Paradox

214 A BRIEF HISTORY OF THE PARADOXreturned to the same place of departure as the sun,wherefore the long voyage had brought the gain oftwenty-four hours, as is clearly seen.(Pigafetta 1969, I, 147–48)It turns out that one of Buridan’s young colleagues, NicoleOresme, wrote extensively on this paradox. (Lutz 1975, 70)(Oresme may have picked up the paradox from Syriangeographers.) In “Traitié de l’espére,” Oresme describestwo imaginary travelers Jehan and Pierre who go aroundthe equator in opposite directions and rendezvous simultaneouslyat their point of departure. Each covers 30 degreesof longitude per 24-hour day. Jehan, who goes west, reportsthat his journey took eleven days and nights. Pierre, whogoes east, says that it lasted thirteen days and nights. As acontrol, there is a third man, Robert, who remains at thestarting point. Robert says that only twelve days and nightshad elapsed since both travelers had set out. Oresmerealized if you travel in the same direction that the sunappears to move, you will lengthen the interval to the nextsunset or sunrise. After a complete circuit, the increases willadd up to a whole day.Lewis Carroll (1850, 31-33) embellishes the circumnavigator’sparadox by imagining a strip of land circling the earthin which everyone speaks English. You embark Tuesday fromLondon at 9 A.M. and travel quickly enough to keep the sunin the same position in the sky. As you go along, you checkthe time by asking the locals, “What time is it?” They alwaysanswer, “9 A.M.” Indeed, that is the answer when, 24 hourslater, you return to London. But the Londoners also reportthe day as Wednesday rather than Tuesday. So where didWednesday begin?