We’ve seen a lot of big numbers this week.
NASA discovered a humongous earth-like planet that has water vapor and rain clouds, but it’s 110 light years away from us. One light year is about 5.8 trillion miles, so do the math on that one.
The Alaska Permanent Fund Corporation’s board of trustees announced that the fund grew by $1.4 billion last year.
ConocoPhillips publicized a new oil and gas project on the North Slope, called the “Willow project,” that could add hundreds of millions of dollars to the state economy, although critics say the project will further irreparable environmental changes to local villages.
And I am currently writing this column in the tail end of Typhoon Faxai, a major storm that has traveled several thousand miles from the coast of Japan, where it left two dead and 700,000 people without power, to southwestern Alaska, where, in a much weakened state, is expected to bring strong winds and a few inches of rain.
While we normally correlate numbers with mathematics, especially huge numbers like these, it’s good to think about how language informs how these numbers are perceived, and how, indeed, language creates numbers.
Take the word thousand, for instance. Thousand is an English word of Germanic origins. The Old English used þusend, from the Proto-Germanic thusundi, which meant ten times one hundred. In other European languages before the modern era, though, the word could also refer to a general great multitude. In fact, the literal meaning of the word thousand is “swollen hundred.”
We get that meaning from its Proto-Indo-European roots. Thousand is a combination of two roots: teue and dekm. Teue means to swell, which we see in words such as tumor, thumb, and even butter (which makes sense if you think about milk “swelling” in a way to make butter and cheese). And dekm is the foundational root of the concept of ten, hence words like decade, dime, decathlon, and hundred.
Latin and Greek had other words that more exactly meant 1,000: mille and khilias, respectively. But Germanic and English translators must have found their word thousand suitable and used it in translations, thus giving thousand it’s more exact sense of ten times a hundred.
European explorers of the Saint Lawrence River region between Ontario and New York, though, must have had the “swollen” meaning of thousand in mind when they designated an archipelago at the northeast corner of Lake Ontario as Thousand Islands. There aren’t a thousand islands there, but it sure looks like it on a map. And, yes, this is where my favorite salad dressing was invented.
A similar “swollen” meaning is in the origins of the word million, too. In its French and Italian roots, million literally meant a great thousand or even just a very great number. The Greeks and Romans had no name for numbers greater than ten or one hundred thousand respectively. One million in Latin, for instance, is decies centena milia (ten hundred thousand). Although, even before the third century C.E., India had names for numbers beyond a billion, but those words never found their way west of the Caucasus Mountains.
In 1475, a French mathematician named Jehan Adam was studying exponents and wrote down the words bymillion and trimillion. About a decade later, another mathematician, Nicolas Chuquet, noted those words in “The Science of Numbers in Three Parts”, but they meant something different: Chuquet’s billion today means trillion, and his trillion is today’s quintillion.
That’s because Chuquet’s lens was exponents. His one billion equaled one million squared (1,000,0002); the “bi” in billion, after all, means two. But, today, our one million squared equals one trillion. Chuquet’s trillion: since the “tri” in trillion means three, one million to the third power equals, for us today, one quintillion.
For almost 300 years, that’s how it worked. Billion then meant trillion today; trillion then meant quintillion today. What we call billion today was “thousand million” back then (or the really weird-sounding “milliard”).
From the late 17th century into the 18th, as numbers grew larger, mathematicians realized their system (today called long-scale) wasn’t very user-friendly. So they developed what’s called a short-scale system, which, using base 10 calculations, divided these long numbers into groups of three, referring to the additional power of three for each numerical unit: 103 equals thousand, 106 equals million, 109 equals billion, etc.
So one billion, the term, went from meaning 1,000,000,000,000 to 1,000,000,000.
The math and numbers didn’t fundamentally change. Language changed. And it still does.