# Thinking in Numbers

Slate published an excerpt from the Daniel Tammet book  Thinking In Numbers: On Life, Love, Meaning, and Math:

It seems the Pirahã make no distinction between a man and a group of men, between a bird and a flock of birds, between a grain of manioc flour and a sack of manioc flour. Everything is either small (hói) or big (ogii). A solitary macaw is a small flock; the flock, a big macaw. In his Metaphysics, Aristotle shows that counting requires some prior understanding of what “one” is. To count five or 10 or 23 birds, we must first identify one bird, an idea of “bird” that can apply to every possible kind. But such abstractions are entirely foreign to the tribe.

Lest anyone should think tribes such as the Pirahã somehow lacking in capacity, allow me to mention the Guugu Yimithirr of north Queensland in Australia. In common with most aboriginal language speakers, the Guugu Yimithirr have only a handful of number words: nubuun (one), gudh-irra (two), and guunduu (three or more). This same language, however, permits its speakers to navigate their landscape geometrically. A wide array of coordinate terms attune their minds intuitively to magnetic north, south, east, and west, so they develop an extraordinary sense of orientation. For instance, a Guugu Yimithirr man would not say something like, “There is an ant on your right leg,” but rather “There is an ant on your southeast leg.” Or, instead of saying, “Move the bowl back a bit,” the man would say, “Move the bowl to the north-northwest a bit.”

We are tempted to say that a compass, for them, has no point. But at least one other interesting observation can be drawn from the Guugu Yimithirrs’ ability. In the West, young children often struggle to grasp the concept of a negative number. The difference between the numbers two (2) and minus two (-2) often evades their imagination. Here the Guugu Yimithirr child has a definite advantage. For two, the child thinks of “two steps east,” while minus two becomes “two steps west.” To a question like, “What is minus two plus one?” the Western child might incorrectly offer, “Minus three,” whereas the Guugu Yimithirr child simply takes a mental step eastward to arrive at the right answer of “one step west” (-1).

There is something profound here about how the languages we use constrain the possibility sets we consider: it has a parallel in how the software we design affects the work we produce with it.