Maps and Territories

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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.

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