Multi-Dimensions 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 group-I. The next ten chapters i.e. chapter 9 to 18 constitute a primary group-II. 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 group-I. Next 20 chapters i.e. chapters 31 to chapter 50 cover central group-II 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 group-I and chapters 66 to 70 constitute sculptural group-II.

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 4-space and ends with the chiseling of third eye of Lord Shiv, the overlord of real 5-space, 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 E² (space) × E³ (time). In terms of this dimensional order we shall be manifesting working geometric domain within the spacetime frame (E²)⁴ (space) x E³ (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 E³ (space) × E¹ (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 un-manifest.

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 6-space. It admits 4-space in the role of dimension while modern thought, mathematics, science and technology centre around 3-space 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 re-examine 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 /3-space body/ 3-space setup or in the general, 3-space 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 0-space (body) accepts 1-space format, moving 1-space (body) accepts 2-space format; moving 2-space body accepts 3-space format, and as a logical consequence the moving 3-space body shall be requiring 4-space format. And in general, moving n-space 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 5-space 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 multi-dimensional 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 (A¹) and 2 boundary points (2A⁰) Square has area (A²) and 4 boundary line (4A¹) and cube has volume A³ and 6 boundary surfaces (6A²).

A¹:2A⁰, A²:4A¹ and A³.6A² suggest a common formulation Aⁿ.2nA^n-1, n=1, 2, 3.

This formulation would hold for all values of n. In particular, for n=4 5 & 6 we shall be getting A⁴:8A³, A⁵:10A⁴ and A⁶:12A⁵. The geometric message is that boundary of 4-space body is constituted by 8 cubes while the boundary of 5-space body is constituted by 10 hypercubes-4 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.

(Advet-tarko 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 6-space.

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 4-space; five heads of Lord Shiv and five dimensions of 5-space; and six heads of incarnations of Lord Vishnu and six dimensions of 6-space. 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 3-space and as such three lines together constitute a three dimensional frame. This in fact is a particular case of general rule that (n-2) space plays the role of dimension of n-space. In modern mathematics as well mental constructs of higher dimensional spaces have been speculated but their dimension always remains a line i.e. 1-space. Obviously this concept is bound to recoil as it would make dimension and space indistinguishable at least in 1-space where 1-space 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 Kag-Bhushandi a difference remained only of two Anguls till Brahman-lok. 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 4-space plays the role of dimension of 6-space.

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)	Hypercube-4
5	Lotus	Four space
6	Lotus seat	Hypercube-4 as domain
7	Lotus feet	Hypercube-4 as boundary
8	Lotus eye	Hypercube-4 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 Hypercube-4.

Sr.No	Idol of Lord Brahma	Geometrical set up of hypercube-5
1	Four heads	Four dimensions
2	Two eyes	Spatial dimensions 2-space as dimension of 4-space
3	Eight petals	Eight solid boundary components (A⁴:8A³)
4	Heart	Origin / Centre
5	Lord of Lord Brahma	5-space as origin of 4-space
6	Ten Brahmas	10 hypercubes-4 as boundary of hypercube-5 (A⁵:10A⁴)

(Dr. Dharmesh Shukla has worked out the details in his doctoral thesis titled “Some properties of real 4-space 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 Hypercubes-5.

Sr.No	Idol of Lord Shiv	Geometrical set up of hypercube-5
1	Five heads	Five dimensions
2	Three eyes	Solid dimensions / 3-space as dimension of 5-space
3	Ten arms	Ten hypersolid boundary components (A⁵:10A⁴)
4	Heart	Origin / Centre
5	Lord of Lord Shiv	6-space as origin of 5-space
6	Dwadas Adityas	12 hypercubes-5 as (12 Suns) boundary of hypercube-6 (A⁶:12A⁵)

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 3-space content/lump manifesting as “volume” of the cube is wrapped within 2-space surface (2-space content/sheets). Further, we know that this is the organization which admits linear dimensional order i.e. 1-space in the role of dimension. Now, if we concentrate upon the center of the cube, we shall be noticing that 8 sub-cube 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 3-space by dimensional frame into 8 octants. As such, the formulation A⁴:8A³ of hypercube-4 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 4-space.

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/3-space/cube/macro world is the first manifestation layer with 1-space playing the role of dimension, 2 -pace playing the role of boundary, 3-space playing the role of domain and 4-space playing the role of origin. Likewise, the world of Lord Brahma i.e. the real 4-space, is the micro world manifestation layer of second order as 2-space plays the role of dimension, 3-space plays the role of boundary, 4-space plays the role of domain and 5-space plays the role of origin. In general, the manifestation layer of order n shall be accepting n-space 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 5-space 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 5-space format is a multi-dimensional 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 4-space reality which takes us to 5-space 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 tri-monad i.e. the dimensional constituent i.e. monads as of three parts. This tri-monad 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 1-space or in other words, we shall be having 3 versions of an interval designated as close interval, half-open 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 half-open 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 2-space 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 3-space, we shall be having 1-space as dimension. The flux of time would be of spatial order. 2-space 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 4-space. This is how the spatial time flux shall be working out transition from linear dimensional order / space i.e. 3-space to spatial dimensional order / space i.e. 4-space. Likewise, in 4-space, we shall be having 2-space as dimension and 3-space as flux of time. 3-space admits 7 versions. The dimensional order of 3-space admits 7 versions. The dimensional order of 4-space 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 5-space. This is how the solid time flux shall be working out transition from spatial dimensional order space i.e. 4-space to solid dimensional order space i.e. 5-space.

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 6-space. This may be depicted as study-zone 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) lotus-like feet kissed by the waving lines of bee-like crowns of the kings of various gods. (Manasara Chapter-1 Shaloka 2)

Chapter LXX : The Chiseling of the Eye

1-2 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.

3-96 …………….

97. The Chief architect should show (to the idol) the Mudra signs (with his hands as the concluding ceremony) amidst music and songs.

98-111 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).

99-114 ………..

115-118. 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 5-space. Sri Sri Shiv Mahapuran is a text book of real 5-space. The organizational format of Sri Sri Shiv Mahanpuran is the organizational format of real 5-space. The scripture is organized as Samhitas parallel to 7 dimensions of 7-space.

5-space plays the role of dimension of 7-space 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 5-space in the role of dimension.

These 7 Samhitas are organized as 12 parts. This is parallel to 12 boundary components of real 6-space. Each boundary component of real 6-space is a 5-space set up. Therefore, these 12 parts are the organisation of 7 Samhitas of Sri Sri Shiv Mahapuran as boundary of 6-space.

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 5-space. The knowledge content of each chapter and the orgnizational format of each chapter work out one or other aspect of real 5-space.

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 4-space. As such the first chapter of the first Samhlta takes us to the format of hypercube-4 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 4-space 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 5-space playing the role of origin and remaining in dormant state in the sealed origin. Therefore, content-wise, Shi Sri Shiv Mahapuran beings with the geometric format of hypercube-4 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 5-space coming into play and 4-space content resoling back to the boundary of 5-space.

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 4-space playing the role of dimension for the organisational format of the great design of Bindu Sarowar and 5-space playing the role of boundary there of and 6-space manifesting as their domain fold and 7-space 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 7-space flows as 7 streams of Divya Ganga from core of the Sun; the sun being the body of 6-space and its core being the 7-space as origin of 6-space. The Divya Ganga flow from core of the sun (6-space) takes to the Sanatana base (5-space in the role of boundary of 6-space). 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 (5-space) 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 6-space within 5-space boundary. With the help of the geometric set up of hypercube-6 as representative body of real 6-space on synthetic format of di-monad i.e. monad of two parts would provide us domain-boundary ratio A⁶:12A⁵. The complete Jyoti flow from core of the Sun ( 6-space) into the Sanatana base ( 5-space) 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 6-space as the god of the measuring-rod.

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 hypercube-4 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 hypercube-6. 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 6-space. Six space in the role of dimension shall be taking us uptill 9-space in the role of origin. In fact this Jyoti Bindu flowing from the core of the Sun is accepting 6-space (Sun) as dimension, 7-space (Sapt-rishi) as boundary, 8-space (Asht-prakriti) as domain and 9-space (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 Nav-Brahm as of 9 units, the second component of Ardha-Matra as of 7 units, the third component as Tri-Pundarm 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, Sapt-rishi and Ashta-prakiti get unified with Nav-Brahm 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 life-span 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 4-space dimensional order of the Sun transforms into the next generational order of 5-space in the role of dimension. It is this generational transformation from dimensional order of 4-space to the dimensional order of 5-space 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 5-space. With this we shall be attaining 5-space and hence the remaining 5 chapters and scripture to end with the chiseling of the third eye of Lord Shiv, the overlord of real 5-space.

MEASURES AND MEASURING-ROD

The concept of measures and measuring-rod 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 measuring-rod. Therefore, the relevant knowledge of measures and measuring rod of chapter 2 Manasara deserve to be read thoroughly.

The verses 64 & 65 describe the measuring-rod as that: Measuring-rod should be one cubic long, one anguls (three fourth inch) broad, and its thickness is stated to be a half Angul. The yard-stick (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 yard-stick and the (measuring) rod.

Further, verse 75 enlightens us that: Vasuki (serpent-god) 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 (n-2) 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 Kag-Bhushandi 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 multi-dimensions 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 E²×E³ space time model. The spatial boundary in the role of dimension manifests real 4-space and the solid domain in the role of dimension manifests real 5-space.

This spacetime model works out smooth transition and continuum from real 4-space to real 5-space 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 4-space and ends with the chiseling of third eye of Lord Shiv, the overlord of real 5-space. Precisely, this enlightenment of the transcendence phenomenon of real 5-space is the subject matter of instructions of Sri Sri Shiv Mahapuran, the text book of real 5-space. 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 4-space to the transcendence phenomenon on the format of real 5-space.

SPHERICAL MODEL OF TIME AND SPACE

Like cube, sphere is another representative regular body of 3-space. 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 E²×E³ as the surface boundary of the sphere shall be manifesting hypercube-4 while the solid domain of the sphere would be manifesting hypercube-5.

The domain-boundary 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 3-space 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 4-space and real 5-space. 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 & 5-space we shall be requiring spacetime frame of spatial dimensional order of real 5-space. Linearly, real 4-space is A⁸ and the solid flux shall be yielding 7 geometries of 3-space 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 5-space. The 7 geometries of 3-space 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 & 5-space would be filled with the help of 2 space sequentially stitching the boundary of 3-space. This sequential stitching mechanism of the boundary of 3-space 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 2-space playing the role of domain fold shall be admitting 3-space 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 2-space to the origin of 3-space is the life span. It is this span which works out the age of everything.

MULTI-DIMENSIONS OF TIME AND SPACE

The multi-dimensions 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 & 5-space, 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 6-space, Vishnu-lok, a point of the manifestation layer with 4-space in the role of dimensions, 5-space in the role of boundary, 6-space in the role of domain and 7-space 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 3-space 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 3-space or space into dimensional space or of 3-space content as volume into 3-space 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, (n-2) space playing the role of dimensional of n-space and the domain-boundary ratio of hypercube-n comes to be Aⁿ:2nA^n-1. This makes the dimensional order of space of two prongs distinct for odd and even dimensional spaces as much as that odd (2n-1) dimensional space shall be having linear dimensional order as (2n+1) x (2n-3) x …….. x3x1 and for even (2n) dimensional space to have linear dimensional order as 2n x (2n-2) x (2n-4) x …… x6x4x2.

Further the domains boundaries sequence shall be yielding sequential ratios for hypercube-n as Aⁿ: 2nA^n-1: 2n x 2(n-1) x A^n-2 : 2n x 2 (n-1) x 2 (n-2) x A^n-3 …….. (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 Kag-Bhushandi 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 Bⁿ = (A+2)ⁿ which means the hypervolume Bⁿ remains only as (B-2)ⁿ and the remaining content stands consumed by the boundary for wrapping the domain (B-2)ⁿ.

Now if we work out the above Bⁿ = (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 B¹ = A¹+2A⁰. This straight way follows from the domain-boundary formulation for 1-space body. For n=2, we shall be getting B²=A²+4A¹+4A⁰. Here the first pair of terms follow straight from the domain-boundary formulation of 2-space body. The second term 4A¹ would yield 8A⁰ 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 (8A⁰) = 4A⁰. Likewise, for n=3, we shall be getting B³=A³+6A²+12A¹+8A⁰. Here as well the first pair of terms follows straight way from the domain-boundary formulation of 3-space body. The third term which shall be taking us to the boundary of the boundary would accordingly can be computed as ½ (4×6A^2-1) = 12A¹. By the same logic we shall be reaching the next term as 1/3 (2x12A^1-1) 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 Bⁿ = (A+2)ⁿ for n=1 yields the geometric set up of close interval as length (A¹) with two end points (2A⁰), for n=2 yields the geometric set up square as area (A²) with four boundary lines (4A¹) and four end points (4A⁰) and for n=3 yields the geometric set up of cube as volume (A³) with six surface plates (6A²), 12 edges (12A¹) and 8 corner points (8A⁰).

This will help us appreciate the greatness of Vedic model. Further this will also help us appreciate how Bⁿ remains (B-2)ⁿ as domain in the synthetic set up and the remaining content is consumed by the boundary of (B-2)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 ad-infinitum reduction and this will prove the Fermat’s last theorem as that zⁿ = Xⁿ + yⁿ and (z-2)ⁿ = (x-n)ⁿ + (y-2)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 6-space. The seat of Lord Vishnu is the heat of Lord Shiv. 6-space is located at the organ of 5-space. Dwadash Adityas (12 suns) are the 12 boundary components of hypercube-6. As many as 12 hypercube-5 are required to constitute the boundary of hypercube-6. Lord Shiv meditates upon His Lord Vishnu and multiplies 12 folds into Vishnu-lok. 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 hypercube-4 while nucleus itself concepts for format of hypercube 4 while nucleus of the nucleus would accept the format of hyupercube-6, Mansara accepts Lord Vishnu, the overlord of 6-space 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 hypercube-6 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 hypercube-4 transcending into hypercube-5. 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 3-space in the role of dimensions. The spatial boundary of the cube shall be creating 4-space while the solid volume shall be creating 5-space. 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 3-space in the role of dimension. With 3-space as dimension we shall be creating 5-space domain with 4-space in the role of boundary and 6-space 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 3-space domain.

Cube and sphere are the representative regular bodies of 3-space. They are miniatured replicas of linear manifestation layers. With sealed origin and un-manifest dimensions, the other two folds namely, spatial boundary and solid domain when come in action would create transition through transcendence from hypercube-4 to hypercube-5. 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 tri-monad 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 4-space in linearly A8 would help us appreciate the interconnection of the artifices of whole numbers 3 & 7 in the context of 3-space. 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 3-space at the boundary of 4-space 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

VEDIC GANITA

Multi-Dimensions of Time and Space in Manasara