Glimpses of Vedic Ganita
[Authored (1990) by Prof.
Krishnaji, Prof. of Physics and ExProVice Chancellor, Allahabad University,
Allahabad, India.]
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 of4space. 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 6space. 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 6space. 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

(n2) space content

(n1) space content

nspace 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 (n2)

Space fold (n1)

Space fold n

Space fold (n+1)

(n+1)th

Space fold (n1)

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 multilayer physiological existence. The start with state of
existence is that of waking state which is parallel to the expression of 1space
as dimension into 3space domain. Sequentially, the existence phenomenon unfolds
until seventh state of consciousness which would be corresponding to the 7space
as dimension into 9 space domain. The origin point of the 6space, being the
7space setup, the human body, geometrically, turns out to be hypercube6 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 6space. 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.
Nondifferentiation of the same is bound to deprive us of most of the results in
specific forms.