From: Ian Goddard (Ian@Goddard.net)
Date: Fri Sep 25 1998 - 14:24:17 MDT
At 01:39 PM 9/25/98 -0400, Doug Bailey wrote:
>Ian Goddard wrote:
>
>> The analysis of synthetic numeric identities here-
>> in allows us to see and thereby prove: (a) that
>> identity is conserved, expressed via the real num-
>> bers as a constant zero-sum, since, for example, n
>> is always as much more than x as x is less than n;
>> (b) that identity is therefore symmetrical; (c)
>> that Relative identity is holistic, since all non-
>> zero identity attributes are derived from other-
>> difference; and (d) that the Absolute (nonrelative)
>> identity of each and every thing equals zero.
>
>I guess at this point I am wondering what kind of useful insights can
>be drawn from the conclusions above. I can not find any. I'd rather
>identify to what end such a conclusion might contribute before
>wondering whether it is valid.
IAN: For starters, union of previously assumed to
be paradoxically related, or contrary, philosophies:
o---------------------------------------------o
o---------------------------------------------o
LOGICAL MODEL & PROOF OF THE PHILOSOPHY OF YOGA
Originating in India in the 5th century AD, the
system of numeration used throughout the world
today has proven to facilitate extreme accuracy
in the modelling of the physical universe.
As we shall observe, the Hindu number system
also accurately models -- and thus explains and
validates as logical -- the core metaphysics of
the Hindu philosophy of yoga, or mystical union.
BRAHMAN: CONTRADICTION OR TRUTH?
The supreme truth in Hinduism is Brahman. Deities
such as Shiva and Vishnu represent mere aspects of
Brahman. According to Hindu scripture, "Brahman is
all"[1] and yet "Brahman is without attributes."[2]
Having zero attributes, Brahman is called "sunya,"
which is Sanskrit for void and the number zero.
"Sunya: void; the Nothing which is All.
Sunya Brahman: [the brahman as the
Void]; Supreme Nothingness."
Glossary of Sanskrit terms [3]
According to scripture, Brahman contains all forms
and yet is formless; is the knower, knowledge, and
the known and yet is "bereft of knower, knowledge,
and known."[4] How can Brahman be all and nothing?
How can Brahman be and also not-be x, y, and z?
This all-and-nothing paradox is the nexus of centur-
ies of confusion and dispute, not only between East
and West but within Eastern philosophical systems.
Here then is the resolution of this Hindu "paradox"
via, appropriately enough, the Hindu number system.
NUMBERS: MAPPING THE FACE OF REALITY
The claim that x is equal to all and x is equal to
nothing is true if, and only if, all is equal to
nothing; for, if x = a and x = 0, then a = 0. But
how could everything possibly be equal to nothing?
Hindu scripture says that "Brahman is one" (is an
undivided unity) but appears to be many due to the
process of "differentiation." [5] The mathematical
definition of difference is that which is obtained
by subtraction.[6] The operation of subtraction is
therefore both the indicated and logical model of
the process by which Brahman appears to be many.
"Treat the laws and relationships
of integers like those of the
celestial bodies." George Cantor
The subtraction table models a system wherein that
one system (the whole table) is populated with many
attributes by the same process that Brahman is pop-
ulated by many: by the process of differentiation:
(fixed-pitch font required)
0 1 2 3
____________
0 | 0 1 2 3 |
| |
1 |-1 0 1 2 |
| |
2 |-2 -1 0 1 |
| |
3 |-3 -2 -1 0 |
--------------
Just Like Brahman
THE TABLE IS ALL & NOTHING
Exactly like Brahman, the whole table (as a model
of a whole universe, or the All) contains all and
yet is itself equal to nothing, because the sum of
all differences between all differentiated numbers
will always equal zero no matter how many or few
numbers are differentiated. All difference = 0.
The significance of difference lies in the fact
that difference -- from zero difference, or same
as, to nonzero differences -- defines the causal
structure of identity, which in turn defines the
fundamental nature of every thing and existence.
Therefore, using the example of the zero-sum of
all difference to model the supreme identity is
not arbitrary, but is the exact model indicated.
ERGO: it's a mathematic fact that the sum (yoga)
of all differences (Brahman) equals zero (sunya).
The all-and-nothing Brahman paradox is therefore
not a contradiction but is in fact logically true
with respect to the nature of the identity of the
All, where the All is a whole system wherein all
members are derived from differentiation, which
is the means by which Brahman appears to contain
many and by which any identity n is defined as n
(a number n is primary its difference from zero).
(The differentiation table, or identity matrix,
serves as a comprehensive model of the structure
of identity; a more complete analysis of this is
found here: http://ian.goddard.net/identity.htm)
MORE YOGA PUZZLES SOLVED
The differentiation table explains not only how
Brahman can be all and nothing, but it explains
many if not all aspects of yogic philosophy such
as the profoundly mystical and seemingly absurd
principle of "Ajati," which declares that nothing
ever exists or is ever actually created (the same
is referred to in Buddhism as the "nonarising" of
all apparent phenomena). The nonarising of things
defines their void-like, or nonexistent, nature.
As the Hindu scripture Mandukya Upanishad says:
"[N]either the mind nor the objects perceived
by the mind are ever born. ... That which is
non-existent [0] in the beginning and in the
end, is necessarily non-existent [0] in the
middle. The objects we see are illusions,
still they are regarded as if real."
Mandukya Upanishad [7]
If there is no difference, and then difference
arises, yet the sum of All difference is equal
to no difference(0), then in fact only nothing
arises, hence the nonarising known as "Ajati."
LOGICAL UNION OF ATMAN AND BRAHMAN
Yoga means "union," the union of the identity
of the individual, the Atman, with the iden-
tity of the supreme Brahman, which is the All.
As the differential matrix shows, the identity
of each thing relative to itself is zero, which
is the same identity as the identity of the All.
The zero of self-relation defines the Absolute,
or nonrelative, nature of identity expressed in
the differentiation n - n = 0, which means that
there is no (0) difference between n and n, and
therefore n = n -- the definition of identity.
So the Absolute identity of each thing (0) is
the same as, and thus is united with, the Abso-
lute identity of everything (0); which also ex-
plains why Hindu scripture proclaims that the
absolute nature of things is nonexistent (0).
THE GOAL OF YOGA EQUALS ZERO (SUNYA)
The goal of the practice of yoga is to condition
the mind to become like zero and in so doing, to
establish an identity-union between the finite
self, the Atman, and the infinite All, Brahman.
"Everything is 'I', and I am no thing."
Ramesh Balsekar, "The Final Truth" [8]
The traditional yoga lifestyle strives toward the
goals of asceticism, which seeks to zero-out all
desires, attachments, emotions, and ego clinging.
The goal of yoga is essentially to cause the mind
to become like zero. In fact, the goal of medita-
tion (the central feature of the yoga lifestyle)
is to zero-out thoughts, to zero-out the mind and
realize the true condition of reality... zero. To
know the supreme become like the supreme... zero.
"He who contemplates on sunya...is absorbed
into space. . . think on the Great Void un-
ceasingly. The Great Void, whose beginning
is void, whose middle is void, [and] whose
end is void...By contemplating continually
on this, one obtains success [nirvana]."
The Siva Samhita [9]
Buddhists agree with Hindus:
"[I]t is only through the understanding of
voidness that liberation from cyclic exist-
ence is possible. ...Insight into voidness is
therefore called 'the gateway to liberation.'"
Geshe Rabten, "Echoes of Voidness" [10]
IN CONCLUSION
The central teachings of the philosophy of yoga
amount to a logical description of the differen-
tial structure of identity and the zero-sum of
all differences, proving that (1) the "All" can
be all and nothing (zero); (2) the arising of
infinite differences cannot constitute a devia-
tion from nothing (zero); and (3) the Absolute
(i.e., nonrelative) identity of each individual
entity, which is zero, equals the Absolute iden-
tity of the All, hence their logical union (yoga).
This essay clearly proves that the most radically
"mystical" and heretofore inexplicable aspects of
the Hindu philosophy of yoga are in fact logical.
__________________________________________________
--- (c) 1998 Ian Williams Goddard ---
- free to copy nonprofit with author attribution -
--------------------------------------------------
References________________________________________
[1] "The Upanishads," translated by Eknath Easwaran.
Petaluma California: Nilgiri Press, 1987, page 60.
[2] "Viveka-Cudamani," by Sri Sankaracarya, trans-
lated by Mohini M. Chatterji. Adyar India: The Theo-
sophical Publishing House, 1932, verse 469, p. 177.
[3] Glossary of Sanskrit Terms in Integral Yoga
Literature: http://www.miraura.org/lit/skgl.html
[4] "Thus Spake Sri Sankara," Madras India:
Sri Ramakrishna Math, 1969, page 35.
[5] "The Siva Samhita," translated by Srisa Chandra
Vasu. New Delhi India: Munshiram Manoharlal Publishers,
1979, chapter 1, verse 67, page 10.
[6] "The Penguin Dictionary of Mathematics," edited by
J. Daintith & R.D. Nelson. Penguin Books, 1989, p. 95.
[7] "The Mandukyopanishad." Mysore India: Sri Rama-
krishna Ashram, 1974, chapter 4, verse 28, p. 31.
[8] "The Final Truth, Guide To Ultimate Understanding,"
by Ramesh S. Balsekar. L.A.: Advaita Press, 1989, p.77.
[9] "The Siva Samhita" (for details, see ref. [5]),
chapter 5, verses 47, 160, and 161, pages 61 and 79.
[10] "Echoes of Voidness," by Geshe Rabten, translated by
Stephen Batchelor. London: Wisdom Publications, 1983, p.128.
***************************************************************
VISIT Ian Williams Goddard ---------> http://Ian.Goddard.net
_______________________________________________________________
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