Mathematics of consciousness and self-awareness

 There is a philosophical idea called panpsychism which argues that consciousnesses is everywhere. This is very appealing to me, and seems like a very logical and naturalistic idea. However, man proponents of this idea tend to have some mystic view that whatever the consciousnesses is, we do not know but it is some unknown trait soon-to-be discovered.

I hold another view which I like to call panpsychistic materialism. This is different from regular materialism in that also in regular materialism there is some mystic ingredient of emerging phenomena giving rise to consciousness. Instead, I would like to argue that no such emergence is needed. Instead all that is needed is already there. Consciousness in its simplest form can instead be described by the most fundamental mathematical operators we know of such as

This is the differentiation operator and a particle that obeys it is conscious of momentum. Equations of motion for a system with interaction describe particles conscious of the other particles in that system.

This way, consciousness is really very simple, it is a systems capability to interact.

Taking this thought a slight bit further, self-awareness can simply be described as self-interaction. A very simple model for this is the feedback-mechanism often seen control systems (of the human body for that matter):

 

With this description, there is nothing strange with consciousness or self-awareness either for that matter. It is simply how the material world operates.