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Cahill-Keyes M-layout world map silhouette including Antarctica
Cahill-Keyes 1975

Gene Keyes
1973-09-10
1979-02-15   2nd ed., revised and expanded
2009-07-18   3rd ed., further revised and expanded

10 Principles for a Coherent World Map System
Note: This is the précis for what was intended to be a revised, enlarged version of my 1973 M.A. thesis, originally entitled "Six Principles for a Unified Map System (Applied to the China-Russia Situation)" (Carbondale: Southern Illinois University, Government Dept., 1973) 217 p. + 49 maps. It included a test sequence using hand, photo, and computer-drawn maps (20 cm) to show China and Russia together at 1/50,000,000, from 1950 B.C. to 1950 A.D. (19 panels), then zero in to Chenpao / Damansky Island at 1/5,000, the site of their almost-nuclear-war in 1969 (20 panels).

The basic projection for the System in the thesis was Buckminster Fuller's 1954 icosahedral model, but this later proved unsatisfactory due to its contortion of East Asia, unwieldy layout, and totally irregular graticule. In 1975, after the thesis, I supplanted Fuller with my re-design of B.J.S. Cahill's octahedral world map. Among innumerable trial panels, I have drawn by hand a 2 x 2 meter world map at 1/20,000,000 (5° graticule); a 1 x 2 meter world map also at 1:20,000,000 (with a 1° graticule plus national borders); a 1 square meter panel of Canada's Atlantic provinces at 1/1,000,000; a 40 cm panel of Denmark at 1/1,000,000; the one-meter octant graticule for a 1/10,000,000 map with 1° graticule; and 16 one-meter test panels of the 1° graticule for a Mega-Map at 1/1,000,000.

Personal exigencies sidelined the map project in 1984, but after retirement in 2003, I resumed it, along with my study of Cahill’s unpublished cartography. Whether or not this "Coherent World Map System" can be implemented in whole or in part is problematic. Since my thesis 36 years ago, there has been a whole new era in computer graphics, the Internet, online maps, and Google Earth, et al. Perhaps they have made this entire endeavor moot. Nonetheless, and incomplete though it is, I am presenting some components here on my website.

Meanwhile, Google maps are still stuck in the 16th century of Mercator, and all the wonders of the Web are still a veneer on deep geographic ignorance. So I will keep developing this hobby-horse in hopes that sooner or later it might be of use to general education.

As stated in my critique of Fuller's map, I want a single, general purpose, world map projection, with high fidelity to a globe, suitable at all scales from smallest to largest, good for one country or the whole planet. I want a world map and globe as a synoptic pair, comparable to each other at a glance, or in detail. I want globes and maps each to have at least a 5° graticule. I want geography learners at any age to be able to grasp the globe and world map as readily as do-re-mi. Cahill is the key.

Earlier versions of this paper were presented at the Canadian Association of Geographers (1974), the International Studies Association (1975), and the Canadian Cartographic Association (1979).
Dr. Gene Keyes
Berwick, Nova Scotia
2009-07-18

Précis

Most world maps are notoriously distorted and open-ended. Most other political- historical maps are a chaos of unrelated projections and perspectives, scales and sizes, grids and graticules, shapes and formats: orphans with no complete parent world map nor globe. Regional sections focus on Europe or America; shrink Africa and Asia. So-called "authoritative" political maps are seldom available, except as secret weapons of international conflict. Thus, geopolitical ignorance remains endemic, however well-drawn a particular map, series, atlas, or GIS specimen.

To facilitate comprehension of the entire earth as a finite frame of natural and human events, a "Coherent World Map System" is herewith propounded. All of its sub-squares are based on the same Master World Profile (revised Cahill projection) in a specified scale progression from tiny to giant; at constant sizes, perspectives, and graticules; with geocells of 1° or at least 5°; and formatted so that hierarchical miniatures relate all main maps and globes in the system to one another: the whole earth to the street where you live. All panels belong to a millimeter matrix on a proposed 1/1,000,000 "Megamap" version 40 meters long, and its correlates: reduced, enlarged, or detached.

The Coherent World Map System is engendered by the precise interlinkage of these ten requisites:


1) PROJECTION: The Master World Profile, encompassing every map in the system, is B.J.S. Cahill's octahedronal transformation (1909), as modified by Gene Keyes in 1975 (top of page; also, large diagram here). Despite gradated compression averaging 14% of nominal scale, the design evinces better felicity, symmetry, and overall fidelity to a globe than any other single-world-map projection. It shows every continent unbroken, as well as all 64,800 one-degree geocells in close proportion to each other.


2) SCALE: The system has 15 main scales, in a macro-micro range of 30, increasing at a 2× - 2× - 2.5× progression from a moon's-eye view of the earth (1:2,000,000,000) to a mole's-eye view (l : 0.5). (See table below.)


3) SIZE: The system has 12 set sizes (4 back-up, 4 main, 4 super), increasing at the same progression, from a one centimeter cell to the 40 meter Megamap. (See table below.)


4) SHAPE: All panels in the system are square. Besides graphic consistency, this shape enables:
(a) the viewer's apparent altitude to equal the map's kilometer span;

(b) any sub-map to join its neighbors in a mosaic congruent with the grid of the Master World Profile;

(c) any map in the system to represent an integral span in tenfolds of only 1, 2, 4, 5, or 8 metric units.
(.A rectangular exception can be made for doub1e-square world maps at super sizes where ceiling heights or floor space constraints are a factor.)


5) PERSPECTIVE: To enhance the viewer's perception of the earth's entirety as well as its finitude, the system emphasizes:
(a) The delimited, self-enclosing nature of the Cahill-Keyes world profile: its octants are pre-numbered to form a "Basic Eight" for the learner's mental grasp of the planet; they can be re-arranged into other patterns and extensions.

(b) The comprehensive nature of map sub-sets: the system stresses wholistic vistas of geo-historical areas and epochs, from stable viewpoints (e.g., Eurasia, not just European Russia), as well as large-scale close-ups of critical locales.

(c) The constant relation of any sub-map to the Master World Profile by means of a metric grid proportionate to its scale: smaller-size world maps in the system are direct reductions of the Megamap and its grid; and smaller-scale regional maps are direct cut-outs from the grid of a complete Cahill-Keyes world profile. (However, larger-scale plans — cities, etc. — may be adapted from conventional sheets to accord with the system's size, shape, and alignment.)

6) GRID: The system's nexus is the 1/1,000,000 Master World Profile, the Megamap, as inscribed within the length of a 40,000 x 40,000 millimeter grid. A corresponding matrix recurs in every other panel of the system. The grid can:
(a) specify the map equivalent of any square kilometer on earth with an 11-character lower-left coordinate, e.g., my old Halifax neighborhood: 12879x24899. (Three more decimal places could specify any square meter on earth);

(b) extract any existing or potential map in the system at any combination of scale or size by prefixing their codes to the lower-left coordinate; e.g., my old Halifax neighborhood at 1/5,000 centered in a 1 square meter map: 15,03:12877x24897. (Thus, 17 characters in all, or 25 to identify a terrestrial square meter.)

(c) replicate the Master World Profile into junior index maps at every other main scale or size in the system. A 200 x 200 millimeter preview grid tessellates a Scale 1, Size 1 "Mini Master Map", the given "standard size" of the system. Each cell enlarges progressively through the first 8 scales, the millimeter lengths being 1, 2, 4, 10, 20, 40, 100, and 200, where, at Scale 8, or 1/1,000;000, every original cell has dilated to the standard 200 mm size, and forms an accent matrix on the intervening millimeter grid of the Master World Profile. The new sub-cells enlarge in a variant progression of 2× - 2.5× - 2× until they show 1 square kilometer in a 1 square meter map (1/1,000), the millimeter lengths being 1, 2, 5, 20, 50, 100, 200, 500, and 1,000, where another millimeter sub-matrix can depict terrestrial square meters, if desired.
Update 2011-06-07: with reference to the digital version of the Megamap, as programmed by Mary Jo Graça, the full length of it is now set within a grid span of 40,000 mm x 20,000 mm: a "double-square" rectangle rather than a square with 40,000 mm on each side. Also, the km coordinates are read from a zero point at the upper left, rather than lower left, and therefore the y-axis goes from 0 to 20,000 mm, instead of 0 to 40,000 mm as in my original notion.

7) GRATICULE: The system's graticular design emphasizes visibility, symmetry, regularity, and proportionality; all maps are to show a complete 1° graticule at scales of 1/20,000,000 or larger, and 5° for the 3 smaller main scales, including globes. While the Master World Profile has a conventional north-up alignment, the sub-maps' meridians are not necessarily vertical, and tend toward 60° either way, incident to the x-axis of the grid.


8) GEOCELLS: Defined hereby as one degree of latitude and longitude, geocells are central to the Cahill-Keyes map design. Its touchstone is proportionality of each adjacent geocell, one to the next. Not only does the System insist upon 1° or at least 5° resolution, but also that rows and columns of geocells not deviate perceptibly in height or width from their contiguous counterparts (while allowing for the projection's gradual shrinkage toward the center of each octant).


9) FORMAT: The system's map sets exhibit these graphic determinants:
(a) Conspicuous scale distinction, re-accentuated by the grid-cell size;

(b) Total span in kilometers of each panel, shown at its lower right (plus miles);

(c) Absence of top and right margins, enabling edge-to-edge assemblies;

(d) An array of 21 back-up maps in 3 columns, 7 rows, relating any main panel to the entire system; each miniature is twice the scale of the one to its left, 10 times that above it, and 1/10 as long as its major counterpart.

10) SYNOPTIC GLOBAL FIDELITY  Creating a globe/map partnership, the system calls for
a) complementary octant-marked 1° or at least 5° political globes at the same scale as counterpart world maps; in particular, globes with diameters in inches of 2.5, 5, 10, 25, and 50.  (See table below; inches happen to work better than centimeters as a globe diameter with metric scales, e.g., 1/50,000,000 is a 10-inch globe.)

b) octant-marked 1° or at least 5° orthographic (global) maps, of at least the first 5 main scales, as well as counterpart geophysical and/or satellite-image globes, whole-earth photos, and remote images.

c) a synoptic globe-plus-map pairing whereby the equator and the two main Cahill-Keyes great-circle meridians are the same length in either spherical or flat-map form (the interchangeable cognate scale of the globe and map pair);

d) a metric understanding of the global basis of a kilometer and a meter and a millimeter;

e) a correspondingly easy-to-grasp set of rational metric scales such as 1/200,000,000 and 1/100,000,000 and 1/50,000,000 and 1/20,000,000, etc.

In short, the Coherent World Map System derives all of its offspring from a single Master World Profile, dovetailing them with corresponding globes and satellite imagery. It could provide a common canvas for world history and current affairs; it could help renovate geography teaching and social studies mapwork.


Appendix 1:

Table of Scales and Sizes
For the Coherent World Map System



Scale
Code for
Scale
OR Size

Size
(length)

Globe diameter
at given scale

(Earth diameter = 12,735 km, but inches  are better for globe size)






inches
cm


Aa

1 cm



Back-up
Scales



Back-up
Sizes





"
1/2,000,000,000
A
"
2 cm

1/4 in
0.6 cm
"
 1/1,000,000,000
B
"
4 cm

1/2 in 1.3 cm
"
 1/500,000,000
C
"
10 cm

1 in
2.5 cm
Main Scales


Main
Sizes






1/200,000,000
1
"
20 cm
Mini Master Map (notebook)
2.5 in
6.3 cm
"
1/100,000,000
2
"
40 cm
(desk)
5 in
12.7 cm
"
1/50,000,000
3
"
1 m
(poster)
10 in
25.4 cm








"
1/20,000,000
4
"
2 m
Jr. Master Map (wall)
25 in
63.5 cm

1/10,000,000
5
Super
Sizes

4 m
Sr. Master Map
(big wall)
50 in
127 cm
"
1/5,000,000
6
"
10 m

100 in
254 cm








"
1/2,000,000
7
"
20 m

250 in
(21 ft)
637 cm
"
1/1,000,000
8
"
40 m
Megamap (plaza or gym floor)
500 in
(42 ft)
1,274 cm
(12.7 m)
"
1/500,000
9

100 m











"
1/200,000
10





"
1/100,000
11





"
1/50,000
12













"
1/20,000
13





"
1/10,000
14





"
1/5,000
15





Ultra
Scales


Ultra
Sizes





 
1/2,000
16






1/1,000
17






1/500
18














1.200
19






1/100
20






1/50
21














1/20
22






1/10
23






1/5
24














1/2
X






1/1
Y






1/0.5
Z






 
Appendix 2:

These are some related papers I have presented or circulated:


1) "Six Principles for a Unified Map System" (Canadian Association of Geographers Annual Meeting, Toronto, 1974-05) 7 p.

2) "Prospectus for a Unified Map System" (International Studies Association Annual Meeting, Washington, D.C., 1975~02) 5 p. + 2 wall maps.

3) "World Maps, World Politics, and World Vision: An Appreciation of B.J.S. Cahill (1866-1944)" (Unpublished Paper, 1975-04; abstract online, updated 2009-06-01 in item #7 below) 46 p.

4) "Geopolitical Chaos: A Critical Survey of Historical Atlases and World Affairs Mapping" (Canadian Political Science Association Annual Meeting, London, Ontario, 1978-05) 36 p.

5) "'Mega-Map': Proposal for a 1/1,000,000 Outline Map of the World in a Single Frame" [including this précis] (Canadian Cartographic Association, Fourth Annual Meeting, York University, Toronto, 1979-05) 10 p. + 2 maps.

6) "Geocells and the Megamap" (Presented at Canadian Learned Societies Annual Meeting: Planetary Association for Clean Energy, 1983-06-02; updated 2007-03-31) 6 p.

7) "Notes on Scaling Cahill and Cahill-Keyes Maps" (1982-06-23; updated 2009-03-07) ca. 5 p. online, 2 illus.

7) "Evolution of the Dymaxion Map: An Illustrated Tour and Critique" (2009-06-15) 17 web-pages, profusely illustrated

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