Humanity 64 concerns not just time, but space. To that end, we divide the world into 64 “squares,” formed by the intersections of 8 lines of latitude (spaced 22.5 degrees apart) and 16 lines of longitude (spaced 45 degrees apart). At the Arctic Circle, the squares are more like triangles, and the squares become more trapezoidal and almost rectangular — not to mention much larger — when we reach the equator. It is well worth noting that there is decent mathematical harmony between octal (base-8) system of the chessboard, the sexagesimal (base 60) system of timekeeping, and sexagesimal-like system of latitude and longitude,
Speaking of mathematical harmony, it’s good to know that sexagesimal comes to us from the ancient Sumerians via the ancient Babylonians, by virtue of the magic of the number 60, which also can be said to lay the framework for our system of latitude and longitude. Base 8 was used by some Native American Tribes (who counted on their knuckles rather than fingers), and may well be the most logical counting system of all:
For tho’ all nations count universally by tens (originally occasioned by the number of digits on both hands) yet 8 is a far more complete and commodious number; since it is divisible into halves, quarters, and half quarters (or units) without a fraction, of which subdivision ten is uncapable….” In a later treatise on Octave computation (1753) Jones concluded: “Arithmetic by Octaves seems most agreeable to the Nature of Things, and therefore may be called Natural Arithmetic in Opposition to that now in Use, by Decades; which may be esteemed Artificial Arithmetic.” Hugh Jones, 1745.
Hugh Jones, 1745
One point of Humanity64 geography is that by using squares within squares, we can pinpoint any location on earth, in a way that is more relatable than GPS. Thus, each “square” can be divided into 64 subsquares, and each of those can be divided into 64 subsquares, and so on. Perhaps not surprisingly, one only needs to go down a few levels to get pinpoint accuracy:
Latitude
Note that the sides on the latitude side are constant. The length of any meridian is 12,429.9 miles. Divide that by 8 to get the sides of any “square”:
1. 12,429/8 = 1553.625
2. 1553.625/8 = 194.203125
3. 194.203125/8 = 24.275390625
4. 24.275390625/8 =3.03442382813
5. 3.03442382813/8 = 0.37930297851
6. 0.37930297851/8 = 0.04741287231 = 250.52961731 feet
7. 0.04741287231/8 = 0.00592660903 = 31.3162021637 feet
8. 0.00592660903/8 = 0.00074082612 = 3.91452527046 feet
Longitude
24901 is the earth’s circumference, So divide that by 8 a few times:
1: 24901/8 = 3112.625 — a1
2. 3112.625/8 = 389.078125 a1b2
3: 389.078125/8 = 48.634765625 – a1b2c3
4. 48.634765625/8 = 6.07934570313 a1b2c3d4
5. 6.07934570313/8 = 0.75991821289 a1b2c3d4e5
6. 0.75991821289/8 = 0.09498977661, ie 501.925979614 feet a1b2c3d4e5f6
7. 0.09498977661/8 = 0.01187372207, i.e. 62.7407474518 feet a1 b2c3d4e5f6g7 – a square that is about 32 feet by 62 feet
8. 0.01187372207/8 = 0.00148421525; ie. 7.8425 9343147 feet a1 b2c3d4e5f6g7h8 – a square that is about 4 by 8 feet.
Note that the “longitudinal” dimension here is at the equator, and as latitude goes up (or down, from equator), longitudinal dimension shrinks (such that every “square” on the chessboard is really a trapezoid). the circumference of the earth at any point is the circumference at the equator times the cosine of the latitude at that point, e.g.
The exact value of cos 22.5 degrees is 0.92387953, so the length of the parallel at is 23005.5241765.
The approximate value of cos 45 is 0.7071.
Cos 67.5 = 0.38268343 so the length of that parallel is 9529.2003
So, a cascade of 8 squares brings us to our personal space (4 by 8 at the equator), and it’s easy to see that any cascading beyond that soon get you as much precision as you might desire.
