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But there is a second way of counting. Take your apples and put each next to an orange. If they match up, you can easily see they are equal in number. “Look,” I say, “I have the same number of apples as oranges.” This method is more primitive and does not require the concept of numbers, but it is very useful. If I’m a shepherd I can hold a set of counters in a bag, one for each sheep. To ensure all my flock are gathered in for the night I drop one counter into the bag as each sheep enters the enclosure. I don’t need to give the counters number names.

The Munduruku tribe, from the Amazon rainforest, have no concept of number names beyond five. Their counting system simply goes one, two, three, four, five, many. Yet this second way of counting allows them to function successfully, deciding whether two groups of things have the same number of elements, even if there are more than five of them. For example, if they need to determine if they have enough spears for a hunt, each person simply stands next to their spear. If everyone has one, they’re ready. If not, then the empty handed Munduruku simply make one. No need for pesky numbers or mathematics lessons.

This second way of counting is particularly useful when tackling infinity because we are not sure what infinity is. Treating it the same way the Munduruku treat the number ‘many’ is the safest thing to do. The first question we would like to answer is whether all infinite things are the same.

[Image of indigenous people holding spears]

Spears and Hunters

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