Understanding Counting Systems in English, German, and French
If we think about the numbers one to twelve in English, we notice that each number has its own unique form, before a repetitive pattern begins to emerge for thirteen, fourteen, fifteen and so on, meaning three-and-ten, four-and-ten, five-and-ten. When we reach twenty, we have a consistent pattern: twenty-one, twenty-two, twenty-three. Then we have thirty, forty, fifty, sixty, seventy, eighty, and ninety – all in blocks of ten. Therefore, the English counting system is founded on a base of ten.
Why Do English and German Have Unique Names for Eleven and Twelve?
So why separate numbers for eleven and twelve? These are the historic remains of a base-12 format of counting. We can still count in base twelve, with expressions such as one dozen, two dozen and so forth. However, our numbers are firmly rooted in a base-10 means of expression. Even so, twelves are convenient for division purposes, which is why this method of counting took hold – plus older counting systems often matched some biological feature. Indeed, in this case, if you look at your fingers, you’ll notice that each of your four fingers has three distinct sections – and there are twelve therefore in total across both your hands. These make for handy portable abacus substitutes. It is also no accident that numbers are also called digits!
We see the same feature in German, where each of the numbers has its own form up to twelve, before the base-10 system of counting comes into play.
Why Are French Numbers Unusual?
However, base-10 and base-12 are not the only counting methods. You’ll notice in French that the numbers all the way up to 16 are all unique. This is likely the result of a base-16 being used to perform arithmetic. Again, looking at our hands, we have four fingers on two hands that could help us with arithmetic. Sixteen is simply double the amount of these 8 digits. In fact, numbers in base-16 split conveniently down from 32 to 16 to 8 to 4 to 2. Historically, this may have been useful for purposes such as taxation or dividing estates.
Mixed into this older base, we have the modern base-10, or rather the decimal system. Again, biology helps here: we have ten fingers (or digits), when we include the thumbs. It means that it is visually convenient to count in batches of tens. Numbers in English, German and French (up to 69) follow this pattern.
Why Is Eighty in French Expressed as quatre-vingts?
Twenty was also an important base for counting – ten digits on the hands and ten on the feet. So, from a human perspective, counting in batches of twenty is also natural – and we see this in the French number for eighty, which is expressed as quatre-vingts, or rather four twenties.
While this can seem strange today, what we are seeing is echoes in languages of historical counting systems reflected in the names for numbers. French has a healthy mix of base-16, base-10, and also base-20!
