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Adhyāsa is the Sanskrit term for the superimposition or false attribution of properties of one thing on another thing.
According to Advaita Vedanta error arises on account of the superimposition of one reality on another. Adi Shankara defines Adhyasa as "the apparent presentation, to consciousness, by way of memory of something previously observed in some other thing".
Adhyasa is the illusory appearance, in another place, of an object seen earlier elsewhere. It is similar in nature to recollection. For instance on seeing a rope in dim light and not recognizing it as a rope, a person mistakes it for a snake which he has seen elsewhere. The snake is not absolutely unreal, because it is actually experienced, and produces the same effect, such as fear and so on, as a real snake would. At the same time, it is not real, because it is no longer seen when the rope has been recognized. It is therefore described as Anirvachaneeya or what cannot be classified as either real or unreal.
Adi Shankara further points out in his Adhyāsabhāṣya on the Brahma Sutras that, when there is superimposition of one thing on another, the latter (the substratum) is not affected in the least by the good or bad qualities of the former. (e.g., nacre does not become more valuable because it is mistaken for silver, nor does a rope get the qualities of the snake which it is mistaken for). The implication of this statement is that the self which is identical with Brahman does not undergo any of the changes, nor does it experience any of the joys and sorrows, of the body, mind and organs which are superimposed on it. It is, however, only because of this mutual superimposition of the self and the non-self that all action, both secular and religious, including the study of Vedanta, becomes possible. The self, by itself, is neither a doer of actions, nor an enjoyer of the results. It becomes a doer and an enjoyer only because of this superimposition, as a result of which, as Adi Shankara says, the real and the unreal, namely, the self and the non-self, are blended into one, as it were.. All action, including the various rites laid down in the Vedas, thus come within the sphere of Avidya or nescience, which is the cause of the superimposition.
Adhyasa is of two kinds. When a rope is mistaken for a snake, the snake alone is seen. The existence of the rope is not known at all. Here the snake is said to be superimposed on the rope. This is known as Svarupa-Adhyasa. The second kind of superimposition is when a crystal appears to be red in the proximity of a red flower. Here both the crystal and the flower are seen as existing, and the redness of the flower is attributed to the crystal also. This is known as Samsarga-Adhyasa. Both these kinds of Adhyasa are present in the mutual superimposition of the self and the non-self.
Because of the superimposition of the non-self on the self, the existence of the self is not recognized at all, and the non-self, (that is, the body, mind and organs), is alone recognized as existing. This is Svarupa-Adhyasa. In the superimposition of the self on the non-self, only the existence and consciousness aspects of the self are attributed to the body, mind and organs. This is Samsarga-Adhyasa. The result of this mutual superimposition is that every one identifies himself with the body. This is the root cause of all suffering. Giving up this wrong identification with the body-mind complex and realizing that one is the self which is beyond all suffering and all the pairs of opposites such as heat and cold, success and failure and so on, is Vidya or knowledge. It is this knowledge that is contained in the Upanishads.
Svarupa-Adhyasa is also known as Nirupadhika-Adhyasa or superimposition without a limiting adjunct or Upadhi. The superimposition of an illusory snake on a rope is of this type. Upadhi has been defined by Bhaskararaya in his commentary on the name Nirupadhih (No.154) in the Lalitāsahasranāmabhāsya as Upa samipe adadhati sviyam dharmam that which imparts its own quality to an object near it. A red flower which makes a transparent crystal near it look red is an upadhi. The superimposition of the red colour on the crystal is a superimposition with upadhi and it is known as Sopadhika-Adhyasa, which is the same as samsarga-adhyasa.
In the superimposition of the snake on the rope, the substratum is considered to be the rope. But the snake itself is not real, and is a superimposition on Brahman or pure Consciousness. Therefore it is said in Vedanta that the substratum is Rajju-upahita chaitanyam or pure Consciousness apparently limited by the rope. Every object in this world should therefore be looked upon as Brahman limited by that object or Brahman in the form of that object Sarvam khalu idam brahma. The illusory snake is described as Pratibhasika or illusory; the rope, like everything in this world, is Vyavaharika or empirical reality. Brahman alone is Paramarthika or absolute reality. The aim of Vedanta is to enable one to attain this realization.