the Pair of Knowing and Object I am searching for a precise understanding of what Buddhist authors mean by the "pair" of "knowing" and "object". For example


  ...we see that what we call "self" is simply the pairwise progression of knowing and object.


A second example


  In all perception, at each event of noting, there is always this twin
  pair, the object and the mind,  which observes the object. These two
  elements of the object and the knowing mind always arise  in pairs,
  and apart from these 2, there does not exist any other thing in the
  form of a 'person',  an 'observer', an 'experiencer', nor any 'Ego',
  'Subject', or  any 'Self'! No identity is present! Similarly is there
  no 'observed object', or  any 'substance' "out there" independent of
  the mind!


Can this "pair" of "knowing" and "object" be explained precisely? Or is it subject to many interpretations?

What insight is gained from discussion of this pair of knowing and objects?
The "pair" or "dyad" of "knowing" and "object" is found in the Pali scriptures, as follows:


  At Savatthī. “Bhikkhus... there is
  this (internal) 'group' ('kaya': of five aggregates) and external minds-and-bodies: thus this dyad (pair). Dependent on the
  dyad (pair) there is contact. 
  
  https://suttacentral.net/en/sn12.19


~~~ 


  Owing to a dyad (pair), monks, consciousness comes into being. And how, monks, does consciousness come into being owing to a dyad?
  
  Owing to the eye and forms arises eye-consciousness. The eye is impermanent, changing, 'becoming-otherwise.' Forms are impermanent,
  changing, 'becoming-otherwise.' Thus this dyad is fleeting and
  transient; impermanent, changing and 'becoming-otherwise.' 
  
  Owing to the ear and sounds arises ear-consciousness. The ear is impermanent...
  
  Owing to the nose and scents arises nose-consciousness. The nose is impermanent...
  
  Owing to the tongue and savors arises tongue-consciousness...The tongue is impermanent.
  
  Owing to the body and tangibles arises body-consciousness. The body is impermanent...
  
  Owing to the mind and ideas arises mind-consciousness. The mind is impermanent...contacted, monks, one feels. Contacted, one intends.
  Contacted, one perceives. Thus these states also are fleeting and
  transient; impermanent, changing, 'becoming-otherwise.'
  
  SN 35.93


~~


  The six internal media should be known. The six external media should be known. The six classes of consciousness should be
  known.
  
  MN 148


The 1st example in the opening post is incorrect understanding. For example, what is called "self" is not included in the pairwise occurring of knowing and object. The mind can know an object but be empty of 'self' because 'self' is a product of thought/thinking (sankhara) while knowing an object is a product of sense consciousness (awareness: vinnana). 

The 2nd example in opening post is correct understanding, in that when the dyad operates, there is no 'self' in its operation. However, the thought of 'self' can arise quickly afterwards (called 'becoming'), as described in the following quote: 


  "Who, O Lord, has a sense-impression?"
  
  "The question is not correct," said the Exalted One.
  
  "I do not say that 'he has a sense-impression.'... The sixfold sense-base is a condition of sense-impression and sense-impression is
  the condition of feeling.'
  
  "Who, O Lord, feels?"
  
  "The question is not correct," said the Exalted One.... And to that the correct reply is: 'sense-impression is the condition of feeling;
  and feeling is the condition of craving.'"
  
  "Who, O Lord, craves?"
  
  "The question is not correct," said the Exalted One. "I do not say that 'he craves.'...the correct reply is: 'Feeling is the condition of
  craving, and craving is the condition of clinging.'"
  
  "Who, O Lord, clings?"
  
  "The question is not correct," said the Exalted One, "I do not say that 'he clings.'... 'Craving is the condition of clinging; and
  clinging is the condition of the process of (self) becoming.' Such
  is the origin of this entire mass of suffering.
  
  SN 12.12


However, to assert there are no objects "out there" independent of the mind goes too far. It is an extreme view because to assert there are no objects independent of mind asserts the mind is 'God' or 'Brahma'; that the mind is the 'Creator' of the external world.

The Pali scriptures state, for example, the Laws of Nature exist "out there" regardless of whether they are known by a human mind or not, as follows: 


  Monks, whether or not there is the arising of Tathagatas, this property stands — this steadfastness of the Dhamma, this orderliness
  of the Dhamma: All processes are inconstant. All processes are
  unsatisfactory. All phenomena are not-self. The Tathagata directly
  awakens to that, breaks through to that. Directly awakening &amp; breaking
  through to that, he declares it, teaches it, describes it, sets it
  forth. He reveals it, explains it, &amp; makes it plain
  
  Dhamma-niyama Sutta


The insight gained in knowing this pair of knowing and objects is explained in SN 35.93 quoted above, namely: (i) the mind can clearly identify or be aware of them and not create 'self-becoming' &amp; suffering in relation to them; (ii) the mind can see they arise &amp; pass; are impermanent &amp; not-self. 

For example, an object of sight comes to be when eye-consciousness functions &amp; an object of sight ceases to be when the eye-consciousness ceases to function. If this is watched, the mind will realise all sense objects are impermanent each time the eye blinks.