Astralica
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.
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~"
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 more horizontal strokes, the more power it has
> 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.
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. Note this is optional
the concept is almost the same when we say "thousand" or "million" or "billion",
but instead of a digit of 3, here we have a digit of 4 going on
with this we can say up to 16 digits, since "so" and "ro" are power 0, we can choose to omit them, but adding them to the number word is still grammatically correct, is an optional choice.
​
here the underscores are used to represent the digits of a large number and verticle lines are added to separate the group:
​
_ sa _ sæ _ si _ (so) ra | _ sa _ sæ _ si _ (so) ræ | _ sa _ sæ _ si _ (so) ri | _ sa _ sæ _ si _ (so) (ro)
​
so 0xCA256 can also be "to ri - dæ sa - næ sæ - li si - læ", or as simple as "to dæ næ li læ"
​
but if we are dealing with bigger numbers, we will need to use math symbols,
which will be covered in the next chapter.
​
​
​
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 previously said base.
Here are some English, Chinese, Astralica examples
so in Astralica, we do the same things, but in base16, here are some examples:
but if the line of zeros stops in the middle of the number, use "no" for the line of zeros,
and the next non-zero number is the head and the rule keeps going
if 1 is a head number, the number name can be omited as well, but the base power name is required
you might be thinking about how we are going to say cardinal numbers and ordinal numbers,
we will talk about this in Volume 2.