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Introduction

In this section, we will be exploring and learning about the Aloukik Ganit a.k.a the "Absolute Numeral System" in Jainism.

What is "Absolute Numeral System"?​

Absolute Numeral System (referred as Alaukik Ganit) is the mathematical number system that has excerpts from the ancient scriptures dated approximately 200 B.C.

This system has clear definitions, explanations and bifurcations of the Numerables (the number system Modern Maths deals with), Innumerables and Infinite. Yes, in Jainism; the term "Infinity" is not Abstract, but very well defined quantity.

Since Karnanuyog Jainism Scriptures explain the Universe, Metaphysics, etc. and the quantities are in the scale of Infinite; this system is very important to be established to explain in great detail.

"Alaukik Ganit" is one of the base for reading Karnanuyog scriptures and thus basic understanding is always helpful to grasp it well.

Introduction​

The Absolute Numeral System is divided broadly into three types :

  1. Numerable (Sankhyaat)
  2. Innumerable (Asankhyaat)
  3. Infinite (Anant)

Numerable​

The Numbers that can be perceived or understood just by representing with digits or symbols fall under Numerable category. They are finite. Numerable starts from 2 as the minimum.

Innumerable​

The Numbers that cannot be perceived or understood by represented with digits or values are known as Innumerable numbers. Thus, different visualization methods, intuitive methods are used to represent them. Though they are extremely large in value, but are finite.

Infinite​

Infinite is that quantity that is unchanged even on performing mathematical operations like addition, subtraction, etc. on it. There are 9 major types of Infinity, and are well defined on how to calculate them.It is not 'Relative' or 'Undefined' term as considered in Modern Mathematics.

Types of Numerable​

Numerable numbers are classified in majorly 3 types:

  1. Minimum = 2 (jaghanya)
  2. Intermediate (madhyam)
  3. Maximum (utkrutsht) (this is the maximum value a normal human can perceive with the help of digits)

Types of Innumerable numbers​

Innumerable numbers are classified in majorly 2 types:

  1. Value-based (proper calculation methods are used derive and perceive its value)
  2. Intuition-based (intuitive and visualization methods are used to derive and perceive its value)

Value-based​

Value-based Innumerable numbers are bifurcated further into 3 types (and totalling to 9 types):

  1. Paritasankhyat
    1. Minimum (Jaghanya)
    2. Intermediate (Madhyam)
    3. Maximum (Utkrusht)
  2. Yukasankhyat
    1. Minimum (Jaghanya)
    2. Intermediate (Madhyam)
    3. Maximum (Utkrusht)
  3. Asankhatasankhat
    1. Minimum (Jaghanya)
    2. Intermediate (Madhyam)
    3. Maximum (Utkrusht)

Intuition-based​

Intuition-based Innumerable numbers are bifurcated further into 3 types (totalling to 8 types):

  1. Palya and Saagar
  2. Suchyangul, Pratarangul and Ghanangul
  3. Jagatshreni, Jagatpratar and Jagatghan
‎

Some equations to compute Innumerable numbers:

1. Min Pariasankhyat = Max Numerable + 1
2. Min Yukasankhyat = Max Partiasankhyat + 1 
3. Min Asankhayatsankhayt = Max Yukatasankhat + 1 
4. (Min Paritasankhat) ^ (Min Paritasankhat) =  Min Yuktasankhyat 
5. (Min Yuktasankhat) ^ 2 = Min Asankhayatsankhayt

Types of Infinite numbers​

Infinite numbers are bifurcated into 3 types (totalling to 9 types).

  1. Paritanant
    1. Minimum (Jaghanya)
    2. Intermediate (Madhyam)
    3. Maximum (Utkrusht)
  2. Yukanant
    1. Minimum (Jaghanya)
    2. Intermediate (Madhyam)
    3. Maximum (Utkrusht)
  3. Anantanant
    1. Minimum (Jaghanya)
    2. Intermediate (Madhyam)
    3. Maximum (Utkrusht)
‎

Some equations to compute Innumerable numbers:

1. Min. Paritanant = Max. Asankhayatsankhayt + 1
2. Min Yukatanant= Max. Paritanant + 1
3. Min Anantanant = Max Yukatanant+ 1
4. (Min Paritanant) ^ (Min Paritanant) = Min Yuktanant
5. (Min Yuktanant) ^ 2 = Min Anantanant

Some practical examples of these large numbers​

  • The total maximum number of humans at any time in the Universe is finite and are equal to: 79,228,162,514,264,337,593,543,950,336
  • The total number of Stars in the Universe are finite and are equal to: 2 X 68,975 X 10^14
  • The Max Life span of Humans in 1st ERA is 3 Palya.
  • The Dimensions of the Universe is 14 X 7 X 7 Rajju (which is an Innumerable Quantity).
  • The total number of concentric islands in the Middle Realm(Madhyalok) falls under Innumerable category.
  • The age of the Universe, the total number of Souls, total number of matter particles is Infinite of corresponding type.
  • The total number of Gods (Siddhas) in Siddhalya of the Universe is Infinite of its correspondning type.