Science recognizes objects and describes relations between them. It means that it belongs to the dual reality.

My understanding of an object is anything I can focus my attention on. It could be a physical object (a chair, a desk, a screen), external sensation – (a sound, a smell, a flavour), internal sensation (fear, pain, guilt) or an abstract sensation (a thought). The main quality of an object is that it cannot be noticed without its background. For example, you would not notice (focus on) these letters without the white space between them, physical objects would not be noticed without the space around them, sounds would not exist without silence, thoughts would not exist without breaks between them. It makes objects seemingly separated from each other. Therefore they belong to the dual reality.

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Science cannot describe the nondual reality because it is objectless.

The nondual reality is objectless because it has no background. An example of non object can be space (without ‘the’). As you know there is a lot of space inside every atom. It means that space we see between physical objects also permeates them. Space does not end when a physical object starts, it goes through it. Space is everywhere around and inside you. Space has no beginnig or end, it has no color, no taste, no texture or smell. It is borderless and featureless. It is a common background of all physical objects and physical objects emerge from it. Space is not an object because you cannot focus on it or describe it. You can replace space by silence, emptiness, awareness, being, etc… The same rules apply. See this link now.

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In order to focus on something and describe it (measure, scientifically research, etc…) you need to separate yourself from it first. With the act of separating you create the dual reality with at least two objects — you and the one you are describing. Scientific research is impossible in the nondual reality because in the nondual reality you cannot separate. You cannot step out of space in order to describe it because it is everywhere. You cannot explain silence by talking about it. You cannot show stillness by moving around it. You cannot explain Being by doing something. You cannot show nothingness by pointing at it and you cannot measure infinity.
So I think, scientific struggle to describe nonduality is a pointless exercise.

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However the dual reality is not placed next to, above or along the nondual reality. Dual reality is within the nondual one. Objects emerge from space and there are space at the same time. Sounds emerge from silence and there are filled with silence at the same time (which is easy to notice when you listen to a sound with low-frequency). Everyone’s individual awareness emerges from within Awareness and it is Awareness at the same time, etc

It would indicate that 
’duality is within nonduality’ and ‘nonduality is within duality’
, movement is stillness’ and ‘stillness is movement’
 ‘doing is being’ and ‘being is doing’
, etc…

Both realities are intimately intertwined and interconnected. They exist together. There are equally real and IT DEPENDS ON US WHICH OF THEM WE PERCEIVE. It really depends on the style of our attention. For example, we can focus on objects and create dual reality. Using this style of attention we can measure things, use numbers and apply a scientific approach. On the other hand we can diffuse our attention (defocus, broaden our focus) and become aware of space between, and within objects. Everything becomes unified, quiet, still and timeless.

We are making the reality dual or nondual. It makes us the creators of our world in a very literal way.

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Now, a few examples.

You can focus your attention on physical objects around you and clearly see they are separated from each other. When you diffuse your attention and become aware of space which is between objects and permeates them (including you) you are aware of the nondual reality.

When they focused on slits and measured which of them is passed by electron they created a particle (the dual reality). When they let go measurement electron was showing features of a wave (the nondual reality).

The letters on the screen you are looking at now, occupy pixels of the screen as well as the space around them. When you focus on the letters or the white space you see the dual reality. When you defocus and see the screen as the whole you are aware of nondual.

Every single equation is an expression of dualism (when you focus on its sides). However, when you widen your focus and notice the whole equation with an equal sign in the middle it becomes an expression of nondualism.

In these examples, once we focus (narrow our attention) we perceive separated objects. When we defocus (diffuse, broaden our attention) we become aware of unity and oneness.

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So, I guess, my point is that while it is not possible to scientifically describe the nondual reality you can experience it through science as well as through everything else. Science can be useful in sensing the nondual reality for those who feel inclined to it (this is my case). The only thing to remember is that in order to discover it we need to practice diffusing our attention. In other words we need to become attention flexible.