Most of us have little trouble working out how many millilitres are in 2.4 litres of water (it’s 2,400). But the same can’t be said when we’re asked how many minutes are in 2.4 hours (it’s 144).

That’s because the Indo-Arabic numerals we often use to represent numbers are base-10, while the system we often use to measure time is base-60.

Expressing time in decimal notation leads to an interaction between these two bases, which can have implications at both the cognitive and cultural level.

Such base interactions and their consequences are among the important topics covered in a new issue of the Philosophical Transactions of the Royal Society journal, which I co-edited with colleagues Andrea Bender (University of Bergen), Mary Walworth (French National Centre for Scientific Research) and Simon J. Greenhill (University of Auckland).

The themed issue brings together work from anthropology, linguistics, philosophy and psychology to examine how humans conceptualize numbers and the numeral systems we build around them.

Despite using numeral bases on a daily basis, few of us have reflected on the nature of these cognitive tools. As I explain in my contribution to the issue, bases are special numbers in the numeral systems we use.

Because our memories aren’t unlimited, we can’t represent each number with its own unique label. Instead, we use a small set of numerals to build larger ones, like “three hundred forty-two.”

That’s why most numeral systems are structured around a compositional anchor — a special number with a name that serves as a........

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