Beautifully detailed portolan charts present historians with a puzzle: How were they made? A mathematical analysis offers some clues.
One
of the most remarkable and mysterious technical advances in the history
of the world is written on the hide of a 13th-century calf. Inked into
the vellum is a chart of the Mediterranean so accurate that ships today
could navigate with it. Most earlier maps that included the region were
not intended for navigation and were so imprecise that they are
virtually unrecognizable to the modern eye.
With this map, it’s as if some medieval mapmaker flew to
the heavens and sketched what he saw — though in reality, he could never
have traveled higher than a church tower.
The person who made this document — the first so-called portolan chart, from the Italian word portolano,
meaning “a collection of sailing directions” — spawned a new era of
mapmaking and oceanic exploration. For the first time, Europeans could
accurately visualize their continent in a way that enabled them to
improvise new navigational routes instead of simply going from point to
point.
That first portolan mapmaker also created an enormous
puzzle for historians to come, because he left behind few hints of his
method: no rough drafts, no sketches, no descriptions of his work. “Even
with all the information he had — every sailor’s notebook, every
description in every journal — I wouldn’t know how to make the map he
made,” says John Hessler, a specialist in modern cartography at the
Library of Congress.
But Hessler has approached the question using a tool that
is foreign to most historians: mathematics. By systematically analyzing
the discrepancies between the portolan charts and modern ones, Hessler
has begun to trace the mapmaker’s tracks within the maps themselves.
The
oldest portolan chart in the Library of Congress collection, drawn
between 1290 and 1350, depicts the Mediterranean Sea and the western
Black Sea.
Library of Congress Geography and Map Division
From Butterflies to Maps
Hessler’s path to mathematical cartography began with
butterflies. A frustrated chemical engineer and a passionate amateur
lepidopterist, he decided in 2000 to take a one-year contract job in the
French Alps, studying the evolutionary relationships among the many
butterfly species endemic to the region. He learned to use mapping
software to track different butterflies’ geographic locations and
deployed a technique called morphometrics to assess the relationships
between the precise placement of the spots on their wings.
In his analyses, Hessler began by conceptualizing each
wing as if it were drawn on a thin metal plate. In a computer
simulation, he twisted and bent the plate to move the spots on the wing
so they matched those on the wing of a butterfly in another region. He
then calculated how much energy it would take to distort the metal into
the new shape. The less energy required, the more similar the positions
of the spots — and, perhaps, the more closely related the butterflies.
When his adventure in the Alps ended, Hessler’s newfound
mapping expertise landed him a job as a curator at the Library of
Congress, where one of his duties was to maintain the vault that holds
the institution’s most rare and important maps.
There, for the first time, he saw a portolan chart, a
coffee table-size map of the Mediterranean Sea. The rendering, created
in 1559, was so accurate that it almost looked modern. The sole of
Italy’s boot had its improbable, graceful arch. He could make out each
cove around Tunis. Tarifa and Tangier reached toward one another, like
teeth, at the Strait of Gibraltar. It was a far cry from earlier
Ptolemaic maps (see “Mapping the World,” below), in which Italy’s boot
was painfully twisted and the teeth at the Strait of Gibraltar were
stretched into flat hammer faces.
The portolan chart’s inland portions were decidedly less
modern, but they showed no shortage of imagination, featuring pictures
of Italian dukes and, in Africa, unicorns and elephants illustrating
“travelers’ tales.” But Hessler paid little attention to the fanciful
characters. “The minute I saw one of the portolans, I was interested in
its structure,” Hessler says. “It’s so different from the mathematical
structure you see in [modern] maps.”
The basic mathematical problem every mapmaker confronts is
that the Earth is spherical and maps are flat. Imagine flattening a
portion of a paper globe: You’ll either have to tear the paper or
crinkle it up to squish it down. Many modern maps solve this problem by
using so-called Mercator projections, which turn the lines of latitude
parallel to the equator and the lines of longitude that converge at the
Earth’s poles into a tidy grid of perpendicular lines on a flat plane.
What Hessler saw on the portolan chart was a different
solution: a seemingly random pattern of lines showing the 16 directions
(north, northeast, east-northeast and so on), spreading out from various
locations. It seemed as though this helter-skelter mess of lines served
as a kind of skeleton for the map — its “mathematical structure” — just
like the tidy grid does for modern maps.
Fresh from his work using morphometric analyses to compare
Alpine butterfly species, Hessler realized that a similar approach
might allow him to compare a portolan chart with modern maps — and maybe
even shed some light on the mystery of how they were made. Perhaps, he
thought, he would find uniform distortions that would give a hint about
how the portolan mapmakers approached their art.
Mysterious Method
To begin, Hessler studied the charts’ history. Before the
first portolan charts were drawn in the 13th century, Mediterranean
sailors had no reliable drawings to guide them; instead, they relied on
compass measurements combined with experience and lore to navigate the
sea. Their sailing records consisted of nothing more than lists of ports
in the order that ships would encounter them, along with annotations
including estimated directions, sailing times between ports and perhaps
some sketches of geographic contours visible from afar, such as
headlands projecting into the sea.
Hessler pictured the first portolan mapmaker at work,
methodically working out some way to improve ships’ odds of making it
safely from port to port. He suspected the mapmaker began with one
sailor’s notes and sketches from a single voyage, starting at a single
port — say, Naples. Then, perhaps, he drew a line to the next port,
using the recorded sailing direction and time as his guide. He would
have traced the journey to the next port, and then the next, making a
circuit of the Mediterranean until his pen brought him back to Naples.
But the mapmaker would have run into a problem: The
vagaries of wind, sea and imperfect records inevitably threw off the
measurements, so that upon completing his vicarious journey, the
mapmaker wouldn’t land exactly on his starting spot. So he would have
had to nudge his ports around to spread out the error. If he did the
same thing again using a different set of sailing records, he would end
up with ports in slightly different locations, and he would need to
tweak the results again. No two of his charts would be exactly the same,
and none would be quite right. The mystery is how he managed to
reconcile all this contradictory, incomplete information into one
brilliantly precise chart of the Mediterranean that allowed mariners to
visualize, for the first time, the sea on which they’d spent their lives
sailing.
John Wolter/A Portolan Atlas of the Mediterranean Sea and Western European Waters/Library of Congress
What Are the Key Features of a Portolan Chart?
This chart comes from a portolan atlas of the
Mediterranean Sea and western European waters. Dating from about
1550, it is rare, since few such atlases from this period have survived.
It has been attributed to Joan Oliva, the most prolific member of a
large family of Catalan chart-makers. The chart exemplifies many key
characteristics of portolan charts.
Rhumb lines (1): These lines run out in
16 directions from points on the chart. It is unknown why these
particular points were chosen and why certain points are illustrated
with a compass rose whereas others are not.
Distortions (2): Portolan mapmakers
lavished care on the Mediterranean because of the volume of
maritime commerce there. Around Britain, the inaccuracies are greater.
Details of coastline (3): The coastline is drawn with incredible accuracy, including the precise shapes of coves that a sailing ship couldn’t enter.
Port names (4): The name of each port is
written alongside it, giving the coastline a soft appearance at a
glance. Every aspect of the chart is drawn by hand.
To
examine the underlying structure of this 1475 portolan chart, Hessler
took a grid on a modern map and transferred it point by point to the
chart. This method revealed a fairly consistent rotation of 8.5 degrees,
which corresponds to the declination (the difference between magnetic
and true north) at the time the chart was drawn.
John Hessler/Library of Congress Geography and Map Division
Clues in the Errors
Hessler began to look for clues within the portolan charts
themselves. Borrowing the morphometric techniques he used to track
movement of the Alpine butterflies’ spots, he transferred each point
from a modern Mercator map of the Mediterranean onto the equivalent
point on the oldest
portolan chart at the Library of Congress. According to carbon dating of its calfskin substrate, this document was created sometime between 1290 and 1350.
portolan chart at the Library of Congress. According to carbon dating of its calfskin substrate, this document was created sometime between 1290 and 1350.
The resulting grid on the portolan chart was slightly
distorted in various small ways — not surprising, given the imprecise
sailing data with which the mapmaker likely had to work. But it was also
fairly consistently rotated by 8.5 degrees counterclockwise. Why?
Hessler suspected the skew was an artifact of compasses,
which had arrived in Europe from China not long before the map was
created. He knew that compasses respond to the Earth’s magnetic field,
which is generated by molten iron moving in the Earth’s outer core. But
magnetic north doesn’t line up perfectly with true north, the point
where the Earth’s axis hits the surface (and above which the North Star
sits). The difference between magnetic and true north, called magnetic
declination, varies slightly with time and place, reflecting shifts in
the flow of the molten iron. Modern mapmakers correct for declination by
adding or subtracting the appropriate number of degrees for particular
locations.
Working from compass measurements but not correcting for
declination could cause just the kind of rotation Hessler’s analysis
revealed. So he went on the hunt for information about historic
declination and found a book that provided mathematical models
estimating how the declination has changed over time. He consulted the
estimates for around 1300, and bingo: 8.5 degrees. Now Hessler
had strong evidence that the mapmaker, relying on sailors’ records,
didn’t correct his measurements for declination. After all,
Mediterranean mariners had no need to worry about how their charts were
oriented with respect to the globe — they just needed a reliable guide
for the region.
Hessler’s detective work turned up one other clue to the
mapmaker’s method: Although the rotation was close to 8.5 degrees
throughout the chart, it varied a bit. Italy was rotated only 6 degrees,
while the Black Sea was rotated up to 8.8 degrees. That suggested the
mapmaker created the chart using different observations made at
different times. The result “highlights one of the most interesting
problems that historical cartographers faced,” says Hessler. How did the
mapmaker decide which records to draw on? “Faced with all this data
from different places and times, how did they know what was more
accurate?” he adds.
Hessler analyzed other portolan charts in the same way,
and each time, the correspondence with his book’s predictions was nearly
exact. Between 1300 and 1350, the declination in the Mediterranean fell
by 2 degrees — and in keeping with that change, portolan charts drawn
by the end of that period were about 2 degrees less rotated. By 1500,
declination was back at 8.5 degrees, and so were most of the charts
Hessler examined. Over the next 150 years, the declination shifted
again, to 11 degrees, and the rotation of the charts followed suit.
To track how portolan charts’ accuracy changed over time,
Hessler drew again on the methods he used to quantify butterflies’
evolutionary relationships. As with the butterflies’ wings, he imagined
each chart drawn on a metal plate and simulated bending it to move the
landmarks on the medieval chart to meet their locations on a modern map.
The less energy required to distort the metal into the new shape, the
more accurate the chart.
Curiously, he found, in the first several decades after
the first portolan chart was drawn, subsequent charts’ accuracy declined
a bit. Hessler speculates that the first portolan mapmaker’s technique
spread quickly, but those who adopted his methods initially lacked his
skill, so their efforts were less precise. As mapmakers’ skills steadily
improved over the next two and a half centuries, so did the accuracy of
their maps.
Across the Atlantic
As he pieced together answers to some of the questions
that had vexed historians, Hessler says, “So many things amazed me: how
much mapmakers of early portolan charts knew, how they updated their
data so quickly, how accurate their compasses were, how geographic
information flowed around the world in ways that we don’t understand.”
Portolan charts paved the way for the age of exploration.
Now, sailors could travel down the coast of Africa and around the cape.
Eventually, maps were made that extended across the Atlantic to the New
World. But paradoxically, the age of exploration that followed the
creation of the portolan charts eventually led to their downfall, as
increasingly sophisticated techniques of shipbuilding and mapmaking made
them obsolete.
The problem was the portolan mapmakers’ lack of a
systematic way of reducing the spherical Earth to a flat map. That was
of little consequence for short journeys but mattered much more when
sailing longer distances. In 1569, the Belgian geographer and
cartographer Gerardus Mercator created his method for presenting a
spherical world on a flat map, the one familiar to us today. This
mapmaking technique, though it stretched and compressed landmarks and
distances between them, had the great advantage that a straight compass
course was represented by a straight line on the map.
Mercator’s projections began to be used to sail the open
seas by the early 1800s, by which time portolan charts had pretty much
disappeared. But their importance is undeniable. “The development of
these maps revolutionized how people perceived space, much like Google
Earth has done in our lifetimes,” Hessler says. “Understanding how the
technology was developed gives us insight into how we got here, and
perhaps into where we’re going.”
This depiction of the world as Ptolemy knew it, published in a 1482 edition of Geographia, was
printed from carved wood blocks. Any maps Ptolemy himself created have
been lost, but later scholars created maps based on his information.
Hain Collection , Library of Congress Geography and Map Division
This
16th-century portolan chart of the Mediterranean is vastly more
accurate than any Ptolemaic map. Designed for marine navigation, the
chart includes labeled seaports, giving the coastline a fuzzy
appearance.
Library of Congress Geography and Map Division
This
1797 chart uses a Mercator projection. Devised by Gerardus Mercator in
1569, these projections, with their perpendicular lines of latitude and
longitude, dominated nautical cartography by the 1800s.
Library of Congress Geography and Map Division
Mapping the World
The second-century Greek mathematician, astronomer and geographer Claudius Ptolemy founded the Western science of cartography.
From his study in Alexandria, Ptolemy assigned coordinates
of latitude and longitude to 8,000 geographic locations, compiling the
information into his Geographia, an atlas of world geography that included colored maps depicting regions of the then-known world.
Although Ptolemy’s data were inaccurate, his work
(translated into Latin in the early 1400s) influenced cartographers and
explorers more than a millennium after Geographia’s publication.
[This article originally appeared in print as "The Mapmaker's Mystery."]
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