Counting Systems & Their Peculiarities

Having spent the past month or two immersed in an attempt to familiarize myself with (I hesitate to say “learn”) the French language I have been exposed to several interesting characteristics of the language.  Most I shrugged off as interesting but not earth-shattering or worthy of serious thought; one, however, has captivated my interest.

In English (as well as many languages), the counting system is based on ten and as a result there are ten different names for the numbers represented as 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. I would venture to say the general assumption of the monolingual Anglophone is that this is the way the entire world’s population sees numbers (just in their own respective languages). Well one need not travel far to discover this is by no means the truth. In fact one could argue that French is as close to English as any living language is (save some local dialects in England that resemble English but are indeed different languages) and yet in French we find things already get thorny.

I won’t be able to describe it any better than the numbers themselves; take a look at the following:

Number                  French Name                English Literal Translation

10                           dix                                   ten

20                           vingt                                twenty

30                           trente                               thirty

40                           quarante                           forty

50                           cinquante                          fifty

60                           soixante                            sixty

70                           soixante-dix                       sixty-ten

80                           quatre-vingts                      four-twenties

90                           quatre-vingts-dix                four-twenties-ten

91                           quatre-vingts-onze             four-twenties-eleven

92                           quatre-vingts-douze            four-twenties-twelve

Et cetera, et cetera, I could expand but I think you get the picture. They have words up until sixty just like English but for some reason after their sixty-nine instead of having another word for seventy they say sixty-ten (followed by sixty-eleven, sixty-twelve, etc). Really? It just seems almost too bizarre, but it gets even worse. For “eighty” they have “four-twenties” and all the way up to one hundred their words from 80 on start with “four-twenties.” If we were to do this in English it would look like this:

·         four-twenties one (81)

·         four twenties two (82)

·         four twenties ten (90)

·         four-twenties eleven (91)

·         four twenties nineteen (99)

·         one hundred

The absolute strangeness of this system to a native English-speaker is difficult to describe. Keep in mind that these aren't fancy mathematical terms, these are the every day, trip-to-the-local-market names of these numbers. In the Francophone mind, the symbols 99 are every bit as much "four-twenties nineteen" or, actually and more literally, " four-twenties ten-nine" (quatre-vingts-dix-neuf) as they are "ninenty-nine" to you and me. The system appears to be inefficient yet the mere fact that it exists and has survived countless generations of linguistic evolution shows that it is easily within the realms of the human brain’s idea of efficiency.

A more manageable way of looking at this is that while French has a ten-based (decimal) system from 0-69, it becomes twenty-based (or vigesimal) at 70 until 100. And if you are asking yourself how in the world this could come into existence in the first place (many of French’s romance neighbors such as Spanish have fully ten-based systems like English), it is an inherited trait that the earliest French speakers picked up from the Vikings and/or Celts whose languages were fully vigesimal. At one time in Old French you could state the majority of numbers in either their base-ten or base-twenty forms, but after the French Revolution they froze it the way it is now in an attempt to unify the country’s counting system (which varied from the vigesimal coasts to the inner regions of France which used a decimal system).

I love this quote I found on an online forum by some random guy discussing this very topic:

“A friend of mine worked a switchboard once and though he's bilingual, he complained about the French numbering. He had to type phone numbers into his board and sometimes the caller would say "quatre-" (and he would type a 4) "-vingt-" (and he would curse to himself, hit backspace and change it to an 8) "-douze" (and he would curse again, backspace again and change it to a 9).”

Perhaps important to add is that Abraham Lincoln pulled a similar move in English in his Gettysburg Address (Four score and seven years ago…), yet for some reason when I was younger I always viewed that as just a “cute” way of saying it and it never dawned on me that it could represent another way of counting and naming numbers entirely. I suspect that if this is the case with me, then it could be the case of others; in fact if I had to guess I’d say it’s likely the case with the majority of English speakers not fluent in a language with a different counting system.

Also important to add is that while the above is the system of the standard dialect of French (i.e. the one Parisians use) not all French dialects are this way and some have words for “seventy”, “eighty”, and “ninety”, even if the words they use are more or less localisms and are completely unused in standard French. I say that to say that there do exist native French speakers who could read this and say “That’s not how I talk!”

As one might expect once exposed to the strange French system (French is, after all, quite a close relative of ours), there are languages that get far stranger still.  

Bengali is a language spoken in Bangladesh, India and a handful of other places; its speakers (about 230 million of them, representing the sixth most spoken language on earth) must essentially memorize the lower numbers because a concrete counting pattern only emerges in the higher numbers.

The Welsh language however has perhaps my favorite example of screwy counting systems. It is entirely vigesimal; consider the following of its more bizarre constructions:

10      -        deg, deng         

11        -      un ar ddeg ("one on ten")

16      -        un ar bymtheg ("one on five-ten")

18      -        deunaw ("two nine")

21      -        un ar hugain ("one on twenty")

30      -        deg ar hugain ("ten on twenty")

40      -        deugain ("two twenty")

I guess my point with all this is that it is truly humbling how you can speak (and in this case count) one way your entire life, eventually becoming convinced that is how everyone on earth must do it, only to find out you couldn’t be farther from the truth. The variance in human language is remarkable!