How little information do you need to be able to draw a map? This zen-like question provided the basis for a short article in the May 21st, 1971 issue of Nature, intriguingly entitled Construction of Maps from “Odd Bits of Information”.
The article, according to its author David G. Kendall of Cambridge University’s Statistical Laboratory, starts from a “rather general principle in historical geography”, i.e. that maps can indeed be produced from apparently inadequate data, and goes on to describe a research programme based on that principle, carried out by Kendall’s lab.
The research concentrated on setting up a suitable (dis)simularity matrix believed to “lie naturally” in a Euclidian space of k dimensions, making use of a computer programme called MD-SCAL. The article mentions two experiments, the first one involving the mapping of eight parishes of the district of Otmoor in Oxfordshire. Amazingly, a fairly accurate map for the eight parishes was extrapolated solely from data on the intermarriage rates between them for the period 1600-1850.
The second experiment involved a map of 88 French departments (excluding the Corsican and Parisian ones), with the only information available being “whether or not one of the 3,828 pairs of departments shares a common boundary.” The map thus computer-produced is one “in which each department is represented by a point, but this system of linked points is converted to a honeycomb of cells by exploiting a natural duality.”
Mr Kendall finally mentions a future experiment with MD-SCAL: “The next step [...] will be to attempt to reconstruct a fifteenth century manor from the abuttals in a contemporary cartulary.”
These maps show France as it really is, and France reconstructed from abuttal data. Please note that the departments are numbered not in the usual alphabetical order, but by “an alternative which approximately orders the departments first by longitude and then by latitude.”
Many thanks to Randall B. Irmis, the paleontologist who sent in these maps, and whose attention was originally drawn to the article following this one, on the dinosaur species called Hypsilophodon.
Wow, it’s impressive how accurate the abuttal data map is, but I wonder, what would hve happened if they included the parisian disctrict? Not much? Or it would have ruined completely the map?
Comment by POL — October 26, 2009 @ 2:44 pm
And they came out mainly hexagonal too…
Comment by disgruntled — October 26, 2009 @ 3:12 pm
[...] Shared Voronoi Diagrams – France, Reconstructed from Apparently Inadequate Data. [...]
Pingback by Flow » Blog Archive » Daily Digest for October 26th - The zeitgeist daily — October 26, 2009 @ 3:22 pm
That’s astonishing. I would love to see more examples; how would this work on a state-by-state map of the United States, or a county-by-county map of any state?
Comment by Mark — October 26, 2009 @ 4:09 pm
I fiirst saw this map when it was reproduced in Trends in Biochemical Sciences around 20 years ago. I was very impressed, but I felt that its use to justify a claim that you can deduce how things are arranged by looking at what they touch was exaggerated, because the départements of France have a number of features that are quite unusual.
First of all, they are all (with the exceptions mentioned) more or less the same size, they don’t have seriously weird shapes, they have very few enclaves (and those they do have, as with the Vaucluse, are not taken into account). They have these characteristics because they were artificially created after the Revolution and were deliberately NOT based on historical boundaries. Finally, metropolitan France is approximately hexagonal in shape (and is about the only country that is), enough to be referred to as l’Hexagone by its inhabitants, and a hexagon is what you’ll get if you join up a lot of elements each of which has about six borders apart from those around the edge.
I’m pretty these were the reasons why France was chosen for the illustration rather than a geographical entiity with boundaries that result from history, wars, marriages, etc. You would get a much worse result with other regions. It is easy to do by hand, for example, with the countries of the Americas, ignoring islands, the Canal Zone and Alaska. If you do (as I have done) you’ll get a result that looks nothing like the reality. About the only recognizable component will be Brazil, which needs to be made big in order to accommodate so many frontiers.
The other point is that the French map includes correct features that cannot be deduced from the data: it is correctly oriented, for example, and of the two indistinguishable mirror images the correct one is illustrated.
Comment by athel — October 26, 2009 @ 4:43 pm
I am more curious about the methodology for creating a map based on intermarriage rates.
Comment by clamshell — October 26, 2009 @ 6:23 pm
I don’t get the reconstructed France map. For instance, look at 78, 79 and 88. Why is that a peninsula rather than a topologically-identical bay, with 78 and 88 poking out and around 79? More generally, if you perturbed the side lengths of any of the “departments” you could get an almost arbitrarily different map.
Comment by DU — October 26, 2009 @ 6:28 pm
Interesting to see how in the derived map, 46 and 56 make up a huge portion of the western border of Switzerland with France, but in reality they account for a very small area of it. Yet the shape remains the same …
Comment by David Kendall — October 26, 2009 @ 6:49 pm
Oh, and for some reason *this* fact didn’t even jump out at me, but I feel I *must* respond: I am *not* the David G. Kendall of the article! (Probably didn’t jump out because my middle initial isn’t G.)
Comment by David Kendall — October 26, 2009 @ 6:50 pm
@ David “Not G.” Kendall:
That is rather weirdly nice!
Comment by strangemaps — October 26, 2009 @ 10:01 pm
Sympa de voir que l’Héxagone restera toujours ainsi formé… :-)
Comment by friscolex — October 26, 2009 @ 11:33 pm
[...] 419 – France, Reconstructed from Apparently Inadequate Data (" “whether or not one of the 3… "How little information do you need to be able to draw a map? This zen-like question provided the basis for a short article in the May 21st, 1971 issue of Nature, intriguingly entitled Construction of Maps from “Odd Bits of Information”." [...]
Pingback by links for 2009-10-26 « Fantasising Zombies — October 27, 2009 @ 1:07 am
Far out.
Comment by michael5000 — October 27, 2009 @ 5:49 am
I wonder if the method can be extended to include one additional piece of information–land area (acknowledging athel’s concern). If it could, I think a reconstructed “map” of the U.S. by state would be very interesting. Or would it just be trivial at that point?
Comment by ebow — October 27, 2009 @ 12:40 pm
@ebow: I think it still wouldn’t be terribly accurate. The USA has so many internal borders defined by geography (mountains, rivers, etc) that putting together a map without that info would result in random blobs. Off the top of my head, at the very least Michigan, Maryland and West Virginia would be total messes.
You might be able to sort-of generally be able to figure out what you’re looking at, but only if you have a pretty good knowledge of the layout of the country already – which really defeats the need for a map in the first place.
Comment by Pete — October 27, 2009 @ 1:28 pm
@14/15: It’s hard to say without seeing someone actually do it, but I’m guessing a map of the states formed this way would shrink the western half of the country relative to the eastern half. I also suspect that Missouri and Tennessee could get somewhat distorted by the fact that they touch eight other states.
Comment by Daniel — October 28, 2009 @ 3:04 am
Incidentally, although not directly related to maps, the problem of reconstructing things from grossly inadequate data has been a serious topic of research. If anyone’s interested I recommend Marcello Barbieri’s book “The Organic Codes”, which contains some impressive examples, where, for example, he shows that you can recreate an image remarkably well on the basis of 10% of the information that is theoretically necessary.
Comment by Athel Cornish-Bowden — October 28, 2009 @ 7:44 am
Multidimensional Scaling, which this map uses, is now a fairly standard multivariate statistical technique. I have used it to build a ‘map’ of musical taste on last.fm. You can see it at my website.
Comment by Nik Shah — October 28, 2009 @ 11:43 am
This reminds me of Languagehat’s post of Sept. 13, 2003, called RDIAENG. If all words in a written communication have their letters scrambled, except the initial and final, the message still gets through to the reader.
It seems that the various forms of communication can be stripped of redundancy and still communicate.
Comment by iakon — October 28, 2009 @ 5:28 pm
Why use a wrong numerotation for the départements ? There does exist a standard numerotation for them (by alphabetical order, accounting for historical modificiations, for exemple Paris has kept the number 75 from the old Seine département), this would have made reading the map easier.
(Remembering the départements by number is a fun occupation for children here).
Comment by Jérôme ^ — October 29, 2009 @ 1:06 pm
“The other point is that the French map includes correct features that cannot be deduced from the data: it is correctly oriented, for example, and of the two indistinguishable mirror images the correct one is illustrated.” ==> I totally agree with you.
Comment by Pogo — October 30, 2009 @ 3:51 am
Weird and puzzling… are there mathematical theories about strange maps that appear in coffee grounds ?
Comment by lp — October 30, 2009 @ 6:23 pm
Fascinating post!
One reason why this ‘works’ for France is that the country has been in slow formation as a cultural and political entity over a period of 1000 years. It might not for the USA – so many boundaries are arbitrary work of Congress and surveyors.
The point about marriage and the Oxford map implies so much about the relationship of human culture to space, while the creation of the French national map is suggestive of ‘laws’ of ‘organic’ geographic development.
The work of the literary critic Moretti on the geography of the novel is a far flung, but related topic.
Comment by lichanos — October 31, 2009 @ 2:10 pm
lichanos: As post #5 by athel already pointed out, the French departements were artificially created, in order to obscure historical borders. Many U.S. states are more the result of historical development than French departements.
Comment by Varana — November 12, 2009 @ 12:03 am
@Varana #24:
Hmmm…good point. Of course, the boundaries weren’t drawn with a compass or straightedge, as in the USA. Still, Athel’s points are all really good.
Which leaves me wondering, why is this map so intriguing? Roughly the same size and no weird shapes – that’s the key. Perfect for generating Voronoi/Thiessen polygons, which is probably close to what they did here…
I’ve tried the same to generate a property map when I have only centroids of lots but no boundaries. Of course, the results aren’t very believable, but as far as apportionment of area goes, they’re not too bad.
Comment by lichanos — November 12, 2009 @ 2:55 am
Varana:
I forgot to ask what you meant
Many U.S. states are more the result of historical development than French departements.
The vast majority of the states were drawn up from territories, bought or conquered, and carved up for land grants. All surveyor’s work. Even in the older eastern states.
Comment by lichanos — November 12, 2009 @ 2:57 am
Yep, but there are certain historical influences. When they carved out the Midwestern states, no one would have created mini-territories like Rhode Island. The Florida panhandle wouldn’t exist if not for historical reasons. I meant that on this level – small old colonies in the East, large and square states in the Midwest and West, the enormous size of Texas, etc. These may all be the result of surveyors, but from different times under varying circumstances. :)
Comment by Varana — November 19, 2009 @ 9:38 pm
As Nik Shah mentioned, the technique is “multidimensional scaling”, which generates a “map” of points where the distance between each point tries to represent their abstract “distance” based on some relationship. The late great geographer Peter Gould liked to cite one example where the points were characters in Shakespeare’s “Romeo and Juliet”, and the “distance” was the number of lines spoken between the characters. The “map” which resulted showed a “Montague space” and a “Capulet space”, with the Nurse in the middle, acting as a sort of “bridge”.
Comment by Jkellymap — November 21, 2009 @ 2:13 pm