Number Systems as Metaphors
Gozzi, Raymond, et Cetera
We tend to think of numbers as pure, abstract ideas, untouched by the messiness of material things. Numbers underlie science, one of our culture's big enterprises, but they tend to give science its authority, its ability to approach some "truth."
I remember when I first read Oswald Spengler's description of the Classical Greek understanding of numbers. The ancient Greeks thought of numbers as being concrete, definite magnitudes. But later in history, European civilization defined numbers more abstractly, as a relation, a variable, or as a function. Spengler showed how a culture's understanding of number was affected by what was going on in the culture itself. "There is not, and cannot be, number as such" (Spengler, 1922/1987, p. 59).
If numbers themselves are cultural artifacts, then we may think of them as metaphorical, since they translate experiences from one domain to another. In fact, Buckminster Fuller defines numbers as experiences (1975, p. 237). In my search for the ever-present metaphor, I started wondering about the ways that numbers are organized into systems. Our everyday counting system is based on the number ten. We have ten digits in our system, zero through nine. To count higher than nine, we need to start combining the digits, using a tens place, a hundreds place, a thousands place, etc. This seems completely natural to us. We use the number system to the base ten to count our money. The decimal system of numbers is our constant companion as we strive to make sense of the world.
I am convinced that we use the number system to the base ten because we all learn to count using our fingers and thumbs. We have ten fingers and thumbs. To get a grasp on something, we like to use them all. Therefore, I would say that our number system is a metaphor for our activity with our hands.
However, we know that it is possible to have number systems based on numbers other than ten. Digital computers, for example, use a number system to the base two. There are only two digits in this number system, zero and one. To count over one, you need to combine the digits, and use a two place, a four place, an eight place, etc. …