Maps and Territories


One of my favorite maps, available for purchase here

It’s odd how the mind works.  If you’d asked me last night if I’d ever heard the phrase “stackable probabilities,” I would have said that I had not. Yet this morning, I woke up from a dream in which I was looking at a photograph of the surface of the Moon while a voice in the background explained that “a map is not an image depicting a territory, it is a graphic representation of related sets of stackable probabilities.”

I woke up before the voice could explain what that meant. Since I have never studied statistics, and did not know until I googled it that there really is such a phrase as “stackable probabilities,” probably the only way a voice in a dream of mine could explain it would be if I were sleeping in a room where someone was giving such an explanation.  Making it even stranger that such a phrase would pop into my head, most of the results for “stackable probability” that came up in that Google search were from gaming forums, and I haven’t spent any time playing or discussing electronic games since about 1983.

Anyway, it is in fact plausible that someone might describe a map as graphic representation of related sets of stackable probabilities. As I understand it, a set of probabilities is stackable if it is made up of a series of variables, each of which is dependent on the item preceding it in the series but independent of the item following it.  So there can be river systems only where the parts of a landmass vary in elevation, but parts of a landmass can vary in elevation where there are no river systems.

It becomes plausible to think of maps as summaries of probability structures rather than as images of territory when we consider that maps of large areas of the Earth’s surface do not feature cloud formations, and that maps of coastlines do not show the tide either coming in or going out. It’s virtually certain that a satellite photo of a continent or an ocean would show at least a few clouds, and utterly certain that the seas continuously show tidal motion, but there is no relationship between the probability that any particular cloud formation or state of the tides will prevail at a given moment and the probability that a user will consult the map at that moment.

Standard features of large-scale maps of populated areas, features such as mountains, rivers, roads, cities, centers of extractive industry, coasts, political boundaries, etc, are likely to be there and to be of interest to a user of the map. Moreover, these standard features are also the features most plainly related to each other. Roads connect cities to each other and to centers of extractive industry, unless mountains, coastlines, or political boundaries block them; rivers flow from mountains to coasts and cities grow along them; etc.

In my dream, I was looking at a photograph of the surface of the Moon. There are no rivers, roads, cities, industries, coasts, or political boundaries there. So, what is the difference between a photograph of the Moon’s surface and a map of the Moon’s surface? Add labels naming the mountains, craters, maria, etc, add notations of the elevation of those features, and isn’t the result a map?

I’m inclined to think not. Several times Apollo astronauts lost their way on the Moon; the best-known such episode came during the Apollo 14 extra-vehicular activity, when Alan Shepard and Edgar Mitchell lost so much time trying to orient themselves that they did not manage to reach the rim of Cone Crater, a key mission objective. Many have accused  Admiral Shepard of showing a cavalier attitude to the geological aspects of the mission; most notable of these is perhaps David Reynolds, author of a well-regarded book called Apollo: The Epic Journey to the Moon, 1963-1972 (Zenith Press, 2013.) Be that as it may, Captain Mitchell is a famously conscientious man (as witness his willingness to sound rather odd at times,) and it is difficult to believe that he did not use every available resource to prepare himself for such an important assignment.

I suspect the problem was that the resources available to Captain Mitchell and his superior officer included too many photographs and too few real maps.  On a surface where the horizon is so much closer than it is on the Earth, people do not have conventional reference points and cannot rely on reflexive mental habits to determine their location. The essential visual aid for such travelers is therefore one which illustrates, not the surface features which their experience on Earth has not prepared them to interpret, but such statistical relationships among those surface features as are likely to shape their journey.

“Literal Meanings”

The other day, Slate magazine posted a map titled “Literal Meanings of Places in the US.”  It’s a fun graphic, I recommend it, but I will also mention a couple of caveats.  These caveats may be obvious in themselves, but perhaps I can express them in a way that will suggest interesting thoughts.

First, what is the “literal meaning” of a name?  When I think of that phrase, I ask two questions.  First, is the name likely to bring that meaning to the minds of most of the people who are likely to hear it?  And second, can the name be used independently to signify that meaning?  For example, the name “Newfoundland” likely brings to the minds of most English speakers, not only the place Newfoundland and the breed of dogs named after it, but also the idea that a land has been newly found.  With just a little typographical liberty, we can refer to places other than Newfoundland as new-found lands.  So I don’t object to saying that new-found land is the “literal meaning” of Newfoundland.

What we see on this map are not, in that sense, the “literal meanings” of North American place names.  They are etymological meanings, that is to say, meanings that have, at one time or another, been associated with words that have influenced the development of those names.  For example, “New York” is supposed to “literally mean” “New Yew-Tree Village.”  When the Latinism Eboracum was coined sometime before the year 95 of our era it probably represented an attempt to spell in Roman letters a Celtic word that meant “Place of the Yew Trees.”   And Eboracum, evolving in tandem with that Celtic word, changed its pronunciation over the centuries to become “York.”  But of course only scholars hear the word “York” and think “Place of the Yew Trees.” And by the time the word came to be pronounced “York” it was centuries past any connection with yew trees.  I suspect that no one has ever looked at a place of yew trees and called it a “York.”

I think it would be reasonable to imagine the history of a word as something like an archaeological site, in which collections of material from different periods of history can be found concentrated on on top of another.  So, two thousand years ago, Eboracum and its Celtic root may have meant “Place of the Yew Trees” to most of the people concerned with settlements in the far northeast of Roman Britannia.

At a a higher stratum, that is to say, a later period, very different meanings are associated with the word.  The acts of the British crown which created the Province of New York in 1664, 1665, and 1674 and thus introduced the name “New York” into the English language were executed by a king who was not only ignorant of the Celtic etymology of the name “York,” but who was not likely giving much thought to the city of that name.  The province was created under the patronage of the king’s brother, the Duke of York, and was named for him.  That nobleman later became King James II of England and VII of Scotland, the last of the Stuart dynasty.  James was York by title, but doesn’t seem to have been greatly involved with the city or its affairs, and he never visited the North American territory claimed in his name.  It is as if we found that someplace named New Newfoundland was named, not for Newfoundland, but for a particular dog of the Newfoundland breed.  At that point, the etymology of the name might have been glossed as something like “James’ new province,” or, considering James’ awkward position within the royal house in 1664, “We still care about you, James.”

If we dig further down to an earlier period, the root word might have meant something quite different.  Various Celtic languages include words similar to Eboracum that refer to various trees; perhaps the root of those words meant something other than “yew tree.”  It is possible that Phoenician merchants, whom we know to have been active in Cornwall and southern Ireland in Roman times, brought with them a word cognate with the Coptic ebu, “ivory,” and its Latin derivative ebor, eboris, and that this word was the base of those Celtic words.  This may not be a particularly likely etymology, but I have never been one to miss an opportunity to bring up the Phoenicians.

A second point enters in with glosses like “of the monks” for Des Moines, Iowa.  This appears to be a folk etymology that white settlers applied to mooyiinkweena, a name that the Peoria people used for certain neighbors of theirs.  The opinion the Peoria had of those neighbors can be surmised from the fact that the parts of the word mooyiinkweena appear to be mooy, meaning “dung,” and iinkwee, meaning “face.”  So, when they pointed at the site where Des Moines now stands and said mooyiinkweena, they were telling the whites that the people who lived there were shit-faces.  I should add that the erudite sources I link to above are not where I first learned the etymology of “Des Moines”; I first saw it last week on Cracked.

Originally, the folk etymology of Des Moines might have been a mistake.  But words mean what people use them to mean, not what they are supposed to mean.  If Des Moines residents and others who are concerned with the city have thought that the meaning “of the monks” is part of the name’s history, then it is part of that history.   And the fact that the name is now “Des Moines” rather than “Mooyiinkweena” is an example of the role that the folk etymology plays in that history.  Therefore, a map listing etymological meanings of North American place names would have to include both “of the monks” and “shit-faces” for Des Moines.   To return to the image of an etymology as an archaeological site stratified into layers, we might think of a three-dimensional map, on which both the geographic location of the places and the temporal development of the names’ meanings could be represented.

Even the two-dimensional map on Slate must be the result of a great deal of work; a three-dimensional map would require a great deal of drudgery, and even then it would be a severe oversimplification.  So I mention it only to illustrate the point, not to find fault with the map or to take back my recommendation that everyone look at it.

Wednesday links

Zach Weiner explains very succinctly why it’s so hard to be a pacifist, Eve Tushnet reads about single mothers, John Wilkins doesn’t believe politicians have mandates, some guy named “Zippy Catholic” decides that women’s suffrage and abortion rights are inseparable (and therefore women’s suffrage must go!,) Laura Flanders and Eve Ensler have never talked to each other about their vaginas and don’t plan to start,  this map does a terrific job of encapsulating the results of the 2012 US presidential election, xkcd is hilarious, and Jim Goad can think of ten good reasons not to assassinate Barack Obama.

Mercator Rotator

Usually when we think of the Mercator Projection, we think of this map with the geographic North Pole at the top, Antarctica at the bottom, and the relative size of the Northern Hemisphere severely exaggerated:

Months ago, this picture appeared on a site called Apathy Sketchpad:

The map is also the Mercator Projection.  Mercator’s contribution was not in putting north at the top, but in developing a particular mathematical formula for representing the planet’s roundish surface on a flat map.  As the author of Apathy Sketchpad puts it, “the Mercator projection doesn’t need to make Africa small and Greenland big. It can do anything you want it to.”  Producing a map with Africa at the top, he explains:

In principle a Mercator projection can be continued infinitely in the vertical direction, and in this case the ‘north’ pole is in Africa, so the map would be Africa all the way up. The level of detail would, source image notwithstanding, get bigger and bigger until eventually sub-atomic particles started to appear. Theoretically, you could exploit this to produce a map where Britain opened out as Africa has at the top, and extend the map up to include a road map of England, including  a large-scale street map of Manchester, eventually opening out to provide a floor-plan of one particular building, then room, and eventually the layout of one table. This, however, seems like it would be very difficult so I haven’t bothered.

In the comments on this post, I remarked that I’d long thought someone should create a flash app called “Mercator Rotator” which would enable a user to put “north” wherever s/he liked and see the resulting Mercator map of the earth.  I have no intention to produce such an application myself, but if you, the reader, have the requisite computer savvy and some time on your hands, I recommend that you do so and let us know about it in the comments.