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Q: Does nature observe itself in the universe or is it observed?

Krishna:
Image source: Freepic

An 'observer' is a person in the classical world who watches, notices, or studies something, often without actively participating, such as a spectator, eyewitness, or an official representative at a meeting. They are also experts who analyze fields, like political observers. Synonyms include spectator, viewer, witness, onlooker, bystander, and commentator.

Nature observes itself through sentient life, acting as a part of the universe that has developed the capacity for self-awareness and measurement. As complex structures within the cosmos—humans and potentially other life forms—we are the universe experiencing and analyzing its own existence, blurring the line between observer and observed. Here the observer also 'actively participates' in the universe's (observed) affairs! Even 'observing' becomes the participation process!
If there is no life, there won't be any observers. Then Nature, although it exists, is not observed.
No humans. No “observers”. Just quantum vs. classical, interacting.

Let us also deal with quantum mechanics  and the concept of an “observer”.
In Quantum Mechanics, an “observer” is simply a classical (as in, non-quantum) thing interacting with the quantum system. Depending on the experimental configuration, that “observer” can be a human, an instrument, a cat, even a brick.

 The “act of observing”, i.e., the interaction between the quantum system and the classical system, confines the quantum system to this classical state with respect to the “observable”, i.e., whichever parameter of the quantum system participates in the interaction.

When a quantum system comes into contact with  an instrument, some of its parameters are briefly confined to numerical values (so-called eigenvalues). This is the most counterintuitive aspect of quantum physics: It can be “interpreted” either as a discontinuous (and retroactive!) “collapse” of the system’s state to the observed value, or we may choose to accept that the present-day evolution of the state of a quantum system is influenced (albeit in a way that has no observable consequences) by the system’s future encounter with the “instrument” so that it acquires the observed value in quantum mechanical (so-called “unitary”) evolution.

This encounter with instruments is what counts as an “observation” in quantum physics. The instrument is the “observer”. Note that it does not imply sentience, consciousness, or anything of the sort. For all we know, the “observer” is just an instrument . Moreover, we must keep in mind that such instruments exist only as mathematical idealizations. Actual bricks (or cats, or people, or electronics) are made up of a large but finite number of quantum particles, so while their quantum behaviour is averaged out (they are “almost” perfectly classical things “almost” all the time) it’s not completely absent.

In short, when you read the word “observer” in the quantum mechanical context, always keep in mind that for all you know, that “observer” is a dumb piece of a non-living entity. Do not read more into the word than that.

Getting back to the classical world ....

Nature Observing Itself: Because human beings are made of star-born materials and are integral parts of the universe, our observation of the cosmos is nature observing itself. This suggests that consciousness and awareness are inherent products of the universe's evolution.
Humans are made of the same matter and energy as the rest of the cosmos. At the level of atoms, chemical elements, and physical laws we are not external observers; we are processes embedded in and produced by the universe.
Consciousness and cognition are emergent properties of complex information-processing systems (brains). Those properties arise from arrangements of matter in specific manners and thus are a natural unfolding of the universe’s dynamical possibilities. In that sense we are the universe’s internal mode of self-representation.

The Observer Effect: Physicist Werner Heisenberg stated, "what we observe is not nature itself, but nature exposed to our method of questioning". This implies that nature is not merely a passive object but reacts to how it is queried, and the act of observation is part of the process of creation, self or otherwise, and evolution.

"Observing" is a physical interaction—photons hitting retinae, neurons firing, instruments mediating information. 
All physical senses in evolved beings help in this process too.

A Self-Regulating System: The universe operates as a whole that, through constant interactions, self-regulates and "observes" itself without needing special outside consciousness.

Unity of Observer and Observed: Many philosophical views conclude that there is no fundamental separation between the observer and the observed; they are part of a single, undivided process. The "observer is the observed," meaning humanity is a window through which the universe looks out at itself.

It is a paradox where nature is both the observer and the observed, manifesting awareness through its own internal complexity. 
That duality—being literally made of the universe while serving as its internal observer is an amazing feeling.

And seeing ourselves as part of the system strengthens  responsibility towards our environment and the entire universe too!

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