Summer Surmises: Thoughts about Thinking About Number

Yom Sheni, 12 Tammuz, 5782.
David Orenstein, Toronto, Canada
david.orenstein@alumni.utoronto.ca

You might have noted that my blog posts are dated both in English, on the Gregorian Calendar, and in Hebrew (though in Roman letters), on the Jewish Calendar.

The days of the week in English honour astronomical bodies, Germanic gods, and Roman deities: Sun Day, Moon Day, Tiu’s Day, Wodin’s Day, Thor’s day, Freja’s Day, Saturn’s Day. By contrast Jewish days are a straight count up, to the Sabbath, with today being Yom sheni = <Day second> = “Second Day”. Or for a complete list:

Sunday = Yom rishon = <Day first> = “First Day”
Monday = Yom sheni = <Day second> = “Second Day”
Tuesday = Yom shlishi = <Day third> = “Third Day”
Wednesday = Yom revi’i = <Day fourth> = “Fourth Day”
Thursday = Yom chamishi = <Day fifth> = “Fifth Day”
Friday = Yom shishi = <Day sixth> = “Sixth Day”
Saturday = Shabbat = <Seventh> = “Sabbath”

Since, at its most fundamental, Mathematics is about number and shape, while English speaking children were learning a hodgepodge of pagan deities, Jewish children were learning their ordinal numbers and getting an initial insight into modular arithmetic.

In English, is it similarly opaque when you start counting with cardinal numbers?

For me these numbers are practically a single thought unit:

One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. 

There is no clear way that any of them could be produced from the others. They just have to be memorised. Once you’ve learned to write, you might see a hint of “two” and “ten” in “twelve”. But if you only have the sounds to go on, there’s little in common. After all, “two” sounds like <too>, not <twoo>. But it’s also a homophone of the word “too”, implying “two” is “one in addition to one”.

English also has many synonyms of “two”: pair, couple, brace, other, etc. Does this help to learn maths or hinder? On the one hand, you could see that these are different labels of the same concept, that you could then more easily abstract. Or on the other hand, you could get lost in the forest of concrete cases, seeing only the practical examples.

How might this work in other languages? I decided to explore counting systems in a group of languages that I’m not familiar with. In my case, that would exclude the Germanic languages (German, Dutch, Danish, etc.), Romance (French, Italian, Catalan, Roumanian, etc., and Jewish (Hebrew, Yiddish, Ladino, etc).

That way I could consider with fresh eyes and ears how your language disposes you towards mathematics. Last year’s BSHM/CSHPM/HOMSIGMAA joint conference being held virtually in St. Andrew’s, Scotland, was a sign that I should learn how to count in the six modern Celtic languages: Manx, Cornish, Breton, Welsh, Gaelic, Erse. Maybe even in Scots.

But that’s another story!