PART I: The difference between Sri Aurobindo's "integral advaita" and other forms of non dualism - in his own words
Don Salmon
Integral Yoga and Other Paths
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I do not agree with the view that the world is an illusion, mithyā. The Brahman is here as well as in the supracosmic Absolute. The thing to be overcome is the Ignorance which makes us blind and prevents us from realising Brahman in the world as well as beyond it and the true nature of existence.
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The Shankara knowledge is, as your Guru pointed out, only one side of the Truth; it is the knowledge of the Supreme as realised by the spiritual Mind through the static silence of the pure Existence. It was because he went by this side only that Shankara was unable to accept or explain the origin of the universe except as illusion, a creation of Maya. Unless one realises the Supreme on the dynamic as well as the static side, one cannot experience the true origin of things and the equal reality of the activeBrahman. The Shakti or Power of the Eternal becomes then a power of illusion only and the world becomes incomprehensible, a mystery of cosmic madness, an eternal delirium of the Eternal. Whatever verbal or ideative logic one may bring to support it, this way of seeing the universe explains nothing; it only erects a mental formula of the inexplicable. It is only if you approach the Supreme through his double aspect of Sat and Chit-Shakti, double but inseparable, that the total truth of things can become manifest to the inner experience. This other side was developed by the Shakta Tantriks. The two together, the Vedantic and the Tantric truth unified, can arrive at the integral knowledge.
But philosophically this is what your Guru's teaching comes to and it is obviously a completer truth and a wider knowledge than that given by the Shankara formula. It is already indicated in the Gita's teaching of the Purushottama and the Parashakti (Adya Shakti) who become the Jiva and uphold the universe. It is evident that Purushottama and Parashakti are both 
eternal and are inseparable and one in being; the Parashakti manifests the universe, manifests too the Divine in the universe as the Ishwara and Herself appears at His side as the Ishwari Shakti. Or, we may say, it is the Supreme Conscious Power of the Supreme that manifests or puts forth itself as Ishwara Ishwari, Atma Atma-shakti, Purusha Prakriti, Jiva Jagat. That is the truth in its completeness as far as the mind can formulate it. In the supermind these questions do not even arise: for it is the mind that creates the problem by creating oppositions between aspects of the Divine which are not really opposed to each other but are one and inseparable.
This supramental knowledge has not yet been attained, because the supermind itself has not been attained, but the reflection of it in intuitive spiritual consciousness is there and that was what was evidently realised in experience by your Guru and what he was expressing in mental terms in the quoted passage. It is possible to go towards the knowledge by beginning with the experienceof dissolution in the One, but on condition that you do not stop there, taking it as the highest Truth, but proceed to realise the same One as the supreme Mother, the Consciousness-Force of the Eternal. If, on the other hand, you approach through the Supreme Mother, she will give you the liberation in the silent One also as well as the realisation of the dynamic One, and from that it is easier to arrive at the Truth in which both are one and inseparable. At the same time, the gulf created by mind between the Supreme and His manifestation is bridged, and there is no longer a fissure in the truth which makes all incomprehensible. If in the light of this you examine what your Guru taught, you will see that it is the same thing in less metaphysical language.
As for Adesh, people speak of Adesh without making the necessary distinctions, but these distinctions have to be made. The Divine speaks to us in many ways and it is not always the imperative Adesh that comes. When it does, it is clear and irresistible, the mind has to obey and there is no question possible, even if what comes is contrary to the preconceived ideas of the mental intelligence. It was such an Adesh that I had when I came away to Pondicherry. But more often what is said is an intimation or even less, a mere indication, which the mind may 
not follow because it is not impressed with its imperative necessity. It is something offered but not imposed, perhaps something not even offered but only suggested from the Truth above.
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If Shankara's conception of the undifferentiated pure Consciousness as the Brahman is your view of it, then it is not the path of this yoga that you should choose; for here the realisation of pure Consciousness and Being is only a first step and not the goal. But an inner creative urge from within can have no place in an undifferentiated Consciousness – all action and creation must necessarily be foreign to it.
I do not base my yoga on the insufficient ground that the Self (not soul) is eternally free. That affirmation leads to nothing beyond itself, or, if used as a starting-point, it could equally well lead to the conclusion that action and creation have no significance or value. The question is not that but of the meaning of creation, whether there is a Supreme who is not merely a pure undifferentiated Consciousness and Being, but the source and support also of the dynamic energy of creation and whether the cosmic existence has for It a significance and a value. That is a question which cannot be settled by metaphysical logic which deals in words and ideas, but by a spiritual experience which goes beyond Mind and enters into spiritual realities. Each mind is satisfied with its own reasoning, but for spiritual purposes that satisfaction has no validity, except as an indication of how far and on what line each one is prepared to go in the field of spiritual experience. If your reasoning leads you towards the Shankara idea of the Supreme, that might be an indication that the Vedanta Adwaita (Mayavada) is your way of advance.
This yoga accepts the value of cosmic existence and holds it to be a reality; its object is to enter into a higher Truth-Consciousness or Divine supramental Consciousness in which action and creation are the expression not of ignorance and imperfection, but of the Truth, the Light, the Divine Ananda. But for that, surrender of the mortal mind, life and body to that Higher Consciousness is indispensable, since it is too difficult for the 
mortal human being to pass by its own effort beyond mind to a supramental Consciousness in which the dynamism is no longer mental but of quite another power. Only those who can accept the call to such a change should enter into this yoga.
02.10.1938
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I don't know that I can help you very much with an answer to your friend's questions. I can only state my own position with regard to these matters.
1. Shankara's Explanation of the Universe
It is rather difficult to say nowadays what really was Shankara's philosophy: there are numberless exponents and none of them agrees with any of the others. I have read accounts given by some scores of his exegetes and each followed his own line. We are even told by some that he was no Mayavadin at all, although he has always been famed as the greatest exponent of the theory of Maya, but rather, the greatest Realist in philosophical history. One eminent follower of Shankara even declared that my philosophy and Shankara's were identical, a statement which rather took my breath away. One used to think that Shankara's philosophy was this that the Supreme Reality is a spaceless and timeless Absolute (Parabrahman) which is beyond all feature or quality, beyond all action or creation, and that the world is a creation of Maya, not absolutely unreal, but real only in time and while one lives in time; once we get into a knowledge of the Reality, we perceive that Maya and the world and all in it have no abiding or true existence. It is, if not non-existent, yet false, jaganmithyā; it is a mistake of the consciousness, it is and it is not; it is an irrational and inexplicable mystery in its origin, though we can see its process or at least how it keeps itself imposed on the consciousness. Brahman is seen in Maya as Ishwara upholding the works of Maya and the apparently individual soul is really nothing but Brahman itself. In the end, however, all this seems to be a myth of Maya, mithyā, and not anything really true. If that is Shankara's philosophy, it is to me unacceptable and incredible, however brilliantly ingenious it may be and however boldly and incisively reasoned; it does not satisfy my reason and it does not agree with my experience.
I don't know exactly what is meant by this yuktivāda. If it is meant that it is merely for the sake of arguing down opponents, then this part of the philosophy has no fundamental validity; Shankara's theory destroys itself. Either he meant it as a sufficient explanation of the universe or he did not. If he did, it is no use dismissing it as Yuktivada. I can understand that thorough-goingMayavadin's declaration that the whole question is illegitimate, because Maya and the world do not really exist; in fact, the problem how the world came to existence is only a part of Maya, is like Maya unreal and does not truly arise; but if an explanation is to be given, it must be a real, valid and satisfying explanation. If there are two planes and in putting the question we are confusing the two planes, that argument can only be of value if both planes have some kind of existence and the reasoning and explanation are true in the lower plane but cease to have any meaning for a consciousness which has passed out of it.
2. Adwaita
People are apt to speak of the Adwaita as if it were identical with Mayavada monism, just as they speak of Vedanta as if it were identical with Adwaita only; that is not the case. There are several forms of Indian philosophy which base themselves upon the One Reality, but they admit also the reality of the world, the reality of the Many, the reality of the differences of the Many as well as the sameness of the One (bhedābheda). But the Many exist in the One and by the One, the differences are variations in manifestation of that which is fundamentally ever the same. This we actually see as the universal law of existence where oneness is always the basis with an endless multiplicity and difference in the oneness; as, for instance, there is one mankind but many kinds of man, one thing called leaf or flower but many forms, patterns, colours of leaf and flower. Through this we can look back into one of the fundamental secrets of existence, the secret which is contained in the one Reality itself. The oneness of the Infinite is not something limited, fettered to its unity; it is capable of an infinite multiplicity. The Supreme Reality is an Absolute not limited by either oneness or multiplicity but simultaneously capable of both; for both are its aspects, although the oneness is fundamental and the multiplicity depends upon the oneness.
There is possible a realistic as well as an illusionist Adwaita. The philosophy of The Life Divine is such a realistic Adwaita. The world is a manifestation of the Real and therefore is itself real. The reality is the infinite and eternal Divine, infinite and eternal Being, Consciousness-Force and Bliss. This Divine by his power has created the world or rather manifested it in his own infinite Being. But here in the material world or at its basis he has hidden himself in what seem to be his opposites, Non-Being, Inconscience and Insentience. This is what we nowadays call the Inconscient which seems to have created the material universe by its inconscient Energy, but this is only an appearance, for we find in the end that all the dispositions of the world can only have been arranged by the working of a supreme secret Intelligence. The Being which is hidden in what seems to be an inconscient void emerges in the world first in Matter, then in Life, then in Mind and finally as the Spirit. The apparently inconscient Energy which creates is in fact the Consciousness-Force of the Divine and its aspect of consciousness, secret in Matter, begins to emerge in Life, finds something more of itself in Mind and finds its true self in a spiritual consciousness and finally a supramental Consciousness through which we become aware of the Reality, enter into it and unite ourselves with it. This is what we call evolution which is an evolution of Consciousness and an evolution of the Spirit in things and only outwardly an evolution of species. Thus also, the delight of existence emerges from the original insentience, first in the contrary forms of pleasure and pain, and then has to find itself in the bliss of the Spirit or, as it is called in the Upanishads, the bliss of the Brahman. That is the central idea in the explanation of the universe put forward in The Life Divine.
3. Nirguna and Saguna
In a realistic Adwaita there is no need to regard the Saguna as a creation from the Nirguna or even secondary or subordinate to it: both are equal aspects of the one Reality, its position of 
silent status and rest and its position of action and dynamic force; a silence of eternal rest and peace supports an eternal action and movement. The one Reality, the Divine Being, is bound by neither, since it is in no way limited; it possesses both. There is no incompatibility between the two, as there is none between the Many and the One, the sameness and the difference. They are all eternal aspects of the universe which could not exist if either of them were eliminated, and it is reasonable to suppose that they both came from the Reality which has manifested the universe and are both real. We can only get rid of the apparent contradiction – which is not really a contradiction but only a natural concomitance – by treating one or the other as an illusion. But it is hardly reasonable to suppose that the eternal Reality allows the existence of an eternal illusion with which it has nothing to do or that it supports and enforces on being a vain cosmic illusion and has no power for any other and real action. The force of the Divine is always there in silence as in action, inactive in silence, active in the manifestation. It is hardly possible to suppose that the Divine Reality has no power or force or that its only power is to create a universal falsehood, a cosmic lie – mithyā.
4. Compounds and Disintegration
No doubt, all compounds, being not integral things in themselves but integrations, can disintegrate. Also it is true of life, though not a physical compound, that it has a curve of birth or integration and, after it reaches a certain point, of disintegration, decay and death. But these ideas or this rule of existence cannot be safely applied to things in themselves. The soul is not a compound but an integer, a thing in itself; it does not disintegrate, but at most enters into manifestation and goes out of manifestation. That is true even of forms other than constructed physical or constructed life-forms; they do not disintegrate but appear and disappear or at most fade out of manifestation. Mind itself as opposed to particular thoughts is something essential and permanent; it is a power of the Divine Consciousness. So is life, as opposed to constructed living bodies; so I think is what we call material energy which is really the force of 
essential substance in motion, a power of the Spirit. Thoughts, lives, material objects are formations of these energies, constructed or simply manifested according to the habit of the play of the particular energy. As for the elements, what is the pure natural condition of an element? According to modern Science, what used to be called elements turn out to be compounds and the pure natural condition, if any, must be a condition of pure energy; it is that pure condition into which compounds including what we call elements must go when they pass by disintegration into Nirvana.
5. Nirvana
What then is Nirvana? In orthodox Buddhism it does mean a disintegration, not of the soul – for that does not exist – but of a mental compound or stream of associations or saṃskāras which we mistake for ourself. In illusionist Vedanta it means, not a disintegration but a disappearance of a false and unreal individual self into the one real Self or Brahman; it is the idea andexperience of individuality that so disappears and ceases, – we may say a false light that is extinguished (nirvāṇa) in the true Light. In spiritual experience it is sometimes the loss of all sense of individuality in a boundless cosmic consciousness; what was the individual remains only as a centre or a channel for the flow of a cosmic consciousness and a cosmic force and action. Or it may be the experience of the loss of individuality in a transcendent being and consciousness in which the sense of cosmos as well as the individual disappears. Or again, it may be in a transcendence which is aware of and supports the cosmic action. But what do we mean by the individual? What we usually call by that name is a natural ego, a device of Nature which holds together her action in the mind and body. This ego has to be extinguished, otherwise there is no complete liberation possible; but the individual self or soul is not this ego. The individual soul is the spiritual being which is sometimes described as an eternal portion of the Divine, but can also be described as the Divine himself supporting his manifestation as the Many. This is the true spiritual individual which appears in its complete truth when we get rid of the ego and our false separative sense of individuality, realise 
our oneness with the transcendent and cosmic Divine and with all beings. It is this which makes possible the Divine Life. Nirvana is a step towards it; the disappearance of the false separative individuality is a necessary condition for our realising and living in our true eternal being, living divinely in the Divine. But this we can do in the world and in life.
6. Rebirth
If evolution is a truth and is not only a physical evolution of species, but an evolution of consciousness, it must be a spiritual and not only a physical fact. In that case, it is the individual who evolves and grows into a more and more developed and perfect consciousness and obviously that cannot be done in the course of a brief single human life. If there is the evolution of a conscious individual, then there must be rebirth. Rebirth is a logical necessity and a spiritual fact of which we can have the experience. Proofs of rebirth, sometimes of an overwhelmingly convincing nature, are not lacking, but as yet they have not been carefully registered and brought together.
7. Evolution
In my explanation of the universe I have put forward this cardinal fact of a spiritual evolution as the meaning of our existence here. It is a series of ascents from the physical being and consciousness to the vital, the being dominated by the life-self, thence to the mental being realised in the fully developed man and thence into the perfect consciousness which is beyond the mental, into the supramental Consciousness and the supramental being, the Truth-Consciousness which is the integral consciousness of the spiritual being. Mind cannot be our last conscious expression because mind is fundamentally an ignorance seeking for knowledge; it is only the supramental Truth-Consciousness that can bring us the true and whole Self-Knowledge and world-Knowledge; it is through that only that we can get to our true being and the fulfilment of our spiritual evolution.
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The sentence1 is rather loose in expression. It does not mean that Maya is Brahman's freedom, but “the doctrine ofMaya simply comes to this that Brahman is free from the circumstances through which He expresses Himself.” This limited play is not He, for He is illimitable; it is only a conditioned (partial) manifestation, but He is not bound by the conditions (circumstances) as the play is bound. The world is a figure of something of Himself which He has put forth into it, but He is more than that figure. The world is not unreal or illusory, but our present seeing or consciousness of it is ignorant, and therefore the world as seen by uscan be described as an illusion. So far the Maya idea is true. But if we see the world as it really is, a partial and developing manifestation of Brahman, then it can no longer be described as an illusion, but rather as a Lila. He is still more than His Lila, but He is in it and it is in Him; it is not an illusion.