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What changed when zero became a number?

The zero in 205 prevents it from being read as 25. Using zero in an operation such as adding or multiplying is a further step. Historical examples separate these roles: a mark can preserve an empty position long before a mathematical tradition develops rules for treating zero as a number.

3–7 min

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  • Why would a placeholder alone leave questions about arithmetic unanswered?

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Why does a radiocarbon date need a second kind of clock?

History4–5 minA radiocarbon measurement does not translate directly into one calendar year. The amount of radiocarbon in the atmosphere has varied, so dating relies on comparison with material whose age is already known.

History

Reading a buried timeline

A deep object is not necessarily the oldest thing at an archaeological site. A later pit can cut through earlier ground, leaving a sequence that has to be reconstructed from relationships between layers.

12–15 min

Reading a buried timeline

History12–15 minA deep object is not necessarily the oldest thing at an archaeological site. A later pit can cut through earlier ground, leaving a sequence that has to be reconstructed from relationships between layers.

History

When Britain’s railways needed a shared clock

A timetable becomes awkward when the clocks at its two ends disagree. In nineteenth-century Britain, railway journeys helped turn local time into a shared coordination problem, while the telegraph helped distribute an answer.

8–10 min

When Britain’s railways needed a shared clock

History8–10 minA timetable becomes awkward when the clocks at its two ends disagree. In nineteenth-century Britain, railway journeys helped turn local time into a shared coordination problem, while the telegraph helped distribute an answer.

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