Craig Fahman over at FiveThirtyEight has an interview with Caleb Everett, author of Numbers and the Making of Us: Counting and the Course of Human Cultures.
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.