The Origins of Counting

Rather than our usual Tuesday afternoon departmental meeting, the Maths Team left the school walls and decamped to ritzy Central London, for a meeting about the Origins of Counting, at the Royal Society. As always, the cultural disparities between Newham and the Mall were very apparent, from graffiti on walls to oil paintings of old venerable men on walls. An example of number sense in animals other than humans:

From Number Sense to Number Symbols

A talk by Francesco d’Errico, who claimed he would turn everyone in the audience into an archaeologist by the end of his 40 minutes. Many animals have number sense (hyenas can make comparative statements about the size of an enemy pack and use it to make a decision about whether to attack or retreat), but only humans have number symbols. How did this journey happen?

  1. The journey was non-linear. Innovations in symbols happened, were lost, and then re-appeared later on, often in different cultures.
  2. Homo Sapiens was not the first species to creat symbols. Neanderthals got there first, 80,000 years ago.
  3. The appearance of number symbols was not due to genetic modification (since many animals have comparable number sense to humans, and neanderthals were able to make number symbols). Rather it was due to the plasticity of the brain, and to communication through culture. Symbols have only been developed in the last 5,000 years – nothing in evolutionary timescales.
Progression of number symbols. x-axis is time (larger x-value means further into the past), and blocks show when different techniques were used. Isolated dots on right show how practices were discovered and then forgotten and then discovered again. 
For a long time we have used symbols to externalise our memory. Outsourcing memory to google is not a new phenomenon.
A summary.

The Deep History of Number Words

By Mark Pagel

Excellent essential question

Language years: if a word is spoken in one language for 5 years and in another for 10 years, then that word has been spoken for 15 language years. “Two” (in its various forms) has been spoken for 148,000 language years. Ridiculous.

Evolution of words, like evolution of genes
Decay of words, like decay of isotopes
The more frequently a word is used, the less it changes. Number words change even slower than this regression would suggest.
The slow evolution of number words is not limited to Indo-European languages.
The only words that change slowly across all three language groups are number words. Number words are special!
Nice inforgraphic

Why do number words change so slowly, across languages and time? Possible answers:

  • A link is built between the number words and the region of the brain links to numerosity. Numerosity is very stable, and so therefore the words are too
  • “Two” is a very clearly defined concept, whereas other words (such as “sofa”) are not.
  • If a word is to be used often, it must be short. There are not many short sounds that are still avaible (they are already words!), so there are no candidates for alternatives to number words.

Implications of Innate Numerosity-Processing Mechanism for Education

By Brian Butterworth, heavyweight academic and oganiser of the conference. He coined the term dyscalculia, and presented here an in-depth analysis of the current neuroscientific research into why some people do not have a strong in-built sense of numerosity.

The speed with which 3 year old children can count dots accurately predicts their numeracy skills at age 11

His rallying cry: dyscalculia is at least as important as dyslexia, and should be treated as such in schools.

Cedric Villani and Marcus du Sautoy in discussion

Two famous popularisers of maths end the conference with their ruminations on what we have learnt. Cedric is a great speaker, his hands wildly gesticulating and accurately representing the mathematical processes that his mouth is talking about. Marcus observes that, contrary to belief, mathematicians do not see the world in numbers – instead they are hypersensitive to structure. We should not be scared of showing children the big meaty ideas in maths, providing them with linguistic structure to tackle deep ideas.


Cedric speaks of this cartoon:



  • We learnt nothing that could be immediately applied in the classroom as maths teachers. But, lifelong learners do not need to be immediately able to apply the new knowledge.
  • We were frustrated by the lack of presentational skills by some of the speakers. Death by powerpoint is never excusable – intellectuals have a responsibility to communicate well.



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