Angel Technologies
Gematria calculator
Numogram
Select a zone or gate to show its pair, current, gate, and channel.
From CCRU: Writings 1997–2003
Training & Development
Syzygies and currents
A syzygy is a pair of zones whose values add to the highest single-digit value. In base 10, each pair adds to 9, so the partner of zone n is 9 − n. The small triangles inside the zone circles identify these pairs.
A current is the major flow shown by a wide arrow. Its destination is the absolute difference between the two zones in its pair. For 0 :: 9, the difference is 9 − 0 = 9, so the current points to zone 9. For 4 :: 5, the difference is 5 − 4 = 1, so the current points to zone 1.
Gates and channels
The smaller circles define gates. The gate from zone n is the nth triangular number: T(n) = n(n + 1) / 2. This is the sum of the integers from 1 to n. The nine visible gates are 1, 3, 6, 10, 15, 21, 28, 36, and 45. For instance, gate 45 starts from zone 9 because 45 is the ninth triangular number.
A channel is the minor flow shown by a thin arrow. To find its destination, add the digits of the gate value. If the result has more than one digit, repeat the digit sum until one digit remains. Gate 28 gives 2 + 8 = 10, then 1 + 0 = 1. Its channel therefore goes from zone 7 to zone 1.
Zone 0 gives gate 0 and a channel back to zone 0. This gate is omitted and not drawn on the numogram.
Lemurian Time-Sorcery
Plex is the 0 :: 9 region. Its current points to zone 9 and stays within the pair. In another base, the Plex region consists of zone 0 and its partner, the highest single-digit zone.
Warp is the 3 :: 6 region. Its current points to zone 3 because 6 − 3 = 3. The destination stays within the pair. This region does not occur in every base.
Torque consists of the six central zones: 1, 2, 4, 5, 7, and 8. Their three pairs connect in a current cycle. The 1 :: 8 pair points to zone 7, the 2 :: 7 pair points to zone 5, and the 4 :: 5 pair points to zone 1. The flow thus returns to its starting pair.
Warp region
Let a be the lower zone and b the higher zone of a Warp pair. The pair must satisfy both a + b = N − 1 and b = 2a. Substitution gives 3a = N − 1, or N = 3a + 1. This makes the difference b − a equal to a, so the current points back to the lower zone of the same pair.
This construction permits only even bases. For N = 3a + 1 to be even, a must be odd. The same condition can be written N = 3M + 1, where M is a positive odd integer. The first bases with a Warp region are 4, 10, 16, 22, and 28. Base 8, for example, has no pair that satisfies this condition.
Construction of the numogram
The table below shows the ninth triangular number in each base.
In base-12, 3 + 9 = 10, therefore 39 reduces to 10. 1 + 0 = 1, so the destination is zone 1. In base 16, d has the value thirteen and f has the value fifteen, so 2 + d = f.
To prevent a zone from pairing with itself, choose an even base: N − 1 is then odd, so two equal integer zones cannot add to it.
| Base | Zone 9 gate | Channel reduction |
|---|---|---|
| 10 | 45 | 45 → 9 |
| 12 | 39 | 39 → 10 → 1 |
| 14 | 33 | 33 → 6 |
| 16 | 2d | 2d → f |
Once the base is fixed, the zone pairs, current destinations, triangular gates, and channel destinations follow from these rules.