Consideration of Maps – I

In this post, I would like to begin a set of postings about maps, mapping and the measurements required to construct maps.

While I’m sure that everyone knows what a map is, we should start at the beginning and deal with the fundamentals: the definition of “map” in the dictionary that came with my computer is: “representation of an area of land or sea showing physical features, cities, roads, etc.”  The OED has a set of definitions, the first and most applicable of them is “A representation of the earth’s surface or part of it, its physical and political features, etc., or of the heavens, delineated on a flat surface of paper or other material, each point in the drawing corresponding to a geographical or celestial position according to a definite scale or projection.” This is probably a pretty good place to start, though I expect to expand this definition over this and the subsequent posts about maps.  A map is generally designed to show certain important aspects based on the use to which the map will be put and the relationships among them.

Maps are designed for specific purposes: I have a property map which shows the boundaries of my property, and specifies exactly what those boundaries are.  It represents the important points for its purpose, and ignores the locations of the trees and bushes.  At one point, our next door neighbor believed that the fence between our houses was incorrectly placed.  She came over to our house and warned us that she had hired a surveyor and we might lose some of the space we thought was ours.  Ooops.  She was wrong, and we gained ten inches along one boundary, based on the surveyor’s use of the property map definitions.

The oldest “map” I’ve been able to find is the one mentioned in an earlier post, found in Hayonim Cave in Israel and associated with the Natufian culture.  The Natufian culture has been dated to 13,000/12,800 to 10,500/300 BP (before the present), so it appeared right at the beginning of when the agricultural revolution may have started – immediately after the end of the last ice age.  I call it a map, but there is some uncertainty to what the limestone slab with the incised lines actually means.  It could be “just decoration” or something else.

There arises the question of whether this design represents an actual phenomenon, serving as a ‘map’ of particular ‘fields’ located in the vicinity of the site, or if it symbolizes some abstract concept of ‘fields’? Unfortunately, 10,000 years of unremitting cultivation, erosion and alluviation made it impossible to trace even the outlines of Natufian fields through aerial photography.1

From the photo of the slab, it does look like it could represent allotments of cultivated land.  The authors also included a schematic drawing of the incising, so that the pattern can be seen more clearly: I would include both, but I don’t have permission to do so.  However, you can review the article at:

http://antiquity.ac.uk/ant/073/Ant0730402.htm

If it is a map, and was used to define property rights, it would mean that among the first uses of measurement and representation of measurement is to define property.  While that is not inconceivable, I think it is unlikely that the first use of mapping was to record property rights.  It just may be that the first map that was preserved in stone was used as such: my guess, and that’s all that it is, is that the earliest maps were probably transitory.

I imagine early map creation this way: two people are discussing going to some place further than can be seen from where they stand.  The one who has been there grabs a stick, and starts scratching on the ground, pointing at a remote rock, saying the equivalent of “if this is that rock, then when you are standing next to it, you will see a boulder balanced on cliff, like here (scratching on the ground).  From the ground below the cliff, bear right, go over the ridge, about here (scratching on the ground again), and then it is a simple walk the rest of the way once you see the mouth of the cave, about here (again scratching).”  The first map?  This would be as close as humans could come to doing the waggle dance of the bees, and would be rubbed out soon thereafter if not by those who were talking, by the wind or water erosion.

Now, our expectation of maps is that they are not only “true” with the relations of roads, highways, byways, trails and paths displayed clearly and accurately, but that they contain the proper landmarks for judging progress.  If someone hand-draws a map with approximations, perhaps just with the landmarks and approximate directions between them, they will at some point either write or say, “by the way, this is not to scale…”

The expectation of maps being either accurate or carefully caveated has caught me a few times, the most notable was when I was visiting in Japan.  I am sure that I am not the only non-Japanese person who has run into problems in Japan, where there are no addresses on streets, but the particular problem I ran into was a printed map with no caveats (in English, anyway), that seemed to have fairly clear directions.  So when my party and I got off the train, we proceeded to follow the map of Nagano to go to Zenkoji Temple, expecting to arrive there shortly, and ending up at a tiny shrine, which we knew couldn’t be the right place.  After losing my temper (I was very bad that day), we finally saw a sign that indicated where to go, followed and an hour later finally arrived at Zenkoji Temple.  To return to the train station took only 5 minutes: we had followed the wrong signs.  The map had been so schematic, and was oriented so differently than what I have come to expect, that getting lost required no special skills, just expectations.

Maps have been made for many purposes other than delineation of property rights and directions, and the definition of maps extends beyond representations of the geographical world.  They are used as well as representations of other kinds of information: indeed, the Human Genome Project had as its goal, to completely “map” the human genome.

What are the characteristics of maps?  I believe that the elements that I have attributed to measurement include many of the characteristics of maps – maps have a social component in that they are used to communicate information, and in fact, they are a way to record measurement, requiring the concepts, standards and scales as part of them.

Chapter One, “The Map Idea”, in a wonderful book by John Noble Wilford called The Mapmakers, is a great introduction to maps.  He mentions some of the history of maps, has comments and anecdotes about them from historical figures, and then provides thumbnail sketches of some more contemporary books about maps that attempt to define what mapping is.  Rather than copy the whole first chapter here, which I thought about, I will select a few quotes, and recommend the book if you are interested in more information about maps.

One book that he provides a sketch of is by Arthur H. Robinson and Barbara Bartz Petchenik called The Nature of Maps, in which they describe some of the best thinking about what the nature of maps is.  After discussing a number of concepts, Wilford quotes what appears to have been their conclusion:

The reason for the common use of mapping as a metaphor for knowing or communicating … has finally become clear: the concept of spatial relatedness, which is of concern in mapping and which indeed is the reason for the very existence of cartography, is a quality without which it is difficult or impossible for the human mind to apprehend anything.2

The basic significance of maps, then, seems to lie particularly in the fact that maps are surrogates of space.3

So, ultimately a map is a tool that represents the results of measuring and presents the measured objects, concepts, etc. in a way that uses spacial relationships for representation.  Magritte’s famous painting, La trahison des images, better known for its inscription, “ceci n’est pas une pipe”, is a simple way to understand the difference between the map and the mapped.  There are objects that exist in the three spacial dimensions of our world: if they are captured by artists in two dimensions on canvas or paper, we see representations of those objects.  At the point where mapping and art come closest, there are pictures of towns and cities from above, done at a time when even climbing to the highest steeple would not give the aerial perspective of the picture, so imagination has been used, and perhaps even some measurement to make sure that the buildings and streets are close to a scaled down and proportionate representation.  But they are still representations of three spacial dimensions in two dimensions.

I emphasize this because maps are like photographs: presenting a static representation at an instant of time.  To map time would require a sequence of maps that are different, and represent a similar interval, say a day or a year apart.  In theory they could be viewed like pages in a flip book, so that the changes appear to be animated, and if set up with the right software on a computer, could be run as a morphing picture, changing from instant to instant.

Although I have seen diagrams that are supposed to represent space-time in two dimensions, they are rarely called maps.  Perhaps maps are a specific type or sub-set of diagrams.

The history of maps and mapmaking is covered in the Wilford book and in others, including Lloyd A. Brown’s The Story of Maps.  Brown started his story with Strabo in 25 BC in Alexandria, Egypt, which seems a little late to me, but the rationale he presented is: “…his Geography [Strabo’s] is the principal key to the history of ancient cartography, simply because the manuscript survived and was published, while the writings and maps of his contemporaries as well as those of the “ancients” before him were lost or destroyed.”4 Brown’s book was originally published in 1949, and the edition I have is from the 1979 Dover Book reproduction.  His book was published before the beginning of the publication of the series of books on China by Joseph Needham, in which the Chinese tradition in maps is shown to considerably precede 25 BC, but does not go back to the Natufian period.  Brown does expand beyond Strabo, discussing cuneiform tablets from the reign of Sargon of Akkad, around 2300 BC, with notes of a real estate (called “cadastral”) survey for tax purposes, and an Egyptian papyrus with a map that “…depicts the triumphal return of Seti I (1366-1333 B.C.) from Syria”.5 He even adds to his list by stating that “The Museum of Naples has a globe two meters in diameter which is doubtless a product of the fourth century B.C. …It may have been built by or for Eudoxus (d. 386 B.C.), the celebrated astronomer and philosopher.”6

Wilford has written about the Chinese tradition, with mention of a town-building prospectus from 1020 BC that included a map which has been lost, and discusses the oldest existing Chinese map, an engraved bronze plate from the fourth century BC.  Later Chinese maps he describes are silk from the second century BC.  He also briefly discusses some Mesopotamian maps which are cadastral maps which he states appear to be quite common both in Mesopotamia and Egypt.  While I was uncomfortable with the Natufian map being one outlining property rights, I am certain that by the second millennium BC, the rulers of stratified societies would have them, if for no other reason than for taxing the owners.  Alas, taxing and taxes too has a long, if not glorious, history, a history of an authority of some sort measuring the obligations of those under its authority to it.  But that is another story for another post.

Representing spacial relationships in maps is not new, since doing so is at least 3000 years old and probably older, though the techniques have undergone considerable change and growth since the earliest maps.7 Some milestones in the making of maps are quite impressive, and I would like to discuss a few that I am especially impressed with.  The first dates from the Greek period, though could have been preceded elsewhere.  Evidently by the time of Aristotle (384-322 BC), there were Greeks, including Aristotle, who believed that the shape of the world was spherical.  Pythagoras around 530 BC, who predates both Eudoxus (the globe owner/builder) and Aristotle, believed it to be spherical, in part because that was the most perfect shape.  Aristotle agreed, but used some independent observations to confirm his belief.  He noted that traveling both south and north caused the stars at the horizon to disappear and new ones to appear at the opposite horizon; he noted that the mast of a ship sailing over the horizon appears to sink rather than become a small dot; and he noticed the shape of the shadow that the earth cast upon the moon during a lunar eclipse.  But the feat that most impressed me is the measurement of the size of this spherical world by Eratosthenes, who used geometry to develop an estimate.

By the time of Eratosthenes, who lived between 276 BC and 196 BC, Euclid’s Elements was in existence, which means that by then, approximately 300 BC, the Greek mathematicians had an extensive grasp of the principals of geometry.  The work was “…built on earlier work by Hippocrates of Chios (c. 470-400 BC), Eudoxus of Cnidos (c. 390 – c. 340 BC) and others.”8 The use of triangles and angles for surveying and for measuring distance was known.

Using the understanding of triangles and angles for measuring land distances, Eratosthenes figured out a method to measure the circumference of the earth.  He assumed that because of the distance to the sun, the rays of the sun were all parallel.  In Syene, a town near what we call the Tropic of Cancer, the sun cast no shadows, and was reflected in the bottom a deep vertical well in Syene, at noon on the day of the summer solstice.  In Alexandria, a known distance from Syene, the sun at noon on the summer solstice did cast a shadow, and he realized by measuring the length of the shadow of an vertical object with a known height, he had sufficient information to calculate the circumference of the earth: the three sides of a triangle, with each of the triangle’s angles.  In both Wilford’s and Brown’s versions, Eratosthenes figured out the angle of the triangle that pointed at the sun was 7 degrees 12 minutes, or approximately 1/50 of a circle.  So he multiplied 50 times the distance from Alexandria to Syene which he figured was approximately 5000 stadia.

In Brown’s version of the story, Eratosthenes thought there was some error in one or another of the measurements, so adjusted his estimate up from 250,000 stadia to 252,000 stadia, approximately 25,000 to 25,200 miles, which compares pretty well to a more modern measure of 24,899 miles.  Wilford tells the same story, but comes up with a figure of 46,000 kilometers, too large by about 6000 km from the current measurement.  Both Brown and Wilford cover the kinds of error that figured into Eratosthenes’ estimate.

The major “dispute” is that since Eratosthenes used as his measure “stadia”, what does 1 stade equal.  Historically there were different values used, but in the book from the British Museum,9 it is conjectured that he used a value of 1 stade = 157.5 meters, which would have put his estimate at 39,690 km, just under the modern measure of 40,075 km.  However, the point that I appreciated is that an estimate this accurate was generated sometime within Eratosthenes’ lifetime, so some time around 200 BC or before.

There is  another aspect pointed out by Brown.  A Greek mathematician named Poseidonius did the same type of measurement around  150 or so years later, his measurement was reported by Strabo as being the equivalent of 18,000 miles.  This dimension was picked up by Ptolemy, despite being about 75% of Eratothenes estimate, and was used for roughly the next 1500 years.

So, shape had been determined and size had been measured.  The tools, both the hardware used to perform the measurements and the concepts, triangles and angle measurements, to generate a usable result, were in existence more than 2200 years ago, and were being used creatively.

Although Ptolemy used the wrong dimension for the size of the earth, and also established the thinking about the heavens incorrectly, he is responsible for the other cartographic feat that impresses me.  That feat shows up in Ptolemy’s Geography, although he was probably a compiler and refiner rather than originator, and that is the current grid system of longitude and latitude.  This is important enough to merit its own post, so that’s what we will look at next.


1 Bar-Yosef, O, & Belfer-Cohen, A. 1999. “Encoding Information: Unique Natufian objects from Hayonim Cave, western Galilee, Israel”.  Antiquity 73, 409.

2 Robinson, Arthur H., and Petchenik, Barbara Bartz, The Nature of Maps: Essays Toward Understanding Maps and Mapping. Chicago, 1976, quoted in Wilford, John Noble, The Mapmakers, Revised Edition, Vintage Books, New York, N.Y. 1981, 2000. p. 14.

3Ibid. p. 13.

4 Brown, Lloyd A., The Story of Maps, Dover Publications, New York, NY, 1979, by permission of Little, Brown and Company, Boston, MA, 1949, 1977. p. 17.

5 Ibid. p. 33.

6 Ibid. p. 34.

7 There is a fascinating map that has been found inscribed on a rock in the Bedolina petroglyphs near Valcamonica, Italy.  A search of Google using Bedolina map returns a number of sites about the map, some with photos and diagrams.  I found a scholarly article that I downloaded at:

archiv.ub.uni-heidelberg.de/…/volltexte/…/11_04_alexander_bedolina.pdf

which discusses the map, tentatively dated to “the Iron Age”, the first millennium BC.  The map includes dwellings, fields and connecting paths.

8 Dilke, O.A.W., Mathematics and Measurement, Volume 2 in the Reading the Past series, 1987 by The Trustees of the British Museum, British Museum Publications Ltd, London. P 19.

9 Ibid. pp. 35-36.

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One Response to Consideration of Maps – I

  1. Steaven Swift says:

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    Steaven Swift
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