th century, and meant a million million: that is, billion = (million) x (million) = (million)². Similarly, trillion = (million)³, and in general thingo-illion = (million)^thingo.

This so-called long scale of illion words still exists in most European languages, including German. The short scale took hold in the US in the 17th century, but it is only in the late 20th century that the short scale has become standard in other English speaking countries. Britain officially switched over in 1974, after which Australia (somewhat less officially) followed suit.

However, there’s a weird twist. Just like the long scale, the short scale originated in France, and for a long time there was the more accepted scale. The short scale was grabbed by the US during its Francophile period, but in 1961 France and the rest of the French-speaking world officially adopted the long scale.

Why did anybody consider that the long scale needed revision? In the long scale, the ratio of consecutive illions is a million, which is a very large factor. Speaking numbers such as 666,666,666,666 with the long scale can be cumbersome. In fact, writing long form numerals is also cumbersome, and it has always been common to place the separating commas at the thousand intervals.

So, there’s a definite advantage to switching to the short scale, either by changing the meanings or by introducing the “arde” words to fill the gaps, as is done in German. But of course what causes endless confusion is having two different systems using the same words. Clearly one system should disappear, and we believe the United Nations should take up this issue as a matter of urgency.

In the meantime your maths master has alerted the Phæno museum to the numerical mistake in their English description. (It appears that he was the first person to do so, in the two years that the exhibit has been around.) The museum promised to fix the wording, but we wonder what will then happen. When “trillion” appears as the translation of Billionen, we can just imagine people on a daily basis alerting the museum to their “mistake”.

 

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator.

Marty Ross is a mathematical nomad. His hobby is smashing calculators with a hammer.

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