16.3: Columbus Again

Last updated
Save as PDF

Page ID: 4704

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

All these results were known to the panel of experts which King Ferdinand appointed to examine the proposal made by Columbus. They turned Columbus down, because using the original value of Eratosthenes, they calculated the westward distance from Spain to India and concluded that the distance was far too great.

Columbus had an estimate of his own. Some historians have proposed that he used an argument like Strabo's, but Dr. Fischer found his claim to be based on incorrect units of distance. Columbus used an erroneous estimate by Ptolemy (whom we meet again), who based it on a later definition of the stadium, and in estimating the size of the settled world he confused the Arab mile, used by El Ma'mun, with the Roman mile on which our own mile is based. All the same, his final estimate of the distance to India was close to Strabo's.

In the end, Queen Isabella overruled the experts, and the rest is history. We may never know whether Columbus knowingly fudged his values to justify an expedition to explore the unknown or if he actually believed India was not too far to the west of Spain. He certainly did call the inhabitants of the lands he discovered “Indians," a mislabeling which still persists.

But we do know that if the American continent had not existed, the experts would have been vindicated: Columbus with his tiny ships could never have crossed an ocean as wide as the Atlantic and Pacific combined.

As for the size of Earth, it has been accurately measured many times since (see item “geodesy" in an encyclopaedia), one notable effort being that of the French Academy of Sciences in the late 1700s. Their aim was to devise a new unit of distance, equal to one part in 10,000,000 of the distance from the pole to the equator (as Eratosthenes showed, it is enough to measure part of that distance). Nowadays that distance is known even more accurately, but the unit introduced by the French academy is still used as the standard of all distance measurements. It is called the meter.

“Another look at Eratosthenes' and Posidonius' Determinations of the Earth's Circumference" by Irene Fischer, Quarterly Journal of the Royal Astronomical Society, vol. 16, p. 152-167, 1975.

A delightful illustrated book for early readers about Eratosthenes, The Librarian who Measured the Earth by Kathryn Lansky (illustrated by Kevin Hawkes), Little Brown and Co., 1988, 1994.