Math : Numbers

Astralica Count differently

Astralica also has its own numbering system.

In this case, Astralica uses position base notation,

Just like normal numbers we write,

each different place of a number represents a quantity of the base raised to a certain power.

"128" under "normal -human-sense" means we have 1 10^2, 2 10^1, 8 10^0

since Astralica is also based on Computer Science, Astralica uses a base-16 system,

aka "hexa-decimal"

Here we have a video talking about Base Systems (Base Positional System)

Astralica has multiple scripts and methods to write the same set of 16 digits,

Each sript is designed and created for different purposes

What is the Extra 16 doing here ?

Some scripts may contain an extra glyph to represent 0x10.

You may be aware that in a base N system,

there are glyphs which are from 0 to N-1, which the Nth is null.

But just like Roman Numerals (X) , Chinese characters (十), and English (ten),

we have a specific symbol/word for the base number.

the glyph 0x10 can be used

when the quantity is directly 16 instead of using 2 glyphs

Digit Scripts

Astralica has multiple scripts and methods to write the same set of 16 digits,

Each sript is designed and created for different purposes

01 : Quadrant Script

02 : Binary Script

03 : Prime Factor Script

04 : Stick Script

Quadrant Script

In this script, the numbers are arranged around the origin point of a 2D cartesian plane with the same direction when an angle is increasing.

In trigonometry, the ending side of an angle starts from the positive side of the X-axis, then rotates anti-clockwise as the angle increases, here the quadrant script reflects this property

the "L"-shape in each glyph represents the X-axis and the Y-axis, with this we can also identify which quadrant they are in

Binary Script

Since Astralica is Base16, hexadecimal can be converted into binary easily.

Here Astralica uses a "stem-based" pattern, each binary glyh has a "stem", with different branches, it represents the quantity of the powers

What is Binary ?

Binary is a Positional Counting System such that it only has 2 glyphs/digits : 0 and 1, in other words, when a digit reaches 2, it needs to be carried to the next digit.

I though Astralica is Base16, how does Binary fit ?

you can try to write a number in binary, and you can treat each chunk of 4 digits as a Base16 glyph/digit. Because 16 is a power of 2, so "chunking" can be applied here.

Prime Factor Script

This script is based on Prime Numbers and factorization.

It is considered as one of the most sophisticated/complicated scripts.

0 and 1

according to the definition, 0 and 1 are not prime numbers, but they behave like booleans, that's why they look a like but 1 is the active version of 0.

2,3 and 5

Here, the prime number 2,3,5 gets their own symbol,

for each of their powers, that glyph will earn an extra horizontal stroke. 2 is inspired from 2 bars, 3 is inspired by a triangle, 5 is inspired by the first 2 strokes of a pentagram star.

7, B(11) and D(13)

these are considered as "annoying numbers", which are prime numbers that is not small enough to be a good fit for 16, so they have the "annoying"/"complex" symbol to start with.

6, A(10), C(12), E(14), F(15)

these are all composite numbers, which can be achieved by multiplying 2 or more prime numbers, as their symbol represents, they are "smushed" from the numbers they are made.

6 is made from 2 and 3,

A is made from 5 and 2,

C is made from 4 and 3,

E is made from 7 and 2,

F is made from 5 and 3.

B1G NUMB3RZ

The Prime Factor Script will allow us to do multiplication and division easier. 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

BASE 64

since huge numbers can be written as one symbol, Astralica can be base64, which is not mandatory.

BASE 64 : prime numbers that are < 64 and not 2,3 or 5

they will be considered as annoying numbers, here there are 2 places where we can insert strokes. the strokes on the right represents "which row it is on ?", the one of the left represents the cardinal order of being annoying on that row.

41, it is on the 2nd row (2 strokes on the right), and it is the first annoying numbers in that row (here we start counting from 0)

in most cases, we won't event use base64, but just incase if we need it, here we have it. But it is not encouraged to use base64 daily, unless this is one of your fetishes.

But why do we have this script ?

The prime Factor Script plays an important role in future chapters, as they are a part of grammatic glyph/symbols construction. the PrimeFactorScript will be combined with other linguistic characters to make other characters afterwards

Stick Script

The Stick Script is heavily inspired by the IK writing system, which is in 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.

LOL, yup, we win

Pronounciation

Primitive Digits

Each digit has its own pronunciation, but unlike other usual language, Astralica follows a straight pattern to say the numbers from 0x0 to 0xF :

næ

læ

dæ

+12

tæ

Normally we would just literally say the digits from left to right

"0xCA256" will be pronounced as " to - dæ - næ - li - ni "

Power Specification

Like in English we have "ones", "tens", "hundreds", "thousands".

Here we have "so"(16^0), "si"(16^1), "sæ"(16^2), "sa"(16^3)

just like in English we have "thousand", "million", "billion", and so on.

Here we have "ro"(16^00), "ri"(16^04), "ræ"(16^08), "ra"(16^12)

To put everything together, we have the following structure :

_ sa _ sæ _ si _ (so) ra | _ sa _ sæ _ si _ (so) ræ | _ sa _ sæ _ si _ (so) ri | _ sa _ sæ _ si _ (so) (ro)

since "so" and "ro" represents "16^0", in most cases you can choose to omit them.

we can also have decimal points in a number, which is pronounced as "pi" (not "pai", "pi" as in "Pikachu")

If we need to write / pronounce something that can more than 16 digits, we jave to use the scientific notation, which will be covered in future chapters

Klari

"Klari" is a mix of different "one"s from Quadrant script, Binary Script, and Prime Factor Script, this symbol is used to represent "quantification". Sometimes, we need this symbol to represent "quantification of some traits". And sometimes when Klari is used with a fundamental group, the symbol pronunciation is cropped to "Kla"

The pronunciation is inspired by "quantity" from English, "liang" from Chinese, and "ryo" from Japanese, by concatenating the underlined parts and altering some of the pieces, we can get "Kaliri", and it is compressed to "Klari"

"Klari" represents a positive quantity, to represent a negative quantity, we can flip the Klari sign upside down, in this case, the pronunciation is "Klæri" (the modification of "Klari")