Friday, March 17, 2017

Numbers as cultural tools

Caleb Everett: My suspicion is that there were many, many times in history when people realized in an ephemeral way that this quantity is the same as that quantity — that this five, in terms of their fingers, is the same as that five, in terms of goats or sheep. It’s no coincidence that many unrelated languages have a numerical structure built around 10 or that the word for five is often the same as the word for hand. Once someone else heard you referring to something as a “hand” of things, it became a cognitive tool that could be passed around and preserved within a particular culture.

Craig Fehrman: Once a particular culture has numbers, what does that allow?

CE: The way our cultures look, and the kinds of technology we have, would be radically different without numbers. Large nation-states aren’t really possible without numbers. Large agricultural societies aren’t possible, either.

Let’s say that two agricultural states in Mesopotamia, more than 5,000 and maybe as many as 8,000 years ago, wanted to trade with each other. To trade precisely, and we can see this in the archaeological record, they needed to quantify. So they cooked up these small clay tokens, with each token representing a certain quantity of a certain commodity like grain or beer. The tokens were then cooked inside a clay vessel that could be transported and cracked open. It was essentially a contract — you owe me this many whatever.
If a culture lacks a number system:
CE: [...] And a few languages and other communications systems, like the Pirahã’s in Brazil, have only imprecise words like hói [one or a couple] and hoí [a few]. Many experiments have shown that without numbers, the Pirahã struggle with basic quantitative tasks. They have a hard time matching one set of objects to another set of objects — lining up, say, eight spools of thread next to eight balloons. It gets even harder when they have to recall an exact quantity later.

It’s important to stress that these people are totally normal and totally intelligent; if you took a Pirahã person and raised them in a Portuguese home, they would learn numbers just fine. But without recourse to a number system, they struggle with counting. It’s an example of how powerful these cognitive tools can be.


  1. "Recent studies in human history, developmental psychology, animal cognition, and neurophysiology provide evidence that the emergence of zero passes through four stages.

    In the first and most primitive stage, the absence of a stimulus (‘nothing’) corresponds to a (mental/neural) resting state lacking a specific signature.

    In the second stage, stimulus absence is grasped as a meaningful behavioral category but its representation is still devoid of quantitative relevance.

    In the third stage, nothing acquires a quantitative meaning and is represented as an empty set at the low end of a numerical continuum or number line.

    Finally, the empty-set representation is extended to become the number zero.

    These different stages of zero-like concepts reflect progressing levels of mental abstraction and pave the way for a full-blown number theory."

    Its a nice paper.

  2. "Zero" is particularly interesting. People were sometimes mystified about something that represented notion. So we go from Arabic ṣifr to zero, but also cipher.

  3. I should go back and read. As I make a speculative leap into something else.

    I would describe the end of engaging with a complex rythmic task I have had diffuclty mastering, as a resting processes and it certainly has provoked the question in the past, why in this place when everything is flying around do I appear to be doing nothing now in the centre of this storm?

    I would have had that down as a last stage question in doing something. Would seem to be the first 'primative' attempt at anlysis.