Note : This article is written for those who
find it difficult to read Hindi. For those who can read Hindi , it is
recommended to read the original material from “ Samyak Gyan Chandrika by
Pandit Todarmalji ”. Here I have tried to simplify the language, however the
original Hindi words are retained as it is since there are no equivalents.
The relationship between numbers is represented by 14 series
in Jainism. The very first is the Sarva Dhara which is nothing but serial
sequence of numbers as 1,2,3,……and so on. However the important difference is
that the last number is keval gyan, which we have seen as the highest infinity
and no number can exceed that. It may also be noted that this number is
believed to be even and divisible by 4. The other series is sequence of even
numbers and odd numbers and so on. But the most interesting is the series of square of 2, number 2 being the
min samkhyat ( Numeral).
The
Series of Square of 2 ( Dwiroop varg dhara)
The series starts with square of 2 being first number and
the subsequent numbers are square of the previous number. This can be seen in
the table below:
Position
|
1
|
2
|
3
|
4
|
5
|
6
|
Number
|
4
|
16
|
256
|
65536
|
4294967296
|
1844-----
|
|
2^21
|
2^22
|
2^23
|
2^24
|
2^25
|
2^26
|
The table shows the first six numbers of this series. Each
position in this series is called Varga Shalaka. For example the number 65536
has varga shalaka of 4 since that is its position in the series. This number is
given the name Panathhi since it begins with number 65. The fifth position is a
10 digit number which is called Badaal since it starts with number 42. The next
number in the series is 20 digit number called Ikathhi since it starts with
number 18. These names itself tell us how important these numbers were in ancient times since they were given
specific names. Another word which needs to be learnt at this stage is called
“Ardhachheda” which is Log2(Number)
, in other words 2 Ardhachheda = Number
For example if Number is 32 then Ardhachheda = 5
since 25 =32
If Number =65536 then ardhachheda= 16 since
Ardhachheda= Log2( Number)
= Log2(2^24)= 24= 16
Another relationship which can be seen is that
Ardhachheda= 2Varga shalaka
We can also derive that Varga shalaka = Log2(Log2Number)=
ardhachheda of ardhachheda
It can be easily seen that although they did not call this mathematics as Logarithms, the principle was just that. Another interesting thing any
student of computer science would have noticed is the remarkable use of series of square of 2, since that forms the
basics of binary system. In Jainism also the decimal numbers were not so much
prominent as the binary numbers to base of 2.
With this introduction we will proceed with our series of
square of 2.
It can be seen that the number grows at a very fast pace in
this series. The sixth position itself give the number as 2^26 = 264
. This number is prominent in Jainism since 264-1 is the total
number of non repetitive letters possible with 64 letters of vocabulary hence
that is the total extent of sruta gyana. Now if we proceed further in this
series , we find that virtually all the important quanitities are part of this
series. This is denoted by indicating its position in the series of square of 2
, as follows:
1)
Position – several samkhyat position ( where
samkhyat represents numerable)
Number = varga shalaka of Min
ParitaSamkhyat ( where Min ParitaSamkhyat
is min innumerable). Note that the number has not reached Min Paritasamkhyat
but its varga shalaka which is far smaller number that Min ParitaSamkhyat (
MPS).
2)
Position – several samkhyat position further
Number = ardhachheda of MPS
3)
Position – several samkhyat position further
Number = square root of MPS
4)
Position -
one position later
Number =
MPS
5)
Position – several samkhyat position after 4)
Number = Min Yuktasamkhyat = One Avali
Where avail is a unit of measurement of
time.
6)
Position – Next position after 5)
Numbet = square of Avali = Prataravali =
Min Asamkhyatasamkhyat
7)
Position – several innumerable steps after 6)
Number = varga shalaka of AddhaPalya
AddhaPalya is a unit of measurement of time
8)
Position – several innumerable steps after 7)
Number = ardhachheda of addhapalya
9)
Position- several innumerable steps after 8)
Number = square root of AddhaPalya
10)
Position- one step after 9)
Number = AddhaPalya
11)
Position – several innumerable steps after 10)
Number = Soochyangul
Where soochyangul is the number of spatial
units(Pradesh) in one Angul space.
12)
Position – next step after 11)
Number=
Pratangul ( square of soochangul)
13)
Position – several innumerable steps after 12)
Number= Cubic root of Jagatshreni
Where Jagatshreni is the height of Lokakash
in spatial units of Pradesh.
14)
Position – several innumerable steps later
Number = Varga shalaka of Min Paritanant
Number = Ardhachheda of Min Paritanant
Number = Square root of Min Paritanant
Number = Min Paritanant
Here four steps are given which occur in
sequence each after several innumerable steps except the fourth which is
immediate next after square root of Min Paritanant.
15)
Position – several innumerable steps later
Number = Min Yuktanant
16)
Position – next step after 15)
Number = Min Anantanant
17)
Position – several Infinite steps after 16)
Number =
Varga shalaka of Jivas
Number = Ardhachheda of Jivas
Number = Square root of Jivas
These three occur after several infinite
steps after each other. Jivas is the number of all life forms in the universe.
18)
Position – Next step after third part of 17)
Number = Jivas
19)
Position – several infinite steps after 17)
Number = Number of Permaanu ( atoms) in the
universe
This shows the relationship between number
of life forms to the matter.
20)
Position – Several infinite steps after 19)
Number = Number of time units from past to
future in units of Samay.
21)
Position – several infinite steps later
Number = Height of the Akash in spatial units of Pradesh.
Here the Akash implies both Lokakash and Alokakash
together. While Lokakash is bound space in which all jivas and matter is
present. Alokakash is inifinite space surrounding the Lokakash wherein no jivas
or matter or time are present.
22)
Position -
Next step after 21)
Number = Number of space units in
Pratarakash
Pratarakash is square of the Akash spatial
elements in height form.
23)
Position – After infinite steps
Number = Number of avibhaag pratichhedas of
Agurulaghutva quality in Dharma and Adharma dravyas
Here abibhaag pratichheda represents the smallest
indivisible unit of the quality of agurulaghutva . Dharma and Adharma are two
primary dravya or elements of the universe. Agurulaghutva is one of the
qualities possessed by all the six prime
dravyas or elements of the universe.
24)
Position – After infinite steps
Number = Number of avibhaag pratichhedas of
the agurulaghutva quality of the single Jiva which increases in six orders of
magnitude namely: infinitesimal increase, innumerable part increase, numerable
part increase, numerable times increase, innumerable times increase, infinite
times increase. The decrease also occurs in a similar six order manner.
25)
Position – After infinite steps
Number = Number of avibhaag pratichhedas of
the min infinitesimal single letter
knowledge of the smallest Nigod Jiva.
26)
Position – several infinite steps later
Number = Number of avibhaag pratichhedas of
the quality of Kshayik labdhi of asamyat samyak drishti Tiryanch (animal) Jiva.
27)
Position – several infinite steps after 26)
Number =
varga shalaka of Keval Gyan
Keval Gyan is the knowledge units of
omniscient.
28)
Position
– several infinite steps later
Number = ardhachheda of keval gyan
29)
Position – several infinite steps later
Number = Eighth square root of the keval gyan
30)
Position - + 1,2,3,4,5,6,7 steps later
Number = 7th, 6th, 5th,
4th, 3rd, 2nd and 1st square root
of keval gyan
31)
Position – Next step after 30)
Number = Avbhaag Pratichhedas of the Keval
Gyana
Thus we see that the series of the square
of 2 contains quite important numbers , namely number of Jivas, Number of
permaanu , number of akash Pradesh, number of time units , as well as Keval
Gyan. Thus in a single series we get to
know the relationship of one with the other.
Series of
Cube of 2 ( Dwiroop Ghan dhara)
The previous series started with square of 2, this series
starts with cube of 2 and the subsequent numbers are square of the previous
ones. The first four positions are shown
below:
Position
|
1
|
2
|
3
|
4
|
Number
|
8
|
64
|
4096
|
|
|
23
|
43
|
163
|
2563
|
The series can be worked out similar to the previous of the
square of 2. It may be noted that this series will not overlap with the
previous one. It means that the same number will not appear in both series. On
the other hand it is complementary to the previous with some important
differences which are highlighted below:
1.
While series of square of 2 has cube root of Jagat
sreni or the height of lokakash as one of the elements {see 14) in previous description}, here Jagat
sreni is the constituent.
2.
While previous series had Number of Jivas as the
elements, here cube of same occurs.
3.
In this series the cube of entire akash i.e.
lokakash and alokakash together is a constituent.
4.
The last number in this series is cube of the
second square root of Keval gyan. If we try to derive the next number then we
find that it becomes cube of the square root of Keval Gyan which will be higher
than kevan gyan . Hence such a number is not possible.
Series of
cube of cube of 2 ( Dwiroop Ghanaghan dhara)
This is the last of the
14 series which are used to describe numbers and their relationship. This
series is that of cube of the cube of 2, and the subsequent numbers are square
of the previous ones.
Position
|
1
|
2
|
Number
|
512
|
262188
|
|
(23)^3
|
((23)^3)^2
|
As can be seen above the series grows at a
very fast pace. The important numbers here are :
1.
The number of Pradesh or units of space of Lokakash.
2.
Several numbers pertaining to the Nigod and
single sensed JIvas and their life span.
3.
Here the last number is the fourth square root
of Keval Gyan
With these 14 series the relationship of most of the
important quantities related to numbers , space, duration and even the bhava
i.e the number of thoughts of the mind
are related to each other and one can understand the magnitude of those
numbers.
Units of Space and Time
Units of
space : Pradesh The smallest
element in the universe is permaanu or atom. However it is not same as the atom
described by our science. In fact it is infinite times smaller than atom
because it is the single particle by which all the atoms and matter has been made. In that sense it is
similar to the God particle described
today. In Jain philosophy such a particle is cause of all the material seen.
The permaanu is indivisible smallest particle of matter which occupies a single
unit of space which is called Pradesh. It is also described as the distance
travelled by one permaanu at slowest speed in one samay where samay is the
smallest unit of time. It is important to note that slowest speed is mentioned
since at highest speed the permaanu can travel from one end of the universe to
the other.
Now permaanus join with one another and create skandh or
molecules. This joining also follows specific laws and is quite scientific.
Interestingly the matter is named Pudgala which itself means one who has
property of associating and disassociating. This is precisely what matter is wherein
the permaanus keep adding or subtracting at any given time. Even infinite
permaanus form the skandh which will still not be visible. The smallest is
called avasannasann skandh. Without going into details we quote the value 811
times of this skandh will be equal to one maize seed. 8 of these equal to one
angul i.e. one finger. This is also known as Soochyangul or Vyavhar angul. However
this is another angul called Prananangul which is 500 times that of previous
one. This corresponds to the finger of Bharat Chakravarti king in the
fourth cycle of Avasarpini kaal
prevailing now. At that time the body of humans was largest equal to 525
Dhanush. His angul is called Praman angul since all measurements with respect
to the seas, oceans and space are related to that absolute measurement. The
table below now shows the relationship
of the space units further.
500 Utsedh Angul
|
1 Praman Angul
|
6 specified angul
|
1 paad
|
2 paad
|
1 vitasti
|
2 Vitasti
|
1 hand
|
2 hands
|
1 rikku
|
2 rikkus, 4 hands
|
1 dand or dhanush
|
2000 dand/ dhanush
|
1 kos
|
4 kos
|
1 yojan
|
500 vyavhar yojan
|
1 praman yojan
|
This praman
yojan is the basic unit by means of which the islands and seas are measured.
For example the diameter of Jambu dweep on which we reside has a diameter of 1 lakh
yojan.
Innumerable soochanguls together equal to one Jagat sreni
i.e the length of lokakash in which all jivas and matter reside. The space is
called Akash which is divided into two parts namely lokaksh and alokakash . In
lokakash all the other 5 dravyas or the elements of the universe are found
namely Jiva, ajiva, kaal, dharmastikaya and adharmastikaya. The volume of
lokakash is equal to cube of Jagat sreni also known as ghan loka. The length of
Jagat sreni is also known as 7 Raju where 343 cube raju is the volume of the
lokakash.
Unit of
Time : Samay As per Jain
scripture the lokakash is packed with units of time known as kaal which is
known as different dravya or one of the six constituents of the universe. The
lokakash is supposed to be comprised of innumerable number ( not infinite) of
pradesh units while alokakash comprises of infinite space units surrounding the
lokakash. While kaal element is packed
through out the universe, it by itself is inert but is the cause of
modification in the jiva and matter at every instant. Hence its function is
that of a catalytic agent. From a practical point of view the time taken by a
single permaanu to cross one pradesh of space is called one samay which is the
smallest unit of time. This is indivisible unit of time far far smaller than
the unit of time which we call “second”.
Innumerable samay units constitute one Avali which is still smaller than second. This
innumerable number is Min Yuktasamkhyat which we have encountered in the
article on infinity ( Jan 09/2017)
The following table represents some of the other time units
Min Yuktasamkhyat
|
1 Avali
|
Numerable Avali
|
1 breath = 2880/3773 seconds
|
7 breaths
|
1 stok
|
7 stok
|
1 love
|
38 ½ love
|
1Ghadi =24 Minutes
|
1 Ghadi= 48 minutes
|
1 Muhurta
|
30 Muhurta
|
24 hours = 1 day
|
30 days
|
1 month
|
12 months
|
1 year
|
However in Jainism the time measurement needed to be far far
higher than years. Even millions of years are not sufficient to define age of a
typical Heaven or Hell resident. Hence another type of unit is used which is
called Upama Maan i.e. the unit defined
by Simile or Anology.
Upama
Maan Imagine a well having the diameter of 1 Praman Yojan and a
depth of 1 Praman Yojan. This filled to the brim with the tips of the hair of
newborn sheep ( which is born in superior Bhoga Bhumi , where the hair is
thinnest). The number of hair in this
well is called one Palya or Palyopam. This number can be computed to be equal
to a 45 digit number. Now take out one hair at an interval of 100 years each.
The period in which all the hair are taken out, measured in number of samay
units is equal to the number of samay in one Vyavhar Palyopam.
Now
multiplying this with number of samay of innumerable years give rise to number
of samay of Uddhar Palyopam. Further multiplying with another number of samay
of innumberable years give rise to number of samay of Addha Palyopam. 10 Koda
Kodi of Addha palya is equal to one Addha Sagar which is a major unit of
measurement of life span in heaven or hell, period of Karmas and so on. One
koda kodi represents one karod karod or 105x105.
Incidentally the analogy of Sagar is
quite apt because this one sagar period would be the time taken to empty the
water of Lavan Sea with surrounds our Jambu dweep taken at a specific rate.
Further
the place like Bharat Kshetra where we reside undergoes time cycle of upward or
downward trend. Currently we are undergoing downward trend known as Avasarpini
Kaal. This duration is total of 10 Koda Kodi Sagar in which we positioned
at about 2500 years of the fifth period
known as Dushma kaal. This cycle would terminate at about 39500 years from now
and the Utsarpini kaal of 10 koda kodi sagar would start. Thus 20 koda kodi
sagar constitute one kalpa kaal.
Conclusion The purpose of such units of time and space
demonstrates the limitless of time and space as told by the omniscient. It also conveys to
us the insignificance of our life span compared to the millions and millions of
years in which we are migrating from one form to another without reaching any
type of destination. If we take a look at the presentation of Panch Paravartan
, it would be more clear to us. Typically the Jivas have a maximum life span of 2000 sagar in
which they take birth as two sensed or
above life form , after which invariably
they revert to one sensed life form in which they may spent unlimited years.
Hence the urgency for self realization is felt more strongly if we keep in mind this
fact.