Summer Surmises: Celtic Counting

Dydd Llun, y cynta Awst / Emancipation Day, Monday, August 1, 2022 / Yom Sheni, 4 Av, 5782.

David Orenstein, Toronto, Canada david.orenstein@alumni.utoronto.ca

Today is Emancipation Day, commemorating the abolition of slavery throughout the British Empire in 1834 on August 1 that year. It’s a day that has been celebrated here in Ontario for well over a hundred years and is on its way to official Canada-wide recognition.

In addition to giving today’s date in English (on the Civil Calendar), and in Hebrew (in the Jewish Calendar), it’s also here in Welsh, the Celtic language whose cardinal numbers we’ve already discussed, in a previous post.

Today let’s look at the cardinals, 1 to 12, in the six modern Celtic languages: Welsh, Cornish, Breton, Erse, Gaelic, and Manx. See Table 1

So, what I chose to do was to build a table of twelve numbers each from a group of six related languages. That is a dozen numbers from half a dozen languages:

Or, half a dozen of a dozen (using the Commutative Property).
Or, half a dozen dozen (Associative Property). 
Or, half a gross (By Substitution: “a gross” = “a dozen dozen”).  
Or, ½ x 12² (By Definition: “a gross” = 12²). 
Or, ½ x 144 (Substitution by Memory: 1 gross = 144). 
Or, 144/2 (Reciprocity of Multiplication and Division). 

That is 72, doing a simple operation of division by two.

Of course, in reality, all this took just a couple of seconds of mental arithmetic.

Why did I tell you this? It’s to illustrate what I’m doing in this series of posts. That’s trying to illuminate how naïve Ethnomathematics can be illuminating for the development of more abstract mathematical systems and for the pedagogy of mathematics. Maybe even for epistemology in general.

We can see many mathematical principles and practices either directly or implicitly in our Table of Celtic Counting.

But that’s another story!