Each language has its own number system, and so does Astralica.
Most languages use the decimal system, or base ten, which has ten symbols to represent the quantity of different powers of ten, which are the normal 0,1,2,3,4,5,6,7,8,9 we know, but decimal is not the only number system we have.
Take Binary for example, or base 2, which only has two symbols to represent the quantity of different powers of two, which is just 0 and 1.
Since Astralica is based on logic and Computer Science, Astralica uses hexadecimal or base16.
Base16 is commonly used in computers because 16 is a power of 2, which can be converted easily between them.
As time evolved, Astralica has different scripts to write the same set of 16 symbols, which are :
Quadrant Script, Binary Script, Prime Factor Script & Stick Script. Each of them has its own purpose.
Quadrant Script
The main concept here is that the numbers are arranged around the origin point with the same direction when an angle is increasing back when we were learning trigonometry. Quadrant script is suitable or addition and subtraction, which is not quite enough.
one thing to clarify, to write "0", just simply write "L".
Binary Script
Since Astralica is Base16, hexadecimal can be converted into binary easily. here are the hexadecimal numbers getting converted into binary:
PS: we use "0x" to say "hey, this is a hexadecimal number~"
0x0 = 0000 | 0x4 = 0100 | 0x8 = 1000 | 0xC = 1100 |
0x1 = 0001 | 0x5 = 0101 | 0x9 = 1001 | 0xD = 1101 |
0x2 = 0010 | 0x6 = 0110 | 0xA = 1010 | 0xE = 1110 |
0x3 = 0011 | 0x7 = 0111 | 0xB = 1011 | 0xF = 1111 |
And this down here is the Binary Script in Astralica
Prime Factor Script
The prime factor script would be one of the complicated script, the main idea is:
we have different symbols for different factors which are prime, which are 2, 3, 5, 7, 11, 13.
although 0 and 1 are not prime, they still have their own symbols.
here is the main logic behind the Prime Factor Script:
> both 0 and 1 can be grouped together, they are designed to look like "off" and "on".
> the base symbol for 2 is just 2 vertical strokes, the more horizontals, the more power it has.
> the base symbol for 3 is derived from a triangle missing one of its sides for simplification.
> the base symbol for 5 is originally a 5-pointed star, but drawing a 5-pointed star is cumbersome, so the first 2 strokes remain.
> you can notice that some numbers are products of two factors, like 10, 6, 12, 14, 15, their symbols are made by combining two symbols together.
> but for 7,11,13, they will be considered as "big prime factors, and cumbersome", so they will share the same base symbol, with additional strokes to represent the "level of cumbersomeness"
the prime factor script will allow us to do multiplication and division easier, and here is why:
the strokes in the middle show the shared power across the bases, if a certain base still requires it's own private power, private strokes are given, here's an example:
With this, calculating fractions and areas and scales are much easier somehow. And since huge numbers can be written as one symbol, Astralica can be base64, which is not mandatory.
one thing to clarify here is the cumbersome prime factors, the horizontal strokes on the right represent how many 16s it is bigger than.
Stick Script
The Stick Script is heavily inspired by the IK writing system, the IK counting system is base20, here we take the concept and apply it to Astralica, this makes addition, subtraction and sometimes multiplication and division easier relative easier to other scripts.
you might be thinking since the stick script is so superior, why do we need the other scripts ?
here, the stick script will be or can be used in mathematical calculations, but the grammatical part of Astralica will use the Prime Factor Script, the prime factor script will be combined with other linguistic characters to make other characters afterwards.
Saying numbers
just knowing how to write numbers is not quite helpful, so here is how we say numbers in Astralica:
here, we are not going to use Astralica letters otherwise you may have a hard time reading this.
| +0 : o | +1 : i | +2 : æ | +3 : a |
+0 : n | 0 : no | 1 : ni | 2 : næ | 3 : na |
+4 : l | 4 : lo | 5 : li | 6 : læ | 7 : la |
+8 : d | 8 : do | 9 : di | A : dæ | B : da |
+12 : t | C : to | D : ti | E : tæ | F : ta |
each number is made by combining different numbers of 4s and 1s. Normally we would just literally say the digits from left to right,
take 0xCA256 for example, it would be "to - dæ - næ - li - læ",
but of course we can also add the bases of 16s into the string.
16^5 | 16^4 | 16^3 | 16^2 | 16^1 | 16^0 |
vras | fras | pras | bras | mras | - |
so 0xCA256 can also be "to fras - dæ pras - næ bras - li mras - læ",
one thing which would be a little bit complicated is Astralica also sometimes uses the "Chinese Logic", which is when a base is not specified, it is expected such that it is 1 base power lower than the previous said base. Here are some English, Chinese, Astralica examples
Numbers | English | Chinese Usual | Direct Translate from Chinese Usual to English |
1500 | one thousand and five hundred | 千五 | thousand five |
2560 | two thousand and five hundred and sixty | 两千五百六 | two thousand five hundred six |
120 | one hundred and twenty | 百二 | hundred two |
250 | two hundred and fifty | 两百五 | two hundred five |
3500 | three thousand and five hundred | 三千五 | three thousand five |
so in Astralica, we do the same things, but in base16, here are some examples:
numbers | Astralica |
0x570 | li bras - la |
0xA200 | dæ pras - næ |
0x1280 | pras - næ bras - do |
you might be thinking about how we are going to say cardinal numbers and ordinal numbers, we will talk about this in Volume 2.
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