MultiDimensions of Time and Space in Manasara
[This Article of Dr. S. K.
Kapoor is published in January 2002 issue of Vedic Vastu Sandesh, Indore,
India.]
PART I : VEDIC WISDOM
VEDIC WISDOM
Vedic wisdom is lively in the
consciousness of living saints. It is also well preserved in the Vedic
literature. The inner evidence of the available Vedic knowledge of the available
Vedic literature makes it out that originally the whole range of the pure
knowledge i.e. Vedic knowledge was vibrating from a single wholesome Ved.
Subsequently this knowledge was organized by Maharishi Ved Vyas as four Veds
namely. Rigved, Yajurved, Samved and Atharvved.
The knowledge of Rigved
admitted 21 branches while the knowledge of other three Veds namely, Yajurved,
Samved and Atharvved respectively admitted 101, 1000 & 9 branches. The
organizational format of each Vedic branch consisted of four folds designated as
Samhita, Brahmana, Aryanak and Upanishad. As such 21+101+1000+9=1131 Vedic
branches had 1131 Samhitas, 1131 Brahmanas, 1131 Arynaks and 1131 Upanishads.
These 1131x4 = 4524 scriptures together came to be known as Vedic wisdom. In
addition corresponding to each Ved, as applied value of the pure knowledge of
the Ved is Upved. The four Upveds are Ayurved, Dhanurved, Gandharvved and
Sthapathyaved. Our present day mathematics, science and technology come within
the range of Sthapatyaupved. Manasara is one such scripture of Sthapatyaupved.
MANASARA :
SCRIPTURE OF STHAPATYAUPVED
Sri Prasana Kumar Acharya had
done a wonderful job of reconstructing the text of Manasara and preparing its
translation in English and by drawing the plates.
The scripture begins with the
prayer to Lord Brahma, the Creator, the supreme and ends with the chiseling of
third eye of the idol of Lord Shiv. The broad organization of the scripture is
of the range of 70 chapters with first eight chapters constituting a primary
groupI. The next ten chapters i.e. chapter 9 to 18 constitute a primary
groupII. Then comes the central part of the Mansara. Chapter 19 to 30 cover
single story building to 12 storied buildings. These 12 chapters constitute a
central groupI. Next 20 chapters i.e. chapters 31 to chapter 50 cover central
groupII and with it the subject of architecture as such is completed. Then
follows the subject of sculptures. The science of sculptures covered in chapters
51 to 70 can be organizationally divided in two sculptural groups. Chapter 51 to
65 constitute sculptural groupI and chapters 66 to 70 constitute sculptural
groupII.
SPACE TIME FRAME
The above topical division of
the text has an organizational message of great importance as in terms of it we
may reach at the geometric format of the organization of the knowledge of the
scripture.
As the scripture begins with
the prayer to Lord Brahma, the overlord of real 4space and ends with the
chiseling of third eye of Lord Shiv, the overlord of real 5space, therefore,
geometric format at the dimensional level is bound to be spatial with the flux
of time being solid.
In short, the spacetime frame
at the dimensional level is going to be E^{2} (space) × E^{3}
(time). In terms of this dimensional order we shall be manifesting working
geometric domain within the spacetime frame (E^{2})^{4} (space)
x E^{3} (solid time). Here (today) we shall be concentrating upon the
concepts and comprehensions of dimensions of space and time in Manasara. In a
way, we shall be taking up the topic of space, time and spacetime in the light
of Vedic wisdom. In the context, it may be relevant to note that the modern
thought, mathematics, science and technology is speculating the general
spacetime frame as E^{3} (space) × E^{1} (linear time).
The modern thought,
mathematics, science and technology centre around linear dimensional reality but
the Vedic systems avail multidimensional reality. The studies of the
organizational formats of various Vedic scriptures reveal that higher
dimensional geometric formats are being availed to organize the pure knowledge.
Illustratively, we may take the case of the oldest book of mankind namely, Sakla
Rigved Samhita.
RIG VED SAMHITA
Fortunately Rigved Samhita is
intact with us from first syllable to the last syllable and as the tradition
goes, the whole range of Vedic knowledge is lively in this scripture of 432000
syllables, out of which 397265 syllables are manifest text while remaining 34735
syllables go deep as organisational format of the text and as such remain
unmanifest.
For the present, we may accept
it an axiom that knowledge and organisation of knowledge are two distinct
aspects of knowledge. Being scriptural text, we get the organised knowledge and
as such both organisation format and the text are to be accepted as the
knowledge content of the scripture. It is like a truck with goods yielding
weight of the truck as well as of the goods loaded in the truck.
Organisation of Rigved Samhita
Total knowledge contents

432000 Syllables

Manifest text

397265 Syllables

Mandals

10

Ashtaks

08

Chapters

64

Anuvaks

85

Suktas

1028

Vargas

2024

Richas

10552

Mathematical Basis
Mathematical basis of the
organisational format of the Rigved Samhita reveals that the Vedic knowledge is
organised on geometric format of real 6space. It admits 4space in the role of
dimension while modern thought, mathematics, science and technology centre
around 3space reality and as such Veds are invincible fort for the modern mind.
As such, we have to learn and understand the Vedic wisdom. For this we have to
reexamine the rationale and basis of our axioms and postulates for accepting
the reality as linear dimensional one. It is only by approaching the Vedic
knowledge, the Vedic way, that we may have real bliss of Vedic wisdom.
PART II : HIGHER
DIMENSIONAL REALITY
MATHEMATICAL
BASIS OF VEDIC LITERATURE
Studies of mathematical basis
of available Vedic literature reveal that 4 and higher dimensional reality was
not only known to the Vedic seers rather the great use thereof was made by them
for organization of pure knowledge.
Let us concentrate upon the
nature of space around us. We can see that straight line is a track of a moving
point while plane is a track of a moving (straight) line. Likewise, moving plane
shall be creating solid space. More precisely, if we reinvestigate this
phenomenon with the help of a point, interval, square and cube, we shall be
noticing that moving point accepts line as its track, moving interval accepts
square as its track and moving square accepts cube as its track. This would pose
a question: What is the nature of the track of moving cube/solid /3space body/
3space setup or in the general, 3space it self?
HYPERCUBES 4, 5,
& 6
To answer the same let us
mathematise this situation as:
Taking point as a
representative regular body of 0 space, interval, square and cube respectively
as representative regular bodies of 1, 2 & 3 space, we may conclude that moving
0space (body) accepts 1space format, moving 1space (body) accepts 2space
format; moving 2space body accepts 3space format, and as a logical consequence
the moving 3space body shall be requiring 4space format. And in general,
moving nspace body shall be requiring (n+1) space format. For convenient
handling.
We may define and designate
four and higher dimensional bodies in continuation of interval, square and cube
as hypercubes. To be precise hypercube 4 shall be a representative regular body
of 5space and so on. Further to facilitate comprehension of main properties of
hypercube and for symbolic representation of the set of properties synthesizing
hypercube it would be desirable to have suitable symbols for them, particularly
for hypercube 4, 5 and 6 for reaching at the concepts and comprehension of
multidimensional spacetime frame being availed for organization of the
knowledge of Manasara.
Let these 3 special symbols of
hypercube 4, 5 & 6 be as:
To have these symbols in
continuity of the geometric setup of interval, square and cube, we have to first
comprehend these geometric setups. As such, let us have a close look at the
geometric setup of interval, square and cube. If we have close look at the
geometric setup of interval, square and cube, we may comprehend that interval
has length (A^{1}) and 2 boundary points (2A^{0}) Square has
area (A^{2}) and 4 boundary line (4A^{1}) and cube has volume A^{3}
and 6 boundary surfaces (6A^{2}).
A^{1}:2A^{0}, A^{2}:4A^{1}
and A^{3}.6A^{2} suggest a common formulation A^{n}.2nA^{n1},
n=1, 2, 3.
This formulation would hold for
all values of n. In particular, for n=4 5 & 6 we shall be getting A^{4}:8A^{3},
A^{5}:10A^{4} and A^{6}:12A^{5}. The geometric
message is that boundary of 4space body is constituted by 8 cubes while the
boundary of 5space body is constituted by 10 hypercubes4 and so on.
The boundary components of
interval, square, cube and hypercubes 4, 5 & 6 are in the ratio 2:4:6:8:12.This
would help us comprehend, appreciate and have the symbols of hypercube 4, 5 & 6
in continuity of and in that sequential order, hypercube 4, 5 & 6 with
boundaries as:
SHANDCHAKRA
FORMAT OF HUMAN BODY
Further it would help us
comprehend and appreciate the Upanishad knowledge regarding the Shadchakra
format of human body as that:
Here are being taken up the
external structural characteristics (of shad chakras format of Human body) These
with respect to the chakras (second to six) which are ahead of the tip of the
nose (first chakra with two characteristics) are four, six, eight ten and twelve
respectively, and in that order.
(Advettarko Upanishad)
The message of great importance
is that Vedic Comprehension of human body is of Shadchakra format which runs
parallel to the geometric formats of representative bodies of first six spaces
and hence this makes Purusha, the being of 6space.
This will help us comprehend
and appreciate the Vedic tradition which accepts Vedic Richas / Mantras as
impulses of one's own consciousness. Here there is another aspect of our
existence phenomenon. One breaths 21600 times a day. Equally one would breath
21600 times during night. This makes day and night breathings as of 43200 units.
Now those who do Pranayam (deep berating) 10 times deep than the normal
breathing, they shall be breathing whole length of Rigved of 432000 syllables.
That is, one breaths, lives and attains consciousness of the order of Rigved
every day and nigh of his existence.
Lord Brahama, Lord Shiv and
Lord Vishnu together are known as Trinity of Gods. Studies into mathematical
basis of the knowledge of Trinity of Gods preserved in the available Vedic
Literature show a complete parallelism between four heads of Lord Brahma and
four dimensions of 4space; five heads of Lord Shiv and five dimensions of
5space; and six heads of incarnations of Lord Vishnu and six dimensions of
6space. The detailed studies of idols of Trinity of Gods further take us to
their geometric formats respectively being of hypercube 4, 5 & 6.
DIMENSIONS AND
SPACES
Since our school mathematics,
we draw three axes as depicted below as three dimensions of three dimensional
frame of three dimensional space.
The message is that we are
accepting line as a dimension of 3space and as such three lines together
constitute a three dimensional frame. This in fact is a particular case of
general rule that (n2) space plays the role of dimension of nspace. In modern
mathematics as well mental constructs of higher dimensional spaces have been
speculated but their dimension always remains a line i.e. 1space. Obviously
this concept is bound to recoil as it would make dimension and space
indistinguishable at least in 1space where 1space is to be accepted as its own
dimension. On the contrary, the rule of difference of space and its dimension as
being of two units is well preserved in Ramayana as well as in Mahrabharatam.
The narrations are that when the Arm of Lord Rama chased KagBhushandi a
difference remained only of two Anguls till Brahmanlok. Likewise when Mother
Yashoda tried to tie child Krishna, She found that every string was short by two
Anguls.
The great message is that the
‘measures’ for the measuring rod are bound to be of two units less. The
Manasara, the scripture of Sathapatyaupved of Atharvved, accordingly accepts
Lord Vishnu (six heads lord) as lord of measuring rod and Lord Brahma (four
heads lord) as lord of measure. In geometric language it means that 4space
plays the role of dimension of 6space.
Mythologically manifestations
as idols, accepts head of the idol as format of dimension and eyes of the head
together to synthesize a dimensional frame for the dimension.
FORMAT OF IDOLS
We may tabulate the following
parallelism between the manifested idols of Trinity of Gods and the geometric
set ups of hypercubes 4, 5 & 6 as geometric formats.
Sr.No

Idol

Representative Geometric body

1

Number of heads

Number of dimensions of head

2

Head

Dimension of the space

3

Number of eyes in the head

Dimensional frame for the dimensions

4

Lotus (of 8 petals)

Hypercube4

5

Lotus

Four space

6

Lotus seat

Hypercube4 as domain

7

Lotus feet

Hypercube4 as boundary

8

Lotus eye

Hypercube4 as dimension

UPNISHADIC
ENLIGHTNMENT
Upanishads and Purans
particularly Sri Sri Brahmpuran, Shivpuran and Vishnupuran enlighten us about
Trinity of Gods as:
Lord Brahma : Lord Brahma is a four heads lord with two eyes in
His each head. He sits majestically on a lotus seat of eight petals. He
meditates on His lord (Lord Shiv) in heart and transcends to Shivlok where He
multiplies Himself as ten Brahmas of four heads each.
The geometric message of the
enlightenment can be decoded in terms of the following complete parallelism
between the idol of Lord Brahma and geometric setup of Hypercube4.
Sr.No

Idol of Lord Brahma

Geometrical set up of hypercube5

1

Four heads

Four dimensions

2

Two eyes

Spatial dimensions 2space as dimension
of 4space

3

Eight petals

Eight solid boundary components (A^{4}:8A^{3})

4

Heart

Origin / Centre

5

Lord of Lord Brahma

5space as origin of 4space

6

Ten Brahmas

10 hypercubes4 as boundary of
hypercube5 (A^{5}:10A^{4})

(Dr. Dharmesh Shukla has worked
out the details in his doctoral thesis titled “Some properties of real 4space
in the light of Vedic knowledge accepted (1994) by H.N. Bahuguna University,
Uttar Pradesh).
Lord Shiv: Lord Shiv is a five heads lord with three eyes in His
each head. He has ten beautiful arms. Sri Sri Shiv Mahanpuran enlightens us that
Hanumanji is incarnation of Lord Shiv. Ramayana enlightens us that Lord Rama,
the incarnation of Lord Vishnu, resides in the heart of Hanumanji.
The geometric message of this
enlightenment can be decoded in terms of the following complete parallelism
between the idol of Lord Shiv and geometric setup of Hypercubes5.
Sr.No

Idol of Lord Shiv

Geometrical set up of hypercube5

1

Five heads

Five dimensions

2

Three eyes

Solid dimensions / 3space as dimension
of 5space

3

Ten arms

Ten hypersolid boundary components (A^{5}:10A^{4})

4

Heart

Origin / Centre

5

Lord of Lord Shiv

6space as origin of 5space

6

Dwadas Adityas

12 hypercubes5 as (12 Suns) boundary of
hypercube6 (A^{6}:12A^{5})

The Thesis of Sh. Bidyadhar
Panda titled “Some Properties of real five space in the light of Vedic knowledge
works out the details of geometric seup of hypercube 5 and real 5 space of Vedic
Comprehension and establishes Sri Sri Shiv Mahapuran as text book of real 5
space.
These two these deserve to be
published for research scholars.
MANIFESTATION
LAYERS
In the light of the above, if
we may have a fresh look at the geometric set up of a cube. We shall be noticing
that the 3space content/lump manifesting as “volume” of the cube is wrapped
within 2space surface (2space content/sheets). Further, we know that this is
the organization which admits linear dimensional order i.e. 1space in the role
of dimension. Now, if we concentrate upon the center of the cube, we shall be
noticing that 8 subcube are synthesized as a cube. We may view center of the
cube as being wrapped within 8 cubes. This is parallel to the cut of 3space by
dimensional frame into 8 octants. As such, the formulation A^{4}:8A^{3}
of hypercube4 being availed by Lord Brahma to manifest as an idol would help us
comprehend that at center of the cube like at the origin of the 3 dimensional
frame is sealed 4space.
The origin/center, the
domain/volume, the boundary/ surface and linear dimension of cube are four
distinct folds of four distinct spaces which together synthesis and manifest
geometric setup of a cube. Therefore, the great geometric message is that our
physical workd/3space/cube/macro world is the first manifestation layer with
1space playing the role of dimension, 2 pace playing the role of boundary,
3space playing the role of domain and 4space playing the role of origin.
Likewise, the world of Lord Brahma i.e. the real 4space, is the micro world
manifestation layer of second order as 2space plays the role of dimension,
3space plays the role of boundary, 4space plays the role of domain and 5space
plays the role of origin. In general, the manifestation layer of order n shall
be accepting nspace in the role of dimension and (n+3) space in the role of
origin.
The Lord Brahma, the Creator of
Supreme, creates reality as manifestation layer of 4 consecutive spaces
synthesizing together. This creation accepts origin in a sealed state. It is a
dormant state. The transcendence from one manifestation layer to another
manifestation layer requires unlocking of the seal of origin fold. This as such
becomes possible only on 5space format. Therefore, Lord Shiv, the transformer
the Supreme, is the Lord of transcendence. Accordingly, in Shivlok exists
vibrant synthetic setup of 5 folds where transcendence from manifestation layer
to another manifestation layer becomes possible.
VIBRANT SYNTHETIC
REALITY
Vedic Model of vibrant
synthetic reality of 5space format is a multidimensional format of space and
time. It takes account of transcendence through manifestation layers as flux of
time. The transition from spatial dimensional order to the solid dimensional
order is worked out as a flux of time of 4space reality which takes us to
5space reality. In concrete terms, the dimensional order of manifested world
being spatial, it attains transition in terms of solid dimensional order of
time, being of solid dimensional order. The time flux crystallizes as a
trimonad i.e. the dimensional constituent i.e. monads as of three parts. This
trimonad format of time when supplied to the manifested bodies of the
manifestation layers, it works out (2n+1) versions of the manifested bodies. In
geometric language, it simply means that the interval, square, cube and
hypercube, as representative regular bodies of the respective dimensional space,
in the roles of domain fold of respective manifestation layers, shall be
accepting (2n+1) versions or in other words, (2n+1) geometries.
Illustratively for n=1, we
shall be having 3 geometries of 1space or in other words, we shall be having 3
versions of an interval designated as close interval, halfopen interval and
open interval. These versions of intervals are having common domain (length) and
they differ only in terms of the boundary components (points). Close interval
accepts 2 boundary points, while halfopen interval accepts one boundary
component and open interval is devoid of both the boundary points. For n=2, we
shall be having 5 geometries of 2space or in other words, we shall be having 5
version of a square in terms, of 4, 3, 2, 1 & 0 boundary lines and for n=3, we
shall be having 7 geometries / versions of 3 space / cube in terms of 6, 5, 4,
3, 2, 1, 0 surface plates and so on.
In 3space, we shall be having
1space as dimension. The flux of time would be of spatial order. 2space admits
5 geometries. The 3 dimensions plus 5 versions would give us 3+5=8 order. In
terms of it, we shall be attaining 8 = 2x4 i.e. 4 spatial dimensions which shall
be constituting dimensional order of 4space. This is how the spatial time flux
shall be working out transition from linear dimensional order / space i.e.
3space to spatial dimensional order / space i.e. 4space. Likewise, in 4space,
we shall be having 2space as dimension and 3space as flux of time. 3space
admits 7 versions. The dimensional order of 3space admits 7 versions. The
dimensional order of 4space would yield 2x4 order. This 2x4 order plus 7
versions shall be yielding 8+7 = 15 order. In terms of it we shall be attaining
15=3x5 i.e. 5 solid dimensions which shall be constituting dimensional order of
5space. This is how the solid time flux shall be working out transition from
spatial dimensional order space i.e. 4space to solid dimensional order space
i.e. 5space.
Therefore for proper
appreciation of vibrant synthetic reality of Vedic comprehension, we have to
work out the Vedic Knowledge, the Vedic way. The geometric continuum is at play
around us. The organizational format of Srimad Bhagwad Gita, the eternal song of
Lord Krishna, makes complete use of real 6space. This may be depicted as
studyzone of Srimad Bhagwad Gita as under :
The organization of Manasara
runs parallet to the study zone of Srimad Bhagwad Gita. This also runs parallel
to the Shad Chakra format of Human body. The organizational format of nucleus of
the nucleus as well avails this zone where Jyoti flows from core of the sun into
the core of the Sanatana base as 7 streams. This flow is channelised on Om
Formulation of 4 components as a Divya Ganga flow. This is a complete discipline
in itself. At present we may not be in a position to enter into the details of
this Vedic discipline of channelization into the Sanatana base but it may not be
out of context to make a mention that advanced students of Vedic Science and
Technology have to learn about it.
PART III :
ORGANISATION OF MANASARA
PRAYER OF LORD
BHAHMA TO CHISELING OF EYE OF LORD SHIV
Opening Prayer of Lord Brahma
He (Brahma), while causing the
creation, the preservation, and the destruction of the worlds, brings forth
earth, water, fire, air, and the sky. I bow to (His) lotuslike feet kissed by
the waving lines of beelike crowns of the kings of various gods. (Manasara Chapter1 Shaloka 2)
Chapter LXX : The Chiseling
of the Eye
12 the chiseling of the eye of
the (idols of the ) gods, goddesses, and devotees, and the purification
(cleansing) of the phalli (of Shiva) will be described in order of the subject.
396 …………….
97. The Chief architect should
show (to the idol) the Mudra signs (with his hands as the concluding ceremony)
amidst music and songs.
98111 The circumambulation of
the village by the idol.
98.Thus is described the
chiseling of the eye. After this should be (performed) the circumambulation of
the village (by the idol).
99114 ………..
115118. This great science (of
architecture) was at first revealed by Brahma, Indra, and all other gods: It is
from their statements that this Manasara (the essence of measurement) has been
complied as a guide book (for the architects ) for the benefit of the people.
Thus in the Manasara, the
science of architecture, the seventieth chapter, entitled.
The description of the
chiseling of the eye (of image). The Manasara is complete.
SRI SHRI SHIV
MAHAPURAN
Lord Shiv is the overlord of
real 5space. Sri Sri Shiv Mahapuran is a text book of real 5space. The
organizational format of Sri Sri Shiv Mahanpuran is the organizational format of
real 5space. The scripture is organized as Samhitas parallel to 7 dimensions of
7space.
5space plays the role of
dimension of 7space and as such each of the 7 Samhitas of Sri Sri Shiv
Mahanpuran enlightens us about one or the other aspect of the knowledge of real
5space in the role of dimension.
These 7 Samhitas are organized
as 12 parts. This is parallel to 12 boundary components of real 6space. Each
boundary component of real 6space is a 5space set up. Therefore, these 12
parts are the organisation of 7 Samhitas of Sri Sri Shiv Mahapuran as boundary
of 6space.
The 7 Samhitas of Sri Sri
Mahapuran consisting of 12 parts are further organised as chapters and chapters
are further organised as Shlokas. These organisations accept formats of real
5space. The knowledge content of each chapter and the orgnizational format of
each chapter work out one or other aspect of real 5space.
The first chapter of first
Samhita of Sri Sri Shiv Mahapuran posses a question as (that): What is the
shortest way to salvation? And the great Rishi remembers Lord Shiv and gets
prepared for answering the same. This that way would help us comprehend and
appreciate that the question being posed and the answer which is going to follow
is to be about Lord Shiv.
The manifestation which is
being talked to be transcended through is the manifestation of real 4space. As
such the first chapter of the first Samhlta takes us to the format of
hypercube4 with a sealed origin. The great concern being shown by the sages
(Munis) to the great Rishi is about the spatial nature of the setup of 4space
and the question being raised is how this manifestation can be transcended
through.
Naturally, the great Rishi
concentrates upon the origin and prepares for answering the question by
remembering Lord Shiv. Who is the overlord or real 5space playing the role of
origin and remaining in dormant state in the sealed origin. Therefore,
contentwise, Shi Sri Shiv Mahapuran beings with the geometric format of
hypercube4 with sealed origin. Likewise, the Manasara opens with the prayer to
Lord Brahama and ends with the chiseling of an eye with which the seal of the
origin would be unlocked and transcendence would take place and the 5space
coming into play and 4space content resoling back to the boundary of 5space.
The knowledge content of Sri
Sri Shiv Mahapuran deserves to be imbibed by all the students of mathematics,
science and technology of Vedic Order. Sri Sri Shiv Mahapuran is a complete
course in itself and it may not be possible to go into details at present.
ORGANIZATIONAL
FORMAT OF MANASARA
The great design of nature is
imprinted in each grain of Nature. Vedic Comprehension of this design
conceptualises as Bindu "Sarowar". This grand unification of Trinity of Gods in
each point reservoir of nature (Bindu Sarowar) may be viewed as the Trinity of
Gods as first three folds and their unification as the fourth fold. In concrete
terms, this amounts to 4space playing the role of dimension for the
organisational format of the great design of Bindu Sarowar and 5space playing
the role of boundary there of and 6space manifesting as their domain fold and
7space as origin thereof.
It is this grand design which
is availed by the Vedic scriptures to organise the pure knowledge. The aim of
Manasara as well is to avail this grand design of nature. The 7space flows as 7
streams of Divya Ganga from core of the Sun; the sun being the body of 6space
and its core being the 7space as origin of 6space. The Divya Ganga flow from
core of the sun (6space) takes to the Sanatana base (5space in the role of
boundary of 6space). Being vibrant synthetic reality this flow is going to be
of vibrant and synthetic as reality. It is going to be of two parts.
Accordingly, the Jyoti flowing from core of the Sun shall be flowing into the
Sanantna base on either side of the Sun. This would help us appreciate and
comprehend the Jyoti flow of 7 streams into Sanatana base (5space) as of 7x5
=35 units on either side of the Sun and thereby we shall be having the flow rate
of 35+ 35 = 70 units. It is this flow rate which runs parallel to the first
organisation fo the knowledge of Manasara as of 70 chapters.
The whole range of organization
of 70 chapters is in fact the organization of the great design of the Bindu
Sarowar. This range with definite end points shall be making it a close range of
1+70+1 = 72 units. This would completely wrap 6space within 5space boundary.
With the help of the geometric set up of hypercube6 as representative body of
real 6space on synthetic format of dimonad i.e. monad of two parts would
provide us domainboundary ratio A^{6}:12A^{5}. The complete
Jyoti flow from core of the Sun ( 6space) into the Sanatana base ( 5space) as
boundary of 12 components as through 6 dimensions of the Sun, (this flow) would
be at the rate of 12x6 = 72 units. This also would help us comprehend and
appreciate the sequential state of the this organization in the sequential order
of 2x1, 2x2, 6x3, 8x4, 10x5 & 12x6 of the atomic organization. In fact this six
steps long sequential order would take us uptill the nucleus of the nucleus of
the atom. This also would help us comprehend and appreciate the Manasara
accepting Lord Vishnu, the lord of 6space as the god of the measuringrod.
Now if we have a close look at
the subject matter of the 70 chapters of Manasara, we shall be noticing that
first 8 chapters constitute one topic. This is parallel to the boundary of
hypercube4 being of 8 components. Therefore the organizational format of the
first 8 chapters of Mansara is the format of 8 components of boundary of
hypercube 4. The next 10 chapters constitute one topic. This is parallel to 10
components boundary format of hypercube 5.
The next set of 12 chapters
i.e. chapter 19 to 30 topically take up one story building to 12 storied
building. This is parallel to the 12 components boundary of hypercube6. With
this we shall be reaching the state where we have to tap the Jyoti flow from the
core of the Sun.
The Sun is a body of 6space.
Six space in the role of dimension shall be taking us uptill 9space in the role
of origin. In fact this Jyoti Bindu flowing from the core of the Sun is
accepting 6space (Sun) as dimension, 7space (Saptrishi) as boundary, 8space
(Ashtprakriti) as domain and 9space (Nav Brahm) as origin. This 4 folds Jyoti
Bindu flow is the Divya Ganga flow of 4 folds. Jyoti Bindu flow is the Divya
Ganga flow of 4 folds on the format of OM as formulation of 4 components, first
as the Bindu Sarowar of NavBrahm as of 9 units, the second component of
ArdhaMatra as of 7 units, the third component as TriPundarm of 3 units and
fourth component as Swastik Pada as of 1 unit. Total being of 20 units.
And these 20 units flow would
be on either side and as such we shall be having 20+20 = 40 unit flow which
shall be covering the remaining range of 40 chapters. Topically the 20 chapters
from chapter 31 to 70 would be completing one topic. The organization of the
remaining 20 chapters would get a division, in the context of Manasara as of 15
chapter and 5 chapters.
I have worked out the details
of organizational format of Manasara as 138 graphics as separate compilation
under Vedic Geometrical Series as a treatise for Indian Institute of Mahraishi
Vedic Science & Technology. These graphic plates of the organizational format of
the Manasara take up the organization right uptil the verses and even subverses
of each chapter. Of these, I am using them now to illustrate how the Manasara is
availing geometric format of the great design of the nature in its each grain as
a Bindu Sarowar where in Trinity of Gods unify.
As per this great design we are
getting a great message as that from within the Bindu Sarowar flows a Jyoti
Bindu Sarowar where the Sun, Saptrishi and Ashtaprakiti get unified with
NavBrahm as the origin. This phenomenal emergence of Jyoti Bindu Sarowar from
within the Bindu Sarowar is the transcendental transformation. This
transcendental transformation phenomenon is at work which helps sequential
attainment of consciousness state. Also this transcendental transformation
phenomenon is at work which takes us from seed to the tree and tree to the seed
as a lifespan and a sequential generational flow.
The Jyoti flows from the core
of the Sun into the Sanatana base at boundary of the Sun potentialised the
‘boundary space’ to play the dimensional role. With this 4space dimensional
order of the Sun transforms into the next generational order of 5space in the
role of dimension. It is this generational transformation from dimensional order
of 4space to the dimensional order of 5space is the attainment through the
Divya Ganga flow of Jyoti from core of the Sun. This would help us appreciate
how the organization of chapters 51 to 55 i.e. the set of 15 chapters is one
topic as 15=1+2+3+4+5 which would be conversing the sequential range of 5space.
With this we shall be attaining 5space and hence the remaining 5 chapters and
scripture to end with the chiseling of the third eye of Lord Shiv, the overlord
of real 5space.
MEASURES AND
MEASURINGROD
The concept of measures and
measuringrod of Manasara is of central importance. In fact Mana means measure
and Sara means essence and as such Manasara means essence of measures. The
science of Architecture and Sculpture centers around the essence of measures and
the exactness of the measuringrod. Therefore, the relevant knowledge of
measures and measuring rod of chapter 2 Manasara deserve to be read thoroughly.
The verses 64 & 65 describe the
measuringrod as that: Measuringrod should be one cubic long, one anguls
(three fourth inch) broad, and its thickness is stated to be a half Angul. The
yardstick (lit, cubic measure) should be accurately marked.
The verse 68 enlightens us
that: Vishnu is stated to be the tutelary god of (the wood for) both the
yardstick and the (measuring) rod.
Further, verse 75 enlightens us
that: Vasuki (serpentgod) is the presiding deity of the (measuring) rope,
and Brahama is known as the presiding deity of measurement.
Lord Brahma is a 4 head lord.
Lord Vishnu is a 6 head lord,. Lord Brahama is born from the lotus whose reed
springs from navel of Lord Vishnu. This Puranic comprehension is the Vedic
enlightenment of real 4 space playing the role of dimension of real 6 space and
in general (n2) space plays the role of dimension of n space and thereby there
being always a difference of 2 units between the domain and dimension which
would help us comprehend and appreciate, the knowledge preserved in the epic
stories of the arm of Lord Rama and KagBhushandi of Ramayana and Yashoda Trying
to tie Lord Krishna but every string found to be short by two units.This
fundamental result is at the base of the mathematics which would help avail the
results of arithmetic into geometry and vice versa. In terms of it only, we may
comprehend and appreciate the multidimensions of time and space of Manasara as
well as of other Vedic Scriptures.
PART IV : MULTI
DIMENSIONS OF TIME AND SPACE
CUBIC MODEL OF
TIME AND SPACE
The cubic model of time and
space is E^{2}×E^{3} space time model. The spatial boundary in
the role of dimension manifests real 4space and the solid domain in the role of
dimension manifests real 5space.
This spacetime model works out
smooth transition and continuum from real 4space to real 5space by attaining
transcendence from the manifestation layers. This precisely is being availed in
the organizational of Manasara.
The scripture opens with the
prayer of Lord Brahma, the overlord of real 4space and ends with the chiseling
of third eye of Lord Shiv, the overlord of real 5space. Precisely, this
enlightenment of the transcendence phenomenon of real 5space is the subject
matter of instructions of Sri Sri Shiv Mahapuran, the text book of real 5space.
Therefore, the cubic model of spacetime is the basic spacetime model for working
out the geometric continuum from manifestations layers on the format of real
4space to the transcendence phenomenon on the format of real 5space.
SPHERICAL MODEL
OF TIME AND SPACE
Like cube, sphere is another
representative regular body of 3space. Therefore, parallel to the cubic model
of the spacetime, we shall be having spherical model of spacetime. Here as well
essentially the Cartesian expression for the spacetime frame would be E^{2}×E^{3}
as the surface boundary of the sphere shall be manifesting hypercube4 while the
solid domain of the sphere would be manifesting hypercube5.
The domainboundary ratio of
the cube as well as of the sphere being identical, as such both cubical and
spherical models can be worked parallelly. However, both these models have their
distinct characteristics and hence their distinct utilities and applied values.
The glaring difference between the geometric set ups of cube and sphere lies in
the set ups of their boundaries.
The boundary of cube is
synthetic set up of as many as 6 surface plates while on the other hand the
spatial boundary of the sphere is a single integrated sheet. As such the
architectural designs of vibrant synthetic reality would depend upon our
capacity to exploit the geometric richness of the representative regular bodies
of 3space in the role of dimensions as spacetime formats.
SPACE, TIME AND
SPACETIME OF MANASARA
For proper appreciation of
space, time and spacetime frame of Manasara, we may have a fresh look at the
organizational format of the Manasara. The architectural and sculptural
achievement of this scripture lies in bridging the deep void between the
geometric set up of real 4space and real 5space. It really is bound to be a
mental holocaust to imagine being on the one bank of this deep void and thinking
of reaching the other bank of this deep void.
How to fill the gap in between
the two consecutive integral dimensional spaces? Is the question which is going
to be the cause for mental holocaust as the logic would fail the bridge the deep
void causing holocaust. Mind would feed the meditative brain the supreme order
of nature as a working mechanism of the geometric continuum which runs through
the deep voids in between the integral dimensional spaces in terms of the
spacetime frames with time being one step ahead of the dimensional order of the
start with integral space.
In the instant case of the deep
void in between real 4 & 5space we shall be requiring spacetime frame of
spatial dimensional order of real 5space. Linearly, real 4space is A^{8}
and the solid flux shall be yielding 7 geometries of 3space of linear
dimensional order and hence we shall be having 8+7 = 15 linear dimensions which
shall be working out 15 = 3×5 i.e. 5 solid dimensions for real 5space. The 7
geometries of 3space would be parallel to cube devoid of surfaces; cube with 1
surface, cube with 2 surfaces, cube with 3 surfaces and so on cubes with all the
6 surfaces. Therefore, the deep void of real 4 & 5space would be filled with
the help of 2 space sequentially stitching the boundary of 3space. This
sequential stitching mechanism of the boundary of 3space is the supreme
mechanism of nature in terms of which the geometric continuum is being attained
by having transition through transcendence. Two space as 0 manifestation layer
with 2space playing the role of domain fold shall be admitting 3space in the
dormant state at its origin in a sealed state. With activisation of the dormant
origin, seal of the origin would be unlocked and there would be phenomenal
transformation with transcendence from 0 manifestation layer to 1 manifestation
layer. This transcendence phenomenon starting with the origin of 2space to the
origin of 3space is the life span. It is this span which works out the age of
everything.
MULTIDIMENSIONS
OF TIME AND SPACE
The multidimensions of time
and space as timespace frame for bridging the deep void in between two integral
dimensional spaces and consequential attainment of geometric continuum for the
vibrant synthetic reality of transcendence phenomenon through manifestation
layers is the basic subject of interest for the scientists and technologists.
When like the mechanism of
bridging of the deep void between real 4 & 5space, the deep voids between real
5 & 6 spaces and between real 6 & 7 space stand worked out, it may be possible
for us to have the bliss of Vedic comprehension of the Bindu Sarowar as the
constituent of 6space, Vishnulok, a point of the manifestation layer with
4space in the role of dimensions, 5space in the role of boundary, 6space in
the role of domain and 7space in the role of unity state.
The blissful state is the unity
state of consciousness which can be attended by all of us the Vedic Way through
Transcendental meditation, a phenomenon of 5 space format, parallel to the
transcendence phenomenon which would fill the deep voids between the different
states of consciousness as well as between the different manifestation layers.
PART V : SUM UP
KNOWLEDGE AND
ORGANISATION KNOWLEDGE
We can appreciate the
distinction of knowledge and organization of knowledge in term of an affine
space and metric affine space. In general terms, we may approach this
distinction in terms of space and dimensional space. In more concrete terms, we
can approach it in the context of our physical world in terms of ‘volume’ as
attribute of 3space content and the volume organized as a ‘cube’. The
organization of a cube requires points, lines and surface plates in addition of
the volume, lines and surface plates. All these set ups of points, edges,
surfaces and volume are to be made out of the available content. The unique
mechanism of transformation of an affine space into metric affine space or of
space into dimensional space or of 3space or space into dimensional space or of
3space content as volume into 3space lump as cube has real mathematics which
deserves to be learned.
Great Vedic comprehension of
this mechanism as that the vibrant synthetic reality accepts synthetic monads,
is responsible for manifestation layers with sealed origin, (n2) space playing
the role of dimensional of nspace and the domainboundary ratio of hypercuben
comes to be A^{n}:2nA^{n1}. This makes the dimensional order of
space of two prongs distinct for odd and even dimensional spaces as much as that
odd (2n1) dimensional space shall be having linear dimensional order as (2n+1)
x (2n3) x …….. x3x1 and for even (2n) dimensional space to have linear
dimensional order as 2n x (2n2) x (2n4) x …… x6x4x2.
Further the domains boundaries
sequence shall be yielding sequential ratios for hypercuben as A^{n}:
2nA^{n1}: 2n x 2(n1) x A^{n2} : 2n x 2 (n1) x 2 (n2) x A^{n3}
…….. (till the term A0 ). This sequential order with the above linear
dimensional order for dimensional space and the concept of synthetic monad of n
parts making each part as 1/n, when worked together would yield the answer for
the above great mechanism of nature, which in the language of Ramayana would
mean a difference of two Anguls (measuring units) between the arm of Lord Rama
and KagBhushandi and in the language of Shri Bhagwad Mahapuran that every
string used by Mother Yashoda to bind Lord Krishna turned out to two Anguls
short.
In mathematical language, it
means that the representative regular bodies of dimensional spaces i.e.
interval, square, cube and hypercubes shall be working out a linear sequential
order which shall be transforming respective affine spaces into respective
metric spaces or spaces as dimensional space or space contents (hyper volumes)
as hypercubes which can be expressed as B^{n} = (A+2)^{n} which
means the hypervolume B^{n} remains only as (B2)^{n} and the
remaining content stands consumed by the boundary for wrapping the domain (B2)^{n}.
Now if we work out the above B^{n}
= (A+2)^{n} equation for n=1, 2, 3, 4, and so on, we shall be convincing
ourselves about the above mechanism of the nature. For n=1, we shall be getting
B^{1} = A^{1}+2A^{0}. This straight way follows from the
domainboundary formulation for 1space body. For n=2, we shall be getting B^{2}=A^{2}+4A^{1}+4A^{0}.
Here the first pair of terms follow straight from the domainboundary
formulation of 2space body. The second term 4A^{1} would yield 8A^{0}
boundary components. But here we shall be reaching boundary of the boundary
which means, we shall be taking a synthetic step of two parts to reach the
boundary. This will make each part being of ½ value. Applying this, we shall
be getting boundary of boundary as ½ (8A^{0}) = 4A^{0}.
Likewise, for n=3, we shall be getting B^{3}=A^{3}+6A^{2}+12A^{1}+8A^{0}.
Here as well the first pair of terms follows straight way from the
domainboundary formulation of 3space body. The third term which shall be
taking us to the boundary of the boundary would accordingly can be computed as ½
(4×6A^{21}) = 12A^{1}. By the same logic we shall be reaching
the next term as 1/3 (2x12A^{11}) for n=4, 5, 6 and so on.
Now let us appreciate the above
mathematics in terms of the geometric set ups of close interval, square and cube
and we shall be comprehending that the equation B^{n} = (A+2)^{n}
for n=1 yields the geometric set up of close interval as length (A^{1})
with two end points (2A^{0}), for n=2 yields the geometric set up square
as area (A^{2}) with four boundary lines (4A^{1}) and four end
points (4A^{0}) and for n=3 yields the geometric set up of cube as
volume (A^{3}) with six surface plates (6A^{2}), 12 edges (12A^{1})
and 8 corner points (8A^{0}).
This will help us appreciate
the greatness of Vedic model. Further this will also help us appreciate how B^{n}
remains (B2)^{n} as domain in the synthetic set up and the remaining
content is consumed by the boundary of (B2)^{n} as domain and this
would be a never ending sequence which impliedly means, we shall be exhausting
the contents and even logically would be demanding the existence in a void, the
impossibility, which is the rule of adinfinitum reduction and this will prove
the Fermat’s last theorem as that z^{n} = X^{n} + y^{n}
and (z2)^{n} = (xn)^{n} + (y2)^{n} can not hold
simultaneously. Accordingly, every Vedic scriptural organizational has a great
mathematics in store for us.
LORD SHIV, SUN,
MAN, ATOM AND MANASARA
Lord Vishnu, is the Lord of
real 6space. The seat of Lord Vishnu is the heat of Lord Shiv. 6space is
located at the organ of 5space. Dwadash Adityas (12 suns) are the 12 boundary
components of hypercube6. As many as 12 hypercube5 are required to constitute
the boundary of hypercube6. Lord Shiv meditates upon His Lord Vishnu and
multiplies 12 folds into Vishnulok. Isha punished enlightens us that Purusha,
in the sun is Lord Vishnu. Ayurved enlightens us that Pursuha is constituted by
6 Dhatus and Atman is the 6th Dhathu. First five Dhatus are Panchmahabhut. Lord
Shiv is the Lord of Panchmahabhut. Lord Vishnu is the Atman. The studies of the
set up of the atom also leads us to the conclusion that electronic configuration
around the nucleus i.e the micro world accepts for format of hypercube4 while
nucleus itself concepts for format of hypercube 4 while nucleus of the nucleus
would accept the format of hyupercube6, Mansara accepts Lord Vishnu, the
overlord of 6space as the Lord of the measuring rod. Lord Brahama, the four
head lord is the Lord of measure. Manasara begins with the prayer of Lord Brahma
and ends with the chiseling of the eye of the Lord. As such the conclusion comes
to be that Manasara adopts the orgnizational format of hypercube 5 at the
boundary of hypercube6 which would be parallel to the worlds of Lord Shiv,
Aditya, Panchmahabhut and nucleus of the atom.
SPACETIME FRAM OF
MANSARA
The spacetime frame of Manasara
as such is the spacetime frame of hypercube4 transcending into hypercube5.
This is a transition through transcendence from the spatial dimensional order
into solid dimensional order. As such practically this would amount to
acceptance of cube or sphere as representative bodies of 3space in the role of
dimensions. The spatial boundary of the cube shall be creating 4space while the
solid volume shall be creating 5space. This really is very exciting role of
vibrant synthetic world being tamed by the Manasara.
THREE SPACE IN
THE ROLE OF DIMENSION
To have proper comprehension
and appreciation of the organizational set up of Manasara we have to learn the
mathematics & geometry of 3space in the role of dimension. With 3space as
dimension we shall be creating 5space domain with 4space in the role of
boundary and 6space in the role of origin. This is the Panchmahabhut world. We
may compare it with our present day thought mathematics, science and technology
which accepts physical world as a 3space domain.
Cube and sphere are the
representative regular bodies of 3space. They are miniatured replicas of linear
manifestation layers. With sealed origin and unmanifest dimensions, the other
two folds namely, spatial boundary and solid domain when come in action would
create transition through transcendence from hypercube4 to hypercube5. To have
proper appreciation of this phenomenon, we may have a fresh look at the
geometric set up of the cube by viewing it as a cube of 10 units length, 10
units breadth and 10 units height.
We shall be having 1000 unit
cubes synthesized as a single cube of 1000 units volume. If we want to know that
how many edges / pillars we shall be having of this set up of 1000 cubes, then
the answer of Vedic mathematics would be simple in terms of Devnagri numerals 3
and 6 being reflection images of each other like reflection pair 01 and 10. The
trimonad i.e. the monad of three parts shall be yielding 363 and then the
length being 10 units so we shall be having the figure 3630. Let us count for
ourselves and verify this answer.
Now this reflection property of
the light and the visible light spectrum of 7 colours on the one hand and the
need of only seven edges to sequentially connect all the 8 edges on the other
hand and the property that real 4space in linearly A8 would help us appreciate
the interconnection of the artifices of whole numbers 3 & 7 in the context of
3space. In this background, we shall be having a bliss of the first quarter of
fist Mantra of the Atharvved.
Yeh Trishapta Prayanti Vishwa
Trishapta (3&7) wraps Vishwa (this world)
The message is that 3space at
the boundary of 4space is a geometric set up of 3 linear dimensions which can
take us sequentially uptill 7 linear steps.
The domain and boundary are
distinct set ups. If domain represents and becomes the Vedic domain, the
boundary would represent and would becomes the Upved. Sthaptyaved being Upved of
Athavved and Manasara being the scripture of Sthaptyaupved, therefore, we shall
be requiring comprehension of the Vishwa as is the enlightenment of the first
quarter of the first Mantra of the Atharvved to appreciate the organization of
Mansara.
Therefore the conclusion of all
conclusions for us is that for proper learning of Vedic science & technology,
there is a need for redrawing the school mathematics syllabi.
Om Tat Sat Iti
The sole syllable Om is the essence of pure knowledge and it is the truth and
the ultimate