How are we to describe unity, how know it? Only by experiment can we discover the nature of its action on any given number. In certain minor respects, this action exhibits regularity. We know, for example, that it uniformly transforms an odd number into an even one, and vice versa; but that is practically the limit of what we can predict as to its action.
We can go further, and state that any number soever possesses this infinite variety of powers to transform any other number, even by the primitive process of addition. We observe also how the manipulation of any two numbers can be arranged so that the result is incommensurable with either, or even so that ideas are created of a character totally incompatible with our original conception of numbers as a series of positive integers. We obtain unreal and irrational expressions, ideas of a wholly different order, by a very simple juxtaposition of such apparently comprehensible and commonplace entities as integers.
There is only one conclusion to be drawn from these various considerations. It is that the nature of every number is a thing particular to itself, a thing inscrutable and infinite, a thing inexpressible, even if we could understand it.
In other words, a number is a soul, in the proper sense of the term, an unique and necessary element in the totality of existence.
Aleister Crowley, “What is a ‘Number’ or a ‘Symbol’?” 1924
Along the banks of Brazil’s Maici River, the Pirahã people kick it “without numbers or time.” Former chair of Pitt’s linguistics department Daniel Everett has spent his career documenting these and other aspects of the Pirahã language, many of which confound the predictions of linguistics’ most popular paradigms.
In their everyday lives, the Pirahãs appear to have no need for numbers. During the time he spent with them, Everett never once heard words like “all,” “every,” and “more” from the Pirahãs. There is one word, “hói,” which does come close to the numeral 1. But it can also mean “small” or describe a relatively small amount — like two small fish as opposed to one big fish, for example. And they don’t even appear to count without language, on their fingers for example, in order to determine how many pieces of meat they have to grill for the villagers, how many days of meat they have left from the anteaters they’ve hunted or how much they demand from Brazilian traders for their six baskets of Brazil nuts.The debate amongst linguists about the absence of all numbers in the Pirahã language broke out after Peter Gordon, a psycholinguist at New York’s Columbia University, visited the Pirahãs and tested their mathematical abilities. For example, they were asked to repeat patterns created with between one and 10 small batteries. Or they were to remember whether Gordon had placed three or eight nuts in a can.
The results, published in Science magazine, were astonishing. The Pirahãs simply don’t get the concept of numbers. His study, Gordon says, shows that ”a people without terms for numbers doesn’t develop the ability to determine exact numbers.”
Rafaela von Bredow, “Living without Numbers or Time” SPIEGEL Magazine 5/3/06
Do the Pirahãs really not grok the concept of number, or do they just not want it? Would its adoption help them to “live here and now” (a core cultural value, according to Everett) or hinder them from doing so?
In his last book Island, Aldous Huxley has mynah birds squawk “Here and now! Here and now!” to remind his Utopians to live in the moment, but the Pirahãs appear not to need such reminding. Though the Korzybski-Whorf-Sapir-Nietzche-Burroughs-etc. hypothesis (basically that language influences, or even determines, perception [and, by extension, culture]), at least admits the possibility of a culturolinguistic phenomenon like Pirahã, a model that would fully account for its profound weirdness and uniqueness has yet to be formulated. Still, I do wonder what those guys would have made of it.
I also wonder what this Daniel would make of the Pirahãs and their apparently numberless headspace.
Finally, according to the Manchester Evening News, Britain’s weather-themed Cool Cash lottery game was recently canceled after only one day because too many players didn’t understand that negative numbers are inverse quantities. What would the Pirahãs, or Crowley, make of that?
Perhaps not much.
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Tags: Aldous Huxley, Aleister Crowley, Alfred Korzybski, Benjamin Whorf, Cool Cash lottery, counting, Daniel Everett, Daniel Tammet, Edward Sapir, here and now, imaginary numbers, infinity, inverse quantities, irrational numbers, Island, linguistics, living in the moment, Living without Numbers or Time, Maici River, negative numbers, number, Peter Gordon, pi, Piraha, psycholinguistics, quantity, Rafaela von Bredow, SPIEGEL Magazine, unity, What is a Number or a Symbol?