Hannah Fry writes:

In “A History of Data Visualization and Graphic Communication” (Harvard), Michael Friendly and Howard Wainer, a psychologist and a statistician, argue that visual thinking, by revealing what would otherwise remain invisible, has had a profound effect on the way we approach problems. The book begins with what might be the first statistical graph in history, devised by the Dutch cartographer Michael Florent van Langren in the sixteen-twenties. This was well into the Age of Discovery, and Europeans were concerned with the measurement of time, distance, and location. Such measurements were particularly important at sea, where accurate navigation presented a considerable challenge. Mariners had to rely on error-prone charts and faulty compasses; they made celestial observations while standing on the decks of rocking boats, and—if all else failed—threw rope overboard in an attempt to work out how far from the seabed they were. If establishing a north-south position was notoriously difficult, the spin of the Earth made it nearly impossible to accurately calculate a ship’s east-west position.

In 1628, van Langren wrote a letter to the Spanish court, in an effort to demonstrate the importance of improving the way longitude was calculated (and of giving him the funding to do so). To make his case, he drew a simple one-dimensional graph. On the left, he drew a tick mark, representing the ancient city of Toledo, in Spain. From this point, he drew a single horizontal line on the page, marking across its length twelve historical calculations of the longitudinal distance from Toledo to Rome. The estimates were wildly different, scattered all across the line. There was a cluster of estimates at around twenty degrees, including those made by the great astronomer Tycho Brahe and the pioneering cartographer Gerardus Mercator; others, including the celebrated mathematician Ptolemy, put the distance between the two cities closer to thirty degrees. All the estimates were too large—we now know that the correct distance is sixteen and a half degrees. But the graph was meant to show just how divergent the estimates were. Depending on which one was used, a traveller from Toledo could end up anywhere between sixty miles outside Rome and more than six hundred miles away, on the plains of eastern Bulgaria.

Van Langren could have put these values in a table, as would have been typical for the time, but, as Friendly and Wainer observe, “only a graph speaks directly to the eyes.” Once the numbers were visualized, the enormous differences among them—and the stakes dependent on those differences—became impossible to ignore. Van Langren wrote, “If the Longitude between Toledo and Rome is not known with certainty, consider, Your Highness, what it will be for the Western and Oriental Indies, that in comparison the former distance is almost nothing.”

Van Langren’s image marked an extraordinary conceptual leap. He was a skilled cartographer from a long line of cartographers, so he would have been familiar with depicting distances on a page. But, as [Edward] Tufte puts it, in his classic study “Visual Explanations” (1997), “Maps resemble miniature pictorial representations of the physical world.” Here was something entirely new: encoding the estimate of a distance by its position along a line. Scientists were well versed in handling a range of values for a single property, but until then science had only ever been concerned with how to get rid of error—how to take a collection of wrong answers and reduce its dimension to give a single, best answer. Van Langren was the first person to realize that a story lay in that dimension, one that could be physically seen on a page by abstracting it along a thin inked line. [Continue reading…]