Sommaire:

The most common numeral system is decimal, based on our ten fingers, but countless other systems exist and have been used throughout history. They use a different "base" or "radix". Traces of these alternative systems are still present today: when we buy a dozen eggs, use base 24 and 60 for timekeeping, or hear a French speaker say ``four-twenty four'' to mean eighty-four, a vestige of a vigesimal (base-20) system. We use our fingers to count in the same way that we may use our feet to measure lengths. We rely on these anthropocentric standards to communicate, but we expect natural phenomena to be independent of the language we speak, the metrics we choose, and even the kind of numbers we use. Both numbers and units should be informed by nature, not human conventions. To illustrate this radical idea, I will explore examples from the capillary dynamics of droplets and bubbles, and from explosions—two classical subjects of scaling. Starting with a single power law, I will show that its eventual breakdown is actually a necessity if the associated phenomenon is to be independent of our human imprint. No power law can extend indefinitely.

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