Mapmaking is a tricky business. There are many issues that must be worked out. In addition, for a cartographer of times past, there was the question of figuring out what the world actually looks like.
Perhaps the most basic question for a cartographer to answer is what shape the map should be. Over the centuries, many models have waxed and waned in popularity. Today, the most popular map is a rectangular one, using the Mercator projection, such as this one:
The motivation for this map goes something like this: for some reason, we want to put the map on a rectangular piece of paper. Now, since the Earth is spherical (more or less), distances can’t be preserved. At least, east-west distances won’t be preserved; we stretch it out in this direction. But, perhaps we’d like to preserve the shapes of land masses. In order to do that, we have to stretch the map in the north-south direction. So, distances aren’t preserved, by shapes are. Also, the Mercator projection is useful for sailors, since lines on it have constant bearing.
This style of map wasn’t always the most popular. Of course, before Mercator (in the 16th century), this style was unknown. But even after he published his map, it took centuries before the Mercator projection because the standard way of making maps. The previous standard was the dual hemisphere map, such as this one by John Senex in the 18th century:
As a mathematician, I find this style of map very appealing: one of our favorite models of a sphere consists of two disks (hemispheres) glued along their boundaries. Generally, we glue them along the equator rather than along a meridian, but the idea is the same. In the case of mapping the earth, this model is particularly compelling since North and South America fit so well in one hemisphere, while Europe, Asia, Africa, and possibly Australia (to the extent it was understood by European mapmakers) fit in the other.
Other considerations abound. Until recently, maps were considered to be works of art, just as much as they were supposed to be informative. So, mapmakers would draw illustrations on the maps, both around the edges (especially if the map is to be printed on rectangular paper but is not rectangular in shape) and in the map itself. Here’s a rather ornate map by Martin Waldseemüller, from 1507:
Unfortunately, the image above is too small to see many details. There are many images on the map of the world: an elephant in southern Africa, for instance, and a ship in the southern Atlantic Ocean. Like many other maps of the time, the world is flanked by heads blowing wind onto the world. At the top, we see a portrait of Amerigo Vespucci, after whom two continents are named, as well as one of Ptolemy. Images of important cartographers could frequently be found on the periphery of maps. A description of the panels on this map can be found here.
Of course, the shapes of the continents were not always well-understood. Medieval maps did not include the Americas, as they had not been discovered by European explorers yet. And, while various lands were being actively explored, maps of these places varied radically. Since the research that had been done was far from definitive, cartographers used the scholarship available to them and used their own speculation to fill in the gaps.
The first continent whose geography was well-understood was Africa. All other continents proved problematical for European explorers. The eastern portions of Asia were too far away for them to reach for a while; not until 1542 did Fernão Mendes Pinto reach Japan. Northern Europe posed still greater difficulties. Explorers were unable to determine the northern boundary of Scandinavia and Russia for many centuries. And, while not the first to reach Australia by any means, James Cook as late as 1770 was the first to make its existence and geography well-understood in Europe. It starts to appear on maps in the late 17th century, albeit with much blurriness.
As for the Americas, South America was much easier to work out than North America. In fact, a long-standing open question was over the existence of a Northwest Passage through Caanda. That question was finally resolved in the affirmative only in 1851, and only due to a very curious instance of someone Being wrong. (A portion of the story is told beautifully in that marvelous book.) So, for a long time, the northern and western boundaries of North America were highly speculative, with each cartographer having a different conjectural take on the matter.
Curiously, while Antarctica was not discovered formally until around 1820 (and even then, I don’t think it was really demonstrated to be a continent), its existence had long been suspected. The reasoning is that more continents seemed to exist in the northern hemisphere than in the southern one, so there ought to be an extra southern continent to counterbalance the north. Questionable logic indeed, but it did turn out to be right!
In Peter Whitfield’s new book The image of the world: 20 centuries of world maps, one can find descriptions of dozens of maps spanning the past two millennia. It’s a gorgeous book, full of spectacular illustrations with a short (roughly one page) description of each map. Evidently, this book is intended to be a coffee-table book rather than one to be read cover-to-cover (although I did the latter). It’s a surprisingly scholarly text, full of fun historical tidbits. The geography lover I was once very actively, and still am somewhat more passively, was able to find a lot of pleasure in this book. And even if one doesn’t want to read the text, it’s still worth checking out this book for the pictures.