10 Principles for a Coherent World Map System

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.