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.
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.
