In modern mathematics, there is a practice of passing to a quotient structure from a parent structure which has been formalised as a standard method during the 20th century. A simple example. Let all integers be reduced to their remainder when divided by 7. This would mean there are only seven numbers now, namely: 0,1,2,3,4,5, and 6. Every other number would be reduced to one of these, uniquely. Thus `zero' would represent all multiples of 7, `1' would represent all numbers which leave a remainder 1 when divided by 7 and so on. Now these seven `representative numbers' can be added and multiplied. The result would be one of these numbers (since any number is reduced to one of these). These can also be subjected to the process of subtraction and division (- this would take a little bit of mathematical routine, but we shall skip it here). Thus, at the end, we have an algebraic structure on this new set derived from the structure on the parent set. In fact the algebraic structure on the parent set of an infinity of numbers has now induced an
analogous (strictly the same, in a certain mathematical sense) structure on the smaller set containing only seven entities, which may now be called the quotient set. Another way of saying this is that all the numbers are `partitioned' into exactly seven entities or classes. These entities or classes have now a structure of addition, subtraction, multiplication and division. Mathematicians call this a quotient structure. The standard way of describing this is to say that the quotient structure is obtained by `killing' or `nullifying' all multiples of seven. This `nullification' is actually an adhyaropa-apavada technique of Vedanta.

'adhyAropa'  means superimposition; wrong imputation;

attribution of a false characteristic; assumption.

'apavAda'  means negation, withdrawal, denial, rescission,

elimination of what has been imputed, attributed, assumed or superimposed.

Put all multiples of seven into one class – this is adhyaropa; and then treat that whole class as nothing but `zero' in the quotient structure – this is apavAda.

This `simple' (!) procedure is used to explain similar `nullifying' operations, for example, among geometrical shapes, to introduce the concepts of topology – a 20th century invention. There are several other quotient structures, introduced in more complicated ways, in various parts of mathematics and its applications. What will interest us here, is the application of this idea to the explanation of mAyA in relation to Absolute Reality.

The entire visible universe is MAyA – that is the advaita contention. By nullifying it, that is, by putting all that is MAyA into one class and treating it as zero of the new quotient structure, there now remains only one class, because there is nothing in the universe that is not under the influence of MAyA. In other words the quotient structure obtained after nullifying mAyA, contains only one single class (the class containing that
mAyA: Note that the class containing mAyA is not mAyA; it is different from mAyA; in mathematics also, the class containing some contents is different from the contents!) and that is The Absolute reality, says advaita! The adhyAropa or superimposition is the worldly habit of treating all that is mAyA as real. The apavAda or eradication of it is the nullification or `killing' of that mAyA.

Listen to Tayumanavar in Tamil :


kaDattai maNNenal uDainthapodo inthakkarumac-  

caDalattaip-poy enal iRanthapodo collattarumam


Do we have to call the pot but clay only when it is broken? Do we have to call this body as false only when it is dead?.The body has to be called jaDa (inert) even before the so-called death occurs. The clay-pot is only clay even when it is not broken. By calling it the clay-pot we are still in the adhyAropa stage only. If we can remove the pot-idea, even when it is not broken, then we have done the apavAda of the adhyAropa. In the teaching of advaita also, they allow you to go on with the idea that the universe and all that we see, hear and feel are real along with the teaching and the teacher. This is the adhyAropa or superimposition on Reality. In fact even the Iswara concept and the Bhakti towards that Iswara are all part of this adhyAropa. At the end of it all they help you realise that what you have been through is nothing but part of the Mayic play of the Lord and so apavAda, the eradication of this mAyic goings-on even when it is going on, is what is needed to be Brahman itself!


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© 2017 by V. Krishnamurthy