Heptimal system
The number system of Solaria is a positional system in base 7, 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 moves on 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 equals seven in decimal, 100 equals forty-nine in decimal (7x7), 1000 equals three hundred forty-three in decimal (7x7x7), and so on.
Seven is therefore not a visible digit, but the principle that governs the passage from one order to the next. This characteristic also has a symbolic value: seven represents the completion of the cycle, not an element internal to the cycle itself.
Sunvash, the seven
Seven has no digit of its own: it is written 10. Its name is therefore built like our “ten,” that is, as the name of a position: sun (one) plus -vash (cycle), “one cycle.” It is the word used to count (seven days, seven people, seven steps are sunvash), but also that of the passage: seven is the single turn that closes and leads to the next order. In the same way, 100 (49) is sanvash, “two cycles,” that is, a cycle of cycles (all the names are in Reading a number).
The cycle fulfilled in all its parts, however, is not seven but eighty-four (7 × 12): it does not serve to count, but to divide time, just as sixty divides the hour into minutes for us. Eighty-four also has two words, one to count it and one to think it, and the second is ulvash, the root from which -vash comes. More on this later, in 84.
Graphic signs
The system is graphically founded on the numbers 1, 2, and 5. The 5 has the shape of an S, the 2 that of a Z: the two signs are mirror images of each other and constitute the generating pair of the system. The mirroring also carries over into the names, which, compared to Earth letters, are swapped, as if the digits had been read in a mirror: the 2, which has the shape of a Z, is called san in kudamaf; the 5, which has the shape of an S, is called zan (all the names are in The names of numbers). This is a deliberate choice: Solaria is the mirror of our world, and so are its numbers.
Above: the Earth Z and S and, beyond the mirror, the Solarian digits of the same shape with their names swapped. Below: the two halves recombine. The letters s and z are the right half and the left half of a cell, and joined together they give sh*; in the same way 2 and 5 joined together give 0,* shan*.*
0 is represented by a shape similar to a vertical 8. This sign arises from the graphic union of 2 and 5: the two mirror-image S’s, joined together, produce a double figure that recalls infinity. For this reason, the zero of Solaria is not understood merely as the absence of value, but also as a sign of union, recomposition, and fulfillment.
The fusion of the two main numbers indicates the completion of a cycle and the beginning of a new order. The play of the mirror also returns in the Solarian alphabet: the letter s is the right half of the cell, z the left half, and sh contains both. This is why zero, which arises from the union of 2 and 5, is said with sh: shan.
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 numbers
In kudamaf, numbers are said the way they are drawn. Each name is a single syllable, made of three parts: the consonant tells the basic shape, the vowel tells the dash, and the final -n closes the number.
| Value | Name | Base shape | Dash |
|---|---|---|---|
| 0 | shan | sh: 2 and 5 joined | — |
| 1 | sun | s: the 2 | u: below, minus one |
| 2 | san | s: the 2 | a: none |
| 3 | sen | s: the 2 | e: above, plus one |
| 4 | zun | z: the 5 | u: below, minus one |
| 5 | zan | z: the 5 | a: none |
| 6 | zen | z: the 5 | e: above, plus one |
The vowels are not chosen at random: in writing, u has the two low bars, e the two high bars, a all three. The vowel thus echoes the position of the dash. The seven drawn digits are in Writing System.
Reading a number
Just as Italian has ten, hundred, and thousand, kudamaf has a word for every power of seven, that is, for every position of the digit. Each name is a single word, made of the digit that counts the zeros and of -vash, the same root as ulvash, the completed cycle of eighty-four: a sunvash is a cycle, a sanvash is a cycle of cycles.
| Earth | Solarian | Zeros | Name | As for us |
|---|---|---|---|---|
| 7 | 10 | 1 | sunvash | ten |
| 49 | 100 | 2 | sanvash | hundred |
| 343 | 1000 | 3 | senvash | thousand |
| 2401 | 10000 | 4 | zunvash | ten thousand |
| 16807 | 100000 | 5 | zanvash | hundred thousand |
| 117649 | 1000000 | 6 | zenvash | million |
A number is read as it is for us: each digit followed by the name of its position, from the highest to the lowest. Units are said alone, zeros are not said, and before a power the 1 is omitted, as in “hundred” and “thousand.”
| Earth | Solarian | Reads as |
|---|---|---|
| 7 | 10 | sunvash |
| 14 | 20 | san sunvash |
| 19 | 25 | san sunvash zan |
| 37 | 52 | zan sunvash san |
| 84 | 150 | sanvash zan sunvash |
| 147 | 300 | sen sanvash |
| 378 | 1050 | senvash zan sunvash |
| 588 | 1500 | senvash zan sanvash |
| 7239 | 30051 | sen zunvash zan sunvash sun |
30051 is read the way we would read “thirty thousand fifty-one”: three at the fourth position, five at the second, one at the units, and the zeros in between stay silent. The mirror pair is also heard aloud: 25 is san sunvash zan, 52 is zan sunvash san.
Beyond zenvash no other names are needed: just as we say “a thousand million,” whatever comes before the last six digits is read as a number on its own and is followed by zenvash. Thus 10000000 (823543) is sunvash zenvash.
One can also read digit by digit, including zeros, as we do with a phone number: 30051 becomes sen shan shan zan sun. This is the way to dictate codes and long numbers, not the way to count.
Ordinals
The ordinal is formed by adding -esh to the last word of the number.
| Position | Solarian | Ordinal |
|---|---|---|
| first | 1 | sunesh |
| second | 2 | sanesh |
| third | 3 | senesh |
| fourth | 4 | zunesh |
| fifth | 5 | zanesh |
| sixth | 6 | zenesh |
| seventh | 10 | sunvashesh |
| eighth | 11 | sunvash sunesh |
| eighty-fourth | 150 | sanvash zan sunvashesh |
| forty-ninth | 100 | sanvashesh |
The ordinal states the place, the collective states the group. Besides the suffixes of every root (verb, adjective, adverb: senat to triple, senen triple, sunen unique), numbers have the collective in -ur: sanur duo, senur trio, zunur quartet, zanur quintet, zenur sextet. Senesh is the third in a row; senur are three people together.
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 search for unity, one and sun share the same name.
Converter
Write an Earth number and see how it is written and spoken on Solaria; with “from Solaria” the reverse happens.
Significant numbers
25 and 52
Due to the symbolic value attributed to 2 and 5, the combinations 25 and 52 also take on a special importance: the first arises from the movement from 2 toward 5, the second from the reverse movement, from 5 toward 2. It should be noted, however, that in the heptimal system, 25 corresponds to decimal 19 and 52 corresponds to decimal 37.
The two numbers are therefore formed by the same signs arranged in mirror 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
Eighty-four arises from a multiplication: 7 × 12. Seven is the cycle, that is, the base of the system; twelve is the number of parts into which each cycle is articulated, like the twelve notes of the chromatic scale. Seven cycles of twelve parts give eighty-four.
To understand the role of eighty-four, just think of sixty. We count in base 10, but the hour does not have a hundred minutes: it has sixty, and the minute has sixty seconds. Sixty is not the base of the system, it is a number chosen to divide time. For the Solarians, eighty-four does the same job: they count in base 7, but a Solarian hour has 84 minutes and a minute has 84 seconds. And just as our 60 is written with a trailing zero, eighty-four in their writing also has one: 150.
Besides time, eighty-four returns in the cycle of fifths and in the seven stages of life: all its uses are gathered in the page Eighty-Four. For this reason it also has its own symbol: 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 immediately represented: not an isolated quantity, but a completed cycle.
Just as the circle stands alongside the digit 150, so in kudamaf eighty-four has two words: one to count it, one to think it.
Sanvash zan sunvash, the eighty-four that is counted
150 is read like any other number: sanvash zan sunvash, a cycle of cycles and five cycles. It is the word of quantities and measures: an hour has sanvash zan sunvash minutes, a minute has sanvash zan sunvash seconds.
Ulvash, the completed cycle
Ulvash is the root from which -vash comes, and it is eighty-four as an idea: the cycle unfolded in all its parts, which closes and returns to the starting point. It is the word of the circle. It does not indicate a quantity and is not used to count eighty-four objects: it is used when eighty-four is a symbol. An hour is sanvash zan sunvash minutes; the whole hour, seen as a completed turn, is an ulvash. In the same way, ulvash is the life that passes through all seven of its stages (see Ciclo della vita).
Symbolic value
Solaria’s number system links number, shape, and cycle. 2 and 5 represent the fundamental mirror 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 where duality is recomposed. For this reason it is associated with truth, harmony, and fulfillment.
Seven represents the complete cycle. In positional writing it does not appear as an independent 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 is fulfilled and passes to a higher order.
Eighty-four represents the cycle of seven unfolded and fulfilled in its individual articulations divided into twelve parts.