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Cahill-Keyes M-layout world map silhouette including Antarctica
Cahill-Keyes 1975
Why Cahill? What about Buckminster Fuller?

Evolution of the Dymaxion Map:
An Illustrated Tour and Critique

Part 9.6

by Gene Keyes

Summary: I love Bucky, but Cahill's map is a lot better. Here's how.

Click inside boxes to open other sections in separate windows.
1) Introduction and
Background Notes

2) 1943:
Split Continents

3) 1944:
Whole Continents

4) 1946:
The Dymaxion Map Patent

5) 1954
Whole Continents

6) 1967 ff:
Later Editions and
World Game Versions

7) 1995 ff
Dymaxion Maps
on the Internet

8) Notes on Scaling Dymaxion Maps
9) Critique:
Dymaxion Map Compared to Cahill

9) Critique: Seven Design Flaws of Fuller's Map as Compared to Cahill's
9.1) Layout assymetrical
9.2) Graticule irregular
9.3) Korea distorted
9.4) Scalability poor
9.5) Anti-metric edges
9.6) Globe fidelity poor
9.7-a) Learnability poor
9.7-b) Learnability poor
9.8) Conclusion

Part 9.6
Poor to zero comparison with any equivalent globe

Fig. 9.6.1 below: Despite the drawing below, and the nifty animation already shown in Part 7, a Dymaxion map does not have a cognate globe with which it can be compared.
Dymaxion map unfolding diagram
Source: verso text of smaller ODT Raleigh map, 2009
Scanned by Gene Keyes

Fig. 9.6.2 below: One of the buzzwords in Fuller's lexicon is "modelability". But it is Cahill, not Fuller, who models the globe to perfection with his map, and vice versa. A Cahill map is the alter ego of a globe.
B.J.S. Cahill's rubber-ball globe-map
Source: 1919 brochure by Cahill; scanned by Gene Keyes

Fuller's map, on the other hand, is a sophisticated geodesic abstraction. It is not a hands-on model that any pupil can use for immediate and comprehensible comparison to a globe. (Nor to an atlas.) Yes, there is that graphic animation of globe to icosahedron to map, but it is a quick and passive piece of digital legerdemaine. Yes, there is a fold-up icosahedron; but it is a flat-faceted novelty, not a globe. These badly lack what I describe later in Parts 9.7-a and 9.7-b, a synoptic view of globe and map together.

Instead, what we see in the Dymaxion sketch above, is a partial view of a globe, minus its graticule; then a partial sketch of an icosahedron, minus its graticule; then the map unfolding to its flat form, minus its graticule. Indeed, there is no actual spherical-icosahedral globe a la Fuller at all (except for one I improvised, shown in Part 9.7-a, where I will further discuss and illustrate the Dymaxion map's poor fidelity to a globe.)

But meanwhile, let us return to the 5°, 50-inch "President's Globe" for FDR and Churchill, depicted in Part 2. I first saw it in the March 1, 1943 Life, then I saw it in real life at the Library of Congress in Washington, DC. Why should that be the only earth-sphere with a 5° graticule? Why not every globe of any size? (Most globes have 15° graticules; a few have 10°.)

Below I will show four big pictures of the FDR globe, plus three of the same pictures enhanced as if with Cahill-type octants. The point of this next set of images is to underscore that for purposes of comparison, a globe and a world map should have a 5º grid. Until the Internet, these President's Globe images were as rare and almost impossible to find as a 5º globe itself.

My educational purpose here is no secret: a 5º globe next to any 5º world map — except Cahill — will show up all other world maps for their distortions: and that goes for Fuller as well. The Dymaxion map's failure to show a 5º grid is a major indicator of its lack of fidelity to a globe. (And if it did have 5º, so much the worse, as we saw in my Grip-Kitrick examples in Part 9..2.)

On the other hand, a 5º Cahill world map, plus a 5º globe, are the foundation for an accurate and proportional concept of the Earth.

Fig. 9.6.3 below: There is, or was, perhaps, another 5° globe, desk size, not floor size: seen in a photograph of prominent cartographer Arthur H. Robinson (1915-2004), none other than the producer of the President's Globe. If my astigmatic eyes do not deceive me, I believe that in this picture of Robinson, his globe has a 5° graticule. Was it a working model for the 50-inch goliath? Or a small replica? (Image shown here at double its Internet original.)
For a smaller size of this picture, click in it once;
to restore enlarged size, click in it twice.

Arthur H. Robinson and 5-degree desk globe?
Source: http://www.geography.wisc.edu/history/faculty/images/arthur_robinson_jpg.jpg

Fig. 9.6.4 below: FDR himself looking at the giant 50-inch globe, which is on floor beside his desk. Again, I have doubled the Internet original of this picture.
For a smaller size of this picture, click in it once;
to restore enlarged size, click in it twice.

FDR looking at his 50-inch 5-degree globe

Source: Library of Congress:

Fig. 9.6.5 below: President's Globe in FDR's office. One of those full-size Life photos from the Google-Life archive.
For a smaller picture size, click in it once; to restore full size, click in it twice.

FDR 50-inch 5-degree globe

Source: http://tbn0.google.com/hosted/images/c?q=9cace840c302e172_large

Fig. 9.6.6 below: Now, imagine any size of 5° globe enhanced at the octant division lines a la Cahill. This is Fig. 9.6.5, as changed by me:
For a smaller picture size, click in it once; to restore full size, click in it twice.

FDR 50-inch 5-degree globe with Cahill-Keyes octants

Source: http://tbn0.google.com/hosted/images/c?q=9cace840c302e172_large
Cropped at top and bottom, and octant division lines added by Gene Keyes.

9.6.7 below: Another closeup of the President's Globe; repeated here from Part 2.
For a smaller picture size, click in it once; to restore full size, click in it twice.

FDR 50-inch 5-degree globe

Source: Google Images Life Magazine archive: http://images.google.com/hosted/life
Via this search: roosevelt globe  (otherwise hard to find)
Date taken, 1943; photographer, Thomas D. Mcavoy
Original caption: "View of globe in President Franklin D. Roosevelt's office."

Fig. 9.6.8 below: Another octant-enhanced view of the President's Globe, as changed from Fig. 9.6.7 above.
For a smaller picture size, click in it once; to restore full size, click in it twice.

FDR 50-inch 5-degree globe with Cahill-Keyes octants

Source: http://tbn0.google.com/hosted/images/c?q=764046a9c4937dfd_large
Other source details at Fig. 9.6.7, ibid
Octant lines added by Gene Keyes.

Fig. 9.6.9 below: President's Globe, in color; I have doubled the Internet original of this picture.
For a smaller size of this picture, click in it once;
to restore enlarged size, click in it twice.

FDR 50-inch 5-degree globe, in color

Source: http://www.loc.gov/exhibits/churchill/interactive/_html/_items/wc0001.jpg

Fig. 9.6.10 below: One more enhanced President's Globe, from Fig. 9.6.9.
FDR 50-inch 5-degree globe, in color, with Cahill-Keyes octants

Source: http://www.loc.gov/exhibits/churchill/interactive/_html/_items/wc0001.jpg
Octant lines added by Gene Keyes.

Fig. 9.6.11 below: Back in 1976, I had already done a similar octant enhancement with my ten-inch Replogle globe. Like most, this one has a faint 15° graticule. I applied a Letraset black line to highlight the Cahill octants; relatively easy. For the next 33 years, I wished it had a 5º graticule, but didn’t want to go to the bother again, as I had in 1974, of drawing 5° on a 12-inch globe for an icosahedral net. (See Part 9.7-a.)
Replogle 10-inch globe with 15 degree grid and Cahill-Keyes octants

Source: Photo by Gene Keyes, 2009

Fig. 9.6.12 below: Then, for the sake of this website, I gritted my teeth and penciled in an improvisational 5° grid. It only took me five days. (Don't worry; I have a life, and can afford the time, being retired. ;-)

In a real, commercially-produced version, the 5º lines would be more precise and not as thick.
Replogle 10-inch globe with 5-degree geocells added by Gene Keyes, and Cahill-Keyes octants

Source: Photo by Gene Keyes, 2009

Appendix: Behind the Scenes of that 5º Penciled Globe

Fig. 9.6.13 below: Perhaps I should scrounge up a bunch of money, and commission a professionally drafted 5º globe with Cahill-Keyes octants; or else should have printed out some 5º globe-map gores and pasted them onto a sphere. (And I'd still prefer 1º as well, but that's quite a job . . .) Meanwhile, to demonstrate the principle in a dummy format, I used an existing 1975 Replogle globe. Its surface is very slick, and difficult to write on; I couldn't dare use a pen or marker (except for the Cahill lines), so pencil it was. The globe's semi-circular holder was unsuitable as a drawing aid, therefore, to do the meridians, I used a flexible curve (spline), which had to be affixed to the globe with a piece of sewing elastic, clamped to the spline. (Below.) I had made tics with a (costly!) ten-point divider to split the 15º meridians into three. Doing the parallels was even more difficult; closer to the poles, I could use a compass. Then, remounting the globe in a different spindle, I was unable to clamp the pencil firmly enough to the outer rim, and eventually had to get Mary Jo to hold the pencil against the rim, while I oscillated the globe back and forth enough times for the line to show up.
Gene Keyes pencilling 5-degree grid on 10-inch globe.

Source: Photo by Mary Jo Graça, 2009

As mentioned, in 1974 I had drawn a similar 5º grid on a different globe and enhanced it with map pins and yarn to replicate a Dymaxion spherical icosahedron. This endeavor, illustrated in the next part, was yet another confirmation to me that the Fuller map was not a good teaching and learning tool.

Go to Part 9.7-a
Learnability: synoptic view, globe and map

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Text cc. 2009 by Gene Keyes; Cahill-Keyes Map c. 1975, 2009  by Gene Keyes