[Proj] No argument from me about Peters
mikeo2106 at msn.com
Thu Sep 20 09:06:02 EDT 2007
[First, Id like to clarify that, in my definition of linear approximate
projections, when I said north-south scale, I didnt mean it in the usual
sense, of scale measured along meridians. I mean, instead, the factor that
relates latitude difference to Y distance on the map. The scale with regard
to the Y distance between latitudes.]
Thanks for the note. I want to emphasize that I only meant to mention an
advantage of the Peters projection itself, along with the Galls Orthographic
projection, and other cylindrical equal-area proposals such as Behrmann,
Balthazart, and Tristan-Edwards (in the more extreme form in which it was
actually printed). Those projections have value, for accurate position
measurement by those willing to do a brief calculation, and also wanting
equal area. Of course their LA counterparts would allow exact position
measurement by linear interpolation, while slightly compromising equal area.
I agree with what you say about the promotion of the Peters projection by
Arno Peters and others. Yes, that was a bit brazen, the claim that Peters
was the only map thats fair to the equatorial countries, and that it was
the only equal-area projection.
The claim that Peters is the only equal area projection is an outrage
whether or not Peters knew the statement wasnt true.
As for tropical fairness, in fact, Peters makes a mess of the map appearance
of the equatorial countries. I dont call that fairness.
Peters and Gall Orthographic are similar enough that I could have just said
Gall, and not Peters. But the cylindrical equal area is best known to
the public as the Peters projection, and I guess I intentionally used the
Peters name because, whether we like it or not, Peters is the publics
name for cylindrical equal-area, and so I just wanted to emphasize that the
map has a use, and hopefully is sometimes used for what its good for. Its
good to find a silver lining.
I agree that it shouldnt really be called the Peters projection, because,
as you pointed out, Lambert proposed the cylindrical equal area projections
in 1772, and especially because Gall had proposed a nearly identical version
of it a century before Peters.
Of course another regrettable thing about the promotion of the Peters
projection is the claim that its the best for all purposes and
applications. But I only praised it, and the similar CEA projections, for
one narrowly-defined purpose.
Ive brought Peterss unsuitability as a general purpose map to the
attention of a few librarians at libraries that have the Peters Atlas.
Someone with professional credentials should write to libraries, bookstores
and organizations about the greatest scam and fiasco in the history of
cartography. Maybe its already been done.
So, the use for Gall orthographic, Peters, Balthazart and Tristan-Edwards is
: Precise position measurement, if the latitude isnt too high, if
equal-area is desired, and if a brief calculation is acceptable (other than
For instance, as I was saying, Gall Orthographic has more map Y distance
corresponding to a given latitude difference, as compared to a sinusoidal of
the same width, up to latitude 60, and, of course, more X distance
corresponding to a given longitude difference everywhere. For example, at
latitude 40, Gall Orthographic allows 30% more accurate longitude
measurements and 53% more accurate latitude measurements, as compared a
sinusoidal of the same map-width, fitting on the same page-width. Thats the
advantage of maps like Galls orthographic and Peters. Its an advantage if
the important thing is position measurements on the map.
But the downside is that, with Galls Orthographic or Peters, a small square
on the equator is expanded north-south so that its north-south dimension is
twice its east-west dimension. In other words, at the equator, north-south
distance is doubled with respect to east-west dimension. Thats a tremendous
shape distortion. Yes, Mollweide distorts shape too, but its
shape-distortion is plausible, rather than ridiculous looking.
I have to say that puts Galls and Peters value in question. Borneo on
those maps doesnt look like Borneo. One knows that its Borneo only because
its where Borneo should be. Of course those maps do a similar thing to
Africa and South America. It seems a bit questionable how useful the
equal-area property is when some parts of the map look so unlike the places
that they map. I mean, one expects an equal-area map to give an intuitive
view of where and how big.. How intuitively clear can that view be when
tropical regions are shown so unlike its their actual shape?
Additionally, as opposed to making measurements on the map, a data map is
often glanced at to get an impression of what is where. How good is that
impression when shapes are so distorted?
FYI, the sinusoidal is by far the best equal area projection based on
scientific tests of accuracy.
Yes, even a glance at an interrupted sinusoidal shows that. Its shape
accuracy is unmatched by any other equal-area world map.
Of course, as an added bonus, the sinusoidal is the only linear equal-area
map. It is for that reason that I advocate the sinusoidal as the best data
map when equal-area is desired.
I only praised the cylindrical equal area maps for one narrowly-defined
purpose: maximally accurate position-measurement on the map, for an
equal-area map, for a given map-width, fitting on a given page-width--for
people willing to do a little more calculation than linear interpolation.
But the severe shape distortion of such maps as Gall Orthographic and Peters
may lessen their value as equal-area maps and as data maps.
Read the literature.
Im sure that it would be fascinating to look at, and I intend to do so.
But, as I said, a glance is sufficient to show the superiority of the
interrupted sinusoidal as an equal-area world map.
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