Xiako Can't Count

Xiako is a typical teenager. Self-absorbed and rebellious, she would fit right in at any American high school. Not to say that she isn’t different. She is a member of the Piraha tribe, a small, self-isolating community in the heart of the Amazon Rainforest.

Imagine that she’s visiting the United States for the first time as part of some sort of cultural exchange program. She’s smart, hard-working, and enjoys taking care of younger children. Of course, language is an issue. Her language isn’t at all like English. (In fact, it’s not at all like any other living language.) But Xiako has a much bigger problem: Xiako can’t count!

Because she can’t count, she can’t do even the simplest math. Her host family is making great progress teaching her English, but they’re having no luck at all with arithmetic.

How come? You said she was smart, and I can see that from the progress she’s made learning English; so, what’s up with her numbers?

Well, for one thing, she doesn’t have any! (Yup, you read it right: she doesn’t have any numbers.) The Piraha don’t distinguish 1 from 2 or 2 from 10, so no wonder she finds math difficult. Try solving the simplest math problem without using numbers…See what I mean?

Without a concept of number, all attempts to teach Xiako the simplest arithmetic were doomed to failure. Even 1 + 1 = 2 made no sense to her. There’s no 1 to begin with, so there’s no 1 + 1 and if there’s no 1 + 1, how than there be a 2 (whatever ‘2’ might mean)?

So, what’s up with the Piraha? How can they get by without numbers?

Turns out, the Piraha get along quite nicely thank you, that is, until they cross paths with folks like us, i.e., folks from ‘number enabled’ cultures like ours. When that happens, there’s trouble, not violence (the Piraha are a peaceful people), but trouble! For example, how can you conclude a modern commercial transaction when one party uses numbers, and the other party doesn’t?

Imagine that I run a trading post several miles downriver from a Piraha village. I have a customer! And my customer wants fish. I’d like to be able to ask, “How much fish would you like?” or “How many fish do you want?” or “How much do you want to spend?” but I can’t say any of those things.

I can’t put the fish on a table and count them; I can’t put them on a scale and weigh them, and I have no idea how to communicate what I mean by ‘price.’

Why do we have numbers while the Piraha don’t? Perhaps because we understand the world as a collection of objects and/or events. In mathematics, a collection of things is often referred to as a set. I immediately want to know the size of my set, how many members does it have? How many apples? How many oranges?

The Piraha have no idea of sets. Each event stands on its own. “One is one and all alone and evermore shall be so.” But Being Piraha doesn’t mean being lonely. Far from it. The Piraha are extremely social.

Many cultures have a less developed number system than ours. For example, there are cultures that rely on just 3 numbers: One, two, many.

Inconvenient? Yes. Impossible to work with? No. With just the numerals 1, 2, >2, we can work through any transaction. It just might take a ‘bit’ (pun intended): remember, computers do all that they do with only two numbers: 0 and 1. Big Blue won Jeopardy using nothing but 0’s and 1’s. But Xiago has no 0 and no 1.

We’re having great success teaching her English, why can’t we teach her math?

The difference is that Piraha understand ‘language’ (they have one) but not ‘numbers’ (they have none). To move from Piraha to English is difficult but possible. To move from no numbers, not even a concept of ‘number,’ to the Set of Real Numbers might just be impossible.

This total lack of numeracy in Piraha culture caught anthropologists by surprise. There are roughly 7,500 distinct human cultures. 7,499 apparently have a concept of number, one does not. Guess which one!

David Cowles is the founder and editor-in-chief of Aletheia Today Magazine. He lives with his family in Massachusetts where he studies and writes about philosophy, science, theology, and scripture. He can be reached at david@aletheiatoday.com.