Ancient Indo-Europeans may have counted in eights

Following on from last week’s blog, one correspondent asked about the peculiarity that all Western Latin-derived languages change their means of counting around the number 16-17.

To explain again specifically: for the numbers 15-18, Classical Latin had quindecim, sedecim, septendecim, duodeviginti – derived literally from ‘five-ten’, ‘six-ten’, ‘seven-ten’ but then ‘two-from-twenty’.

French and Italian have, respectively, quinze/quindici, seize/sedici, dix-sept/diciasette, dix-huit/diciotto – in each case literally ‘five-ten’, ‘six-ten’ but then (unlike Latin) ‘ten-seven’, ‘ten-eight’.

Spanish changes order one further back: it has quince, dieciseis, diecisiete, dieciocho – thus ‘five-ten’ but ‘ten-six’, ‘ten-seven’, ‘ten-eight’.

Here, it is over to you – why did all three shift from Latin, with Spanish shifting one further?

One thing which is immediately apparent, however, is that most Indo-European languages show a common trait around the number ‘nine’. This is, in French, Italian and Spanish respectively, neuf, nove, nueve. It is no coincidence that this is similar to the word for ‘new’: neuf, nuovo, nuevo. As far back as Proto-Indo-European, from which Classical Latin, Ancient Greek, Sanskrit and Proto-Germanic were derived, the word for ‘nine’ showed a striking resemblance to the word for ‘new’. The reason is quite simple: it was a new digit. Originally, Indo-European speakers counted only to ‘eight’.

It is thought we now use Base Ten as our counting system because that is the number of fingers we have (including thumbs), but the linguistic evidence is that millennia ago we ignored the thumbs. Counting in Base Eight is fairly logical after all – it allows for constant doubling, from two to four to eight to sixteen as so on; computer scientists, no less, typically use Base Eight or Base Sixteen (or simply Base Two, i.e. binary).

(It should be noted no specific evidence has been found in Eurasia for ancients having counted in Base Eight; though there is none that they counted in Base Ten either. There is evidence from the Americas of humans counting in Base Eight; alongside significant evidence of Base Twelve and even a system based around Sixty used by the Babylonians.)

What is interesting is that the subsequent moves in Latinate languages towards a shift in order around the number sixteen demonstrates that there is still something innately important about that number. It is also just about possible that although Classical Latin was consistent from 11-17 (including, unlike its daughter languages, 17 itself), spoken Latin was not and that there was always a split in the spoken language around 16.

Any thoughts on this more than welcome!


5 thoughts on “Ancient Indo-Europeans may have counted in eights

  1. korhomme says:

    The Babylonians used base 60 in their ‘posh’ mathematics, from which our minutes and seconds of time are derived, and the 360 degrees in a circle. They probably used base 12 in everyday transactions, as 12 can be easily divided by 2, 3, 4 and six in the markets. (Base 10 can only be divided by 2 and 5.)

    Base 8 also has this problem, divisible by 2 and 4. If you measure in 8s, how you do you get a third of it?

    There is some linguistic evidence of base 20; we still have a ‘score’, and the French have quatre-vingt rather than ‘octant’ (which they do use in Canada, along with nonant). In English, we have a ‘dozen’ as evidence of once using base 12; and think of the difference between eleven and twelve, and then thirteen, fourteen etc. With 13, the construction of the name changes, and 13 is ‘three-ten’.

    And while we can count to what we call ten on our fingers, and start with ‘1’, the numeral 0 (zero) is a fairly recent Indian invention—even Arabic numerals are actually Indian. Dennis the Dwarf, when constructing a chronology of the Christian world, at the behest of the pope, didn’t know about 0. So, 1BC was immediately followed by AD1.

    And these ‘newfangled’ Arabic numerals scared early Italian bankers, who preferred proper Roman numerals; this, supposedly, is why we write the amount on a cheque in words, just to be sure.

    • Spot on on all counts. That post should be promoted to an addendum!

      One very marked use of the ‘score’ is Danish, which retains numbers based on twenties all the way from 20-90 – much to the confusion of Nordic neighbours, who otherwise don’t!

  2. tthef says:

    Ian, I am not convinced by the argument. 🙂 Just couple of thoughts.

    Base-8 means you have 8 independent symbols getting reused; I don’t see any evidence for that, and I think the etymological argument from ‘nine’ being like ‘new’ is weak (etymological argumants are generally fairly useless because the assignment of linguistic signs is entriely arbitrary, and their meaning is always differential — even if 9 is derived from ‘new’, the ‘new’ only gets its meaning from a contextual oposition with some ‘old’, and there is an endless number of possibilities of what that ‘old’ might have been at the point it was put into a new oposition with 8 and 10, the ‘new set of hands’ is only one possibility).

    The benefits of base-8 are, I think, overstated/anachronistic. The benefit of the ‘constant doubling’ is really the benefit of base-2, and is only a benefit if handling more than two independent symbols is difficult. The modern uses of base-8 and 16 are entirely as a proxy for the humanly impractial base-2. (Base 12 is far more practical because of the divisibility by 2,3,4, and as a previous comment notes, is attested by the likes of ‘thirteen’.)

    I think we tend to over-estimate what formal properties of language can tell us about the mindset of those using the language. One of the most signficant forces in language formation is the ease and economy of use. When encountering an interesting linguistic phenomenon, I tend to ask ‘how did it make the language easier to use’, I wonder if that might not apply to the number formation here as well.

    • That’s all sound stuff (I’ve long thought if we encounter a master civilisation somewhere else in the Milky Way, we will find it counts in Base 12!), though it still leaves us with the original problem.

      Why did the Romans, apparently, go two back from each ten but stick with a regular form through 17/27/37 (albeit one the other way around from 11-17), only for their successors to irregularise (or partially regularise, depending on how you look at it) this, and to do so around 16?

      It doesn’t, apparently, make it easier to use – essentially the numbers from 11-17 in each Latinate language (with the exception up to a point of Italian) need to be learned individually, whereas they didn’t in Latin and don’t in Germanic languages.

      It is a marked exception to the quite correct rule you identify.

  3. Deirdre Devlin says:

    That’s the most interesting thing I’ve read in ages!!! You should definitely write a book Ian.

    Best D

    Sent from my iPad

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