• John Snyder covers “2000 years of map projections” in his book.
• By 1800 the key map projections we use today had been developed, so the
year indicators in the title are overambitious.
• This presentation: focus on and intriguing subject from history of geodesy: my
PhD study on portolan charts.
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• The story of Eratosthenes may be a popularised version of his method, which
may explain the arbitrary extra 2000 stades of his result.
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• Ptolemy developed two pseudo-conical projections, of which this is the
“Second projection” , and he developed the perspective projection, in which he
was well ahead of Google Earth!
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• Mappamundi – Cloth of the world: altarpieces, intellectual spiritual elite.
• Qualitative, religious view of the world; even an anti-quantitative view.
• Christian symbolism dominating factor, not any perceived need to map the world in a
geometrically correct manner.
• The Hereford map is an elaborate T-O map. It is meant to be directed east-up (our word
‘orientation’ comes from such maps. The vertical bar of the ‘T’ in the name is the
Mediterranean, in simpler T-O maps often represented as a thin strip. The cross-bar is the
river Don (in the north) and the Nile in the south. These two rivers were believed to be the
boundaries of the continents Europe-Asia and Africa-Asia. The ‘O’ is the ocean
surrounding the inhabited world.
• Earth was understood to be a sphere; no idea how to represent that in maps.
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• Around mid 13th century, like a bolt from the blue, portolan charts start to appear
• No development path leading to their apearance; hardly development after that
• Not a replacement of the mappamundi, but parallel with.
• New type of map: a nautical chart; highly realistic; inland features very
inaccuarate.
• Appearance of these charts: one of the most important events in the history of
cartography
• Researched very intensively: enormous amount of literature, however, mostly
qualitative.
• My research: geodetic, quantitative focus
• Manuscript maps on vellum (parchment)
• Appeared in Italy; Pisa or Genoa
• Maritime commercial world; not from intellectual elite
• Clearly based on measurements; not on a mental image
• ~10° counterclockwise rotation; associated with unrecognised magnetic declination
• First maps to be drawn to scale (scalebars)
• Very characteristic, at first sight chaotic line pattern (to remain a char. of naut.charts
18th c)
• Portolan charts have a map projection (best fit: Mercator)
• Enigma is how this is possible in a period in which the necessary geodetic
knowledge and skills cannot be assumed to have existed.
• Controversial maps: pseudo-science claims; however, 99.9% of map historians are
convinced of a medieval origin
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• Used to lay out (cross-basin) courses; this is a guess.
• Maps too small-scale to be of much use in coastal navigation
• 16 points regularly spaced on the perimeter of a hidden circle
• Based on (?) Greek antiquity: 8 wind system – Medieval Italian names
• Colour coding of main (black), half (green) and quarter (red) winds
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• Many coastal features are enlarged by a factor 10 or more
• No sophisticated cartographic characteristic: not consistently applied and not
an exact scale enlargement
• More like a rough sketch superimposed on an accurate coastline.
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• Geodetic contradiction.
• Mapping works geodetically from the detail to the whole, not the other way
around.
• Measurement errors propagate from the detail (small) to the whole (larger)
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• Method: Points identified on and scaled off from portolan chart (800 – 1000).
Corresponding points scaled-off from modern map (Digital Chart of the World).
• Least Squares solution, solving for optimum fit by applying projection formulas
with superimposed affine transformation (Mercator + Equirectangular)
• Residuals squared and added. RMSE is measure for accuracy of the chart
• Chart scale ~ 1:5.5 mln (dimensions: 102 x 75 cm)
• Variation by chart occurs (I analysed 5) but more commonalities than
differences
• Portolan charts were largely copied from the early ones; hardly
development in coastlines of core area.
• Analysis confirms that a portolan chart is a composite of smaller parts.
• Parallel appearance of these sub-charts produced in their own region is
nowadays assumed
• Remarkable: overlaps between sub-charts: appear to have been used
to fit sub-charts together
• Suggests that scale and orientation of sub-charts were precisely known.
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• Red line is the reference coastline on a Mercator projection.
• Mercator projection was ‘invented’ by Gerard Kremer mid 16th century
• Mathematics by Edward Wright end 16th century
• Remarkable, because the Mercator projection is a mathematical relationship
between latitude/longitude and X,Y map coordinates
• NOTE: In the narrow latitude band of the Mediterranean the Mercator
projection in portolan charts cannot be established with absolute certainty.
The Mercator projection can hardly be distinguished from the Equirectangular
or Equidistant Cylindrical projection in that area, but the charts have more
characteristics of the Mercator projection than of the Equirectangular.
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For those who don’t remember what the Mercator projection looks like.
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Assumption: very disciplined navigation by dead reckoning; every few hours estimation
of distance travelled and course direction. All dutifully recorded.
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• The medieval origin story is unsatisfactory, inconsistent. Generally
acknowledged, but “it’s all we’ve got”.
• Mariner’s compass introduced only early 14th century. Portolan charts already
existed.
• Before that: floating compass, i.e. magnetised needle stuck through a straw,
floating in a bowl of water; unsuitable for surveying and mapping.
• Role of the compass in charting therefore disputed
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• Round ships: potbellied sailing vessels with lateen rig (length to beam ratio 3:1)
• Galleys: large rowing gigs (length to beam ratio 10:1) – notoriously poor sailers
• Running before the wind was the only option; enormous leeway on other courses
• Dominant wind direction (summer): NW – N (west Med) and NW (east Med)
• Consequence: Dominant trade routed mainly along northern Mediterranean coasts.
• Navigation by dead reckoning: distance by piece of wood thrown in at the bow;
passage estimated by reciting a rhyme.
• Course direction by compass is assumed; however, the charts precede the time of
introduction of the mariner’s compass, i.e. compass card fixed to needle: early 14th
century.
• My accuracy model of medieval navigation: most favourable accuracy: standard
deviation of 17% of the length of a route. Course bearing within a compass point).
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• ‘Portolani’: sailing guides with written courses (“From A to B so many miles at
such and such a course”), plus information on ports and anchorages.
• Consensus assumption: navigation data collected and improved in accuracy by
averaging over a large number of measurements. From this data the first
portolan chart was constructed (hence the name “portolan” chart).
• I have statistically analysed the oldest portolan (1296):
• ~1400 routes (distance and bearing) – along the coast and across open
sea
• Conclusions
• Distance: (standard deviation of 15% for cross-sea routes and 37% for
coastal distances)
• Bearing: (standard deviation of 9.5° for cross-sea routes and 25° for
coastal distances)
• Short courses have the worst accuracy, which does not make sense,
unless scaled off from a chart. In that case the coastal feature
exaggeration causes this effect.
• No accurate averages. Scaled off from a chart.
• Calculation of the arithmetic mean (‘averaging’) is anyway a “presentism”, a
modern idea that has been transposed to the past.
• The first experiment that demonstrates some awareness of variation in
measurements date from 1538.
• Tycho Brahe used the mean to eliminate systematic errors and the first
recorded application of the calculation of the mean to improve precision is from
the geodetic expeditions to Lapland and Peru in the 18th century (Clarke 1880,
not the ellipsoid, but the book!
• Medieval seamen ahead of their intellectual contemporaries? Centuries ahead
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• The total root mean squared error of the chart is the value (per sub-chart)
shown in Slide 14.
• However, in slide 14 I divided the total sum of the squared residuals in a
latitude and a longitude component. The square root of each constitutes
roughly the semi-major and the semi-minor axis of the mean error ellipse for an
arbitrary point. Only the length of the semi-major axis is reported in slide 15.
• In the above analysis the sum of the squares of all residuals are counted.
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• The results shows an algebraic impossibility: the sum of a number of squares
must always be greater than (or equal to) any of its components.
• Plane charting introduces such large distortions in the network that the shape
of the coastline is materially different from that of a portolan chart.
• The propagation of the accuracy of navigation hasn’t even been assessed
here: even with GPS this wouldn’t work out!
• Ergo:
• portolan charts were not constructed by plane charting
• their map projection is not an artefact of the charting method either and
must therefore have been applied intentionally
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