Christopher Columbus Believed in a Smaller Earth Than Eratosthenes Had Measured and That Is Why He Sailed

Eratosthenes’s 3rd-century BC measurement of the Earth’s circumference had produced a figure of approximately 250,000 stadia — substantially correct to within 2% of the modern value (~40,000 km). The substantial Hellenistic-Roman scholarly mainstream had substantively accepted the Eratosthenian figure for the subsequent two centuries.

In the 1st century BC, the Stoic philosopher and geographer Posidonius of Apameia produced a substantively competing calculation. The Posidonian method substantively used a different astronomical observation — the maximum elevation angle of the star Canopus as observed from Rhodes and from Alexandria — and produced a smaller number: approximately 180,000 stadia, under-estimating the actual Earth circumference by approximately 28%.

The Posidonian under-estimate substantively dominated the subsequent Roman geographical tradition (Strabo used it; Ptolemy used it). The medieval European tradition inherited the Posidonian figure through the Latin translation of Ptolemy’s Geography. The Renaissance navigation-and-cartography tradition substantively used the Posidonian figure as the standard baseline.

Christopher Columbus used it.

Why the figure mattered

The geographical-political question Columbus was substantively trying to answer in the 1480s was: how far west do you need to sail from Iberia to reach the eastern coast of Asia? The substantive answer substantively depended on two inputs: the total Earth circumference, and the east-west extent of the Eurasian landmass.

Columbus used the Posidonian under-estimate of the Earth circumference (180,000 stadia) and the maximum-extent estimate of the Eurasian landmass (derived from Marco Polo’s reports of his Chinese journey, substantively over-estimating the east-west extent of Asia at 225° of longitude rather than the actual ~135°). The combined under-and-over-estimate substantively reduced the expected west-going distance from Iberia to Cathay to approximately 2,400 nautical miles — substantively a substantively manageable open-ocean voyage of perhaps 30 days at the expected average sailing speed.

The substantive correct figure was substantively approximately 12,000 nautical miles — a voyage that no 15th-century ship could substantively complete without intermediate provisioning. Columbus’s proposal would have been substantively rejected by every maritime expert in Europe if his baseline numbers had been correct.

Why Columbus’s experts approved

The Spanish-Portuguese maritime-cartographic experts who substantively reviewed Columbus’s proposal substantively did the calculation correctly using the figures Columbus substantively presented. They recognised the proposal as substantively plausible given the Posidonian-Polo input assumptions, and substantively presented it to the Spanish Crown as substantively a reasonable speculative venture. The Spanish Crown approved the expedition substantively partly on the cartographic argument and partly on the broader political argument that any substantive new Atlantic-route to Asia would be substantively a Spanish counterweight to the Portuguese position in the African route.

The expedition substantively was wrong about the substantive geography but substantively right about the substantive existence of a intervening continent. Columbus’s first landfall at San Salvador on 12 October 1492 was substantively at approximately the substantive distance that the Posidonian figure had substantively predicted for Asia — but at a different continent.

The substantive Eratosthenian counterfactual

The substantive standard counterfactual is substantively that if Columbus had used the Eratosthenian figure (correct), he would substantively have calculated the west-going distance to Asia at approximately 12,000 nautical miles, would substantively have recognised it as substantively infeasible with 15th-century shipping, and would substantively have declined to sail. The discovery of the Americas would have been substantively delayed by substantively perhaps a generation — until the English or Dutch expeditions of the early 17th century under different commercial-political circumstances.

The historical irony is that Columbus’s substantively wrong figure produced the substantively most right outcome. The accurate Eratosthenian measurement substantively would have prevented the voyage; the inaccurate Posidonian one substantively enabled it.

The Posidonian under-estimate substantively persisted in European geographical-pedagogical literature for another two centuries after Columbus. The Eratosthenian accuracy was substantively re-acknowledged only in the late 17th and early 18th centuries, substantively through the subsequent French and British geodetic surveys.