The Sand-Reckoner
Psammites
Even a number as vast as the count of grains of sand needed to fill the entire universe can be named and calculated precisely using an extended numerical system, refuting any claim that some quantities are simply too large to express.
- a notation for numbers beyond ordinary limits
- calculating grains of sand to fill the cosmos
- preserving Aristarchus's heliocentric hypothesis
- an exercise in the limits of numerical notation
- no quantity beyond systematic description
The Sand-Reckoner, addressed to the Syracusan king Gelon II, refutes the assumption that the number of grains of sand is too vast to be counted by devising a new notation for numbers far beyond ordinary Greek numerals, then using it to calculate an upper bound for the grains of sand that would fill the cosmos. Since it is addressed to Gelon as a living ruler, it must predate his death in 216 BC, placing it among Archimedes's later works, after On the Sphere and the Cylinder and On Floating Bodies in Heath's reconstructed chronology. To make the calculation extreme, Archimedes adopts the largest cosmological model available, an early heliocentric universe proposed by Aristarchus of Samos, making the treatise one of the only surviving sources that records Aristarchus's heliocentric hypothesis at all.
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