Yesterday she shared, with great excitement, some of the remarkable things she was discovering about maths as a result of reading the book Here's Looking at Euclid by Alex Bellos. One story that I only half knew about was how some indigenous folks living in the Amazon rain forest have a very unique outlook on things mathematical.
Their number system for example consists of one and two, which are numerically form followed by threeish, fourish, and fivish, terms that I will need to read the book to fully grasp.
Katy also described how there are no standard units of measurement used to measure anything. For example, time is not divided up into units such as seconds, minutes and hours. There are no length or distance measurements such as feet or meters or miles or kilometers. This made me start wondering about how dependent our lives are on every conceivable unit of standardized measurement. There is almost nothing in our lives that cannot be measured with some standardized unit s is illustrated in this Dictionary of Units of Measurement.
I am sure that the indigenous people of the Amazon have units of measurement for some things that are part of their culture and that they all know but they clearly have no need of standard measures with which to communicate with the rest of the world.
So in my class yesterday I asked my undergraduate students to imagine living without standard units of measurement. I posed the question "Suppose you came to class when you felt like it and left when you felt like it or if there was another way of determining when class started and ended" . We didn't have a whole lot of time to get into a deep discussion and I hadn't really had time to think through where I wanted to go with it but the whole idea does make you start to explore how we live. How mathematically our lives are defined by how we used standardized measures.
Perhaps retirement is life without the control of standardized measures?