Transcript Diapositiva 1

Luis A. Robles Macías
[email protected]
24th International Conference on the History of Cartography
Moscow, July 2011
This paper presents the historical evolution of a singular cartographic parameter:
the “Longitude of the Mediterranean” in degrees.
LongMed
Image by Mapsof.net , licensed under CC-BY-SA
I will focus on the difference of longitude in degrees, abbreviated LongMed,
as opposed to the length of the Mediterranean Sea expressed in units of
distance (miles, km…)
Why look at this “LongMed” parameter?
Because:

It was displayed with large errors in maps up to 1700 and even later

In such maps the Mediterranean was often less accurate than far-away
regions only recently discovered by Europeans

Many of those maps were made by cartographers who lived and worked on
the very shores of the Mediterranean

On the other hand, cartographic works with highly accurate values of
LongMed have existed since the High Middle Ages
I will limit myself to plotting the evolution of the error of the LongMed parameter
along time.
I will describe general trends and highlight key cartographic works but will
otherwise refrain from extracting conclusions from the results.
This is a work in progress, your input is most welcome.
Few studies have specifically analyzed the evolution of the error of LongMed
along the history of cartography.
A simplistic but rather frequent opinion states that:
1.
Ptolemy made a big error in estimating LongMed due to an
underestimation of the radius of the Earth.
2. This error persisted until the late 17th century.
3.
It was then corrected thanks to astronomic observations.
However medieval tables of coordinates with highly accurate longitudes have been
known since the 19th century.
In particular Mercè Comes pointed out that the LongMed is much more accurate in
medieval Arabic tables than in Ptolemy’s Geographia but also than in later
European cartographic works like Kepler’s Rudolfine Tables.
Mercè COMES, “Islamic Geographical Coordinates: al-Andalus’ contribution to the correct measurement of the size of the
Mediterranean”, in Science in Islamic Civilization. Studies and Sources on the History of Science (Istanbul: Research
Centre for Islamic History, Art and Culture, 2000), 123-138.
Fuat Sezgin did a quite extensive survey of the historical evolution of LongMed:
 defined LongMed as the difference of longitude between Tangiers and
Iskenderun
 focused mainly on printed world maps
 attempted to prove that the improvement of LongMed on European maps
between 1500 and 1700 was mainly due to earlier Arab-Islamic works
Fuat SEZGIN, Mathematical Geography and Cartography in Islam and their Continuation in the Occident, 3 vols.,
Geschichte des Arabischen Schrifttums (Frankfurt am Main: Institute for the History of Arabic-Islamic Science, 2005)
In my opinion, there remains room for improvement in Sezgin’s study:
 instead of using two arbitrary locations to define LongMed it is more robust
to calculate it as an average of several differences of longitude
 several significant cartographic works were omitted by Sezgin, in particular
manuscript maps with accurate LongMed well before 1700
 in a few cases I have not been able to reproduce Sezgin’s numeric results
For this study I have restricted myself to cartographic works that allow measuring
longitude unequivocally.
•
This excludes, among others, medieval portolan charts
•
I have nevertheless chose to include two maps whose projection is
debatable due to their specific interest for this discussion
I have tried to include as diverse cartographic works as possible
 nature: manuscript maps, printed maps, globes, tables of coordinates
 scope: world, Mediterranean basin, Africa
 origin: Greek, Arabic, Hebrew, Italian, Spanish, French, German, Ottoman…
To calculate the “LongMed error” of each cartographic work, I have taken the
average of as many measurements as possible.
For every cartographic work:
1. Select Western localities
2. Select Eastern localities
3. For each couple of Western and Eastern localities
i. measure difference of longitudes DLold,
ii. look up actual difference of longitudes DLreal, and
iii. compute relative error ( DLwork – DLreal ) / DLreal
4. Calculate average error (E) and standard deviation (s)
Western
localities
A
B
C
Eastern
localities
W
X
D
E
Y
Z
DLol
DLrea
d
l
A–W
53
40
32.5%
A–X
55
41
34.1%
48
42
14.3%
Average E
-
-
28.7%
Std. dev s
-
-
6.3%
Pair of
localities
error
…
E–Z
Vertical axis Y represents the error of LongMed
60%
50%
Each cartographic work is plotted
as a point.
M. Behaim
40%
Its X value is the date at which it
was first created or published.
30%
Its Y value is the value of average
LongMed error E
20%
Vertical error bars represent the
standard deviation of LongMed
error s
10%
1550
1540
1530
1520
1510
1500
1490
1480
1470
1460
-10%
1450
0%
-20%
Horizontal axis X represents time, in years.
Claudius Ptolemy’s Geographia contains the earliest known table of coordinates
that allows measuring LongMed.
The analysis of these tables is not simple due to several reasons:
• lost original
• earliest preserved manuscripts from 13th century
• two different recensions
• large amount of data, 6000 or 8000 localities overall
• questioned date, as some place-names post-date Ptolemy (Bagrow 1945)
The numeric study of these tables is today a fruitful field of research:
Leif ISAKSEN, “Lines, Damned Lines and Statistics: Unearthing Structure in Ptolemy’s Geographia”, presented at the 6th
International Workshop on Digital Approaches in Cartographic Heritage. The Hague, April 2011.
Angeliki TSORLINI, Claudius Ptolemy Γεωγραφική φήγησις (Geographia): Digital analysis, evaluation, processing and
mapping the coordinates of Greece, the Mediterranean and the Black Sea, based on 4 manuscripts and 15 printed
editions, from Vaticanus Urbinas Gr. 82 (13th cent.) until today. The new Catalogue “GeoPtolemy- ϑ” PhD dissertation.
Aristotle University of Thessaloniki, 2011.
Coastlines inferred from Ptolemy’s coordinates overlaid on a modern map. Red
line represents the axis Gibraltar – Iskenderun. Image courtesy of Leif Isaksen.
I have limited myself to an excerpt of 17 localities from the Geographia’s tables →
results to be taken as an order of magnitude only
average error E = 45%
standard deviation s = 5%
Study to be refined based on recently-published research.
Abu Abdallah Muhammad ibn Musa al-Khwarizmi
Kitab surat al-ard (Book of the image of the Earth)
Preserved in a copy made in 1037
60%
50%
Substantially more accurate than Ptolemy
Ptolemy
40%
Same error found later in Toledan tables, Yemenite tables, etc
30%
-10%
1000
900
800
700
Ishaq ibn al-Hasan al-Zayyat, dead before 1059
0%
Eearliest
? known independent table of coordinates
made in Al-Andalus. 298 entries.
1100
Al-Zayyat
Bar Hiyya
Al-Magribi
1275
Al
Kammad
1200
10%
Yemenite tables
Remarkably accurate and internally consistent
-20% one single meridian of reference for all Numerous medieval tables show highly
(i.e.
longitude coordinates).
and Printed
precise
LongMed
Tables of coordinates Manuscriptaccurate
maps Globes
maps
1300
Toledan tables
Marseille tables
20%
Al Marrakushi
Al Magribi 1257
Al-Khwarizmi
Forf illustration purposes only, I have plotted AlZayyat’s coordinates of Western Mediterranean
localities
over a modern map.
Al-Zayyat's
coordinates
44
ROME
42
MERIDA
SARAQUSTA
40
TOLEDO
GENOA
Latitude
DENIA
CORDOVA
JAYYAN
GRANADA VALENCIA
MALAGA MURCIA
ALMERIA
CADIZALGECIRAS
38
36
MAJORCA
SICILY
BIZERTE
ALGIERS
TANGIER
MAHDIYYA
SFAX
JIRBA
34
KAIRAWAN
TRIPOLI ALGHARB
RIBAT
ASFI
32
AGHMAT
MARRAKISH
30
0
5
10
15
20
25
30
35
40
Longitude (from a meridian 18º to the west of Toledo)
Based on data compiled by the late Mercè Comes, kindly provided by Julio Samsó.
Idem for the Eastern Mediterranean.
Longitude based on Toledo = 18º.
Al-Zayyat's coordinates
38
37
CYPRUS
36
ALEPPO
Latitude
35
ANTIOCH
34
JAFFA
TRIPOLI SHAM
TYRE
SIDON
DAMASCUS
QAYSARIYA
33
JERUSALEM
RAMLA
ASQALAN
32
TIBERIAS
DAMIETTA
TINNIS
31
ALEXANDRIA
30
50
52
54
Misr
56
58
60
62
64
Longitude (from a meridian 18º to the west of Toledo)
Based on data compiled by the late Mercè Comes, kindly provided by Julio Samsó.
How did Al-Zayyat manage to ascertain longitudes with a higher accuracy
than either Al-Khwarizmi or Ptolemy?
Later Andalusian and North African tables are even more accurate and
precise than the ones compiled by Al-Zayyat. How were they compiled?
A deeper question remains: how much ‘cartography’ is there in these
tables, which were often mere appendices of astrological works?
In 1923 John K. Wright stated the following, based on his study of the
Marseille Tables:
“How far was the significance of this sort of information understood? How far was it utilized
with a view to giving greater precision to the vague geographical ideas of the time? Reluctantly
we must answer: practically not at all. The geographic importance of the figures seems to have
been almost entirely overlooked.”
In my opinion Wright’s questions are still pertinent but I do not agree with
his answer. I think that a clear conclusion is not easy to reach yet.
60%
Ulm Geography
40%
Ibn F. al-'Umari
30%
M. Behaim
I. Angelo
50%
In the 15th century Ptolemy’s Geographia is
translated into Latin. As a result numerous
European cartographic works start to depict the
Circular world map with graticule
Mediterranean
Contained in the book Masalik
al-absar with a much exaggerated longitude.
by Ibn Fadlallah al-'Umari (ca. 1340)
20%
10%
A.Zacut
1500
1400
1300
0%
-10%
-20%
Abraham Zacut is a late example of highly accurate
table of coordinates, albeit with a few gross errors.
Tables of coordinates
Manuscript maps
Globes
Printed maps
60%
Walters atlas
M.Waldseemüller
B.Agnese
G.Mercator
50%
P.Apian
V.de Maggiolo
G.Gastaldi
40%
O.Fine
J.Ruysch
S.Münster
G.Contarini
30%
A highly elongated Mediterranean becomes the
norm in European cartography.
However, there is not a unique ‘Ptolemaic’ pattern.
For example, Oronce Fine chooses in 1531 a
shorter Mediterranean than Mercator in 1538.
20%
10%
D.Ribero
J.Rotz
B.Agnese
1550
1540
1530
1520
1510
1500
0%
-10%
-20%
At the same time certain European cartographers draw
the Mediterranean accurately. Let’s look at them in detail.
Tables of coordinates
Manuscript maps
Printed maps
Diego Ribero, of Portuguese origin, had the job of “cosmographer” at the
Casa de Contratación of Seville and was therefore responsible for the
Padrón Real.
Carta universal en que se contiene todo lo que del mundo se ha
descubierto fasta agora. Diego Ribero, Seville, 1529.
Facsimile images courtesy of the Library of Congress.
The map does not contain a full grid of coordinates but in my opinion it is quite
likely based on a plate-carrée projection, as it contains five horizontal parallels ;
three vertical meridians ; graduated equator and graduated meridian
Assuming a plate-carrée projection the error of LongMed is remarkably small:
E = -1.3% s = 1.7%
Highly accurate latitudes too. Does not show the usual rotation of portolan charts.
In a text box on the map, Ribero explains that he took latitude data both from
direct astronomical observations and from previous reports by other
geographers.
He does not mention any source of longitude values however.
He is nevertheless aware that his map contains a substantial inconsistency in
terms of longitude. He says that he preferred to exaggerate grossly the width of
the Middle East rather than to deform the Mediterranean “from what is already
used and conceived in the mind.” What did he mean?
World map in two hemispheres in
stereographic projection.
Part of a manuscript atlas entitled
Boke of Idrography made by this
cartographer and navigator from
Dieppe (France) around 1542. Today
preserved at the British Library.
Complete and precise graticule allows
unequivocal
measurement
of
LongMed.
It turns out to be quite accurate:
E = 10% s = 6%
Which were Jean Rotz’s sources?
Two maps showing different values of LongMed coexist in a same cartographic
work: the manuscript atlases drawn by Battista Agnese from 1536 to 1564.
Pages 25-26 of the atlas
Oval world map with
‘ptolemaic’
Mediterranean
Complete graticule
allows unequivocal
measurement of
LongMed:
E = 53% s = 6%
Image courtesy of the Library of Congress.
Pages 9 – 10 of the atlas
‘Nautical chart’ style map
Possibly in plate-carrée
projection but not certain:
• horizontal equator and
Tropics
• one vertical meridian
• graduated equator and
meridian
Assuming a plate-carrée,
LongMed would be very
accurate:
E = - 3% s = 4%
Image courtesy of the Library of Congress.
‘Nautical chart’ style map
Plate-carrée projection (assumed)
E = - 3% s = 4%
Oval world map
E = 53% s = 6%
Why?
60%
Myritius
H.Ahmed
P.Forlani
40%
M.Tramezzino
G.Ruscelli
30%
20%
A.Macar
G.Gastaldi
Anon.(Shirley 174)
Imperial Atlas
G.Mercator
A.Ortelius
50%
J.Martines
G.B.Ramusio
R.Mercator
Anon.(Shirley 169)
T.Porcacchi
J.Cossin
Since 1560 numerous maps begin to
show LongMed with E around 30%.
10%
-10%
-20%
Numerous
maps
follow
thekeeps
Ptolemaic
tradition
(E ca. 40%)
The Dieppe
school
also
on showing
a slightly
too big
Tables of coordinates
Manuscript
maps
LongMed
(J. Cossin
1570,
E = Printed
16%)maps
1600
1590
1580
1570
1560
1550
0%
Abraham Ortelius and Rumold Mercator
adopt this value and make it the de facto
standard of LongMed for the following
InAtthe
second
half
of
the
16th
century
confusion
about thethe
the same time, the Iberian
school the
keeps
on representing
decades.
longitude
of the Mediterranean
reaches
its zenith.
Mediterranean
correctly (D. Homem
1558,
E = -7%)
D.Homem
60%
M.Ricci
50%
Along the 17th century diversity remains.
Nevertheless values of error around 30%
or astronomer,
above are not
rare in maps
from table
the of
In 1627 Johan Kepler, the famous
publishes
a famous
second half
of the
17thtoo
century.
coordinates that shows a Mediterranean
around
25%
long.
Sanson-Jaillot 1691
40%
30%
J.Kepler
20%
A.Arnoldi
W.Blaeu
Sanson-Jaillot 1692
J.Blaeu 1662
A.G.Céspedes
F.de Wit
F.de Wit
J.Blaeu 1664
Robyn
J.Thornton
10%
A.Colom
J.Moxon
E.Halley
-10%
G.Delisle
1700
1680
1660
1640
1620
1600
0%
Printed maps with accurate values of LongMed start to appear in the
1650’s. This trend becomes dominant towards the end of the century.
-20%
Tables of coordinates
Manuscript maps
Printed maps
60%
50%
40%
30%
20%
10%
-10%
-20%
Tables of coordinates
Manuscript maps
Globes
Printed maps
1700
1600
1500
1400
1300
1200
1100
1000
900
?
800
700
0%
65 cartographic works surveyed to date.
The evolution of LongMed error turns out to be quite complex.
Cartographic works with significantly different accuracies coexist in the
same time frame and same location.
Beware of simplistic explanations.
This study is a work in progress. Your input is most welcome!
In memoriam Mercè Comes
I would like to thank the following individuals and institutions:
 Julio Samsó for providing access to Mercè Comes’s unpublished data
and for his kind and helpful advice
Jean-Charles Ducène for providing access to his soon-to-be-published
work on the Yemenite tables
 The Germanische Nationalmuseum and TU Wien for providing projected
images of Martin Behaim’s globe
 Leif Isaksen for his advice on Ptolemy’s Geographia
And of course thank YOU for having watched this automatic presentation!
Luis A. Robles Macías
[email protected]
24th International Conference on the History of Cartography
Moscow, July 2011