[Proj] No argument from me about Peters

Michael Ossipoff mikeo2106 at msn.com
Thu Sep 20 09:06:02 EDT 2007

[First, I’d like to clarify that, in my definition of linear approximate 
projections, when I said “north-south scale”, I didn’t 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.]

Dr. Usery--

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 that’s 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 wasn’t true.

As for tropical fairness, in fact, Peters makes a mess of the map appearance 
of the equatorial countries. I don’t 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 public’s 
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 it’s good for. It‘s 
good to find a silver lining.

I agree that it shouldn’t 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 it’s the best for all purposes and 
applications. But I only praised it, and the similar CEA projections, for 
one narrowly-defined purpose.

I’ve brought Peters’s 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 it’s already been done.

So, the use for Gall orthographic, Peters, Balthazart and Tristan-Edwards is 
: Precise position measurement, if the latitude isn’t too high,  if 
equal-area is desired, and if a brief calculation is acceptable (other than 
linear interpolation).

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. That’s the 
advantage of maps like Gall’s orthographic and Peters. It’s 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. That’s 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 Gall’s and Peters’  value in question. Borneo on 
those maps doesn’t look like Borneo. One knows that it’s Borneo only because 
it’s 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?


You wrote:

FYI, the sinusoidal is by far the best equal area projection based on 
scientific tests of accuracy.

I reply:

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.

You continued:

Read the literature.

I reply:

I’m 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.

Michael Ossipoff

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