Systematic symbols
Systematic symbols are digits that allow a person to represent an arbitrary number in any base with no prior knowledge of any other digits.
The problem with contemporary representations is that most of them start with the decimal digits, sometimes adding more digits larger than 9. This not only causes confusion as to the meaning of the number, but also creates problem with insufficient number of additional digits for large bases which can theoretically be solved with multibase encoding for non-prime bases. An even larger problem is that if there is no agreement upon a "default" base, used for communication then there is no way to communicate what base is actually being used (any base encoded in that base is written as digit-1 followed by digit-2).
The ridiculous approach simply using dots, lines, circles, or other marks with their amount representing the value will not work for extremely large bases.
Due to these factors prime factorisation is used to represent an arbitrary value.
Examples
"Bubbleoid"
Rules:
- 0 is an unfilled crossed circle
- 1 is a line
- 2 is a filled out circle, it is the basis of all the other values
- Each prime number has an outline. Inside this outline is the previous number
- Composite numbers are made up of different primes placed next to one another
| Decimal rep. | Factorisation | Symbol |
|---|---|---|
| 0 | - | ⨂ |
| 1 | - | ∣ |
| 2 | 2 | ⬤ |
| 3 | 3 | (⬤) |
| 4 | 2×2 | ⬤⬤ |
| 5 | 5 | (⬤⬤) |
| 6 | 2×3 | ⬤(⬤) |
| 7 | 7 | (⬤(⬤)) |
| 143 | 11×13 | (⬤(⬤⬤))(⬤⬤(⬤)) |
| 170 | 2×5×17 | ⬤(⬤⬤)(⬤⬤⬤⬤) |
Writing down Pi using these symbols:
| Arabic numerals | Bubbleoid | ||||||
|---|---|---|---|---|---|---|---|
| Decimal | Octal | Dozenal | Base-360 | Decimal | Octal | Dozenal | Base-360 |
| 3 | 3 | 3 | 3 | (⬤) | (⬤) | (⬤) | (⬤) |
| 1 | 1 | 1 | 50 | ∣ | ∣ | ∣ | ⬤(⬤⬤)(⬤⬤) |
| 4 | 1 | 8 | 350 | ⬤⬤ | ∣ | ⬤⬤⬤ | ⬤(⬤⬤)(⬤⬤)(⬤(⬤)) |
| 1 | 0 | 4 | 146 | ∣ | ⨂ | ⬤⬤ | ⬤(⬤⬤⬤(⬤)(⬤)) |
| 5 | 3 | 8 | 304 | (⬤⬤) | (⬤) | ⬤⬤⬤ | ⬤⬤⬤⬤(⬤(⬤)(⬤)) |
| 9 | 7 | 0 | 186 | (⬤)(⬤) | (⬤(⬤)) | ⨂ | ⬤(⬤)(⬤(⬤)(⬤⬤)) |
| 2 | 5 | 9 | 268 | ⬤ | (⬤⬤) | (⬤)(⬤) | ⬤⬤(⬤(⬤)(⬤(⬤⬤))) |
