A Logical Model of Yoga Philosophy

(c) 1998 Ian Williams Goddard


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, our Hindu number system also accurately models -- and thus explains and validates as logical -- central metaphysics of the Hindu philosophy of yoga.



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 centuries of confusion and dispute, not only between East and West but within Eastern philosophical systems. I believe the following resolves this Hindu paradox via, appropriately enough, the Hindu number system



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 populated by many: by the process of differentiation:

Just Like Brahman


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.

ERGO: it is 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 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 in fact the exact model indicated. (for a more comprehensive analysis of difference and identity)



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
in the beginning and in the end, is necessarily non-
[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.



Yoga means "union," the union of the identity of the individual, the Atman, with the identity 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 states 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 Absolute identity of everything (0); which also explains why Hindu scripture proclaims that the absolute nature of things is nonexistent (0).



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 [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 meditation (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 unceasingly. The Great Void,
whose beginning is void, whose middle is void,
whose end is void. . . By contemplating continually
on this, one obtains success

The Siva Samhita [9]

Buddhists agree with Hindus:

"[I]t is only through the understanding of voidness
that liberation from cyclic existence is possible...
Insight into voidness is therefore called
'the gateway to liberation.'"

Geshe Rabten, "Echoes of Voidness" [10]



The central teachings of the philosophy of yoga amount to a logical description of the differential 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 deviation from nothing (zero); and (3) the Absolute (i.e., nonrelative) identity of each individual entity, which is zero, equals the Absolute identity of the All, hence their logical union (yoga).

This essay demonstrates that the most radically "mystical" and heretofore inexplicable aspects of the Hindu philosophy of yoga can in fact be logical.


[1] "The Upanishads," translated by Eknath Easwaran. Petaluma California: Nilgiri Press, 1987, page 60.

[2] "Viveka-Cudamani," by Sri Sankaracarya, translated by Mohini M. Chatterji. Adyar India: The Theosophical Publishing House, 1932, verse 469, page 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 5, verse 161, page 79.

[6] "The Penguin Dictionary of Mathematics," edited by J. Daintith & R.D. Nelson. Penguin Books, 1989, page 95.

[7] "The Mandukyopanishad." Mysore India: Sri Ramakrishna Ashram, 1974, chapter 4, verse 31, page 245.

[8] "The Final Truth, Guide To Ultimate Understanding," by Ramesh S. Balsekar. L.A.: Advaita Press, 1989, page 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, page 128.




(c) 1998 Ian Williams Goddard