1 The Birth of Science - MSRI

3.2 Geodesy and Mathematical Geography 61
earth. Someone who goes back and forth in thought between a drawing
and the world is using, most often unconsciously, correspondence rules —
precisely what we have singled out as an essential characteristic of scientific
method. Indeed, only by making explicit all the underlying assumptions
(which in the case of Eratosthenes were those of optics and of geometry,
the roundness of the earth and the smallness of the earth compared
with the distance to the sun) can one create a theoretical model that, being page 94
approximately applicable to the earth, is also amenable to depiction by a
drawing and so furnishes a logical bridge between the two.
Eratosthenes’ method is a brilliant example of the power of scientific
method: by going back and forth between the real world and the model,
he gained information about the unknown regions of the earth, which no
Ancient had ever seen.
In the second century B.C., mathematical geography progressed thanks
above all to Hipparchus of Nicaea. It was he who, in critiquing the method
of his predecessors, had the idea of finding differences in longitude using
astronomical methods, by measuring differences in local time for the same
lunar eclipse. 57
The study of geography was taken up again in the imperial age, in close
connection with astronomy and spherical geometry, by Marinus of Tyre,
whom we know only through Ptolemy’s criticism, and by Ptolemy himself
(both second century A.D.). But whereas Eratosthenes had found one
degree of meridian to be worth 700 stadia, a quite accurate number also
accepted by Hipparchus a century later, 58 Marinus and Ptolemy adopted
instead the value 500 stadia. 59 Although we do not know why the world
shrank like this in the imperial age, an error of this magnitude must mean page 95
that either the values of certain key geographic data current in Ptolemy’s
time were much less accurate than they had been 400 years earlier, or that
such data were misunderstood or misapplied. Either possibility should
not surprise us, given that Ptolemy was separated from the golden age
57 Strabo, Geography, I, i, 12. Strabo mentions also solar eclipses, obviously by an oversight, which
nonetheless has propagated down the centuries (see, for example, the Encyclopaedia Britannica, 15th
edition, Micropaedia, sub “Hipparchus”).
58 Strabo, Geography, II, v, 7.
59 Apparently this was not just a matter of inconsistent units: Ptolemy really did believe the
meridian was shorter than formerly thought. That the shorter value had already been adopted
by Marinus is mentioned in Ptolemy, Geography, I, xi. Using Ptolemy’s data, a person setting out to
travel westward along the latitude of (say) Palos, Spain, would expect to cover 17,000 km (5/7 of
the actual value of 24,000 km) before returning home. If his goal were to reach Asia by traveling
due west from Spain, he would estimate the length of the voyage by subtracting from 17,000 km
the breadth of Eurasia (about 10,000 km). It turns out that Ptolemy’s error did not affect the size of
the known continents, which he reports with reasonable accuracy; thus the calculated difference
(17,000 − 10,000 = 7,000 km) would be about half the true value (24,000 − 10,000 = 14,000 km). This
may help explain why Columbus grossly underestimated the length of a westward route to Asia.
Revision: 1.13 Date: 2002/10/16 19:04:00