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The theory of Yoga is almost same as Samkhya.. If Vedanta and Saamkhya is theory, then Yoga is Practical.. Knowledge, IMHO, can't be attained by any one single approach. This is the opinion of all the Astika schools.
Yog literally means Union.. It extensively deals with psychology and training which mind and body needs to be given for achievement of supreme knowledge.
It is defined as controlling the tendencies of Mind. (Yog: Chitta Vritti Nirodh:). Control need not necessarily mean oppression. Some times in some conditions, some tendencies need to be over-expressed. So it is relative, and should be governed by Dharma (righteousness and Duty, more fittingly basic nature, in terms of Yoga).
When, tendencies of mind are controlled, the characteristics of mind which is governed by Prakriti of three characteristics slowly change to neutral state of mind. This is called the process of going back towards birth (Prati-Prasava) of these tendencies.
eg. If a person gets angry too often, trying to get rid of this quality by suppressing anger is illogical. Instead, slowly, the quality is taken towards its birth. Finding out the root cause of why one gets angry, and trying to work on the cause. Slowly, the intensity of anger will reduce and eventually vanish. Thus, one Characteristic of the given mind is controlled. Similarly to all characteristics.
When all the characteristics of mind are controlled, person attains a state where the mind and the ego are dissolved. Because, Mind and Ego are said to be characteristics made up by Prakriti and Purusha.
Hence, a seedless state of mind (Nirbeej Samadhi) is attained, where the existence of individual as mind, intellect, and separate identity vanishes and he becomes Kaivalya or Singularity. This is state of Liberation or Moksha - Liberation from one'e mind, body, intellect and even a sense of separate individual existence.
Kaivalya is not same as Ishwara.
Thus we see, Samkhya, Yoga and Vedanta are mutually complementary to each other and belief in God does not matter. There are plenty of complications, though..
The aim of Samkhya-Yoga is to transcend the universe made up of Purush and prakriti made up of trigunas.
Not only the universe, but mind (manas), Intellect (buddhi), Ego as in sense of self (Ahamkar or Atman) are in the domain of tri-guNas. Samkhya-Yoga aims at attaining the stage of Kaivalya where the Sanskaras (attributes) of Prakriti-Purusha at all stages be dissolved.
Maanas to be dissolved in Buddhi.. Buddhi in Ahamkaar... and ahamkaar in Kaivalya...
Ishwar praNidhaan or Bhakti is one of the way of controlling the mind.. Ishwara of Patanjali is more about a psychological measure to control rein-free mind. Nothing more.. The PraNidhaan of Ishwar won't give you Moksha.. What is gained is stability of mind..
Instead of Ishwara, one can do praNidhaana/bhakti on donkey or whatever... controlling random thoughts by focussing on one thought is the concept... Donkey will give you peace of mind, if used as prescribed by Patanjali...
Controlled mind is essential for DharaNa (framework of mind for meditation)...Accomplished DhaaraNa is essential for Dhyaan (meditation) - Dhyaan is concentrating on one Desha (region or idea, nothing/Shunya)...When Dhyaan is accomplished, we experience Samaapatti (Samadhi). Samadhi is state where mind is in unison with subject of meditation. ..Samadhi gives some thing creative to seeker. Hence it depends upon what subject he chooses to meditate upon.
If subject is based on Tarka (logic), it is first stage of Samadhi.... If subject is based on Vichaara (thought/idea), which is refined form of Tarka, we attain second stage..... Samadhi without Vichaara is Nirvichaara Samadhi OR Sananda samadhi where person experiences bliss...
Beyond Saanand is Sam-Pragnyaat samadhi which involved awakening of Pragnaa, an intellectual faculty of mind. In common lingo, the MOMENT when an ORIGINAL IDEA strikes to a person, is the moment of 4th stage of samadhi.... Fifth stage is when a person attains Samadhi without having a need to entertain a thought in mind or intellect. This is one of the higher stages.
However, this is not the highest. In all these stages, Prakriti is involved. In fifth stage, person is in unison with his SELF or ahamkaar or Aatman...
But this seed of "I" as separate identity still lingers.. Hence all these samadhis are known as Sabeej Samadhi (one with seed of identity). When a seeker's karma-vipaak is burnt, that is, when he has either nullified or experienced all his Karma, he attains the supreme Samadhi where this seed is lost. This is known as Nirbeej samadhi (Seedless Samadhi)....
What remains then, is Kaivayla...Singularity... person ceases to exist as separate ego and becomes Singularity...