Round the World
The Earth is roughly spherical in shape, as everyone reading this
knows. What's often more of a surprise is that this part of core
science has been known to humans for some millennia, and has remained
generally accepted and largely uncontroversial. We see mountaintops in
the distance before we see the plains below, and we see that masthead
of an approaching ship before we see the hull. We see the shadow of
the Earth upon the face of the moon during a lunar eclipse, and it is
always circular. At different latitudes, we see different stars at
night, and the sun casts shadows of different lengths during the
day. These pieces of evidence are all documented in ancient times, and
were gathered together in Aristotle's
treatise On
the Heavens (Book II, Ch 14), which means they were all
known by around 350BC at the latest. This led to the prediction that
you could travel in a particular direction and eventually return to
the place from which you started, a hypothesis that was confirmed by
the Magellan expedition nearly 2000 years
later.
The practical importance of this discovery appears in
many engineering situations. It's often necessary for planning and
executing journeys of more than a few hundred miles. It's vital for
understanding weather patterns. It's vital for long-distance
communication: once the railway and the telegraph were standard, it
became apparent quite quickly that some system of coordinated time and
corresponding time zones was necessary to synchronize watches around
the planet. Software engineers dealing with any kind of geographic
application learn very quickly that trying to treat latitudes and
longitudes as Cartesian coordinates is asking for trouble: and if we
go back into the history of mathematics, we find that this is just
what sines and cosines were invented for.
In about 180 BC, Eratosthenes of Alexandria used the
difference in lengths of shadows at midday at different latitudes to
estimate the circumference of the Earth, and this gave a much more
accurate figure than the estimate used by Christopher Columbus to
convince Queen Isabella that the east coast of China was within reach
of a well-provisioned sea voyage. Like many children in school, I read
that Columbus was one of the first people to believe that the Earth
was round. Not true: instead, he was the first to place enough faith
in an optimistically small estimate of the Earth's circumference that
he was willing to risk a westward voyage from Europe to China. In the
event, his ignorance of geography was turned into good fortune thanks
only to the intervention of an unexpected continent in
between.
In between the mathematicians of the ancient world and
the European renaissance lies the period of the Middle Ages. Readers
of many standard histories may be left with the impression that in
this period at least, Europeans in particular believed that the Earth
was flat. This is generally false: the overwhelming majority of
writers who touched on the subject assumed that the reader knows that
the Earth is round. These include Augustine, Bede, Aquinas,
over 70 other
medieval churchmen, and of course a whole range of Arab, Indian
and Chinese scholars and sailors. From around 1000AD, the knowledge
assumed increasing practical importance as the mariner's compass and
sailing into the wind made regular longer voyages possible,
particularly over the Indian Ocean. The European renaissance and
voyages of discovery did not come from nowhere, but from centuries of
gradual technological advances during which common knowledge of the
shape of the Earth played a central part. By the time Copernicus was
able to write his pivotal
work On
the Revolutions of the Heavenly
Spheres, he could state firmly in his second paragraph
that the Earth is spherical, give a short list of demonstrations
similar to those above, and know that every educated reader would
agree with his book thus far.
Given the importance of the Earth's shape in the day to
day life of many professions, why is the story of this knowledge
relatively obscure compared to that of the Earth's movement in the
solar system? Most educated people today can give a reasonable
estimate of when it became known that the Earth goes round the sun:
many will say Copernicus; others will guess at Galileo which is
roughly accurate to within a century. By contrast, if asked "At around
what date did we know that the Earth was round?" many educated people
will admit to not knowing at all, or will guess at a similar time in
the early modern period.
In the rest of this brief essay, I will propose three reasons for this absence: one scientific, one literary, and one religious.
The scientific reason is that the Earth's daily
rotation is intimately linked to its shape, but was demonstrated much
later. Ptolemy of Alexandria (who knew of course that the Earth was
round) considered but dismissed the idea that the sunrise and sunset
were due to the Earth itself rotating, because the surface of the
Earth would have to be moving so fast that there would be enormous
windstorms everywhere. This is the claim that Copernicus challenges
first, before going on to discuss the movement of planets and the
Earth around the Sun. Copernicus argues a kind of least-action
principle – if the Earth rotating once a day is "too fast to
believe", then how much harder is it to believe instead that the
sphere of the immeasurably distant stars rotates once a day? To
explain the lack of permanent hurricanes, Copernicus suggests that
even though gases are attracted to the Earth's surface less strongly
than liquids and solids, still they are attracted and pulled round as
the Earth itself spins. He even goes so far as to suggest that the
moon and sun may similarly attract the things near to them: to explain
the lack of perpetual hurricanes, Copernicus even anticipates the law
of universal gravitation! So Copernicus did contribute
crucially to our knowledge of the Earth's circular motion,
and the history of this discovery can understandably be confused with
the history of our knowledge of the Earth's
circular shape.
The literary reason is that the story of the Earth's
shape lacks drama. It's like trying to write a love story about a
couple who stays happily married for decades – it's dull! There
is no hero thrown in jail, no individual of brilliant insight rejected
by an ignorant public or a corrupt establishment, no centuries of
darkness redeemed by a final enlightenment. Even worse, there's
nothing that makes us today feel superior to people at other times and
places with whom we feel no intellectual kinship. It doesn't fit with
the narrative of modernity: instead of a revolution in thought that
throws out everything that went before, it is an example of
continuity, in which ancient and medieval science built a platform
upon which modern science was built. If it's a dull story that doesn't
fit with the standard narrative, much better to ignore it than to
dwell on it. Or romanticize it: any sensible movie-maker would
probably prefer the popular myth of Columbus as a steadfast and unique
believer in a new idea, rather than an opportunist adventurer who got
lucky in spite of using some very bad data.
The third and most controversial reason is to do with
religion. During the 19th century, books like John William
Draper's History
of the Conflict between Religion and Science and Andrew
Dickson
White's History
of the Warfare of Science with Theology in Christendom dwelt
considerably on a few medieval authors, particularly Cosmas of
Alexandria who taught of a flat earth in a 6th century work
called Christian
Topography. Though we know today that such flat-Earth
believers were the exception rather than the rule, this mistake about
the middle-ages spread into the 20th century and is still
with us (see the Wikipedia article on
the Flat
Earth Myth). The Flat Earth Myth seems to me like an unfortunate
and very human accident – Cosmas' choice of title suggests that
he wanted to promote his views as decidedly Christian, and later
antitheist critics have been more than happy to agree with him on this
score. The story reminds us that we're prone to believe things that
fit with our pre-existing biases, and that fact-checking assertions
about what most scholars did or not did believe in a time as distant
as the middle-ages is difficult.
Science offers two important and readily accessible
methods for avoiding such errors. The first is to read primary
sources. For example, to find out if Copernicus could assume that the
Earth was round, and what other prior knowledge could be safely
assumed, who better to read than Copernicus himself? In
his first
and most revolutionary chapter, parts of which were mentioned
above, Copernicus cites the Pythagoreans, Plato, Aristotle, Ptolemy,
Plutarch, Averroes, Martianus Capella's medieval encyclopedia, and
Psalm 92:4, to name but a few. Even in the cases where he proposes
different explanations (for example, Ptolemy on the movement of the
Earth and Averroes on that of Mercury), he assumes that their
observations were correct. His "prior art" quote for the relativity of
motion comes from Virgil's Aeneid, and that for the sun
lighting all things comes from Sophocles' Electra. So much
for the irrelevance of a liberal arts education! His demonstrations
emphasize continuity with the past wherever possible, partly because
he wants his theory to have the best possible chance of being accepted
by his contemporaries. You might hear a scientist today claim that the
scientific revolution threw out everything that came before: this has
become standard in the retelling, and deriding distant people is
always easier than taking the time to understand them. But for many of
the pivotal minds who made that revolution, their debt to the past was
gratefully and humbly acknowledged.
The second, and most important method, is to observe
the world. Take the time to convince yourself that the Earth is round
– don't take someone else's word for it. Take a pair of
binoculars to the top of a hill and watch the ships at sea. Note the
date of the next lunar eclipse (there's one coming up on April
4th 2015, mainly visible over the Pacific regions) and look
at the Earth's shadow (and first, look at the way the full moon is
opposite to the sun in the sky and convince yourself that what you're
seeing is the Earth's shadow!). If you travel to a distant
place at a different latitude, look for a familiar constellation like
Orion and see that it is higher or lower in the sky at the same time
of night. These are the things that can make us fall in love with the
system of the world: these are the things that make us scientists. And
if you see them, remember with pride that for thousands of years,
people have seen the same things with their own eyes, and in so doing,
have seen beyond themselves.
Dominic Widdows, March 2015.