Financial Mathematics Text

Friday, October 12, 2012

Being Without Numbers

Linguistic anthropologist Daniel Everett has been researching and living with (off and on) an Amazonian tribe called the Pirahã for a few decades now. In Don't Sleep, There Are Snakes: Life and Language in the Amazonian Jungle, Everett gives a semi-autobiographical account of his interactions with the Pirahã.

One of Everett's main claims is that the Pirahã lack recursion in their language. As an example he notes the following statement (pg 227 from the above book):
Hey Paitá, bring back some nails. Dan brought those very nails. They are the same.
Everett points out that we would say something with a relative clause:
Bring back the nails that Dan bought.
This lack of recursion raises questions about Chomsky's thesis of universal grammar. But that debate I'm largely ignorant of and is not the focus of my own interest in the Pirahã. A lack of recursion has other implications.

Recursion runs throughout much of mathematics. As an example consider the Peano axioms. In particular axiom 2 exhibits recursion (if a is a number, the successor of is a number.) The Pirahã lack of recursion is related to their lack of numbers and counting. That's what initially drew my interest.

The Pirahã have no number words in their language and they do not count. Everett spent eight months attempting to instruct the Pirahã on how to count, borrowing the number words from Portuguese language, but was largely unsuccessful.

The Pirahã also have no concept of time. I've wondered if the two are related. According to Immanuel Kant:
Arithmetic attains its concepts of numbers by the successive addition of units in time.
-Prolegomena to Any Future Metaphysics
This has suggested a conjecture on my part. The Pirahã may lack counting and arithmetic but that doesn't necessarily rule out space and geometry (another one of Kant's relationships). 

In any event, Everett's own view of why they lack counting has to do with what he calls The Immediacy of Experience Principle.  The Pirahã are only concerned with those things that they can directly experience in the here and now. As an example of this, Everett actually began his work as a missionary. The Pirahã were not interested Jesus inquiring of Everett what he looks like and whether or not he had met Jesus. The Pirahã lost interest upon realizing that Everett was attempting to tell them about a man whom he had not met.

Regardless of why they don't count, the fact that they don't is quite foreign to us. Much of Western culture is centered around mathematics. Every transaction (and transactions play an important part in our inter-social relationships) results in exchanging quantities  of currency for quantities of goods and services. In addition, most of our knowledge of the world has been mathematized. It would be hard to imagine a physics course without seeing some equations.

Mathematics has often been claimed to be "universal" and "a priori true". It's not entirely clear that the Pirahã rule out these claims but it does raise some interesting questions about who we are and how we view the world.

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