Q:
1) If Atman is perfect, how can it ever be deluded by mAyA?

2) What is the source of avidyA? If there is only brahman, how and why does avidyA exist?

Answers are provided by: Ted, Martin, Shuka, and Dennis.

A (Ted):
1) Atman (i.e. pure limitless awareness) is never really deluded by mAyA (i.e. ignorance), but rather only apparently so.  Given the non-dual nature of reality and, thus, the fact that Brahman-Atma is the only thing — though, of course, pure awareness cannot be said to be a “thing” at all due to its attributeless and unobjectifiable nature — that exists, mAyA is nothing other than Brahman-Atma itself.  That is, it is a power inherent in the very nature of Brahman-Atma.  Ironically, if Brahman-Atma, whose nature is limitless, were limited by the inability to apparently delude itself, it would not be limitless and, therefore, would not be Brahman-Atma :-).

2) As mentioned in the previous response, the source of avidyA (i.e. microcosmic or personal ignorance) is Brahman-Atma (i.e. awareness).  There is no how or why for this.  As a power inherent in pure awareness, ignorance — be it macrocosmic mAyA or microcosmic avidyA — is beginningless and, thus, has no causal explanation for how it came to be.  It simply is.  Why it exists is equally enigmatic.  Since Brahman-Atma is by nature whole, complete, perfect, and full, and therefore inherently desireless, and moreover given the fact that it is not a person with volitional will or ulterior motive or even some anthropomorphic deity with a cosmic agenda or divine plan, there is no purpose for the manifestation, no end it is designed to accomplish.  What could it possibly achieve or attain that limitless awareness needs or does not already have?  If there be any reason for ignorance at all, it might only be guessed that it is for the purpose of its own eradication by means of self-knowledge.  In other words, the self deludes itself in order to “experience” the ecstasy of remembering itself.   Of course, given the fact that pure awareness is not an experiencer, even that doesn’t make much sense.

A (Martin):
1) Atman cannot be deluded by mAyA, simply because mAyA is unreal. According to Shankara mAyA is the illusory causal seed of the world, due to avidyA. The operative mode of avidyA is adhyAsa (a double superimposition: sat – Brahman – on a-sat – the adjuvant body-mind, and a-sat on sat), also following Shankara. This gives rise to the apparent multiplicity of phenomena, that is, to the apparent world. The world is identical in essence with, and has no independent existence from, Atman-brahman. It is not the effect of a cause (brahman), since the effect is not other than, not different from, the cause.  

 2) From the Absolute perspective (pAramArthika) there is no avidyA. Its ‘existence’ is only apparent and ultimately unexplainable, the same as with mAyA. It is said to be indeterminate, meaning that it is not totally unreal, as everyone can attest to from the viewpoint of this empirical world of phenomena, including of course ‘individual’ subjects.  As to the source of avidyA it can only be said that it, and its modus operandi, adhyAsa, are coeval, congenital to the apparent individual. Thus, to ask why avidyA exists is logically illegitimate; besides, who asks the question? To add to the mystery, Shankara avowed that trying to find the locus of avidyA is ‘a wild goose chase’.

A (Shuka): Ajñāna (primordial nescience) consists of three guṇas (qualities), sattva, rajas and tamas, is indeterminable as either real or unreal (sadadbhyāṁ anirvacanīyam)… it is bhāva (positive existence) in nature and not abhāva (non-existence)… it is based upon the experience “I do not know Brahman” and it is removable by self-knowledge… 

 This ajñāna is twofold – māyā and avidyā… That aspect of ajñāna which is sattva-guṇa-pradhāna (predominance of sattva), is called māyā. That aspect of ajñāna wherein sattvaguṇa is less predominant is avidyā. 

 The power of ajñāna is twofold – jñānaṣakti (power of knowledge) and kriyāśakti (power of action). Sattva, not subdued by other two guṇas, is called jñānaṣakti (power of knowledge). Kriyāśakti is two fold again – āvaraṇaśakti (power of concealment), which is tamoguṇa not subdued by other two.. vikṣepaśakti (power of projection) which is rajoguṇa not subdued by other two… 

 āvaraṇaṣakti is the cause for empirical usages such as ‘it does not exist, it is not manifest’. vikṣepaśakti is the cause of the origination of the world… 

 ajñāna is spoken of as avidyā when it is predominant in its power of concealment. It is spoken of as māyā when it is predominant in its power of projection. 

 Consciousness reflecting in māyā is Īśvara, and māyā is controlled by Īśvara. Consciousness reflecting in avidyā is jīva, and avidyā controls jīva.. 

A (Dennis): As with most seemingly difficult questions, they arise because of a confusion of paramArtha and vyavahAra, the ‘absolute reality’ and the ‘empirical world of transactions’. ‘In reality’ there is only Brahman – end of story. But we cannot deny the appearance of the world so that there need to be provisional explanations for it until such time as we can accept that there is, in reality, no world at all separate from Brahman. Once we can accept this, then those provisional explanations are withdrawn as they are no longer needed (and were not actually true anyway). This process is called adhyAropa-apavAda.

So, in answer to your questions:

1)    Atman is never deluded by mAyA. Atma is satyam or real; mAyA is mithyA – it does not really exist as something separate from Brahman; it is only a provisional explanation to account for the appearance.

2)    avidyA is another provisional explanation to account for our failure to appreciate the non-dual reality of Brahman. It is also mithyA in the final analysis.