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Swami Paramarthananda has discussed this subject in his various lectures. The word nirvikalpaka means “divisionlessness.” We experience the world in the form of division of “subject and object.” Hence it is a clear case of dvaita (duality).
World is also presented in another way: without an instrument, “seer” and “seen,” it cannot be experienced. And there has to be a “Creator” of what is seen. He is called “Isvara” (God). With the help of the power of Maya (creative power), he manifests all that is seen. So we can say that the world consists of a “triputi” (group of three), which is Isvara (God), the world and the jiva (individual soul), which sees and experiences the world with the instruments of knowledge with which he is born. Technically, triputi (group of three) is referred to as “subject, object and the instrument of knowledge” – the pramata (knower), pramanam (instrument of knowledge) and prameyam (that which is seen and experienced). In substance, the world is in the form of dvaita (duality). Hence it is called “savikalpaka” (with division).
In Vedanta, nirvikalpakam (divisionlessness) is of two types:
1. Nirvikalpaka avastha – a state of divisionlessness, a state in which all the divisions are resolved. Resolution of vikalpa (division) happens in different ways: in deep sleep, going into a coma stage, death and pralaya (complete dissolution). Thus it can be natural or artificially brought about like yogic samadhi (deep meditation). But all such divisionless states are not really divisionless, because divisions have not gone away but are in a dormant form. In other words, it is only a temporary nivikalpa (divisionlessness) and not real nirvikalpaka (divisionlessness).
In the vision of Vedanta, nirvikalpaka avastha (state of divisionlessness) does not have much value, since such a state solves no problems – in the sense that all the problems are just kept in a dormant state, only to get revived after the state of samadhi (deep meditation) is over. As a temporary measure, of course it is useful; but nothing more.
2. There is another nirvikalpaka samadhi (divisionless deep meditation) which is not a “state” but has the nature of Brahman (the ultimate truth of everything as existence, consciousness and limitlessness). It is a state in which there are absolutely no divisions or any kind of action. It is the state of being Brahman (the ultimate truth).
Brahman (The ultimate truth) is called nirvikalpaka (divisionless) because it is free from all divisions and actions. Brahman is in fact nirvikalpaka vasthu (nature of divisionlessness) and not just a nirvikalpaka avastha (state of divisionlessness). It is so in this nature that all the time and the mithya (existence depending on something else) world cannot disturb it at all.
So our aim is to be that nirvikalpaka vasthu (nature of divisionlessness) and not just reach a state of nirvikalpaka samadhi (divisionless deep meditation). Let the savikalpaka (with division) world appear and disappear (as in deep sleep), but “I” as Brahman am always nirvikalpaka (divisionless).
Matter, being anadhi (beginningless), cannot be created. It was there in potential form before the Creation, it exists as the Creation and gets resolved at the time of pralaya (resolution). All this happens with the power of Maya shakti (creative power). But it is jadam (inert) in its nature. But Brahman is neither manifest nor unmanifest, since it is the non-material consciousness principle. Consciousness is the reality in which the universe manifests and unmanifests; but it is not a part or product of the universe, but the only reality. This reality undergoes no change whatever.
All the Vedantic students should understand this difference and not look forward to just nirvikalpaka samadhi (divisionless deep meditation) as advocated by many of the teachers of philosophy.
Advaitic vision is understanding that all that is manifest here as the universe is divisionless Brahman. Brahman is the ultimate truth of everything as existence, consciousness and limitlessness. My true nature is also existence, consciousness and limitlessness. I am non-separate from Brahman.