Transcendental Basis of Vedic Literature
(Panel of Jury set up by the
Bhartiya Vidya Bhavan to select candidates for Shri Guru Gangeshwaranandaji Veda
Ratna Puraskar-1997 had selected Dr. S. K. Kapoor for his excellence and service
rendered in the field of Vedic Mathematics.
The Panel of Jury had considered
the evaluation report titled "Transcendental Basis of Vedic Mathematics". As
good information about some aspects of Vedic mathematics of the report would be
of great interest for the research scholars working in the field and as such
same is being included here).
My
studies
culminating into the Doctoral Degree for my thesis titled “Mathematical Basis of
Vedic Literature” accepted by Faculty of Mathematics, Kurukshetra University,
Kurukshetra, summed up conclusions as under:
Sum up of the results as
those flow while working florescence-systems on Om formulation within framed
domains are:
1. In a nutshell, the conclusions
are that the mathematics precedes the composition of Rigveda Samhita. Vedic
Mathematics, helped to transform the Universal set of knowledge as a speaking
language and in the process itself as well stood transformed as such and
assimilated its identity into the Vedas. Within Vedas, all disciplines of
knowledge transform their identity and get assimilated into florescence systems
admitting 432000 components channelizable on Om formulation. As such, need is to
rewrite the history of mathematics, even the intellectual history of man well
admitting fundamental unity of human intellect, the message with which the
Rigveda ends “Samanam-astu.........Sushasati”.
2. One line conclusion, of all the
above conclusions, is that the entire Lower Vedic Mathematical domain stands
exhaustively covered by single formula:
3. And the above formulation as well is nothing but the
extended version of Divya Ganga flow through Om formulation. Divya Ganga flow
crystalizes as florescent frames for the Eternal paths beyond and to which the
Vedic florescence systems ultimately transformed.
The thesis is divided
into 12 chapters with contents as:
1. Vedic mathematics
(Introductory concepts)
– To settle the text
2. Om formulation
(Vedic mathematics applications)
– To settle equivalent
formulations:
· Om
· Pranava
· Aum
· Onkar
· Udgitha
· Vashatkara
· Swastik
· Anmoh
3. Vedas
(Mathematics as a speaking
language)
· Rigveda
· Yajurveda
· Samaveda
· Atharvveda
4. Adi Valmiki
Ramayana
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence.
5. Urmahabhartam
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence.
6. Srimad Bhagwad Gita
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence.
7. Sri Vishnu
Shastranam Satotram
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence.
8. Srimad Durga
Saptsati
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence.
9. Upanishads
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence.
– Prasno Upanishad; Derivation of
the frame and systems.
10. Shad Darshan
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence of
· Nyaya Darshan
· Sankhya
· Vaisesika
· Yoga
· Mimamsa
· Vedanta
· Sankarshna
11. Puranas
(Vedic mathematical basis)
– Derivation of the frames and
systems on
Om formulation in terms of framed
domains sequence of Puranas.
– Srimad Bhagwat Puran; Derivation
of frame & system.
12. Devanagri alphabet
(Vedic mathematical basis)
– Derivation of frame and systems of
the alphabet, its structure, forms and formulations of the
letters within Pranava domain on
Om formulation for working out the sunlight
florescene systems within framed domains.
– Maheshwara Sutras and Sanskrit grammar.
– Saraswati Mantras and Vedic grammar.
– Derivation of classical and languages alphabet.
– Mother computer language for all
computer systems.
With respect to the value of
research work, Professor in Structure Engineering, Dr. Anand Parkash of
Civil Engineering Department, University of Roorkee, had conveyed in 1986 to
Prof. L. R. Varmani, Department of Mathematics in Kurukshetra, Kurukshetra:
“It is my pleasure to convey to you
my appreciation of the work undertaken by Mr. S. K. Kapoor in the basis artifice
of our alphabet and number system conveying the basis energies channelization
into atomic frames and their structures. His study of the sunlight reflecting on
the different number frames resulting into all artificial intelligence and value
judgment has the potential of a breakthrough in scientific thoughts bearing on
the understanding of our universe permeating throughout our vedic literature.
I take this opportunity to
congratulate you all the all valuable inspiration and guidance for the brilliant
research output by him.
With regards.”
Simultaneously, Professor Anand
Parkash had enclosed general appreciation of the research result as under:
“It was very satisfying to listen
Mr. Sant Kumar Kapoor to decipher the hidden code in the construction of
alphabets and numbers channelising the basis energies in the atomic frames
constituting their structure. His formulation that there are 108 basic energy
sources constituting the fundamental format of the atomic tables is noteworthy.
His attempt to have breakthrough
with the insight into sunlight being the basic source of all artificial
intelligence and value judgment in this universal, interlinking the modern
scientific knowledge with the vedic thoughts, deserve all encouragement and
support for advancing the cause of applied research.
I with him all success in his
mission.”
Professor J. N. Kapur, a well-known mathematician of our country, having
hundreds of research articles and dozens of books of mathematics, and experience
of more than four decades of actual teaching of mathematics at graduate and
postgraduate levels, and of guiding several research scholars, had occasion to
consider the geometrical validity of the framed domain sequence being arrived at
in the thesis i.e. (an:2nan–1, n=1, 2, 3, 4, ...) and his considered opinion conveyed to
Professor Krishanaji, read as:
“The sequential interpretation of a3/6a2,
a4/8a3, a5/10a4 are valid.
‘n’ dimensional hypercube has ‘n’ dimensional content ‘an’. It has ‘n–1’ dimensional content
‘2nan–1’ and the ratio is ‘an/2nan–1’.
This has also ‘n–2’ dimension, ‘n–3’ dimension, ...... content which I have
discussed in my article.
This part can be rigorously
justified.”
Professor Krishnaji
in his letter dated March 31, 1988 addressed to Hon’ble
Chief Justice of Punjab & Haryana High Court had requested for sparing the
services of mine for institute of Vedic Science for two years conveying as:
“We must congratulation you for
having in your department such a brilliant and creative mind as Sri S. K.
Kapoor, C.J.M., Rohtak, who can authentically expound the foundations of all
order in nature, as the basis of the Vedic literature available to us through
the oral honoured Vedic tradition. The work by him in his Ph.D. thesis is so
basic that the authenticity of the Veda and Vedic literature is established with
such mathematical precisions and credibility that through his work, it is
possible now to establish the traditionally available Vedic literature as the
most orderly and comprehensive literature of a perfect science of life. This has
the potential to revolutionise the education in all parts of the world and bring
perfection to life on Earth.
This revival of the absolute order
with which the unified wholeness of natural law functions and maintains
orderliness at every stage of evolution of life, is a blessing for every one in
this scientific age, which is rising to be the age of enlightenment through
Vedic Science, Maharishi Mahesh Yogi is currently formulating the Vedic
science and will very much appreciate, if Sri S. K. Kapoor’s time and talent are
available for structuring Vedic science at a rapid pace, which is such a perfect
science of life that with its both approaches - subjective and objective, it far
exceeds the benefits of modern science which functions through objective
approach only. We will be grateful to you, if you kindly spare his services for
our Institute of Vedic Science preferably for two years in order to propagate
the results of his research to our universities in Europe and America -
Maharishi European Research University, Switzerland, Maharishi International
University, Norway, Holland and USA and the forthcoming University of Natural
Medicine in Brazil and other institutes of higher learning.
With respectful regards”
The report of work done during two
year (1988 to 1990) as Visiting Professor in the institute with Professor
Krishnaji as Chairman, as submitted by Professor Krishnaji to Hon’ble Chief
Justice of Punjab and Haryana High Court, Chandigarh, is as under:
“Shri Sant Kumar Kapoor, Chief
Judicial Magistrate, Rohtak, was granted leave by your goodself for two years to
carry on research in Vedic Mathematics as a Visiting Professor, in our
Institute. He joined us on 25th May, 1988.
Shri Sant Kumar Kapoor has done
exceptionally meritorious work in Vedic mathematics. He has developed concepts
involved in the structure of “Om” and the two Vedic structures “Know Brahman
quarter by quarter” and “know fourth quarter Brahman as integrated value of the
first three quarters.” He has also developed Vedic concepts of multi-dimensional
geometrical space and structural frames and systems. He has established that the
regular bodies of geometrical domains constitute a framed domains sequence.
an/2nan–1,
where n = 1, 2, 3, 4, ........
and a=dimensional unit.
Using the above concepts, he has
analysed several vedic scriptures. Following are the results of his research
activity:—
(i)
Mathematical concepts and application to structural frames and systems of
Sri Sri Vishnu Sahastranam Stotram.
(ii)
Vedic mathematical concepts and applications to structural frame and
systems of Sama Veda Samhita.
(iii) Vedic mathematical concepts and
application to structural frames and systems of sixteen sutras.
(iv)
Vedic mathematical concepts and application to structural frames and
systems of Shrimad Bhagwad Geeta.
(v)
Vedic mathematical concepts and application to unsolved mathematical
problems – Five proofs of Fermat’s Last Theorem.
All the above have been published
as Institute Reports. The last one “Fermat’s Last Theorem” has been published in
the form of a book. Three Proofs have been published as a research paper in
M.I.U. Journal “Modern Science & Vedic Science” Vol.3, No. 1, pp 75-104, 1989
USA. The two proofs have been submitted as a research paper to “Mathematical
Reports of the Academy of Sciences” Canada. This work has acquired great
importance because the original theorem was proposed by French Attorney and
mathematician Pierre de Fermat in 1637 and nobody has succeeded in getting the
proof inspite of continuous attempts by distinguished mathematicians for more
than 350 years. Shri S. K. Kapoor has been awarded the Ph.D. degree by the
Maharishi Research University, Seelisberg, Switzerland for his work on Sam Ved
Samhtia.
The leave of Shri S. K. Kapoor is
due to expire on 24th May, 1990, hence this report is sent for your information
and official record.”
Simultaneously, Professor Krishnaji
had made a request with Hon’ble Chief Justice for further leave for Institute,
which was allowed and I worked for another two years (1990-1992) as Visiting
Professor and my research results have been summed up in one of the articles by
Professor Krishnaji in Mathematics Today and reproduced as Appendix A of my book
“Fermat’s Last Theorem and Higher Spaces Reality Course”.
"Vedic mathematics was lost to the
modern world over several thousand years. Fortunately, the renowned scholar
Jagadguru Swami Bharti Krisna Tirthahji Maharaj, Shankracharya of Sharda
Peeth and Goverdham Math discovered 16 Vedic Sutras and 13 Upsutras in the
Parishistha of Atharvved. After continuous Sadhana and hardwork, he was able to
decode them and get wide ranging mathematical principles and applications from
them. He found that these Sturas cover all aspects of mathematical science in
depth. He wrote sixteen volumes on Vedic mathematics covering all aspects of
these sutras in depth. Unfortunately, the manuscript was lost which fact was
finally confirmed in 1956. During his last days when his health was failing and
his eyesight was weak, he rewrote from his memory an introductory account of the
subject. He attained Mahasmadhi in 1960. Later in 1965 a book entitled “Vedic
Mathematics” was published. This book is edited by Dr. V.S.Agarwala with the
help of Smt. Manula Trivedi on the basis of manuscript and notes left by Swamijee. This
book is therefore, the first book to give a glimpse of Vedic mathematics and to
reestablished the subject. The book attracted the attention of several Indians
and foreigners. Dr. Narinder Puri of Roorkee University took up the cause of
Vedic Mathematics in right earnest. His Holiness Maharishi Mahesh Yogi spread
the message of Vedic mathematics throughout the world by sending Dr. Puri to
several countries and making it possible for many schools all over the world
start teaching Vedic mathematics. A former minister of Human Resource
Development, in the Government of India, Sh. P.V.Narasima Rao made a reference
in Parliament about the work on Vedic mathematics which created a wider interest
in the nation. Rashtritya Ved Vidya Pratishthan started looking into the matter
and appointed a committee on Vedic Mathematics. During the same period a
controversy arose about the source of these 16 Sutras and the level of
mathematics contained in them. One view was that these Sutras do not have a
Vedic source and that they deal only with simple arithmetical operations.
In the meantime, Dr. Sant Kumar Kapoor, inspired by integrated impact of the
Ganita Sutras, started working on basic aspects of the mathematical structure of
Vedic literature. He got several clues from Ganita Sutras, Maheshwara Sutra and
many other Vedic Mantras. He was inspired by the divine blessing from Yograj Sri
Sripad Babaji of Vrindavan and His Holiness Maharishi Mahesh Yogiji at Maharishi
Nagar. He has been awarded Ph.D. degree by Kurukshetra University, in December
1990 on his thesis titled “Mathematical Basis of Vedic literature”. His work
shows that the potential of Ganita Sutras is much higher than what appears in
the book “Vedic Mathematics” and the mathematical structure of Ganita Sutras is
similar to that of Samved indicating that Ganita Sturas belong to Vedic family.
His work shows that the Devnagri alphabet and the Vedic scriptures are
mathematically organized. Perhaps a more important aspect of his work in the
existence of Real Geometric Spaces of higher dimensions in the form of a
continuum. A comprehensive description of his research is given in the next
section. Dr. Sant Kumar Kapoor is presently working as a Visiting Professor in
the Indian Institute of Maharishi Vedic Science & Technology which is a part of
Maharishi Ved Vigyan Vishwa Vidyapeeth, Maharishi Nagar. Three research students
are working in our institution on the structure and properties of fourth, fifth
and sixth dimensional spaces.
Vedic mathematical Research done by Dr. S. K. Kapoor
Studies reveal that knowledge and organisation of knowledge are two distinct
disciplines. The thesis of Dr. S.K.Kapoor is substantively covering the
organisational aspect of Vedic knowledge. The main results of the thesis and his
subsequent research can be summed as under:
1.
Real 4 and higher dimensional spaces do exist.
Real 4 and higher dimensional spaces were not only known to the Vedic seers but
those were precisely availed by them for organisation of vedic knowledge.
Vedic alphabet format is a precise setup of4-space. The alphabet letters of
Devnagri script, their forms formulations, combinations and rules etc. are
precisely mathematical.
Sakala Rigvedic Samhita is the oldeset scripture of mankind. The organisational
format of this Samhita is precisely that of real 6-space.
Vedic knowledge accepts a measuring rod constituted by regular bodies of the
first six real dimensional spaces which admit formulations as:
The organisational format of Srimad Bhagwad Gita emerges to be of prime
importance as it is parallel to the organising power of the knowledge content of
the scripture. This format tallies with the format of human body on the one hand
and the sun on the other hand as of real 6-space.
The Trinity of Gods namely Brahma, Mahesh, Vishnu are the overlords of real 4, 5
& 6 spaces respectively.
The geometrical continuum expressed
as manifestation layers of 4 folds of consecutive dimensional spaces contents.
These folds of the nth manifestation layer can be represented as under:
|
First Fold
|
Second Fold
|
Third Fold
|
Fourth Fold
|
|
Dimension
|
Frame
|
Domain
|
Origin
|
|
(n-2) space content
|
(n-1) space content
|
n-space content
|
(n+1) space content
|
The transcendence from one manifestation layer to another manifestation layer
giving rise to the following (five steps) chain reaction or five steps which are
possible within the setup of Panch Mahabhut.
|
Manifestation Layer
|
Dimension
|
Frame
|
Domain
|
Origin
|
|
nth
|
Space fold
(n-2)
|
Space fold
(n-1)
|
Space fold
n
|
Space fold
(n+1)
|
|
(n+1)th
|
Space fold
(n-1)
|
Space fold
n
|
Space fold
(n+1)
|
Space fold
(n+2)
|
Transition from one space to
another space is to be had in terms of unlocking of the seals of the origin
points of all the four folds of the manifestation. The modern mathematical
models of transition from straight line to plane deserve serious reexamination.
In particular the axioms of space filling curves and the axioms of ‘one’ without
a predecessor deserve close scrutiny as their rationale emerges to be without
basis.
The role of real numbers additive group (R,+) and real numbers field (R,+,×)
with reference to straight line deserve to be differentiated.
The plane deserves to be studied as four geometrically distinct quarters. One
faced plane and two faced plane are two distinct geometrical setups and they
deserve to be taken up as such.
The concepts of origin and dimension are two concepts with respect to which the
modern geometrical models are not up to date. These two concepts deserves to be
studied in detail as transcendence to the higher dimensional spaces is possible
only in terms of their understanding.
Human body is a compactified phenomenon of multi-layer physiological existence.
The start with state of existence is that of waking state which is parallel to
the expression of 1-space as dimension into 3-space domain. Sequentially, the
existence phenomenon unfolds until seventh state of consciousness which would be
corresponding to the 7-space as dimension into 9 space domain. The origin point
of the 6-space, being the 7-space setup, the human body, geometrically, turns
out to be hypercube-6 and this would explain how the primordial sound, the
planetary effects, the Yajna oblations etc. operate and precisely influence the
individual existence patterns.
Srimad Bhagwad Gita is one such scripture whose organisational format precisely
workout for us the structural set up and frames of the 6-space. The study zone
of Srimad Bhagad Gita can be worked as under:
The organisational setups of Ganita Sutras, Maheshwara Sutras, Saraswati
Mantras, Gyatri Mantra and Om formulation deserve interdisciplinary
explorations.
Sankhay Nistntha and Yoga Nistha are complementary and
supplementary of each other and as such their complementary nature and
supplementary nature deserve to be distinguished well. Non-differentiation of
the same is bound to deprive us of most of the results in specific forms.
Now let me take up how the subject
contents of my different books are indexed in their prefaces. First starting
with “Vedic Mathematical Study of Structural Frames and Systems of Sri Sri
Vishnu Sahastranam Stotram”, published by Maharishi Ved Vigyan Vishwa
Vidyapeetham, Maharishi Nagar–201304, (INDIA) (1991):
“Preface
The present study aims at
approaching the organisation format of the scripture; Sri Sri Vishnu Sahastranam
Stotram. This is a scripture of 107 verses and it composes 1000 names of Lord
Vishnu, who is overlord of real 6-space. Though the modern mathematics too talks
of dimensional spaces higher than three but those are mere mental-constructs.
The modern mathematics has striped the concepts of dimension from geometrical
reality and as such the suffix ‘Real’ before 6-space is of real significance
here in this study.
If it is only while faced with
problems of the classifications of the geometries of dimensional spaces and the
sporadic finite groups, we are really face to face with the intensity and
richness of each space beyond 3 space. Sylvestor’s classification theory of n+1
geometries of n-space is just a property of real 4-space. It is a simple shift
from monad without partes which gives us 1-space as dimension of 3-space to
synthetic monad of two parts of real 4 space with 2-space as dimension. In a
sequence, the real 5-space and 6-space are having synthetic monads of 3 parts
and 4 parts respectively and accordingly their dimensions are 3-space and
4-space.
Vedic literature avails real 4, 5 & 6 spaces for organisation of knowledge.
These spaces respectively contribute 24, 25 and 26 Tatavs (elements /
characteristics properties). The step beyond Sylvester’s classification or n+1
geometries of n-space would be to enter real 5-space where we shall be getting
2n+1 geometries of signatures –n to +n of n-space. The step beyond the 25th
sporautic finite group would be a step into the real 6-space and we straight way
get the number of elements of 26th sporadic finite group as 10×1264.
And with it, the classification assignment over which practically we have
consumed complete nine decades or this century and still 26th group is eluding,
gets answer from ancien wisdom of real spaces. This would help us appreciate the
ancient wisdom to accept the measuring rod of real bodies of first six real
spaces admitting ratios of their domain parts as an:2nan–1,
n = 1, 2, 3, 4, 5, 6.
This all is being added here just
to impress upon the rationale for the choice of Sri Sri Vishnu Sahastranam
Stotram for organisational study. However, I would like to add at the outset
that by all means it is just a preliminary study into the structural frames and
systems of this scripture and the real studies would follow from the pens of
really the real privileged souls who, I pray, should spare moments from their
blissful samadhi to give the desired direction to the flow of intelligence of
the present generation.
Sri Sri Vishnu Sahastram Stotram is
the holiest of the holy scriptures whose enlightenment was the last discourse to
the Pandavas given by great Bishma from his death bed of arrows in the battle
field of Kurukshetra in the presence of Lord Krishna, incarnation of Lord
Vishnu. This, that way, is the scripture of perfection and hence the proper
scripture of the Sankhya nistha as well as the Yoga nishta.
His Holiness Sri Sripad Babaji
initiated me into Sankhya nistha as the science of organisation of the Universe
on the artifice of natural numbers. His Holiness Maharishi Mahesh Yogi has
initiated me further in the subject that the Sankhya nistha is the science of
self-organising power of the pure knowledge. The specific processing lines,
which I describe as Sripad processing line is to know Brahman quarter by quarter
and the Maharishi processing line is to know fourth quarter of Brahman as
integrated quarter of first three quarters. The present study in a way is
nothing but the extent to which I could comprehend only that much and over and
above that are the limitations on language and what not and so the humble
request that they may skip over such stages by their own contemplation which is
the only guide in such like adventures or mortals like me regarding the vedic
scripture of perfection
× × ×
With all humbleness this study is
submitted with the hope that the advanced students of Vedic science and
technology will continue the processing further into this and other scriptures.
Here is a caution for them that the first correction which the modern
mathematics needs in the discipline of geometry is regarding its hypothesis of
space filling curves. This hypothesis deserves to be rejected. The second thing
which I would like to suggest is that the continuum be approached the Vedic way
as manifested layers of four-folds of four consecutive space-contents and not
‘individual dimensional spacewise’ as is being attempted at present by the
modern mathematics. Before submitting the present study for consideration of the
scholars I feel it may duty to share the first principles of decoding the
knowledge content from the organisational format of the Vedic scriptures. The
keyword of this principle is Shardha and culmination is the word nistha. The
principle operate as: Samsayatma Vinasyanti (Gita-4.40). Practical working rule
comes to be that the doubt destroys everything, the scriptural commands deserves
to be approached faithfully, the words of seers deserve to be taken up on their
face value. To have an idea that how difficult it becomes to gain anything from
the Vedic systems the moment one approaches them with an initial doubts, we can
see what mess stands created by the individuals about the powerful systems of
Ganita Sutras.”
Professor Krishnaji has expressed
by way of Forward of this book as:
“I am happy that, I am able to seek
the blessings of H.H Mahairshi Mahesh Yogi on the first publication of the
Indian Institute of Maharishi Vedic Science & Technology in a record time. Shri
S. K. Kapoor, who is Visiting Professor in the Institute has produced, wonderful
work, entitled “Vedic mathematical concepts and its application to structures
and systems of Sri Sri Vsihnu Sahastranam Stotram”. This publication is the
first publication or its kind in which Sh. S.K.Kapoor has introduced the Vedic
geometric formula called “Gurudev formula” and has introduced the concepts of
“Divya Ganga flow” and “Om formulation”. He has explained the basic difference
between conventional geometry and Vedic geometry e.g., the point in Vedic
geometry has a structure whereas the point in conventional geometry is
dimensionless. He has gone into sufficient yet restrained details of the new
concepts and the rules before applying them to the structural systems or the
scripture Sri Sri Vishnu Sahastrannam Stotram. He has shown without any strain
and without any doubt that Vedic mathematical concepts are able to explain
unambiguously, the number of names of Lord Vishnu included in every individual
Shaloka of the scripture. His writing comes directly from his thinking. His gift
of thinking is original but the inspiration given by H. H. Shri Pad Babaji of
Vrindavan and H. H. Maharishi Mahesh Yogi is clearly visible. The knowledge is
drawn from the vast treasure of Maharishi Vedic science and technology but the
representation is original.
In recent year, there has been a
revival of the ancient Vedic knowledge because a very large section of people
have started realising that Vedas are the infinite source of complete knowledge
and have existed from times immemorial. However, there has been an unfortunate
tendency, primarily due to ignorance, of comparing and trying to understand
vedic science in terms of the modern science. Very few people realise that the
modern science utilises only the objective approach whereas Maharishi Vedic
Science utilises both objective and subjective approaches to gaining knowledge
simultaneously.
The epistemological nature of the
ancient Indian knowledge is based on the understanding that the process of
intuitive revelation of true knowledge in the individual mind can be controlled
by eliminating the difference in the operation of emotions and intellect through
their unification by the techniques of Yoga Darshan. It will be of interest to
the student of Vedic science, if they carefully understand the difference
between modern science and Maharishi Vedic science.
Vedic mathematics is one particular
component of Vedic science. Mathematics is called the queen of sciences and is
the fundamental base on which all planning is done and all structures are
raised. Shri S. K. Kapoor is using this as an axiom and has applied the Vedic
mathematics concepts as an integral part of Maharishi Vedic Science and
Technology to investigate in the volume a particular case of structures and
systems of Sri Sri Vishnu Sahastranam Stotram. The readers may find it difficult
to comprehend the subject during the first reading because they are used
conditioned to the usual objective approach of conventional mathematics. The
second and subsequent readings, however, will reveal to them the real meaning of
concepts and therefore, the immense beauty and power of this knowledge.
The Indian Institute of Maharishi
Vedic Science and Technology is a research institute covering all aspects of
Vedic Science & Technology including Vedic philosophy, structure of Vedic
knowledge, Vedic mathematics, Ayurveda, Jyotish, Ganderva Veda Dhanurveda,
Sathapatyaveda etc. The Vedic science covers the widest possible spectrum from
point to infinity and back to the point and the infinitely expanding universe. I
hope that the present publication will re-open the infinite sources to pure
knowledge, which has always existed in the supreme consciousness and has been
frozen in the self referral individual consciousness also from times immemorial.
One will find that before the main text there is an abstract table giving
geometrical coordination of 1000 names of Lord Vishnu. To begin with, it may be
incomprehensible to the understand reader, but it will certainly show that the
Vedic geometry deals with the dimensions higher than 3, that is 4th, 5th, 6th
dimensional frames whereas conventional geometry does not go beyond third
dimensional frame.
The implications of this work are
multidimensional and far reaching. One aspect is the Vedic claim that faithful
recitation of Sri Sri Vishnu Sahastranam Stotram can cure all kinds of fevers.
This can easily be understood because the studies reveal:
“The Vedic sounds are
multi-dimensional domains’ frequencies from within a particular dimensional
domain as the structure of that domain. When the sounds are pronounced, the
frozen frequencies get initiated and the self organising power of the Vedic
sounds sets the frequencies’ potentialisation process into action. It is this
process whose utilisation is the aim of different Vedic scriptures.”
This work is being submitted at the
feet of H. H. Maharishi Mahesh Yogi for his blessing.
Jai Guru Dev!”
The book “Vedic Geometry” of mine
published by M/s. Arya Book Depot, Karol Bagh, New Delhi (in 1994) indexes it
preface as:
“The present introductory volume
aims to introduce the ancient discipline of Vedic geometry. We may formally
define Vedic geometry as a discipline of Geometry based on Vedic concepts.
Studies of mathematical basis of
Vedic literature reveals that 4 and higher dimensional reality was not only
known to Vedic Rishis but also put to practical use by them for organisation of
pure knowledge on geometric formats, particularly, real 4, 5 and 6 space
formats.
Vedic comprehension of geometric reality is characteristically different from
our present-day conclusion. Basic difference in the two approaches viz. modern
approach vis-a-vis Vedic approach can be appreciated in terms of the concept of
dimension. Modern Cartesian dimensional approach makes all dimensional spaces
the linear dimensional spaces as much as that 1-space is to play the role of
dimension for all dimensional spaces while, on the contrary, Vedic comprehension
comes to be that n-2 space plays the role of dimension of n-space.This glaring
difference may well be focussed algebraically as that as per modern model we may
express 4, 5 and 6 spaces as A4, A5 and A6 while
as per Vedic model their expressions comes to be (A2)4, (A3)5 & ((A2)4)6.
The above difference and impact of
n–2 space playing the role of dimension of n-space comes to be that it requires
4 consecutive dimensional spaces to manifest a dimensional body as a 4 fold body
having distinct dimension fold, boundary fold, domain fold and origin fold. Our
well known solid bodies having cubes as their representative regular bodies
avail 1-space as dimension fold, 2-space as boundary fold, 3-space as dimension
fold, and 4-space as origin fold. In general n–2, n–1, n and n+1 spaces together
synthesis and manifest ‘n’ dimensional body which may be designated as n–2
manifestation layer. Also it may be designated as hypercube-n. This makes our
modern set theory or binary compositions a study of 0 manifestation layer and
Euclidean geometry a study of 1-manifestation layer while Vedic geometry takes
up all manifestation layers within its domain.
The beauty of this discipline lies
in its capacity to unify all discipline of knowledge as a single discipline.
Illustratively, human body, sun, nucleus or nucleus of atom, 6-space,
organisation of knowledge of Srimad Bhagwad Gita etc. etc. are all availing the
format of hypercube 6 i.e. 4 manifestation layer. This would help us appreciate
the uniqueness of approach and richness of content of this discipline. But this
is just a first glimpse . Real bliss lies ahead with unification of entire
existence phenomenon as impulses of consciousness.”
This “Vedic Geometry” book has 10
chapters with split-up of contents as under:
Chapter-1
Introduction of the subject
1.1 Vedic geometry
1.2 Vedic knowledge
1.3 Vedic literature
1.4 Organisation of knowledge
1.5 Geometric formats
1.6 Oganisation parallel to
knowledge content
1.7 Four space
1.8 Five space
1.9 Six space
1.10 Trinity of gods.
Chapter-2
Basic concepts and formulations
2.1 Synthetic monads
2.2 Manifestation layers
2.3 Transcendence at the origin
2.4 Regulation acceleration of
transcendence
2.5 Measuring rod
2.6 Generation status of elements
2.7 Place value system
2.8
Power sets
2.9 Reflection operation
2.10 Structural constants
Chapter-3
Trinity of Gods
3.1 Trinity of gods
3.2 Lord Brahma
3.3 Lord Shiv
3.4 Lord Vishnu
3.5 Real 4-space
3.6 Real 5-space
3.7 Real 6-space
3.8 Mathematics of di-moand
3.9 Mathematics of tri-monad
3.10 Mathematics of tetra-monad
Chapter-4
Shadchakras
4.1 Shadchakras
4.2 Shadchakras format of human
body
4.3 First Shadchakra
4.4 Second Shadchakra
4.5 Third Shadchakra
4.6 Fourth Shadchakra
4.7 Fifth Shadchakra
4.8 Sixth Shadchakra
4.9 Coordination of Shadchakras
4.10 States of consciousness
Chapter-5
Vedic geometry
5.1 Vedic geometry
5.2 Mathematics of 4-space
5.3 Mathematics of 5-space
5.4 Mathematics of 6-space
5.5 Science of 4-space
5.6 Science of 5-space
5.7 Science of 6-space
5.8 Technology of 4-space
5.9 Technology of 5-space
5.10 Technology of 6-space
Chapter-6
Vedic number theory
6.1 Vedic number theory
6.2 Parallelism between artifices
of whole number and dimensional spaces
6.3 Chasing organisation of
boundary of 5 space
6.4 Chasing organisation of
boundary of 4 space
6.5 Chasing organisation of
boundary of n space
6.6 Addition and bindary operation
of 1-space
6.7 Substraction and bindary
operation of –1 space
6.8 Real line is solid line
6.9 Dedekind’s cut work out half
open interval.
6.10 Calculus is science of
boundary hypercubes.
Chapter-7
Ganita Sutras
7.1 Ganita Sutas text
7.2 Organisation format of Ganita
Sutras
7.3 Organisation of 16 Sutras
7.4 Organisation of 13 Upsutras
7.5 Organisation of 46 constructs
7.6 Organisation of 520 letters
7.7 To reach at the applied values
of Ganita Sutras:
Ganita Sutra-1
Ganita Sutra-2
Ganita Sutra-3.
Chapter-8
Structural frames and systems of Samved Samhita
8.1
Introduction
8.2
First part of Samved Samhita
8.3
Second and third of Samved Samhita
8.4
Purva Archik; Sum-up
8.5
Chapter-1 Dastis 1-12
8.6
Purva Archik Mantras of chapter-1
Chapter-9
Structural frames and systems of Srimad Bhagwad Gita
9.1
Organisation of knowledge
9.2
Understanding the systems of Srimad Bhagwad Gita
9.3
Organisation of the text of Srimad Bhagwad Gita
9.4
Organisation of the knowledge of 18 chapters.
Chapter-10
Conclusion and their applications to the solution of Fermat’s Last Theorem
10.1
Fermat’s Last Theorem
10.2
Four folds approach
10.3
First proof
10.4
Proof by direct comparison
10.5
Transcendence approach
10.6
Power expression
10.7
Power sets
10.8
Aspects 1 to 12.
International Sanskrit Research
Academy (Regd. Trust), Bangalore in its letter dated June 22, 1996, conveyed its
editorial team’s view regarding Chapter-9 titled “Structural frames and systems
of Srimad Bhagwad Gita” of my book “Vedic Geometry” (pages 433 to 458) as under:
“This is an inter disciplinary
study bringing out the link between the Vedic geometry and the classical text of
philosophy namely Bhagavagita in the Chapter-9. This study can further lead us
to understand the relation of Gita with other important scientific disciplines
in the Indian tradition about which the present knowledge is very meager. This
article is a stimulator for further studies.”
In the Preface to my book “Fermat’s
Last Theorem and Higher Spaces Reality Course” published by M/s. Arya Book
Depot, the subject content is indexed and focused as under:
“Preface
Present phase of intellectual
history of man begins with seventeenth century. Over all these years, one
statement which remained source of intellectual challenge is the statement of
Fermat’s Last Theorem. It is rightly stated that “those non-mathematicians who
really wants to understand the essential nature of mathematics and how it is
created ought to begin with this discussion” (of our recorded history how
bravely we fought to conquer the fort of this statement).
The French Attorney and
mathematician Pierre de Fermat (1601–65) made his assertion in 1637 as the
following note (original in Latin admitting English rendering translation as
given below) in the margin of mathematics book (Bachet’s translation of
Diophantus’ Arithmetica, great classics of ancient Greek mathematics) he was
reading at that time:
It is impossible to separate a cube
into two cubes, a biquadrate into two biquadrate, or in general any power higher
than second into two powers of like degree. I have discovered a truly remarkable proof which this
margin is too small to contain’
Prof. Paulo Ribenboim in his essay
titled “Early History of Fermat’s Last Theorem” highlights amongst other
features, the fact that despite efforts no proof could be traced from the paper
left behind by Fermat and that one school of thought is gaining grounds when he
adds: ‘It is very difficult to understand today how the most distinguished
mathematicians could have failed to rediscover a proof if one had existed.’
This article despite above
reservations earned a hopeful editorial comment: ‘It is amazingly simple
question but whose solution eluded the world, the world of mathematics to this
very hour.’
The present work approaches this
theorem from many angles and put forwards several alternative proofs but the
crowning jewel is the equally simple answer for an amazingly simple question.
The answer runs as that on format of volume of cube;
z3 = x3 +y3 implies
(z–2)3=(x–2)3+(y–2)3 as
a3 = (a–2)3 + 6(a–2)2 + 12(a–1)1+12(a–1)0
Number value cube = volume +
surface area + length of edges + value of corner of geometric cubes.
The law of impossibility of
infinite descent proves the case n=3.
As such the dimensional order of odd hypercube-n such that n=2m+1 comes to be
1×3×5×7×.........2m+1 and for even hypercuebs-n such that n=2m comes to be
2×4×6×8×.........2m, therefore, for all hypercubes-n such that n=4 implies that
dimensional order of hypercube n is divisible by 3. Therefore, n is divisible by
3. Therefore, the general case for n=4 immediately follows from case n=3 as we
can rewrite zn=xn+yn as (zn/3)3=(xn/3)3+(yn/3)3.
The case n=4 was proved by Fermat himself. The initial choice or format of
volume of cube restricts n to be greater than 2. Hence, the general proof.
The source concepts at the base of
above proof is: n–2 space plays the role of dimension of n-space. It is well
preserved in our Vedic literature. Two such references are Uttarkand 79(ka)
Ramcharitmanas and Bhagwad Mahapuran (10.9.15-16).
General Proof (at pages 104-110 of
this book) was sent by the author to Prof. Paulo Ribenboim who referred it to
referee but unfortunately lost it.
To be at most natural answer is an
intellectual satisfaction but his is the beginning of the new wonderful higher
dimensional reality displayed beyond this point. The mathematical truth of this
theorem is the basic foundation stone for jumping from three space reality to
four and higher space reality. Aim of this work is to attempt a school courses
for higher dimensional mathematics to mature the young brains by exposing them
to the geometric formats of mathematics, science & technology of real three,
five and six spaces over a duration of post-middle four years duration of school
education so that present generation may have taste of the bliss of Vedic
wisdom.
The efforts of the author would get
amply rewarded if this work helps the students and teachers of mathematics to
think about the ways and means of coming out of a single space (three space)
model of mathematics, science and technology.
Eternity of Vedic knowledge is
there because of eternal organisation formats of Vedic knowledge. Idols of
Trinity of Gods manifest on formats of hypercubes 4, 5 and 6. These together as
three folds of four manifestation layer with 4,5,6 and 7 space as dimension,
boundary, domain and origin fold constitute a really wonderful format being
availed as organisation format for Vedic wisdom.
Because of it, seven place value system has a unique role
to play. As is evident from the table below, all the six numbers 1 to 6 of seven
place value system acquire same value i.e 1 for power 6.
|
|
|
Digits
|
|
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Powers
|
1
|
1
|
2
|
3
|
4
|
5
|
6
|
|
2
|
1
|
4
|
2
|
2
|
4
|
1
|
|
3
|
1
|
1
|
6
|
1
|
6
|
6
|
|
4
|
1
|
2
|
4
|
4
|
2
|
1
|
|
5
|
1
|
4
|
5
|
2
|
3
|
6
|
|
6
|
1
|
1
|
1
|
1
|
1
|
1
|
|
|
|
|
|
|
|
|
|
As such, it may be very easy to
physically test even case i.e. n–2m cases for n>4 on seven place value system.”
The book “Foundations of Higher
Vedic Mathematics” published by M/s. Arya Book Depot, has indexed in its Preface
as:
“Ved means ‘knowledge’. Studies of
available Vedic literature reveal that Vedic seers had successfully organised
whole range of knowledge as a single discipline as a speaking language. Further,
studies reveal that our ancestors could achieve success par excellence by first
comprehending Reality which ends up as Triloki (three space) as higher
dimensional Reality and secondly, by making use of this comprehension of higher
dimensional Reality for the required geometric formats for organisation of Vedic
knowledge.
Upanishads are the end-product of
Vedic literature. The enlightenment of Upanishads takes us to the fundamental
unity of Reality as much as that Purusha emerges to be the first manifested
incarnation of Brahm (Sri Sri Vsihnu Puran). The specific enlightenment of
Upanishads is that Lord Vishnu, Sun, Purusha, Atman and real six space are
organisationally in unison with each other. It is this enlightened comprehension
which may be taken as the source for unification of knowledge on six space
format.
Further, studies of mathematical
basis of literature leads to the conclusion that the organisation format of
hypercube-6 (being the representative regular body of six space) is structurally
very rich and is capable of organising the whole range of pure knowledge as a
single discipline as a speaking language as real six space, if viewed linearly,
is a space of 2×4×6=48 linear dimensional order.
Upanishad further enlighten us that
Lord Vishnu accepts hypecuube-6 as format for His Idol, Shad-Chakra format of
human body admits coordination through Sushmana Nari and takes us to the core of
sun parallel to the measuring rod of first six hypercubes accepted by Sthapatya
Ved. In fact, every Vedic literature makes use of one or other aspect of
hypercube-6 for organisation of knowledge.
In the opening paragraph of
chapter-1 of present studies it has been made specific that: Vedic mathematics,
as it is, yet to be explored. Though whole domain and the scope of Vedic
mathematics, as it is, yet to be explored but three distinct approaches, to
which we may have access at present, are, firstly, ‘on the artifices of whole
numbers’ of Ganita Sutras, as interpreted by H.H. Swami Bharti Krisna Tirthaji
Maharaj, secondly ‘on the geometric formats’ of Maheshwara Sutras, as is
expounded by H. H. Sri Sripad Babaji Maharaj, and thirdly, ‘on consciousness
state of human physiology’ as unfolded by H.H.Maharishi Mahesh Yogiji Maharaj,
known as ‘Maharishi’s Vedic Mathematics’.
Present studies are titled
‘Foundations of higher Vedic mathematics’ as here attempt is being made to reach
at the foundations of higher Vedic mathematics on which the Vedic knowledge has
been organised as a single discipline as a speaking language. Mahalakshmi Astham
Stotram has been taken as the reference scripture for measure the success of
studies.
Present study for foundations of higher
Vedic mathematics is being divided
into four chapters as four steps. The first step is to introduce the basic
concepts and formats required for reaching at the organisation formats of
different folds of Vedic mathematics text. This as such is the topic of study of
the first chapter.
The inner evidence of available
Vedic literature makes out that Om formulation is the basic formulation without
whose proper understanding it may not be possible to have desired insight into
the working rules of Vedic mathematics at the base of the organisation of Vedic
knowledge and as such the second topic of study of chapter-2 is ‘Om
Formulation’.
The organisation of knowledge being
for working out the systems which end up as Triloki and as such the third topic
for detailed study which need be taken and in fact is being taken up in the
present study as chapter-3 is ‘Structural richness of a cube’.
With Mahalakshmi-Ashtakam Stotram
at the centre and transcendental meditation as the basic technology, attempt has
been made to ascertain the specific properties of a geometric space as the
Santana (eternal format/real 5-space) accepted for the organisation of Vedic
knowledge.
Mahalakshmi Ashtakam Stotram is a
scripture of Stuti Shalokas devoted to Goddess Mahalakshmi. Devotees by
faithfully reciting these Shaloks get blessed with Vibhuti and Shakti of
Vishnu-lok. This is the fruit of pure knowledge, the Vedas.
Devotees just recite the Stuti
shaloks with full faith and get blessed with the godly grace. For all those who
wish to be blessed with such a grace, for them, there is no choice, but to
recite these Shalokas with faith. Such readers may straight-a-way go to the text
of the Stotram (chapter-4) and faithfully recite the same be blessed with godly
grace of Goddess Mahalakshmi.
The conclusion of the studies comes
to be that: Vibhuti and Shakti of the Vishnu-lok manifests at boundary or
Vishnu-lok (real 5-space in the role of boundary) as well as Saptrishi-lok as
stands released with unlocking of the seal of the origin of Vishnu-lok. This is
there because of the Goddess Mahalakshmi, the consort of Lord Vishnu,
manifesting as real 5-space playing the role of boundary of 6-space and
dimensional order of 7-space.
This privileged state of Vibhuti
and Shakti of Vishnu-lok is there because of the Goddess Mahalakshmi. This is
the state whose comprehension and understanding has much education for us who
are interested in sciences, mathematics and technology of higher real spaces,
particularly as to how the continuity of manifestations is being maintained by
the dimensional contents which otherwise remain sealed at the origins of the
dimensional spaces.
The concept of release of higher
dimensional content with unlocking of the seal of the origin and transcendence
setting into action is the most fundamental concept which is not known to the
present day sciences and technologies. Four consecutive dimensional spaces
manifest simultaneously as four fold manifestation sequentially playing the
roles of dimension, boundary, domain and origin with origin normally remaining
in dormant sate but otherwise being capable of being initiative. This in Vedic
technological language would mean chiselling of an eye. In Yogic language it
would mean attaining transcendence state for higher state of consciousness. This
precisely in geometric language would mean the release of next higher
dimensional space.
Though in the present study which
aims to outline some of the steps for foundations of higher Vedic mathematics,
an attempt is being made to make this study a self-contained one but despite
every effort it has not become possible to go for defining each and every
technical term used here and as scuh I feel that one reading of my book on
“Vedic Geometry” may be of great help.
Before presenting the studies to
the readers, I feel it my duty to express that this study simply would have been
without shape, but for the enlightenment of Maharishi’s Vedic mathematics’
statement sharpened and focussed by H.H.Maharishi Mahesh Yogiji Maharaj (as part
of Maharishi’s Absolute Theory of Defence). This has been annexed with the
present studies to give the readers an idea as to what is going to be the final
shape of things in the area of Vedic mathematics, and now wonderful worlds of
higher dimensional Reality are awaiting for us.
Scholars may straight-a-way go to
the Maharishi’s Vedic Mathematics statement. The readers who are not yet exposed
to Vedic geometry and Vedic mathematics, may first go through chapter-3 of the
present studies regarding “Structural Richness of a Cube”. However, the readers
who are already exposed to Vedic geometry and Vedic mathematics, they may start
with chapter-1 titled “Steps for foundations of higher Vedic mathematics”. The
reader who are interested to first to go through Om formulation, they may start
with chapter-2 and the readers who are interested only in godly grace they may
straight-a-way go to chapter-4 titled “Mahalakshmi-Ashtakam Stotram”:
Mahalakshmi Ashtakam Stotram blesses devotees reciting the scripture with faith.
With all humbleness, I share with
the readers that my family has full faith in this scripture and everyone can be
blessed with godly grace just by faithful recitation (three times a day) or
Stuti Shaloks of Mahalakshmi Ashtakam Stotram.
Present study, in fact is a joint
exercise of all the members of my family as every member has contributed for the
completion of the work in his/her won way. Further I would like to share with
the readers that the present studies have become possible only because of the
privilege to be at the feet to H.H. Sri Sripad Babaji Maharaj and had
initiations into the organisation of Vedic knowledge and further being at the
feet of H.H. Maharishi Mahesh Yogiji Maharaj and learnt Transcendental
Meditation for transcendence values needed for reciting at the inner folds of
organisation formats of Vedic knowledge.
Mahalakshmi-Ashtakam Stotram text
is a composition of just 818 letter organised as just 11 Shaloks and its
recitation even by reading the text is an exercise of less than five minutes. By
way of study of chapter-4: “Mahalakshmi-Ashtakam Stotram”, it has been expressed
about the organisation and composition of this scripture as that: The
composition of this scripture as that: The composition range of 818 units is
firstly organised as 352 syllables. These 352 syllables are further organised as
85 Padas (words). The Padas range of 85 units is organised as 22 composition
ranges as half is organised as 22 composition range as half Shaloks of 16
syllables length. Ultimately these 22 composition ranges get organised as 11
Shaloks of 32 syllables each.
The organisation of individual
Shaloks as 32 syllables of equal parts of 16 syllables is parallel to the
organisation of 32 teeth in the mouth grouped as two jaws of 16 teeth each.
The human Nad had ultimately gets
regulated through these 32 teeth arrangement as Shabad (Mantras). The
organisation of Nad of 818 units of Mahalakshmi-Ashtakam Stotram is parallel to
the organisation of the affine space of a cube of 818 units. This organisation
is further parallel to the organisation range of Vedic mathematics text of
precisely 818 units.
Therefore, the organisation of 818
units composition of Mahalkshmi Stotram satisfy the first test of being of the
potentialities of the nature which ends up as our Triloki. As such, everything
what may be attained within human frame is ensured with faithful recitation of
Mahalakshmi-Ashtakam Stotram.
The physical test of the
organisation possible on the affine space within a cube and the intellectual
test of the organisation of the Vedic mathematics text having been done, the
interested readers may further have the satisfaction of the subjective test by
themselves experiencing the taste of the Stotram.
For such interested readers, it is
added that they should have faithful recitation of the scripture three times a
day, initially with the help of written text till the text become fully
enlivened in their consciousness, it would become possible for them to dispense
with the written text and they may enjoy the recitation of the scripture while
siting in Pada-Asan. Though the recitation as such may turn out to be just of
one minute duration and even stage would reach where just attention would
enliven the whole range of the text.
The blessed state of
Mahalakshmi-Ashtakam Stotram getting enlivened just the moment there is
attention to it becomes a permanent state provided one does not deviate from the
laws of pure consciousness state which admits truth as its base/format for
enlivened existence.
To achieve the enlivened state of
existence may not be difficult but to make it a permanent state, one is to be
ever truthful to oneself so that purity of consciousness is not diluted. If at
any stage one feels that some circumstances of consciousness are having tendency
to dilute the purity of consciousness, he should increase the number of
recitations of this scripture to meet those uncalled for tendencies of those
circumstances. Faithful recitation has the potentialities to overcome all such
things.”
This book “Foundations of Higher
Vedic Mathematics” published by M/s. Arya Book Depot, has four chapters with
split-up contents as:
1. Steps for foundations of Higher Vedic Mathematics
1.1 Introduction
1.2 Main results
1.3 Basic geometric formats and concepts
1.4 Vedic mathematics text
1.5 Illustrative case: Fermat’s Last Theorem
1.6 Organisation of Rigved Samhita
1.7 Jyoti Manifestation format
1.8 Triloki & trinity of gods
1.9 Conclusion
2. Om formulation
2.1 Introduction
2.2 First set of rules of Om formulation
2.3 Second set of rules of Om formulation
2.4 Third set of rules of Om formulation
2.5 Fourth set of rules of rules for Om formulation
2.6 Studies: 4 components of Om formulation as first four
dimensional domains
2.7 Illustration I: Structure of an atom
2.8 Illustration II: 120 years cycle of human destiny
2.9 Illustration III: Human physiology: Shadchakra
2.10 Illustration IV: Lagrangian n=8.
2.11 Appendix: Occurrence of ‘Om’ in the ancient literature
and some questions regarding multi-dimensional spaces.
3. Structural richness
of cube
3.1 Cube
3.2 Three space
3.3 Triloki and Lord Vishnu
3.4 Chasing Rigved organisation with cube
3.5 Chasing Vedic knowledge organisation with cube
3.6 Internal structure of a cube
3.7 Structural setups of a cube of edges as ten units
3.8 Bottlenecks of linear mathematics
3.9 Exposure to structural richness of cube
3.10 To arrive at a syllabi
3.11 For transition to course on hypercube-4
4. Mahalakshmi
Ashtakam Stotram
4.1 Introduction
4.2 Text of the scripture
4.3 Text as composition of 818 letters
4.4 Shalokawise structural data
4.5 Gyan Vigyan Yog
4.6 Sri Sri Durgasaptsati
4.7 Goddess Mahalakshmi
4.8 Five as organisation format
4.9 Jyoti manifestation format
4.10 On Sanatana format
4.11 Commentary
My modest work “Patanjali Unison
Discipline” is my first attempt as more in the spirits of a Sadhaka then in that
of scholar, was blessed by my Guru His Holiness Sri Sripad Babaji Maharaj,
with his forward:
“This Indian spiritual wisdom
revealed first in and through the Vedas was well systematised and reconstructed
in the six orthodox systems of Indian philosophy, namely Nayaha, Vaisesika
Sankhya, Yoga, Mimasa and Vedanta. Based on scriptural authority and expounded
by eminent Acaryas, these celebrated Darsanas ensure salavation to the serious
aspirant. It is well known that philosophy in India has not been merely an
intellectual enterprise, but a way of life. And herein lies the Sadhanatmaka
character of Indian thinking.
It is against this background that
the philosophy of Yoga should be understood. While recently there is a craze for
Yoga, there is less seriousness for a correct apprehension of this spiritual
science. An attempt at is oversimplification and devising shortcut is what is
apparent here and there. In fact, Yoga is a mater of eternal inspiration for the
Sadhakas. Hence, the relevance of the repeated and reneweded studies of the
basic texts of these great disciplines has dominated search of the truth since
time immemorial.
In the context of such a huge and
rich literature on the subject, as is amassed on Yoga to-date, it is indeed not
any easy task to write a fresh commentary on the Yoga-sutras of Patanjali, which
number 196, are an example of brevity and perfection with which ancient learning
was preserved at the hands of Rishis. Even an explanation of the aphoristic
expression requires a mastery of the language, as well as a deeper insight into
the field. While the size of the Yoga Sutras is not voluminous, it has been very
rationally classified to present a scientific picture of spiritual ascent. The
first section, dealing with the nature and technique of Yoga is known as Samadhi
Pada, since it is devoted to explain what the Yoga is. The second section has
significantly been termed as Sadhana Pada, since it expounds the reasons for
which one should adhere to the path of Yoga. It aptly analyses the miseries of
life from which liberation is sought, and it prescribes external preparatory
disciplines which attune the Sadhaka to Samadhi. The third section, called as
Vibhuti Pada, lays down the internal Yogic techniques which unfold the mysteries
powers prior to attainment of Samadhi. The last section is naturally Kalvlya
Pada, which thoroughly deals with the basic philosophical doctrine involved in
the Yogic conception of bondage and liberation.
Sri Sant Kumar Kapoor of the
Haryana Civil Service (Judicial), Palwal, has done an humble service by writing
the book titled “Patanjali Unison Discipline”. His modest work is more in the
spirit of a Sadhaka than in that of a scholar. He has attempted a simple
explanation note for each Sutra of the Patanjali Yoga-Sutras. May God grant him
further inspiration in this noble direction, as the Patanjali Yoga Darsana is to
first taste the amrosia of yoga with the supreme, and then to reveal the
experience. The lineage of Sadhakas as well as scholars has worked together on
the Patanjali Yog Sutra from the ages to reveal and to experience the Yoga
Sutras by their living evidence”
His Holiness Sri Sripad Babaji
Maharaj
saint of Vrindavan, the founder of
Vraja Academy, Vrindavan blessed this work and made me His disciple emerging to
His satisfaction of Mahewshwara Sutras for proper channelization of natural
order on the transcendental format of Om as Udgiti of Parvanava, AUM, Onkar and
Vashitakar of Absolute order of Veda:
"The revelation of Eternal wisdom
has been the eternal quest -- the meeting point of alpha and omega in Indian
School of Thought. Lord Krishna reveals this lineage in Bhagvad Gita as:
‘I taught this immortal Yoga to
Vivaswan (Sun-god):
Vivaswan conveyed it to Manu (his son); and Manu imparted
it to (his son) Ikswaku’ IV.1
The transmission of the light of
knowledge from man to man and from age to age is handed down through the great
ancillary of cosmic memory by the enlightened one to the seeker in quest.
Whenever this link of interaction is broken the energy is stagnant and humanity
stands at the crossroad. Symbolically, the churning of divine and demonic forces
comes to the point of creating problems for right discrimination to decipher the
Truth and find the right dimension of consciousness.
Since these ancient links are lost,
intellectual attempts to regain them are being made since several decades. The
present research work within the Vedic mathematical disciplines opens new
horizons for modern science and inspires rational thinking to go back to the
ancient metaphysical courses of the meeting point of thinghness and nothingness,
which the great symbol reveal in the mantras and shruti, in the journey of
consciousness of the Pauranic kathas and in the insight into the in-depth psyche
of the Bhagavadgita. Once again efforts are being made to provide a way to the
rational scientist to link knowledge with the energy of an inscrutable faith
which can open in him the mystic eye or vision. The rejuvenation of this quest
is deeply stressed and aims to arrive at a metamorphosis in the fields of
eternal mathematics introduced here as the first of its kind.
Sri Sant Kumar Kapoor’s quest –
else engaged in the field of jurisprudence – has opened his intuitive faculty of
study ancient scriptures in the light of modern mathematics. These studies were
brought to focus by His Holiness Swami Bharti Krisna Tirthaji Maharaj, the
Sankracharya of Kanchi Peeth around 1965.
As the Shrutis of the Vedas sing in
chorus; “He is full, this is full, if fullness if taken out of fullness there
remains fullness”, so the heart of the Rigveda concludes that our thoughts
should be same, our actions should be same, there should be no diversity between
them, that the fullness of thought, speech and action should meet at alpha and
omega, at-one-ment. To unlock the intuitive forces and dynamic energies in quest
of the churned out Ambrosia the universal syllable AUM is beginning and the end.
This research work is on its way to
arrive at this very conclusion. May the Supreme Divine bless this venture.”