By Andreea Calude 16/01/2018


Unclenching his tiny fist, my son shows me the palm of his hand and says I want this many blueberries. His father asks you want five?. The boy meets his gaze, holds out his hand, and slowly unclenches each finger, one by one, counting slowly but steadily one, two, three, four, five…yes, five. He is extremely pleased and I am wondering if he is pleased that his father had guessed correctly or whether he is pleased at his own ability to count all the way to five – not a mean feat for a small human of only 3. As for me, I am just pleased we still have five blueberries left.

Numbers come early

But why do numbers and number words matter so much, from such a young age? True, they don’t matter to everyone – some cultures do not have number words at all, like the Pirahã, or they only have a limited set, like the Pica, and others described by Alex Bellos in Alex’s Adventures in Numberland. Yet for many Western and Eastern cultures, numbers do matter a great deal and are acquired early in life. Admittedly, what “acquired” actually means is complicated: while some young children might recite the progression from one to ten like a poem or nursery rhyme, they may not necessarily associate these words with actual quantities or measurements; that comes later.

Numbers are often surrounded by a cloak of mystique (13 is unlucky for some English-speakers, 7 often expresses symbolic perfection in biblical texts, 4 symbolises treason and betrayal for the Chinese), not unlike the people whose business it is to study them, mathematicians. Yet studying numbers is not just for mathematicians.

Words for small numbers are old and stable

Using fancy statistics and linguistic theory, evolutionary biologists Mark Pagel and Andrew Meade published a paper in last week’s Philosophical Transactions of the Royal Society B(iology) showing another fascinating side of numbers. It turns out that the words we use to denote numbers are amongst the slowest evolving words in a(ny) language, and what is more, this holds true in hundreds of languages, from the Indo-European family, to the Bantu family, and even the Austronesian family (a family known for languages that do not have elaborate number systems). Put simply, the words denoting small numbers (1-5) are among the oldest words in our languages, fossils of our linguistic past.

Here is another twist: the word for ‘one’ is not especially stable when compared to the words for ‘two’, ‘three’ ‘four’, or ‘five’. Why? This is most likely to do with internal linguistic factors, the word for ‘one’ also functions as a indefinite article in many languages (for example, in Romanian ‘a book’ o carte is the same as ‘one book’), and thus comes under an entirely different set of pressures over time.

Number words in various languages

English Albanian Breton Palauan Chamorro Zulu Swahili
one një unan tɑŋ unu kunye moja
two dy daou ɛrʊŋ dos kubili mbili
three tre tri ɛðe(y) tres kuthathu tatu
four katër pevar ɛwɑŋ kuåttru kune nne
five pesë pem(p) ɛim sinɡku kuhlanu tano

Source for English, Breton, Palauan, and Chamorro.

Source for Zulu and Swahili.

Why are they so stable?

The question is WHY? Why should words for numbers be preserved and only change minimally with the passing of time, instead of being completely overhauled by new combinations of sounds, much like the rest of our words? The answer is still unclear, but here are some suggestions:

(1) Our brains are somehow predisposed to learning and holding on to number words (they appear to be acquired sooner than their frequency would predict).

(2) Number words tend to have a single and clear meaning (there is one and only one way to express the concept of ‘three’ in English, and conversely, ‘three’ expresses a very specific and unique concept, it has no other meaning).

(3) Number words tend to be short and therefore they seem to have achieved their ‘ideal’ length and ‘best’ fitness in the language, hence replacing them proves unnecessary.

In an article last year, Annemarie and I noted that the patterns for deriving higher numbers (20, 25, 30, 35, etc.) from smaller number words also show remarkable stability across the Indo-European family.

All this points to the fact that there is something about numbers that has a hold over the human brain, and it is not just mathematicians who are affected!

References

Alex Bellos, 2011. Alex’s Adventures in Numberland, Bloomsbury.

Stanislas Dehaene, 2011. The Number Sense: How the Mind Creates Mathematics, Oxford University Press.

Mark Pagel and Andrew Meade, 2018. The deep history of number words Philosophical Transactions of the Royal Society B(iology) Vol 373.

Andreea Calude and Annemarie Verkerk, 2016. How to build the Number Line in Indo-European – a Phylogenetic Study. Journal of Language Evolution Vol 2.

Lists of number words in various languages:

Numeral Systems of the World’s Languages

Of Languages and Numbers