How do these results reflect upon the accuracy of Eratosthenes’ measurement of the Earth’s circumference? By today’s standards, these error percentages may seem high. However, for the ancient Greeks, the approximation is remarkably close.
While some modern scholars cling to theories which seem to indicate that Eratosthenes’ approximation was highly accurate, others admire his approximation solely on the soundness of his reasoning and elegance of his argument. Mathematician Irene Fischer, having worked on modern measurements of the Earth, writes with great admiration of Eratosthenes’ method.
[…] the great thing for us about Eratosthenes’ achievement was the method, the introduction of painstaking measurements instead of speculations, and not a specific number for the size of the Earth. It would not be fair to compare the ancient measuring precision, as advanced and sufficient as it may have been for that time, with modern precision in triangulation, astronomy, and satellite geodesy [5, p.159 ].
While it is true that ancient scientists lacked the sophisticated scientific equipment necessary to make precise measurements, it is also necessary to realize that they did not place the same emphasis on precision that we do today. Therefore, assuming that a figure given by an ancient scientist is the most accurate measurement available at that time is not a safe assumption. Nor is it safe to assume that the ancient scientist holds in mind the same rigorously scientific ideals that scientists do today. Scholar of ancient astronomy D.R. Dicks comments on the futility of trying to determine the accuracy of ancient scientific works.
The Greek mentality cannot be judged correctly from the standpoint of the modern scientist, and any attempt to force a spurious accuracy on to ancient measurements and translate them into mathematically exact modern equivalents is bound to have misleading results [2, pp.43-45 ].
Thus the specifics of Eratosthenes’ measurement may elude us simply because Eratosthenes did not have specifics in mind when he conducted this calculation.
Eratosthenes’ approximation of the Earth’s circumference is a beautiful mathematical argument, regardless of the accuracy of its result. The modern length equivalent to the stade used by Eratosthenes may never be known, just as the reason for the addition of 2000 stades may never be discovered. Nonetheless, Eratosthenes helped to lay the foundation for science based on mathematics and empirical observation rather than on mere philosophical speculation. Most importantly, he demonstrated the awesome power of mathematics as a tool to model our world.