Heptimal system
The numerical system of Solaria is a positional base-7 system, that is, a heptimal system, in which the operative digits are seven: 0, 1, 2, 3, 4, 5 and 6. This means that, after 6, the cycle of digits closes and one moves to the next position. The initial sequence is therefore:
0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, etc.
In this notation, 10 is equivalent to decimal seven, 100 is equivalent to decimal forty-nine (7×7), 1000 is equivalent to decimal three hundred forty-three (7×7×7), and so on.
Seven, then, is not a visible digit, but the principle that governs the passage from one order to the next. This feature also carries a symbolic value: seven represents the completion of the cycle, not an element internal to the cycle itself.
Graphic signs
The system is graphically founded on the numbers 1, 2 and 5, where 5 is represented by a shape similar to an S, while 2 is represented by a reversed S. The two signs are thus mirror images of each other and constitute the generating pair of the system.
0 is represented by a shape similar to a vertical 8. This sign arises from the graphic union of 2 and 5: the two mirrored S shapes, joined together, produce a double figure that recalls infinity. For this reason, the zero of Solaria is understood not merely as the absence of value, but also as a sign of union, recomposition and completion. The fusion of the two principal numbers indicates the completion of a cycle and the beginning of a new order.
The other digits derive from 2 and 5 through an upper or lower dash. The lower dash indicates a decrease of one unit; the upper dash indicates an increase of one unit. The number 1 thus derives from 2 decreased by 1, 3 from 2 increased by 1, 4 from 5 decreased by 1, and 6 from 5 increased by 1.
| Value | Glyph description | Symbolic origin |
|---|---|---|
| 0 | vertical 8 shape | union of 2 and 5 |
| 1 | shape of 2 with lower dash | 2 − 1 |
| 2 | reversed S shape | mirror glyph |
| 3 | shape of 2 with upper dash | 2 + 1 |
| 4 | shape of 5 with lower dash | 5 − 1 |
| 5 | S shape | fundamental glyph |
| 6 | shape of 5 with upper dash | 5 + 1 |
The names of the numbers
In kudamaf the numbers are spoken as they are drawn. The letters s and z are mirror images of each other like 2 and 5, and take their place; sh, whose sign fully contains that of s and that of z, is zero, just as the zero glyph arises from the union of the two S shapes. The vowel represents the dash: a, which has all three bars, is the pure digit; u, which has the two lower bars, carries the value of the lower dash; e, which has the two upper bars, the upper one. All names end in -n.
| Value | Name | Composition |
|---|---|---|
| 0 | shan | s + z |
| 1 | sun | s, lower dash |
| 2 | san | s |
| 3 | sen | s, upper dash |
| 4 | zun | z, lower dash |
| 5 | zan | z |
| 6 | zen | z, upper dash |
Whoever knows the digits already knows how to count, and vice versa. Kudamaf has no words for ten, hundred, or thousand: a number is read digit by digit, as it is written. Seven, which is written 10, is said sun shan; 84, that is 150, is said sun zan shan. The mirrored pair can also be heard: 25 is said san zan, 52 zan san.
Seven nonetheless has a word of its own, ulvash, but it does not indicate a quantity: it is the completed cycle.
From the names of the numbers, as from any root, the verb, the adjective and the adverb are formed (senat to triple, senen triple, sunen unique), and in addition the collective in -ur: sanur duo, senur trio, zunur quartet, zanur quintet, zenur sextet.
One, sun, coincides with the English word for “sun.” The coincidence is intentional: on a planet called Solaria, and in a world that tells of the quest for unity, the one and the sun share the same name.
Significant numbers
25 and 52
Because of the symbolic value attributed to 2 and 5, the combinations 25 and 52 also take on particular importance: the first arises from the movement from 2 toward 5, the second from the reverse movement, from 5 toward 2. It should be specified, however, that in the heptimal system, 25 corresponds to decimal 19 and 52 corresponds to decimal 37.
The two numbers are thus formed by the same signs arranged in mirrored order. This inversion recalls the idea of two opposing and complementary forces, distinct yet bound by the same structure. For this reason, 25 and 52 (19 and 37) can be associated with the shape of Ku’s wings, understood as two figures that answer and balance each other.
The sum of 19 and 37 is 56, which in the heptimal system corresponds to 110 (7×7 + 7).
84
The number 84, written 150 in the heptimal system, possesses an autonomous symbolic form, due to its symbolic meanings: the circle. The circle represents the complete cycle, the totality of the parts, and the return to the starting point after traversing the entire structure.
The circle does not replace ordinary numerical writing. In calculations, 84 remains 150 in base 7. On the symbolic plane, however, the circle allows the deep meaning of the number to be represented immediately: not an isolated quantity, but a completed cycle.
Symbolic value
The numerical system of Solaria links number, form and cycle. 2 and 5 represent the fundamental mirrored pair: two elements in dialogue, which can be read as man and nature, or as the relationship between human beings, forces, communities, or complementary principles.
Zero, represented by an 8, embodies their union. Although it has an ordinary mathematical function within the positional system, on the symbolic plane it does not indicate a mere absence, but the point at which duality is recomposed. For this reason it is associated with truth, harmony, and completion.
Seven represents the complete cycle. In positional writing it does not appear as an autonomous digit, but as the passage to 10. On the symbolic plane, however, seven is not merely a quantity: it is the principle of the cycle that completes itself and passes to a higher order.
Eighty-four represents the cycle of seven unfolded and completed in its individual articulations, divided into twelve parts.