Tuesday, December 27, 2011

81: A Billion Frenchmen Can Be Wrong

    Suppose you decide to have a backyard barbeque, and being a Math
Mutation listener, have so many friends you need to order a billion
bratwurst.  You call the local German deli and order.  When the
delivery trucks arrive, you may find a thousand times more sausages
than you expected!  A billion means 10 to the 9th power in the US, but
10 to the 12th power in Germany.  That's why you may sometimes hear in
political or scientific discourse, when someone wants to ensure
clarity or, alternatively, demonstrate how worldly they are to their
uncultured audience, people will sometimes say "a thousand million"
rather than "a billion".  There are similar differences in the usage of
the words trillion, qudarillion, etc.
    But where did this difference come from?  One common explanation
is that the latin derivations led to the terms bi-million for a
million million and tri-million for a million million million, and
these were shortened to billion and trillion, leading to the
supposedly correct European usages.  However, American bumpkins in the
colonies occasionally discussed large quantities and needed a word for
a thousand million, and not having been educated in Latin, thought
"billion" sounded right, and started using it that way.  Thus the
American usage evolved out in the boonies in ignorance of the true
Latin derivation, while the proper Europeans continued to use the
"real" words.  Sounds plausible, right?  Especially if you're one of
our European listeners.
    Fortunately for our American pride, however, this story is simply
false.  The Wikipedia article in the show notes has a detailed
timeline on how the two usages evolved, and ironically enough, *both*
usages of the word billion evolved from the French.  The European
version of a billion as a million million started as early as the
1400s, in articles by French mathematicians Jehan Adam and Nicolas
Chuquet.  During the 17th century, however, French scientists realized
that for practical reasons, they needed a word for a thousand million,
and began using the word 'billion' for this purpose.  The two usages
of the word billion became known as the 'long scale' and 'short
scale'.  As science blossomed in the early 19th century, the short
scale became the standard in France, and the United States followed.
Britain continued to use the long scale as their standard though.
    In the years after World War II, apparently the European nations
wanted to assert their independence from the United States, and the
1948 General Conference on Weights and Measures proposed that the long
scale become the international standard.  But by the 1970s, the
English-speaking world was finding the differences with the US a bit
incovenient, and Australia, Canada, the UK, and various smaller
countries officially switched to the short scale.  Most
non-English-speaking countries kept the long scale, not as much of an
issue since any discussions had to be translated anyway.  To further
confuse things, an odd assortment of countries including Russia,
Turkey, Israel, and Iran use the short scale for most large numbers,
but the old French word 'milliard' instead of 'billion' for 10 to the
    So, if you have occasion to discuss large numbers in mixed
company, or need to make change at your local German deli, be sure to
keep in mind that the word 'billion' may be ambiguous. 
    And this has been your math mutation for today.

  • Math Forum discussion on the word "billion"
  • Wikipedia article on long and short scales
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