Our language does not help because it has developed alongside many ancient counting systems and retains many anomalies that complicate matters for young children. While it might appear obvious to us now that we choose to use base ten as we have ten digits, it was once equally as obvious that we should use base twelve. It is easy to count to twelve with one hand, using the thumb to point to each bone of each finger. This seemed significant at the time as there are roughly twelve lunar cycles in a solar year. The progression of the day could be measured by dividing it into twelve segments and this gave twelve hours of daylight and twelve hours of darkness. We still divide the day into two sets of twelve, although we now start at midnight, and we still buy eggs by the dozen.
With this system, the other hand can be used to keep a tally of the number of times you have counted to twelve – using all five digits gives five sets of twelve, which is sixty. This is the basis of the sexagesimal system developed by the Sumerians five thousand years ago and still used by us today for measuring time and geographic coordinates.
As a result our language makes progress for young children more difficult. We have unique words for ten, eleven and twelve, suggesting they are a continuation of the base numbers, as they once were. We then revert to thirteen, fourteen and so on. There is rightly no symbol for ten, just as there is no symbol for two in the binary system used in computing, just ones and zeros. We use one again in the next place position to the left to represent two in binary or one set of ten in decimal. Had our language developed differently, eleven might have been “eleventeen” or “tenty-one”.
Far Eastern counting languages are structured differently. They use ten-one, ten-two for eleven, twelve and so on, giving a better visual representation of the numbers. It is easier to visualise three tens and six minus two tens and four than hopping back and forth on a number line. While we do have unique words for ten, hundred, thousand and million, we don’t have a unique word for ten-thousand or hundred-thousand, as Far Eastern languages do. French speakers are even more disadvantaged, where eighty-five is expressed as quatre vingt cinq, or four twenties and five.
These skills are learnt in the early years and give Far Eastern language speakers a lifelong advantage. Interestingly, the Welsh language has a similar counting structure to the Far Eastern languages and, strangely, these cultures all revere the dragon, the symbol of the number nine, the largest base number. This is why we call our approach Dragon Maths.
