Brhadaranyaka Upanisad - Upadhi and Self

An upadhi is a thing which communicates its own property to another situated close to it as for instance, when a red flower is placed near a crystal, it imparts its red colour to the glass which then appears red; here the flower is the associate of the crystal.

(from Vichar Sagar by Sadhu Nachildas)

That is the standard example which is of course an analogy attempting to give the sense of a relationship between two objects which are separate. Clearly they must have the capacity to affect each other. An important point is that the nature of both elements is not changed by their association. Away from the rose the crystal is as it always was.

Likewise and similarly the inert mind body becomes aware by being 'close' to pure consciousness. Other expressions of that relationship mention pervasion and saturation.

The intellect being transparent and next to the self, easily catches the reflection of the intelligence of the self. Therefore even wise men happen to identify themselves with it first; next comes the Manas, (mind) which catches the reflection of the self through the intellect; then the organs, through contact with the Manas; and lastly the body, through the organs. Thus the self successively illumines with its own intelligence the entire aggregate of body and organs. It is therefore that all people identify themselves with the body and organs and their modifications indefinitely according to their discrimination.

(from Sankara's commentary on Brh.Up. IV.iii.7)

Thus it is said that the mind is an upadhi (limiting adjunct) of pure consciousness. It, as it were, shrinks it to its own size.

Next Sankara explicates the central advaitic concept of adhyasa (superimpostion) and its relations to upadhi. Later....